| Title: | Portfolio Analysis, Including Numerical Methods for Optimization of Portfolios |
|---|---|
| Description: | Portfolio optimization and analysis routines and graphics. |
| Authors: | Brian G. Peterson [cre, aut, cph], Peter Carl [aut, cph], Ross Bennett [ctb, cph], Kris Boudt [ctb, cph], Xinran Zhao [cph], R. Douglas Martin [ctb], Guy Yollin [ctb], Hezky Varon [ctb], Xiaokang Feng [ctb], Yifu Kang [ctb] |
| Maintainer: | Brian G. Peterson <[email protected]> |
| License: | GPL-3 |
| Version: | 2.1.0 |
| Built: | 2024-12-04 22:03:36 UTC |
| Source: | CRAN |
PortfolioAnalytics is an R package to provide numerical solutions for portfolio problems with complex constraints and objective sets. The goal of the package is to aid practicioners and researchers in solving portfolio optimization problems with complex constraints and objectives that mirror real-world applications.
One of the goals of the packages is to provide a common interface to specify constraints and objectives that can be solved by any supported solver (i.e. optimization method). Currently supported optimization methods include
random portfolios
differential evolution
particle swarm optimization
generalized simulated annealing
linear and quadratic programming routines
The solver can be specified with the optimize_method argument in optimize.portfolio and optimize.portfolio.rebalancing. The optimize_method argument must be one of "random", "DEoptim", "pso", "GenSA", "ROI", "quadprog", "glpk", or "symphony".
Additional information on random portfolios is provided below. The differential evolution algorithm is implemented via the DEoptim package, the particle swarm optimization algorithm via the pso package, the generalized simulated annealing via the GenSA package, and linear and quadratic programming are implemented via the ROI package which acts as an interface to the Rglpk, Rsymphony, and quadprog packages.
A key strength of PortfolioAnalytics is the generalization of constraints and objectives that can be solved.
If optimize_method="ROI" is specified, a default solver will be selected based on the optimization problem. The glpk solver is the default solver for LP and MILP optimization problems. The quadprog solver is the default solver for QP optimization problems. For example, optimize_method = "quadprog" can be specified and the optimization problem will be solved via ROI using the quadprog plugin package.
The extension to ROI solves a limited type of convex optimization problems:
Maxmimize portfolio return subject leverage, box, group, position limit, target mean return, and/or factor exposure constraints on weights.
Minimize portfolio variance subject to leverage, box, group, turnover, and/or factor exposure constraints (otherwise known as global minimum variance portfolio).
Minimize portfolio variance subject to leverage, box, group, and/or factor exposure constraints and a desired portfolio return.
Maximize quadratic utility subject to leverage, box, group, target mean return, turnover, and/or factor exposure constraints and risk aversion parameter.
(The risk aversion parameter is passed into optimize.portfolio as an added argument to the portfolio object).
Maximize portfolio mean return per unit standard deviation (i.e. the Sharpe Ratio) can be done by specifying maxSR=TRUE in optimize.portfolio.
If both mean and StdDev are specified as objective names, the default action is to maximize quadratic utility, therefore maxSR=TRUE must be specified to maximize Sharpe Ratio.
Minimize portfolio ES/ETL/CVaR optimization subject to leverage, box, group, position limit, target mean return, and/or factor exposure constraints and target portfolio return.
Maximize portfolio mean return per unit ES/ETL/CVaR (i.e. the STARR Ratio) can be done by specifying maxSTARR=TRUE in optimize.portfolio.
If both mean and ES/ETL/CVaR are specified as objective names, the default action is to maximize mean return per unit ES/ETL/CVaR.
These problems also support a weight_concentration objective where concentration of weights as measured by HHI is added as a penalty term to the quadratic objective.
Because these convex optimization problem are standardized, there is no need for a penalty term. The multiplier argument in add.objective passed into the complete constraint object are ingnored by the ROI solver.
Many real-world portfolio optimization problems are global optimization problems, and therefore are not suitable for linear or quadratic programming routines. PortfolioAnalytics provides a random portfolio optimization method and also utilizes the R packages DEoptim, pso, and GenSA for solving non-convex global optimization problems.
PortfolioAnalytics supports three methods of generating random portfolios.
The sample method to generate random portfolios is based on an idea by Pat Burns. This is the most flexible method, but also the slowest, and can generate portfolios to satisfy leverage, box, group, position limit, and leverage constraints.
The simplex method to generate random portfolios is based on a paper by W. T. Shaw. The simplex method is useful to generate random portfolios with the full investment constraint (where the sum of the weights is equal to 1) and min box constraints. Values for min_sum and max_sum of the leverage constraint will be ignored, the sum of weights will equal 1. All other constraints such as the box constraint max, group and position limit constraints will be handled by elimination. If the constraints are very restrictive, this may result in very few feasible portfolios remaining. Another key point to note is that the solution may not be along the vertexes depending on the objective. For example, a risk budget objective will likely place the portfolio somewhere on the interior.
The grid method to generate random portfolios is based on the gridSearch function in package NMOF. The grid search method only satisfies the min and max box constraints. The min_sum and max_sum leverage constraint will likely be violated and the weights in the random portfolios should be normalized. Normalization may cause the box constraints to be violated and will be penalized in constrained_objective.
PortfolioAnalytics leverages the PerformanceAnalytics package for many common objective functions. The objective types in PortfolioAnalytics are designed to be used with PerformanceAnalytics functions, but any user supplied valid R function can be used as an objective.
This summary attempts to provide an overview of how to construct a portfolio object with constraints and objectives, run the optimization, and chart the results.
The portfolio object is initialized with the portfolio.spec function. The main argument to portfolio.spec is assets. The assets argument can be a scalar value for the number of assets, a character vector of fund names, or a named vector of initial weights.
Adding constraints to the portfolio object is done with add.constraint. The add.constraint function is the main interface for adding and/or updating constraints to the portfolio object. This function allows the user to specify the portfolio to add the constraints to, the type of constraints, arguments for the constraint, and whether or not to enable the constraint. If updating an existing constraint, the indexnum argument can be specified.
Objectives can be added to the portfolio object with add.objective. The add.objective function is the main function for adding and/or updating objectives to the portfolio object. This function allows the user to specify the portfolio to add the objectives to, the type, name of the objective function, arguments to the objective function, and whether or not to enable the objective. If updating an existing objective, the indexnum argument can be specified.
With the constraints and objectives specified in the portfolio object, the portfolio object can be passed to optimize.portfolio or optimize.portfolio.rebalancing to run the optimization. Arguments to optimize.portfolio include asset returns, the portfolio obect specifying constraints and objectives, optimization method, and other parameters specific to the solver. optimize.portfolio.rebalancing adds support for backtesting portfolio optimization through time with rebalancing or rolling periods.
In addition to the more standard optimizations described above, PortfolioAnalytics also supports multi-layer optimization and regime switching optimization.
Support for multi-layer optimization allows one to construct a top level portfolio and several sub-portfolios with potentially different assets, constraints, and objectives. First, each sub-portfolio is optimized out-of-sample which creates a time series of returns. One can think of the out of sample returns for each sub-portfolio as the returns for a synthetic instrument. Finally, the out-of-sample returns of each sub-portfolio are then used as inputs for the top level optimization. The top level portfolio and sub-portfolios are created as normal using portfolio.spec, add.constraint, and add.objective. The multi-layer portfolio specification object is first initialized by passing the top level portfolio to mult.portfolio.spec. Sub-portfolios are then added with add.sub.portfolio. The multi-layer portfolio specification object can then be passed to optimize.portfolio and optimize.portfolio.rebalancing. See demo(multi_layer_optimization).
Support for regime switching models allows one to change constraints and objectives depending on the current regime. Portfolios are created as normal with portfolio.spec, add.constraint, and add.objective. The portfolios are then combined with a regime object using regime.portfolios to create a regime portfolio specification which can then be passed to optimize.portfolio and optimize.portfolio.rebalancing. Regime switching optimization is implemented in such a way that any arbitrary regime model can be used. See demo(regime_switching).
The PortfolioAnalytics framework to estimate solutions to constrained optimization problems is implemented in such a way that the moments of the returns are set once for use in lower level optimization functions. The set.portfolio.moments function computes the first, second, third, and fourth moments depending on the objective function(s) in the portfolio object. For example, if the third and fourth moments do not need to be calculated for a given objective, then set.portfolio.moments will try to detect this and not compute those moments. Currently, set.portfolio.moments implements methods to compute moments based on sample estimates, higher moments from fitting a statistical factor model based on the work of Kris Boudt, the Black Litterman model, and the Fully Flexible Framework based on the work of Attilio Meucci (NEED REFERENCE HERE). See the Custom Moment and Objective Functions vignette for a more detailed description and examples.
Intuition into the optimization can be aided through visualization. The goal of creating the charts is to provide visualization tools for optimal portfolios regardless of the chosen optimization method.
chart.Weights plots the weights of the optimal portfolio. chart.RiskReward plots the optimal portfolio in risk-reward space. The random portfolios, DEoptim, and pso solvers will return trace portfolio information at each iteration when optimize.portfolio is run with trace=TRUE. If this is the case, chart.RiskReward will plot these portfolios so that the feasible space can be easily visualized. Although the GenSA and ROI solvers do not return trace portfolio information, random portfolios can be be generated with the argument rp=TRUE in chart.RiskReward. A plot function is provided that will plot the weights and risk-reward scatter chart. The component risk contribution can be charted for portfolio optimization problems with risk budget objectives with chart.RiskBudget. Neighbor portfolios can be plotted in chart.RiskBudget, chart.Weights, and chart.RiskReward.
Efficient frontiers can be extracted from optimize.portfolio objects or created from a portfolio object. The efficient frontier can be charted in risk-reward space with chart.EfficientFrontier. The weights along the efficient frontier can be charted with chart.EF.Weights.
Multiple objects created via optimize.portfolio can be combined with combine.optimizations for visual comparison. The weights of the optimal portfolios can be plotted with chart.Weights. The optimal portfolios can be compared in risk-reward space with chart.RiskReward. The portfolio component risk contributions of the multiple optimal portfolios can be plotted with chart.RiskBudget.
PortfolioAnalytics contains a comprehensive collection of demos to demonstrate the functionality from very basic optimization problems such as estimating the solution to a minimum variance portfolio to more complex optimization problems with custom moment and objective functions.
TODO
Several of the functions in the PortfolioAnalytics package require time series data of returns and the xts package is used for working with time series data.
The PerformanceAnalytics package is used for many common objective functions. The objective types in PortfolioAnalytics are designed to be used with PerformanceAnalytics functions such as StdDev, VaR, and ES.
The foreach and iterators packages are used extensively throughout the package to support parallel programming. The primary functions where foreach loops are used is optimize.portfolio, optimize.portfolio.rebalancing, and create.EfficientFrontier.
In addition to a random portfolios optimzation method, PortfolioAnalytics supports backend solvers by leveraging the following packages: DEoptim, pso, GenSA, ROI and associated ROI plugin packages.
Continued work to improved charts and graphs.
Continued work to improve features to combine and compare multiple optimal portfolio objects.
Support for more solvers.
Comments, suggestions, and/or code patches are welcome.
TODO
Ross Bennett
Kris Boudt
Peter Carl
Brian G. Peterson
Maintainer: Brian G. Peterson [email protected]
Boudt, Kris and Lu, Wanbo and Peeters, Benedict, Higher Order Comoments of Multifactor Models and Asset Allocation (June 16, 2014). Available at SSRN: http://ssrn.com/abstract=2409603 or http://dx.doi.org/10.2139/ssrn.2409603
Chriss, Neil A and Almgren, Robert, Portfolios from Sorts (April 27, 2005). Available at SSRN: http://ssrn.com/abstract=720041 or http://dx.doi.org/10.2139/ssrn.720041
Meucci, Attilio, The Black-Litterman Approach: Original Model and Extensions (August 1, 2008). Shorter version in, THE ENCYCLOPEDIA OF QUANTITATIVE FINANCE, Wiley, 2010. Available at SSRN: http://ssrn.com/abstract=1117574 or http://dx.doi.org/10.2139/ssrn.1117574
Meucci, Attilio, Fully Flexible Views: Theory and Practice (August 8, 2008). Fully Flexible Views: Theory and Practice, Risk, Vol. 21, No. 10, pp. 97-102, October 2008. Available at SSRN: http://ssrn.com/abstract=1213325
Scherer, Bernd and Martin, Doug, Modern Portfolio Optimization. Springer. 2005.
Shaw, William Thornton, Portfolio Optimization for VAR, CVaR, Omega and Utility with General Return Distributions: A Monte Carlo Approach for Long-Only and Bounded Short Portfolios with Optional Robustness and a Simplified Approach to Covariance Matching (June 1, 2011). Available at SSRN: http://ssrn.com/abstract=1856476 or http://dx.doi.org/10.2139/ssrn.1856476
CRAN task view on Empirical Finance
https://cran.r-project.org/view=Econometrics
CRAN task view on Optimization
https://cran.r-project.org/view=Optimization
Large-scale portfolio optimization with DEoptim
https://cran.r-project.org/package=DEoptim
Compute the first moment from a single complete sort
ac.ranking(R, order, ...)ac.ranking(R, order, ...)
R |
xts object of asset returns |
order |
a vector of indexes of the relative ranking of expected asset
returns in ascending order. For example, |
... |
any other passthrough parameters |
This function computes the estimated centroid vector from a single complete sort using the analytical approximation as described in R. Almgren and N. Chriss, "Portfolios from Sorts". The centroid is estimated and then scaled such that it is on a scale similar to the asset returns. By default, the centroid vector is scaled according to the median of the asset mean returns.
The estimated first moments based on ranking views
R. Almgren and N. Chriss, "Portfolios from Sorts" https://papers.ssrn.com/sol3/papers.cfm?abstract_id=720041
centroid.complete.mc centroid.sectors
centroid.sign centroid.buckets
data(edhec) R <- edhec[,1:4] ac.ranking(R, c(2, 3, 1, 4))data(edhec) R <- edhec[,1:4] ac.ranking(R, c(2, 3, 1, 4))
This is the main function for adding and/or updating constraints to the portfolio.spec object.
add.constraint( portfolio, type, enabled = TRUE, message = FALSE, ..., indexnum = NULL )add.constraint( portfolio, type, enabled = TRUE, message = FALSE, ..., indexnum = NULL )
portfolio |
an object of class 'portfolio' to add the constraint to, specifying the constraints for the optimization, see |
type |
character type of the constraint to add or update, currently 'weight_sum' (also 'leverage' or 'weight'), 'box', 'group', 'turnover', 'diversification', 'position_limit', 'return', 'factor_exposure', or 'leverage_exposure' |
enabled |
TRUE/FALSE. The default is enabled=TRUE. |
message |
TRUE/FALSE. The default is message=FALSE. Display messages if TRUE. |
... |
any other passthru parameters to specify constraints |
indexnum |
if you are updating a specific constraint, the index number in the $constraints list to update |
The following constraint types may be specified:
weight_sum, weight, leverage
Specify constraint on the sum of the weights, see weight_sum_constraint
full_investment Special case to set min_sum=1 and max_sum=1 of weight sum constraints
dollar_neutral, active
Special case to set min_sum=0 and max_sum=0 of weight sum constraints
box box constraints for the individual asset weights, see box_constraint
long_only Special case to set min=0 and max=1 of box constraints
group specify the sum of weights within groups and the number of assets with non-zero weights in groups, see group_constraint
turnover Specify a constraint for target turnover. Turnover is calculated from a set of initial weights, see turnover_constraint
diversification target diversification of a set of weights, see diversification_constraint
position_limit Specify the number of non-zero, long, and/or short positions, see position_limit_constraint
return Specify the target mean return, see return_constraint
factor_exposure Specify risk factor exposures, see factor_exposure_constraint
leverage_exposure Specify a maximum leverage exposure, see leverage_exposure_constraint
Ross Bennett
portfolio.spec
weight_sum_constraint,
box_constraint,
group_constraint,
turnover_constraint,
diversification_constraint,
position_limit_constraint,
return_constraint,
factor_exposure_constraint,
leverage_exposure_constraint
data(edhec) returns <- edhec[, 1:4] fund.names <- colnames(returns) pspec <- portfolio.spec(assets=fund.names) # Add the full investment constraint that specifies the weights must sum to 1. pspec <- add.constraint(portfolio=pspec, type="weight_sum", min_sum=1, max_sum=1) # The full investment constraint can also be specified with type="full_investment" pspec <- add.constraint(portfolio=pspec, type="full_investment") # Another common constraint is that portfolio weights sum to 0. pspec <- add.constraint(portfolio=pspec, type="weight_sum", min_sum=0, max_sum=0) pspec <- add.constraint(portfolio=pspec, type="dollar_neutral") pspec <- add.constraint(portfolio=pspec, type="active") # Add box constraints pspec <- add.constraint(portfolio=pspec, type="box", min=0.05, max=0.4) # min and max can also be specified per asset pspec <- add.constraint(portfolio=pspec, type="box", min=c(0.05, 0, 0.08, 0.1), max=c(0.4, 0.3, 0.7, 0.55)) # A special case of box constraints is long only where min=0 and max=1 # The default action is long only if min and max are not specified pspec <- add.constraint(portfolio=pspec, type="box") pspec <- add.constraint(portfolio=pspec, type="long_only") # Add group constraints pspec <- add.constraint(portfolio=pspec, type="group", groups=list(c(1, 2, 1), 4), group_min=c(0.1, 0.15), group_max=c(0.85, 0.55), group_labels=c("GroupA", "GroupB"), group_pos=c(2, 1)) # Add position limit constraint such that we have a maximum number # of three assets with non-zero weights. pspec <- add.constraint(portfolio=pspec, type="position_limit", max_pos=3) # Add diversification constraint pspec <- add.constraint(portfolio=pspec, type="diversification", div_target=0.7) # Add turnover constraint pspec <- add.constraint(portfolio=pspec, type="turnover", turnover_target=0.2) # Add target mean return constraint pspec <- add.constraint(portfolio=pspec, type="return", return_target=0.007) # Example using the indexnum argument portf <- portfolio.spec(assets=fund.names) portf <- add.constraint(portf, type="full_investment") portf <- add.constraint(portf, type="long_only") # indexnum corresponds to the index number of the constraint # The full_investment constraint was the first constraint added and has # indexnum=1 portf$constraints[[1]] # View the constraint with indexnum=2 portf$constraints[[2]] # Update the constraint to relax the sum of weights constraint portf <- add.constraint(portf, type="weight_sum", min_sum=0.99, max_sum=1.01, indexnum=1) # Update the constraint to modify the box constraint portf <- add.constraint(portf, type="box", min=0.1, max=0.8, indexnum=2)data(edhec) returns <- edhec[, 1:4] fund.names <- colnames(returns) pspec <- portfolio.spec(assets=fund.names) # Add the full investment constraint that specifies the weights must sum to 1. pspec <- add.constraint(portfolio=pspec, type="weight_sum", min_sum=1, max_sum=1) # The full investment constraint can also be specified with type="full_investment" pspec <- add.constraint(portfolio=pspec, type="full_investment") # Another common constraint is that portfolio weights sum to 0. pspec <- add.constraint(portfolio=pspec, type="weight_sum", min_sum=0, max_sum=0) pspec <- add.constraint(portfolio=pspec, type="dollar_neutral") pspec <- add.constraint(portfolio=pspec, type="active") # Add box constraints pspec <- add.constraint(portfolio=pspec, type="box", min=0.05, max=0.4) # min and max can also be specified per asset pspec <- add.constraint(portfolio=pspec, type="box", min=c(0.05, 0, 0.08, 0.1), max=c(0.4, 0.3, 0.7, 0.55)) # A special case of box constraints is long only where min=0 and max=1 # The default action is long only if min and max are not specified pspec <- add.constraint(portfolio=pspec, type="box") pspec <- add.constraint(portfolio=pspec, type="long_only") # Add group constraints pspec <- add.constraint(portfolio=pspec, type="group", groups=list(c(1, 2, 1), 4), group_min=c(0.1, 0.15), group_max=c(0.85, 0.55), group_labels=c("GroupA", "GroupB"), group_pos=c(2, 1)) # Add position limit constraint such that we have a maximum number # of three assets with non-zero weights. pspec <- add.constraint(portfolio=pspec, type="position_limit", max_pos=3) # Add diversification constraint pspec <- add.constraint(portfolio=pspec, type="diversification", div_target=0.7) # Add turnover constraint pspec <- add.constraint(portfolio=pspec, type="turnover", turnover_target=0.2) # Add target mean return constraint pspec <- add.constraint(portfolio=pspec, type="return", return_target=0.007) # Example using the indexnum argument portf <- portfolio.spec(assets=fund.names) portf <- add.constraint(portf, type="full_investment") portf <- add.constraint(portf, type="long_only") # indexnum corresponds to the index number of the constraint # The full_investment constraint was the first constraint added and has # indexnum=1 portf$constraints[[1]] # View the constraint with indexnum=2 portf$constraints[[2]] # Update the constraint to relax the sum of weights constraint portf <- add.constraint(portf, type="weight_sum", min_sum=0.99, max_sum=1.01, indexnum=1) # Update the constraint to modify the box constraint portf <- add.constraint(portf, type="box", min=0.1, max=0.8, indexnum=2)
This function is the main function for adding and updating business objectives in an object of type portfolio.spec.
add.objective_v1( constraints, type, name, arguments = NULL, enabled = TRUE, ..., indexnum = NULL ) add.objective( portfolio, constraints = NULL, type, name, arguments = NULL, enabled = TRUE, ..., indexnum = NULL )add.objective_v1( constraints, type, name, arguments = NULL, enabled = TRUE, ..., indexnum = NULL ) add.objective( portfolio, constraints = NULL, type, name, arguments = NULL, enabled = TRUE, ..., indexnum = NULL )
constraints |
a 'v1_constraint' object for backwards compatibility, see |
type |
character type of the objective to add or update, currently 'return','risk', 'risk_budget', 'quadratic_utility', or 'weight_concentration' |
name |
name of the objective, should correspond to a function, though we will try to make allowances |
arguments |
default arguments to be passed to an objective function when executed |
enabled |
TRUE/FALSE |
... |
any other passthru parameters |
indexnum |
if you are updating a specific objective, the index number in the $objectives list to update |
portfolio |
an object of type 'portfolio' to add the objective to, specifying the portfolio for the optimization, see |
In general, you will define your objective as one of the following types: 'return', 'risk', 'risk_budget', 'quadratic utility', or 'weight_concentration'. These have special handling and intelligent defaults for dealing with the function most likely to be used as objectives, including mean, median, VaR, ES, etc.
Objectives of type 'turnover' and 'minmax' are also supported.
Brian G. Peterson and Ross Bennett
data(edhec) returns <- edhec[,1:4] fund.names <- colnames(returns) portf <- portfolio.spec(assets=fund.names) # Add some basic constraints portf <- add.constraint(portf, type="full_investment") portf <- add.constraint(portf, type="long_only") # Creates a new portfolio object using portf and adds a quadratic utility # objective. This will add two objectives to the portfolio object; 1) mean and # 2) var. The risk aversion parameter is commonly referred to as lambda in the # quadratic utility formulation that controls how much the portfolio variance # is penalized. portf.maxQU <- add.objective(portf, type="quadratic_utility", risk_aversion=0.25) # Creates a new portfolio object using portf and adds mean as an objective portf.maxMean <- add.objective(portf, type="return", name="mean") # Creates a new portfolio object using portf and adds StdDev as an objective portf.minStdDev <- add.objective(portf, type="risk", name="StdDev") # Creates a new portfolio object using portf and adds ES as an objective. # Note that arguments to ES are passed in as a named list. portf.minES <- add.objective(portf, type="risk", name="ES", arguments=list(p=0.925, clean="boudt")) # Creates a new portfolio object using portf.minES and adds a risk budget # objective with limits on component risk contribution. # Note that arguments to ES are passed in as a named list. portf.RiskBudgetES <- add.objective(portf.minES, type="risk_budget", name="ES", arguments=list(p=0.925, clean="boudt"), min_prisk=0, max_prisk=0.6) # Creates a new portfolio object using portf.minES and adds a risk budget # objective with equal component risk contribution. # Note that arguments to ES are passed in as a named list. portf.EqRiskES <- add.objective(portf.minES, type="risk_budget", name="ES", arguments=list(p=0.925, clean="boudt"), min_concentration=TRUE) # Creates a new portfolio object using portf and adds a weight_concentration # objective. The conc_aversion parameter controls how much concentration is # penalized. The portfolio concentration is defined as the Herfindahl Hirschman # Index of the weights. portf.conc <- add.objective(portf, type="weight_concentration", name="HHI", conc_aversion=0.01)data(edhec) returns <- edhec[,1:4] fund.names <- colnames(returns) portf <- portfolio.spec(assets=fund.names) # Add some basic constraints portf <- add.constraint(portf, type="full_investment") portf <- add.constraint(portf, type="long_only") # Creates a new portfolio object using portf and adds a quadratic utility # objective. This will add two objectives to the portfolio object; 1) mean and # 2) var. The risk aversion parameter is commonly referred to as lambda in the # quadratic utility formulation that controls how much the portfolio variance # is penalized. portf.maxQU <- add.objective(portf, type="quadratic_utility", risk_aversion=0.25) # Creates a new portfolio object using portf and adds mean as an objective portf.maxMean <- add.objective(portf, type="return", name="mean") # Creates a new portfolio object using portf and adds StdDev as an objective portf.minStdDev <- add.objective(portf, type="risk", name="StdDev") # Creates a new portfolio object using portf and adds ES as an objective. # Note that arguments to ES are passed in as a named list. portf.minES <- add.objective(portf, type="risk", name="ES", arguments=list(p=0.925, clean="boudt")) # Creates a new portfolio object using portf.minES and adds a risk budget # objective with limits on component risk contribution. # Note that arguments to ES are passed in as a named list. portf.RiskBudgetES <- add.objective(portf.minES, type="risk_budget", name="ES", arguments=list(p=0.925, clean="boudt"), min_prisk=0, max_prisk=0.6) # Creates a new portfolio object using portf.minES and adds a risk budget # objective with equal component risk contribution. # Note that arguments to ES are passed in as a named list. portf.EqRiskES <- add.objective(portf.minES, type="risk_budget", name="ES", arguments=list(p=0.925, clean="boudt"), min_concentration=TRUE) # Creates a new portfolio object using portf and adds a weight_concentration # objective. The conc_aversion parameter controls how much concentration is # penalized. The portfolio concentration is defined as the Herfindahl Hirschman # Index of the weights. portf.conc <- add.objective(portf, type="weight_concentration", name="HHI", conc_aversion=0.01)
Add a sub-portfolio to a multiple layer portfolio specification object
add.sub.portfolio( mult.portfolio, portfolio, optimize_method = c("DEoptim", "random", "ROI", "pso", "GenSA"), search_size = 20000, rp = NULL, rebalance_on = NULL, training_period = NULL, trailing_periods = NULL, ..., indexnum = NULL )add.sub.portfolio( mult.portfolio, portfolio, optimize_method = c("DEoptim", "random", "ROI", "pso", "GenSA"), search_size = 20000, rp = NULL, rebalance_on = NULL, training_period = NULL, trailing_periods = NULL, ..., indexnum = NULL )
mult.portfolio |
a |
portfolio |
a |
optimize_method |
optimization method for the sub portfolio |
search_size |
integer, how many portfolios to test, default 20,000 |
rp |
matrix of random portfolio weights, default NULL, mostly for automated use by rebalancing optimization or repeated tests on same portfolios |
rebalance_on |
haracter string of period to rebalance on. See
|
training_period |
an integer of the number of periods to use as a training data in the front of the returns data |
trailing_periods |
an integer with the number of periods to roll over (i.e. width of the moving or rolling window), the default is NULL will run using the returns data from inception |
... |
additonal passthrough parameters to |
indexnum |
the index number of the sub portfolio. If |
Ross Bennett
mult.portfolio.spec portfolio.spec optimize.portfolio optimize.portfolio.rebalancing
This function is used to calculate risk or return metrics given a matrix of weights and is primarily used as a convenience function used in chart.Scatter functions
applyFUN(R, weights, FUN = "mean", arguments)applyFUN(R, weights, FUN = "mean", arguments)
R |
xts object of asset returns |
weights |
a matrix of weights generated from random_portfolios or |
FUN |
name of a function |
arguments |
named list of arguments to FUN |
Ross Bennett
generate plots of the cumulative returns and drawdown for back-testing
backtest.plot( R, log_return = FALSE, drawdown_on = 1, plotType = "both", main = NULL, colorSet = NULL, ltySet = NULL, lwdSet = NULL )backtest.plot( R, log_return = FALSE, drawdown_on = 1, plotType = "both", main = NULL, colorSet = NULL, ltySet = NULL, lwdSet = NULL )
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
log_return |
arithmetic return or log return, the default is arithmetic return |
drawdown_on |
the plot will shadow the full time period of the maximum drawdown and recovery of the first portfolio. Use number (e.g. 1, 2, 3) to indicate which portfolio drawdown interval you wish to track, or NULL to not shadow any period. |
plotType |
"cumRet", "drawdown", or the default is both |
main |
users can design title by providing a character of main |
colorSet |
users can design the color by providing a vector of color |
ltySet |
users can design lty by providing a vector of lty |
lwdSet |
users can design lwd by providing a vector of lwd |
Peter Carl, Xinran Zhao, Yifu Kang
This function is called by chart.GroupWeights function if chart.type="barplot"
barplotGroupWeights( object, ..., grouping = c("groups", "category"), main = "Group Weights", las = 3, xlab = NULL, cex.lab = 0.8, element.color = "darkgray", cex.axis = 0.8 )barplotGroupWeights( object, ..., grouping = c("groups", "category"), main = "Group Weights", las = 3, xlab = NULL, cex.lab = 0.8, element.color = "darkgray", cex.axis = 0.8 )
object |
object of class |
... |
passthrough parameters to |
grouping |
|
main |
an overall title for the plot: see |
las |
numeric in {0,1,2,3}; the style of axis labels
|
xlab |
a title for the x axis: see |
cex.lab |
The magnification to be used for x and y labels relative to the current setting of |
element.color |
color for the default border and axis |
cex.axis |
The magnification to be used for x and y axis relative to the current setting of |
Ross Bennett
Compute the Black Litterman estimate of moments for the posterior normal.
black.litterman(R, P, Mu = NULL, Sigma = NULL, Views = NULL)black.litterman(R, P, Mu = NULL, Sigma = NULL, Views = NULL)
R |
returns |
P |
a K x N pick matrix |
Mu |
vector of length N of the prior expected values. The sample mean
is used if |
Sigma |
an N x N matrix of the prior covariance matrix. The sample
covariance is used if |
Views |
a vector of length K of the views |
posterior expected values
posterior covariance matrix
This function is largely based on the work of Xavier Valls to port the matlab code of Attilio Meucci to R as documented in the Meucci package.
Ross Bennett, Xavier Valls
A. Meucci - "Exercises in Advanced Risk and Portfolio Management" https://www.arpm.co/articles/exercises-in-advanced-risk-and-portfolio-management/.
This function computes the Black-Litterman formula for the moments of the posterior normal, as described in A. Meucci, "Risk and Asset Allocation", Springer, 2005.
BlackLittermanFormula(Mu, Sigma, P, v, Omega)BlackLittermanFormula(Mu, Sigma, P, v, Omega)
Mu |
[vector] (N x 1) prior expected values. |
Sigma |
[matrix] (N x N) prior covariance matrix. |
P |
[matrix] (K x N) pick matrix. |
v |
[vector] (K x 1) vector of views. |
Omega |
[matrix] (K x K) matrix of confidence. |
BLMu [vector] (N x 1) posterior expected values.
BLSigma [matrix] (N x N) posterior covariance matrix.
Xavier Valls [email protected]
A. Meucci - "Exercises in Advanced Risk and Portfolio Management" https://www.arpm.co/articles/exercises-in-advanced-risk-and-portfolio-management/.
See Meucci's script for "BlackLittermanFormula.m"
Box constraints specify the upper and lower bounds on the weights of the assets.
This function is called by add.constraint when type="box" is specified. See add.constraint.
box_constraint( type = "box", assets, min, max, min_mult, max_mult, enabled = TRUE, message = FALSE, ... )box_constraint( type = "box", assets, min, max, min_mult, max_mult, enabled = TRUE, message = FALSE, ... )
type |
character type of the constraint |
assets |
number of assets, or optionally a named vector of assets specifying initial weights |
min |
numeric or named vector specifying minimum weight box constraints |
max |
numeric or named vector specifying minimum weight box constraints |
min_mult |
numeric or named vector specifying minimum multiplier box constraint from initial weight in |
max_mult |
numeric or named vector specifying maximum multiplier box constraint from initial weight in |
enabled |
TRUE/FALSE |
message |
TRUE/FALSE. The default is message=FALSE. Display messages if TRUE. |
... |
any other passthru parameters to specify box constraints |
an object of class 'box_constraint'
Ross Bennett
data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) # defaults to min=0 and max=1 pspec <- add.constraint(pspec, type="box") # specify box constraints as a scalar pspec <- add.constraint(pspec, type="box", min=0.05, max=0.45) # specify box constraints per asset pspec <- add.constraint(pspec, type="box", min=c(0.05, 0.10, 0.08, 0.06), max=c(0.45, 0.55, 0.35, 0.65))data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) # defaults to min=0 and max=1 pspec <- add.constraint(pspec, type="box") # specify box constraints as a scalar pspec <- add.constraint(pspec, type="box", min=0.05, max=0.45) # specify box constraints per asset pspec <- add.constraint(pspec, type="box", min=c(0.05, 0.10, 0.08, 0.06), max=c(0.45, 0.55, 0.35, 0.65))
it first estimates the conditional GARCH variances, then filters out the time-varying volatility and estimates the higher order comoments on the innovations rescaled such that their unconditional covariance matrix is the conditional covariance matrix forecast
CCCgarch.MM(R, momentargs = NULL, ...)CCCgarch.MM(R, momentargs = NULL, ...)
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
momentargs |
list containing arguments to be passed down to lower level functions, default NULL |
... |
any other passthru parameters |
Center a matrix
center(x)center(x)
x |
matrix |
This function is used primarily to center a time series of asset returns or factors. Each column should represent the returns of an asset or factor realizations. The expected value is taken as the sample mean.
x.centered = x - mean(x)
matrix of centered data
Compute the centroid for buckets of assets
centroid.buckets(buckets, simulations = 1000)centroid.buckets(buckets, simulations = 1000)
buckets |
a list where each element contains the index of the assets in the respective bucket. The assets within each bucket have no order. The bucket elements are in ascending order such that R_bucket_1 < ... < R_bucket_n |
simulations |
number of simulations |
A common use of buckets is to divide the assets into quartiles or deciles, but is generalized here for an arbitrary number of buckets and arbitrary number of assets in each bucket.
the centroid vector
Ross Bennett
Numerical method to estimate complete cases centroid
centroid.complete.mc(order, simulations = 1000)centroid.complete.mc(order, simulations = 1000)
order |
a vector of indexes of the relative ranking of expected asset
returns in ascending order. For example, |
simulations |
number of simulations |
the centroid vector
Ross Bennett
# Express a view on the assets such that # R_2 < R_1 < R_3 < R_4 centroid.complete.mc(c(2, 1, 3, 4))# Express a view on the assets such that # R_2 < R_1 < R_3 < R_4 centroid.complete.mc(c(2, 1, 3, 4))
Compute the centroid for expressing views on the relative ranking of assets within sectors.
centroid.sectors(sectors, simulations = 1000)centroid.sectors(sectors, simulations = 1000)
sectors |
a list where each list element contains the order of each asset in the given sector |
simulations |
number of simulations |
the centroid vector
Ross Bennett
# Express a view on the assets in two sectors # Sector 1 View: R_2 < R_1 < R_3 # Sector 2 View: R_5 < R_4 x <- list() x[[1]] <- c(2, 1, 3) x[[2]] <- c(5, 4) centroid.sectors(x)# Express a view on the assets in two sectors # Sector 1 View: R_2 < R_1 < R_3 # Sector 2 View: R_5 < R_4 x <- list() x[[1]] <- c(2, 1, 3) x[[2]] <- c(5, 4) centroid.sectors(x)
Compute the centroid for expressing a view on assets with positive or negative expected returns
centroid.sign(positive, negative, simulations = 1000)centroid.sign(positive, negative, simulations = 1000)
positive |
a vector of the index of assets with positive expected return in ascending order |
negative |
a vector of the index of assets with negative expected return in ascending order. |
simulations |
number of simulations |
the centroid vector
Ross Bennett
# Express a view that # R_1 < R_2 < 0 < R_3 < R_4 centroid.sign(c(1, 2), c(4, 3))# Express a view that # R_1 < R_2 < 0 < R_3 < R_4 centroid.sign(c(1, 2), c(4, 3))
This function charts the optimize.portfolio object in risk-return space
and the degree of concentration based on the weights or percentage component
contribution to risk.
chart.Concentration( object, ..., return.col = "mean", risk.col = "ES", chart.assets = FALSE, conc.type = c("weights", "pct_contrib"), col = heat.colors(20), element.color = "darkgray", cex.axis = 0.8, xlim = NULL, ylim = NULL )chart.Concentration( object, ..., return.col = "mean", risk.col = "ES", chart.assets = FALSE, conc.type = c("weights", "pct_contrib"), col = heat.colors(20), element.color = "darkgray", cex.axis = 0.8, xlim = NULL, ylim = NULL )
object |
optimal portfolio created by |
... |
any other passthru parameters. |
return.col |
string matching the objective of a 'return' objective, on vertical axis. |
risk.col |
string matching the objective of a 'risk' objective, on horizontal axis. |
chart.assets |
TRUE/FALSE. Includes a risk reward scatter of the assets in the chart. |
conc.type |
concentration type can be based on the concentration of weights or concentration of percentage component contribution to risk (only works with risk budget objective for the optimization). |
col |
color palette or vector of colors to use. |
element.color |
color for the border and axes. |
cex.axis |
The magnification to be used for axis annotation relative to the current setting of |
xlim |
set the x-axis limit, same as in |
ylim |
set the y-axis limit, same as in |
Peter Carl and Ross Bennett
This function produces a stacked barplot of weights along an efficient frontier.
chart.EF.Weights(object, ...) ## S3 method for class 'efficient.frontier' chart.EF.Weights( object, ..., colorset = NULL, n.portfolios = 25, by.groups = FALSE, match.col = "ES", main = "", cex.lab = 0.8, cex.axis = 0.8, cex.legend = 0.8, legend.labels = NULL, element.color = "darkgray", legend.loc = "topright" ) ## S3 method for class 'optimize.portfolio' chart.EF.Weights( object, ..., colorset = NULL, n.portfolios = 25, by.groups = FALSE, match.col = "ES", main = "", cex.lab = 0.8, cex.axis = 0.8, cex.legend = 0.8, legend.labels = NULL, element.color = "darkgray", legend.loc = "topright" )chart.EF.Weights(object, ...) ## S3 method for class 'efficient.frontier' chart.EF.Weights( object, ..., colorset = NULL, n.portfolios = 25, by.groups = FALSE, match.col = "ES", main = "", cex.lab = 0.8, cex.axis = 0.8, cex.legend = 0.8, legend.labels = NULL, element.color = "darkgray", legend.loc = "topright" ) ## S3 method for class 'optimize.portfolio' chart.EF.Weights( object, ..., colorset = NULL, n.portfolios = 25, by.groups = FALSE, match.col = "ES", main = "", cex.lab = 0.8, cex.axis = 0.8, cex.legend = 0.8, legend.labels = NULL, element.color = "darkgray", legend.loc = "topright" )
object |
object of class |
... |
passthru parameters to |
colorset |
color palette or vector of colors to use. |
n.portfolios |
number of portfolios to extract along the efficient frontier. |
by.groups |
TRUE/FALSE. If TRUE, the group weights are charted. |
match.col |
string name of column to use for risk (horizontal axis). Must match the name of an objective. |
main |
title used in the plot. |
cex.lab |
the magnification to be used for x-axis and y-axis labels relative to the current setting of 'cex'. |
cex.axis |
the magnification to be used for sizing the axis text relative to the current setting of 'cex', similar to |
cex.legend |
the magnification to be used for sizing the legend relative to the current setting of 'cex', similar to |
legend.labels |
character vector to use for the legend labels. |
element.color |
provides the color for drawing less-important chart elements, such as the box lines, axis lines, etc. |
legend.loc |
NULL, "topright", "right", or "bottomright". If legend.loc is NULL, the legend will not be plotted. |
Ross Bennett
Chart the efficient frontier and risk-return scatter of the assets for
optimize.portfolio or efficient.frontier objects
chart.EfficientFrontier(object, ...) ## S3 method for class 'optimize.portfolio.CVXR' chart.EfficientFrontier( object, ..., optimize_method = "CVXR", match.col = "ES", n.portfolios = 25, xlim = NULL, ylim = NULL, cex.axis = 0.8, element.color = "darkgray", main = "Efficient Frontier", RAR.text = "SR", rf = 0, tangent.line = TRUE, cex.legend = 0.8, chart.assets = TRUE, labels.assets = TRUE, pch.assets = 21, cex.assets = 0.8 ) ## S3 method for class 'optimize.portfolio.ROI' chart.EfficientFrontier( object, ..., optimize_method = "ROI", match.col = "ES", n.portfolios = 25, xlim = NULL, ylim = NULL, cex.axis = 0.8, element.color = "darkgray", main = "Efficient Frontier", RAR.text = "SR", rf = 0, tangent.line = TRUE, cex.legend = 0.8, chart.assets = TRUE, labels.assets = TRUE, pch.assets = 21, cex.assets = 0.8 ) ## S3 method for class 'optimize.portfolio' chart.EfficientFrontier( object, ..., match.col = "ES", n.portfolios = 25, xlim = NULL, ylim = NULL, cex.axis = 0.8, element.color = "darkgray", main = "Efficient Frontier", RAR.text = "SR", rf = 0, tangent.line = TRUE, cex.legend = 0.8, chart.assets = TRUE, labels.assets = TRUE, pch.assets = 21, cex.assets = 0.8 ) ## S3 method for class 'efficient.frontier' chart.EfficientFrontier( object, ..., match.col = "ES", n.portfolios = NULL, xlim = NULL, ylim = NULL, cex.axis = 0.8, element.color = "darkgray", main = "Efficient Frontier", RAR.text = "SR", rf = 0, tangent.line = TRUE, cex.legend = 0.8, chart.assets = TRUE, labels.assets = TRUE, pch.assets = 21, cex.assets = 0.8 )chart.EfficientFrontier(object, ...) ## S3 method for class 'optimize.portfolio.CVXR' chart.EfficientFrontier( object, ..., optimize_method = "CVXR", match.col = "ES", n.portfolios = 25, xlim = NULL, ylim = NULL, cex.axis = 0.8, element.color = "darkgray", main = "Efficient Frontier", RAR.text = "SR", rf = 0, tangent.line = TRUE, cex.legend = 0.8, chart.assets = TRUE, labels.assets = TRUE, pch.assets = 21, cex.assets = 0.8 ) ## S3 method for class 'optimize.portfolio.ROI' chart.EfficientFrontier( object, ..., optimize_method = "ROI", match.col = "ES", n.portfolios = 25, xlim = NULL, ylim = NULL, cex.axis = 0.8, element.color = "darkgray", main = "Efficient Frontier", RAR.text = "SR", rf = 0, tangent.line = TRUE, cex.legend = 0.8, chart.assets = TRUE, labels.assets = TRUE, pch.assets = 21, cex.assets = 0.8 ) ## S3 method for class 'optimize.portfolio' chart.EfficientFrontier( object, ..., match.col = "ES", n.portfolios = 25, xlim = NULL, ylim = NULL, cex.axis = 0.8, element.color = "darkgray", main = "Efficient Frontier", RAR.text = "SR", rf = 0, tangent.line = TRUE, cex.legend = 0.8, chart.assets = TRUE, labels.assets = TRUE, pch.assets = 21, cex.assets = 0.8 ) ## S3 method for class 'efficient.frontier' chart.EfficientFrontier( object, ..., match.col = "ES", n.portfolios = NULL, xlim = NULL, ylim = NULL, cex.axis = 0.8, element.color = "darkgray", main = "Efficient Frontier", RAR.text = "SR", rf = 0, tangent.line = TRUE, cex.legend = 0.8, chart.assets = TRUE, labels.assets = TRUE, pch.assets = 21, cex.assets = 0.8 )
object |
object to chart. |
... |
passthru parameters to |
optimize_method |
the optimize method to get the efficient frontier |
match.col |
string name of column to use for risk (horizontal axis).
|
n.portfolios |
number of portfolios to use to plot the efficient frontier. |
xlim |
set the x-axis limit, same as in |
ylim |
set the y-axis limit, same as in |
cex.axis |
numerical value giving the amount by which the axis should be magnified relative to the default. |
element.color |
provides the color for drawing less-important chart elements, such as the box lines, axis lines, etc. |
main |
a main title for the plot. |
RAR.text |
string name for risk adjusted return text to plot in the legend. |
rf |
risk free rate. If |
tangent.line |
TRUE/FALSE to plot the tangent line. |
cex.legend |
numerical value giving the amount by which the legend should be magnified relative to the default. |
chart.assets |
TRUE/FALSE to include the assets. |
labels.assets |
TRUE/FALSE to include the asset names in the plot.
|
pch.assets |
plotting character of the assets, same as in |
cex.assets |
numerical value giving the amount by which the asset points and labels should be magnified relative to the default. |
For objects created by optimize.portfolio with 'DEoptim', 'random', or 'pso' specified as the optimize_method:
The efficient frontier plotted is based on the the trace information (sets of
portfolios tested by the solver at each iteration) in objects created by
optimize.portfolio.
For objects created by optimize.portfolio with 'ROI' specified as the optimize_method:
The mean-StdDev or mean-ETL efficient frontier can be plotted for optimal
portfolio objects created by optimize.portfolio.
If match.col="StdDev", the mean-StdDev efficient frontier is plotted.
If match.col="ETL" (also "ES" or "CVaR"), the mean-ETL efficient frontier is plotted.
Note that trace=TRUE must be specified in optimize.portfolio
GenSA does not return any useable trace information for portfolios tested at each iteration, therfore we cannot extract and chart an efficient frontier.
By default, the tangency portfolio (maximum Sharpe Ratio or modified Sharpe Ratio)
will be plotted using a risk free rate of 0. Set rf=NULL to omit
this from the plot.
Ross Bennett, Xinran Zhao
Overlay the efficient frontiers of different minRisk portfolio objects on a single plot.
chart.EfficientFrontierCompare( R, portfolio, risk_type, n.portfolios = 25, match.col = c("StdDev", "ES"), guideline = NULL, main = "Efficient Frontiers", plot_type = "l", cex.axis = 0.5, element.color = "darkgray", legend.loc = NULL, legend.labels = NULL, cex.legend = 0.8, xlim = NULL, ylim = NULL, ..., chart.assets = TRUE, labels.assets = TRUE, pch.assets = 21, cex.assets = 0.8, col = NULL, lty = NULL, lwd = NULL )chart.EfficientFrontierCompare( R, portfolio, risk_type, n.portfolios = 25, match.col = c("StdDev", "ES"), guideline = NULL, main = "Efficient Frontiers", plot_type = "l", cex.axis = 0.5, element.color = "darkgray", legend.loc = NULL, legend.labels = NULL, cex.legend = 0.8, xlim = NULL, ylim = NULL, ..., chart.assets = TRUE, labels.assets = TRUE, pch.assets = 21, cex.assets = 0.8, col = NULL, lty = NULL, lwd = NULL )
R |
an xts object of asset returns |
portfolio |
same constrained portfolio created by |
risk_type |
type of risk that you want to compare |
n.portfolios |
number of portfolios to extract along the efficient frontier.
This is only used for objects of class |
match.col |
string name of column to use for portfolio object. Must match the name of an objective. |
guideline |
show the risk difference and mean difference between efficient frontiers |
main |
title used in the plot. |
plot_type |
define the plot_type, default is "l" |
cex.axis |
the magnification to be used for sizing the axis text relative to the current setting of 'cex', similar to |
element.color |
provides the color for drawing less-important chart elements, such as the box lines, axis lines, etc. |
legend.loc |
location of the legend; NULL, "bottomright", "bottom", "bottomleft", "left", "topleft", "top", "topright", "right" and "center". |
legend.labels |
character vector to use for the legend labels. |
cex.legend |
The magnification to be used for sizing the legend relative to the current setting of 'cex', similar to |
xlim |
set the x-axis limit, same as in |
ylim |
set the y-axis limit, same as in |
... |
passthrough parameters to |
chart.assets |
TRUE/FALSE to include the assets. |
labels.assets |
TRUE/FALSE to include the asset names in the plot. |
pch.assets |
plotting character of the assets, same as in |
cex.assets |
A numerical value giving the amount by which the asset points and labels should be magnified relative to the default. |
col |
vector of colors with length equal to the number of portfolios in |
lty |
vector of line types with length equal to the number of portfolios in |
lwd |
vector of line widths with length equal to the number of portfolios in |
Xinran Zhao
Overlay the efficient frontiers of multiple portfolio objects on a single plot.
chart.EfficientFrontierOverlay( R, portfolio_list, type, n.portfolios = 25, match.col = "ES", search_size = 2000, main = "Efficient Frontiers", cex.axis = 0.8, element.color = "darkgray", legend.loc = NULL, legend.labels = NULL, cex.legend = 0.8, xlim = NULL, ylim = NULL, ..., chart.assets = TRUE, labels.assets = TRUE, pch.assets = 21, cex.assets = 0.8, col = NULL, lty = NULL, lwd = NULL )chart.EfficientFrontierOverlay( R, portfolio_list, type, n.portfolios = 25, match.col = "ES", search_size = 2000, main = "Efficient Frontiers", cex.axis = 0.8, element.color = "darkgray", legend.loc = NULL, legend.labels = NULL, cex.legend = 0.8, xlim = NULL, ylim = NULL, ..., chart.assets = TRUE, labels.assets = TRUE, pch.assets = 21, cex.assets = 0.8, col = NULL, lty = NULL, lwd = NULL )
R |
an xts object of asset returns |
portfolio_list |
list of portfolio objects created by
|
type |
type of efficient frontier, see |
n.portfolios |
number of portfolios to extract along the efficient frontier.
This is only used for objects of class |
match.col |
string name of column to use for risk (horizontal axis). Must match the name of an objective. |
search_size |
passed to optimize.portfolio for type="DEoptim" or type="random". |
main |
title used in the plot. |
cex.axis |
the magnification to be used for sizing the axis text relative to the current setting of 'cex', similar to |
element.color |
provides the color for drawing less-important chart elements, such as the box lines, axis lines, etc. |
legend.loc |
location of the legend; NULL, "bottomright", "bottom", "bottomleft", "left", "topleft", "top", "topright", "right" and "center". |
legend.labels |
character vector to use for the legend labels. |
cex.legend |
The magnification to be used for sizing the legend relative to the current setting of 'cex', similar to |
xlim |
set the x-axis limit, same as in |
ylim |
set the y-axis limit, same as in |
... |
passthrough parameters to |
chart.assets |
TRUE/FALSE to include the assets. |
labels.assets |
TRUE/FALSE to include the asset names in the plot. |
pch.assets |
plotting character of the assets, same as in |
cex.assets |
A numerical value giving the amount by which the asset points and labels should be magnified relative to the default. |
col |
vector of colors with length equal to the number of portfolios in |
lty |
vector of line types with length equal to the number of portfolios in |
lwd |
vector of line widths with length equal to the number of portfolios in |
Ross Bennett
Chart weights by group or category
chart.GroupWeights( object, ..., grouping = c("groups", "category"), plot.type = "line", main = "Group Weights", las = 3, xlab = NULL, cex.lab = 0.8, element.color = "darkgray", cex.axis = 0.8 )chart.GroupWeights( object, ..., grouping = c("groups", "category"), plot.type = "line", main = "Group Weights", las = 3, xlab = NULL, cex.lab = 0.8, element.color = "darkgray", cex.axis = 0.8 )
object |
object of class |
... |
passthrough parameters to |
grouping |
|
plot.type |
"line" or "barplot". |
main |
an overall title for the plot: see |
las |
numeric in {0,1,2,3}; the style of axis labels
|
xlab |
a title for the x axis: see |
cex.lab |
the magnification to be used for x and y labels relative to the current setting of |
element.color |
color for the default border and axis. |
cex.axis |
the magnification to be used for x and y axis relative to the current setting of |
Ross Bennett
This function is the generic method to chart risk budget objectives for
optimize.portfolio, optimize.portfolio.rebalancing, and
opt.list objects. This function charts the contribution or percent
contribution of the resulting objective measures of a
risk_budget_objective. The risk contributions for optimize.portfolio.rebalancing
objects are plotted through time with chart.StackedBar.
chart.RiskBudget(object, ...) ## S3 method for class 'optimize.portfolio' chart.RiskBudget( object, ..., neighbors = NULL, risk.type = "absolute", main = "Risk Contribution", ylab = "", xlab = NULL, cex.axis = 0.8, cex.lab = 0.8, element.color = "darkgray", las = 3, ylim = NULL ) ## S3 method for class 'optimize.portfolio.rebalancing' chart.RiskBudget( object, ..., match.col = "ES", risk.type = "absolute", regime = NULL, main = "Risk Contribution" ) ## S3 method for class 'opt.list' chart.RiskBudget( object, ..., match.col = "ES", risk.type = "absolute", main = "Risk Budget", plot.type = "line", cex.axis = 0.8, cex.lab = 0.8, element.color = "darkgray", las = 3, ylim = NULL, colorset = NULL, legend.loc = NULL, cex.legend = 0.8 )chart.RiskBudget(object, ...) ## S3 method for class 'optimize.portfolio' chart.RiskBudget( object, ..., neighbors = NULL, risk.type = "absolute", main = "Risk Contribution", ylab = "", xlab = NULL, cex.axis = 0.8, cex.lab = 0.8, element.color = "darkgray", las = 3, ylim = NULL ) ## S3 method for class 'optimize.portfolio.rebalancing' chart.RiskBudget( object, ..., match.col = "ES", risk.type = "absolute", regime = NULL, main = "Risk Contribution" ) ## S3 method for class 'opt.list' chart.RiskBudget( object, ..., match.col = "ES", risk.type = "absolute", main = "Risk Budget", plot.type = "line", cex.axis = 0.8, cex.lab = 0.8, element.color = "darkgray", las = 3, ylim = NULL, colorset = NULL, legend.loc = NULL, cex.legend = 0.8 )
object |
optimal portfolio object created by |
... |
any other passthru parameters to |
neighbors |
risk contribution or pct_contrib of neighbor portfolios to be plotted, see Details. |
risk.type |
"absolute" or "percentage" to plot risk contribution in absolute terms or percentage contribution. |
main |
main title for the chart. |
ylab |
label for the y-axis. |
xlab |
label for the x-axis. |
cex.axis |
the magnification to be used for axis annotation relative to the current setting of |
cex.lab |
the magnification to be used for axis annotation relative to the current setting of |
element.color |
provides the color for drawing less-important chart elements, such as the box lines, axis lines, etc. |
las |
numeric in {0,1,2,3}; the style of axis labels
|
ylim |
set the y-axis limit, same as in |
match.col |
string of risk column to match. The |
regime |
integer of the regime number. For use with
|
plot.type |
"line" or "barplot". |
colorset |
color palette or vector of colors to use |
legend.loc |
legend.loc NULL, "topright", "right", or "bottomright". If legend.loc is NULL, the legend will not be plotted |
cex.legend |
The magnification to be used for the legend relative to the current setting of |
neighbors may be specified in three ways.
The first is as a single number of neighbors. This will extract the
neighbors closest to the portfolios in terms of the out
numerical statistic.
The second method consists of a numeric vector for neighbors.
This will extract the neighbors with portfolio index numbers that
correspond to the vector contents.
The third method for specifying neighbors is to pass in a matrix.
This matrix should look like the output of extractStats, and
should contain properly named contribution and pct_contrib columns.
optimize.portfolio optimize.portfolio.rebalancing chart.StackedBar
This function charts the optimize.portfolio object in risk-return space.
chart.RiskReward(object, ...) ## S3 method for class 'optimize.portfolio.DEoptim' chart.RiskReward( object, ..., neighbors = NULL, return.col = "mean", risk.col = "ES", chart.assets = FALSE, element.color = "darkgray", cex.axis = 0.8, xlim = NULL, ylim = NULL ) ## S3 method for class 'optimize.portfolio.GenSA' chart.RiskReward( object, ..., neighbors = NULL, return.col = "mean", risk.col = "ES", chart.assets = FALSE, element.color = "darkgray", cex.axis = 0.8, ylim = NULL, xlim = NULL, rp = FALSE ) ## S3 method for class 'optimize.portfolio.pso' chart.RiskReward( object, ..., neighbors = NULL, return.col = "mean", risk.col = "ES", chart.assets = FALSE, element.color = "darkgray", cex.axis = 0.8, xlim = NULL, ylim = NULL ) ## S3 method for class 'optimize.portfolio.ROI' chart.RiskReward( object, ..., neighbors = NULL, return.col = "mean", risk.col = "ES", chart.assets = FALSE, element.color = "darkgray", cex.axis = 0.8, xlim = NULL, ylim = NULL, rp = FALSE ) ## S3 method for class 'optimize.portfolio.random' chart.RiskReward( object, ..., neighbors = NULL, return.col = "mean", risk.col = "ES", chart.assets = FALSE, element.color = "darkgray", cex.axis = 0.8, xlim = NULL, ylim = NULL ) ## S3 method for class 'opt.list' chart.RiskReward( object, ..., risk.col = "ES", return.col = "mean", main = "", ylim = NULL, xlim = NULL, labels.assets = TRUE, chart.assets = FALSE, pch.assets = 1, cex.assets = 0.8, cex.axis = 0.8, cex.lab = 0.8, colorset = NULL, element.color = "darkgray" )chart.RiskReward(object, ...) ## S3 method for class 'optimize.portfolio.DEoptim' chart.RiskReward( object, ..., neighbors = NULL, return.col = "mean", risk.col = "ES", chart.assets = FALSE, element.color = "darkgray", cex.axis = 0.8, xlim = NULL, ylim = NULL ) ## S3 method for class 'optimize.portfolio.GenSA' chart.RiskReward( object, ..., neighbors = NULL, return.col = "mean", risk.col = "ES", chart.assets = FALSE, element.color = "darkgray", cex.axis = 0.8, ylim = NULL, xlim = NULL, rp = FALSE ) ## S3 method for class 'optimize.portfolio.pso' chart.RiskReward( object, ..., neighbors = NULL, return.col = "mean", risk.col = "ES", chart.assets = FALSE, element.color = "darkgray", cex.axis = 0.8, xlim = NULL, ylim = NULL ) ## S3 method for class 'optimize.portfolio.ROI' chart.RiskReward( object, ..., neighbors = NULL, return.col = "mean", risk.col = "ES", chart.assets = FALSE, element.color = "darkgray", cex.axis = 0.8, xlim = NULL, ylim = NULL, rp = FALSE ) ## S3 method for class 'optimize.portfolio.random' chart.RiskReward( object, ..., neighbors = NULL, return.col = "mean", risk.col = "ES", chart.assets = FALSE, element.color = "darkgray", cex.axis = 0.8, xlim = NULL, ylim = NULL ) ## S3 method for class 'opt.list' chart.RiskReward( object, ..., risk.col = "ES", return.col = "mean", main = "", ylim = NULL, xlim = NULL, labels.assets = TRUE, chart.assets = FALSE, pch.assets = 1, cex.assets = 0.8, cex.axis = 0.8, cex.lab = 0.8, colorset = NULL, element.color = "darkgray" )
object |
optimal portfolio created by |
... |
any other passthru parameters. |
neighbors |
set of 'neighbor' portfolios to overplot, see Details. |
return.col |
string matching the objective of a 'return' objective, on vertical axis. |
risk.col |
string matching the objective of a 'risk' objective, on horizontal axis. |
chart.assets |
TRUE/FALSE. Includes a risk reward scatter of the assets in the chart. |
element.color |
color for the default plot scatter points. |
cex.axis |
The magnification to be used for axis annotation relative to the current setting of |
xlim |
set the x-axis limit, same as in |
ylim |
set the y-axis limit, same as in |
rp |
TRUE/FALSE to generate random portfolios to plot the feasible space |
main |
a main title for the plot. |
labels.assets |
TRUE/FALSE to include the names in the plot. |
pch.assets |
plotting character of the assets, same as in |
cex.assets |
numerical value giving the amount by which the asset points should be magnified relative to the default. |
cex.lab |
numerical value giving the amount by which the labels should be magnified relative to the default. |
colorset |
color palette or vector of colors to use. |
neighbors may be specified in three ways.
The first is as a single number of neighbors. This will extract the neighbors closest
portfolios in terms of the out numerical statistic.
The second method consists of a numeric vector for neighbors.
This will extract the neighbors with portfolio index numbers that correspond to the vector contents.
The third method for specifying neighbors is to pass in a matrix.
This matrix should look like the output of extractStats, and should contain
risk.col,return.col, and weights columns all properly named.
This function charts the optimal weights of a portfolio run via
optimize.portfolio or optimize.portfolio.rebalancing.
The upper and lower bounds on weights can be plotted for single period optimizations.
The optimal weights will be charted through time for optimize.portfolio.rebalancing
objects. For optimize.portfolio.rebalancing objects, the weights are
plotted with chart.StackedBar.
chart.Weights(object, ...) ## S3 method for class 'optimize.portfolio.rebalancing' chart.Weights(object, ..., main = "Weights") ## S3 method for class 'optimize.portfolio.DEoptim' chart.Weights( object, ..., neighbors = NULL, main = "Weights", las = 3, xlab = NULL, cex.lab = 1, element.color = "darkgray", cex.axis = 0.8, colorset = NULL, legend.loc = "topright", cex.legend = 0.8, plot.type = "line" ) ## S3 method for class 'optimize.portfolio.GenSA' chart.Weights( object, ..., neighbors = NULL, main = "Weights", las = 3, xlab = NULL, cex.lab = 1, element.color = "darkgray", cex.axis = 0.8, colorset = NULL, legend.loc = "topright", cex.legend = 0.8, plot.type = "line" ) ## S3 method for class 'optimize.portfolio.pso' chart.Weights( object, ..., neighbors = NULL, main = "Weights", las = 3, xlab = NULL, cex.lab = 1, element.color = "darkgray", cex.axis = 0.8, colorset = NULL, legend.loc = "topright", cex.legend = 0.8, plot.type = "line" ) ## S3 method for class 'optimize.portfolio.ROI' chart.Weights( object, ..., neighbors = NULL, main = "Weights", las = 3, xlab = NULL, cex.lab = 1, element.color = "darkgray", cex.axis = 0.8, colorset = NULL, legend.loc = "topright", cex.legend = 0.8, plot.type = "line" ) ## S3 method for class 'optimize.portfolio.random' chart.Weights( object, ..., neighbors = NULL, main = "Weights", las = 3, xlab = NULL, cex.lab = 1, element.color = "darkgray", cex.axis = 0.8, colorset = NULL, legend.loc = "topright", cex.legend = 0.8, plot.type = "line" ) ## S3 method for class 'opt.list' chart.Weights( object, neighbors = NULL, ..., main = "Weights", las = 3, xlab = NULL, cex.lab = 1, element.color = "darkgray", cex.axis = 0.8, colorset = NULL, legend.loc = "topright", cex.legend = 0.8, plot.type = "line" )chart.Weights(object, ...) ## S3 method for class 'optimize.portfolio.rebalancing' chart.Weights(object, ..., main = "Weights") ## S3 method for class 'optimize.portfolio.DEoptim' chart.Weights( object, ..., neighbors = NULL, main = "Weights", las = 3, xlab = NULL, cex.lab = 1, element.color = "darkgray", cex.axis = 0.8, colorset = NULL, legend.loc = "topright", cex.legend = 0.8, plot.type = "line" ) ## S3 method for class 'optimize.portfolio.GenSA' chart.Weights( object, ..., neighbors = NULL, main = "Weights", las = 3, xlab = NULL, cex.lab = 1, element.color = "darkgray", cex.axis = 0.8, colorset = NULL, legend.loc = "topright", cex.legend = 0.8, plot.type = "line" ) ## S3 method for class 'optimize.portfolio.pso' chart.Weights( object, ..., neighbors = NULL, main = "Weights", las = 3, xlab = NULL, cex.lab = 1, element.color = "darkgray", cex.axis = 0.8, colorset = NULL, legend.loc = "topright", cex.legend = 0.8, plot.type = "line" ) ## S3 method for class 'optimize.portfolio.ROI' chart.Weights( object, ..., neighbors = NULL, main = "Weights", las = 3, xlab = NULL, cex.lab = 1, element.color = "darkgray", cex.axis = 0.8, colorset = NULL, legend.loc = "topright", cex.legend = 0.8, plot.type = "line" ) ## S3 method for class 'optimize.portfolio.random' chart.Weights( object, ..., neighbors = NULL, main = "Weights", las = 3, xlab = NULL, cex.lab = 1, element.color = "darkgray", cex.axis = 0.8, colorset = NULL, legend.loc = "topright", cex.legend = 0.8, plot.type = "line" ) ## S3 method for class 'opt.list' chart.Weights( object, neighbors = NULL, ..., main = "Weights", las = 3, xlab = NULL, cex.lab = 1, element.color = "darkgray", cex.axis = 0.8, colorset = NULL, legend.loc = "topright", cex.legend = 0.8, plot.type = "line" )
object |
optimal portfolio object created by |
... |
any other passthru parameters . |
main |
an overall title for the plot: see |
neighbors |
set of 'neighbor' portfolios to overplot. See Details. |
las |
numeric in {0,1,2,3}; the style of axis labels
|
xlab |
a title for the x axis: see |
cex.lab |
The magnification to be used for x and y labels relative to the current setting of |
element.color |
provides the color for drawing less-important chart elements, such as the box lines, axis lines, etc. |
cex.axis |
The magnification to be used for axis annotation relative to the current setting of |
colorset |
color palette or vector of colors to use. |
legend.loc |
location of the legend. If NULL, the legend will not be plotted. |
cex.legend |
The magnification to be used for legend annotation relative to the current setting of |
plot.type |
"line" or "barplot" to plot. |
optimize.portfolio optimize.portfolio.rebalancing chart.StackedBar
This function checks if a set of weights satisfies all constraints. This is
used as a helper function for random portfolios created with rp_simplex
and rp_grid to eliminate portfolios that do not satisfy the constraints.
check_constraints(weights, portfolio)check_constraints(weights, portfolio)
weights |
vector of weights |
portfolio |
object of class 'portfolio' |
TRUE if all constraints are satisfied, FALSE if any constraint is violated
Ross Bennett
Estimate cokurtosis matrix using a statistical factor model
cokurtosisMF(beta, stockM2, stockM4, factorM2, factorM4)cokurtosisMF(beta, stockM2, stockM4, factorM2, factorM4)
beta |
(N x k) matrix of factor loadings (i.e. the betas) from a statistical factor model |
stockM2 |
vector of length N of the 2nd moment of the model residuals |
stockM4 |
vector of length N of the 4th moment of the model residuals |
factorM2 |
(k x k) matrix of the 2nd moment of the factor realizations from a statistical factor model |
factorM4 |
(k x k^3) matrix of the 4th moment of the factor realizations from a statistical factor model |
This function estimates an (N x N^3) cokurtosis matrix from a statistical factor model with k factors, where N is the number of assets.
(N x N^3) cokurtosis matrix
Estimate cokurtosis matrix using a single factor statistical factor model
cokurtosisSF(beta, stockM2, stockM4, factorM2, factorM4)cokurtosisSF(beta, stockM2, stockM4, factorM2, factorM4)
beta |
vector of length N or (N x 1) matrix of factor loadings (i.e. the betas) from a single factor statistical factor model |
stockM2 |
vector of length N of the 2nd moment of the model residuals |
stockM4 |
vector of length N of the 4th moment of the model residuals |
factorM2 |
scalar of the 2nd moment of the factor realizations from a single factor statistical factor model |
factorM4 |
scalar of the 4th moment of the factor realizations from a single factor statistical factor model |
This function estimates an (N x N^3) cokurtosis matrix from a statistical factor model with k factors, where N is the number of assets.
(N x N^3) cokurtosis matrix
This function takes a list of objects created by optimize.portfolio
and sets the class name attribute to 'opt.list' for use in generic functions
combine.optimizations(x)combine.optimizations(x)
x |
a list of objects created by |
an opt.list object
This function takes a list of objects created by portfolio.spec
and sets the class name attribute to 'portfolio.list' for use in generic functions
combine.portfolios(x)combine.portfolios(x)
x |
a list of objects created by |
a portfolio.list object
Function to calculate a numeric return value for a portfolio based on a set of constraints and objectives. We'll try to make as few assumptions as possible and only run objectives that are enabled by the user.
constrained_objective_v1( w, R, constraints, ..., trace = FALSE, normalize = TRUE, storage = FALSE ) constrained_objective( w, R, portfolio, ..., trace = FALSE, normalize = TRUE, storage = FALSE, env = NULL )constrained_objective_v1( w, R, constraints, ..., trace = FALSE, normalize = TRUE, storage = FALSE ) constrained_objective( w, R, portfolio, ..., trace = FALSE, normalize = TRUE, storage = FALSE, env = NULL )
w |
a vector of weights to test. |
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns. |
constraints |
a v1_constraint object for backwards compatibility with |
... |
any other passthru parameters. |
trace |
TRUE/FALSE whether to include debugging and additional detail in the output list. The default is FALSE. Several charting functions require that |
normalize |
TRUE/FALSE whether to normalize results to min/max sum (TRUE), or let the optimizer penalize portfolios that do not conform (FALSE) |
storage |
TRUE/FALSE default TRUE for DEoptim with trace, otherwise FALSE. not typically user-called. |
portfolio |
an object of class |
env |
environment of moments calculated in |
If the user has passed in either min_sum or max_sum constraints for the portfolio, or both,
and are using a numerical optimization method like DEoptim, and normalize=TRUE,
we'll normalize the weights passed in to whichever boundary condition has been violated.
If using random portfolios, all the portfolios generated will meet the constraints by construction.
NOTE: this means that the weights produced by a numeric optimization algorithm like DEoptim, pso, or GenSA
might violate constraints, and will need to be renormalized after optimizing.
We apply the same normalization in optimize.portfolio so that the weights you see have been
normalized to min_sum if the generated portfolio is smaller than min_sum or max_sum if the
generated portfolio is larger than max_sum.
This normalization increases the speed of optimization and convergence by several orders of magnitude in many cases.
You may find that for some portfolios, normalization is not desirable, if the algorithm cannot find a direction in which to move to head towards an optimal portfolio. In these cases, it may be best to set normalize=FALSE, and penalize the portfolios if the sum of the weighting vector lies outside the min_sum and/or max_sum.
Whether or not we normalize the weights using min_sum and max_sum, and are using a numerical optimization engine like DEoptim, we will penalize portfolios that violate weight constraints in much the same way we penalize other constraints. If a min_sum/max_sum normalization has not occurred, convergence can take a very long time. We currently do not allow for a non-normalized full investment constraint. Future version of this function could include this additional constraint penalty.
When you are optimizing a return objective, you must specify a negative multiplier for the return objective so that the function will maximize return. If you specify a target return, any return that deviates from your target will be penalized. If you do not specify a target return, you may need to specify a negative VTR (value to reach) , or the function will not converge. Try the maximum expected return times the multiplier (e.g. -1 or -10). Adding a return objective defaults the multiplier to -1.
Additional parameters for other solvers
(e.g. random portfolios or
DEoptim.control or pso or GenSA
may be passed in via ...
Kris Boudt, Peter Carl, Brian G. Peterson, Ross Bennett
constraint, objective, DEoptim.control
constructor for class constraint_ROI
constraint_ROI( assets = NULL, op.problem, solver = c("glpk", "quadprog"), weight_seq = NULL )constraint_ROI( assets = NULL, op.problem, solver = c("glpk", "quadprog"), weight_seq = NULL )
assets |
number of assets, or optionally a named vector of assets specifying seed weights |
op.problem |
an object of type "OP" (optimization problem, of |
solver |
string argument for what solver package to use, must have ROI plugin installed for that solver. Currently support is for |
weight_seq |
seed sequence of weights, see |
Hezky Varon
See main documentation entry in add.constraint.
constraint_v1( assets = NULL, ..., min, max, min_mult, max_mult, min_sum = 0.99, max_sum = 1.01, weight_seq = NULL ) constraint(type, enabled = TRUE, ..., constrclass = "v2_constraint")constraint_v1( assets = NULL, ..., min, max, min_mult, max_mult, min_sum = 0.99, max_sum = 1.01, weight_seq = NULL ) constraint(type, enabled = TRUE, ..., constrclass = "v2_constraint")
assets |
number of assets, or optionally a named vector of assets specifying initial weights |
... |
any other passthru parameters |
min |
numeric or named vector specifying minimum weight box constraints |
max |
numeric or named vector specifying minimum weight box constraints |
min_mult |
numeric or named vector specifying minimum multiplier box constraint from initial weight in |
max_mult |
numeric or named vector specifying maximum multiplier box constraint from initial weight in |
min_sum |
minimum sum of all asset weights, default .99 |
max_sum |
maximum sum of all asset weights, default 1.01 |
weight_seq |
seed sequence of weights, see |
type |
character type of the constraint to add or update |
enabled |
TRUE/FALSE to enabled the constraint |
constrclass |
name of class for the constraint |
This includes the deprecated constructor for the v1_constraint object for backwards compatibility.
Peter Carl, Brian G. Peterson, Ross Bennett
Estimate coskewness matrix using a statistical factor model
coskewnessMF(beta, stockM3, factorM3)coskewnessMF(beta, stockM3, factorM3)
beta |
(N x k) matrix of factor loadings (i.e. the betas) from a statistical factor model |
stockM3 |
vector of length N of the 3rd moment of the model residuals |
factorM3 |
(k x k^2) matrix of the 3rd moment of the factor realizations from a statistical factor model |
This function estimates an (N x N^2) coskewness matrix from a statistical factor model with k factors, where N is the number of assets.
(N x N^2) coskewness matrix
Estimate coskewness matrix using a single factor statistical factor model
coskewnessSF(beta, stockM3, factorM3)coskewnessSF(beta, stockM3, factorM3)
beta |
vector of length N or (N x 1) matrix of factor loadings (i.e. the betas) from a single factor statistical factor model |
stockM3 |
vector of length N of the 3rd moment of the model residuals |
factorM3 |
scalar of the 3rd moment of the factor realizations from a single factor statistical factor model |
This function estimates an (N x N^2) coskewness matrix from a single factor statistical factor model with k=1 factors, where N is the number of assets.
(N x N^2) coskewness matrix
Estimate covariance matrix using a statistical factor model
covarianceMF(beta, stockM2, factorM2)covarianceMF(beta, stockM2, factorM2)
beta |
(N x k) matrix of factor loadings (i.e. the betas) from a statistical factor model |
stockM2 |
vector of length N of the variance (2nd moment) of the model residuals (i.e. idiosyncratic variance of the stock) |
factorM2 |
(k x k) matrix of the covariance (2nd moment) of the factor realizations from a statistical factor model |
This function estimates an (N x N) covariance matrix from a statistical factor model with k factors, where N is the number of assets.
(N x N) covariance matrix
Estimate covariance matrix using a single factor statistical factor model
covarianceSF(beta, stockM2, factorM2)covarianceSF(beta, stockM2, factorM2)
beta |
vector of length N or (N x 1) matrix of factor loadings (i.e. the betas) from a single factor statistical factor model |
stockM2 |
vector of length N of the variance (2nd moment) of the model residuals (i.e. idiosyncratic variance of the stock) |
factorM2 |
scalar value of the 2nd moment of the factor realizations from a single factor statistical factor model |
This function estimates an (N x N) covariance matrix from a single factor statistical factor model with k=1 factors, where N is the number of assets.
(N x N) covariance matrix
create an efficient frontier
create.EfficientFrontier( R, portfolio, type, optimize_method = "CVXR", n.portfolios = 25, risk_aversion = NULL, match.col = "ES", search_size = 2000, ... )create.EfficientFrontier( R, portfolio, type, optimize_method = "CVXR", n.portfolios = 25, risk_aversion = NULL, match.col = "ES", search_size = 2000, ... )
R |
xts object of asset returns |
portfolio |
object of class 'portfolio' specifying the constraints and objectives, see |
type |
type of efficient frontier, see Details. |
optimize_method |
the optimize method to get the efficient frontier, default is CVXR |
n.portfolios |
number of portfolios to calculate along the efficient frontier |
risk_aversion |
vector of risk_aversion values to construct the efficient frontier.
|
match.col |
column to match when extracting the efficient frontier from an objected created by |
search_size |
passed to |
... |
passthrough parameters to |
Currently there are 4 'types' supported to create an efficient frontier:
This is a special case for
an efficient frontier that can be created by a QP solver.
The portfolio object should have two
objectives: 1) mean and 2) var. If the portfolio object does not contain these
objectives, they will be added using default parameters.
The efficient frontier will be created via
meanvar.efficient.frontier.
This is a special
case for an efficient frontier that can be created by an LP solver.
The portfolio object should have two objectives: 1) mean
and 2) ETL/ES/CVaR. If the portfolio object does not contain these
objectives, they will be added using default parameters.
The efficient frontier is created via
meanetl.efficient.frontier.
This is a special
case for an efficient frontier that can be created by CVXR solvers.
The portfolio object should have two objectives: 1) mean
and 2) CSM. If the portfolio object does not contain these
objectives, they will be added using default parameters.
The efficient frontier is created via
meanrisk.efficient.frontier.
This is a special case for multiple efficient frontiers.
The efficient frontier is created via
meanrisk.efficient.frontier.
This can handle more complex constraints and objectives
than the simple mean-var and mean-ETL cases. For this type, we actually
call optimize.portfolio with optimize_method="DEoptim"
and then extract the efficient frontier with
extract.efficient.frontier.
This can handle more complex constraints and objectives
than the simple mean-var and mean-ETL cases. For this type, we actually
call optimize.portfolio with optimize_method="random"
and then extract the efficient frontier with
extract.efficient.frontier.
an object of class 'efficient.frontier' with the objective measures and weights of portfolios along the efficient frontier.
Ross Bennett, Xinran Zhao
optimize.portfolio,
portfolio.spec,
meanvar.efficient.frontier,
meanetl.efficient.frontier
custom.covRob.Mcd uses the robustbase package function covMcd to compute a robust mean vector and robust covariance matrix for a portfolio's asset returns
custom.covRob.Mcd(R, ...)custom.covRob.Mcd(R, ...)
R |
xts object of asset returns |
... |
parameters for covRob.Mcd |
For parameter details, see covMcd in the robustbase Reference Manual at https://CRAN.R-project.org/package=robustbase
a list containing covariance matrix sigma and mean vector mu
custom.covRob.MM uses the RobStatTM package function covRobMM to compute a robust mean vector and robust covariance matrix for a portfolio's asset returns
custom.covRob.MM(R, ...)custom.covRob.MM(R, ...)
R |
xts object of asset returns |
... |
parameters for covRob.MM |
a list containing covariance matrix sigma and mean vector mu
Yifu Kang, Xinran Zhao
For parameter details, see covRobMM in the RobStatTM Reference Manual at https://CRAN.R-project.org/package=RobStatTM
custom.covRob.Rocke uses the RobStatTM package function covRobRocke to compute a robust mean vector and robust covariance matrix for a portfolio's asset returns
custom.covRob.Rocke(R, ...)custom.covRob.Rocke(R, ...)
R |
xts object of asset returns |
... |
parameters for covRob.Rocke |
For parameter details, see covRobRocke in the RobStatTM Reference Manual at https://CRAN.R-project.org/package=RobStatTM
a list containing covariance matrix sigma and mean vector mu
Yifu Kang
This is a function uses the TSGS function from GSE package to compute the Two-Step Generalized S-Estimate, a robust estimate of location and scatter for data with cell-wise and case-wise contamination.
custom.covRob.TSGS(R, ...)custom.covRob.TSGS(R, ...)
R |
xts object of asset returns |
... |
parameters for covRob.TSGS |
a list contains mean and covariance matrix of the stock return matrix
Claudio Agostinelli, Andy Leung, "Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination", 2014.
Diversification is defined as 1 minus the sum of the squared weights
diversification(weights)diversification(weights)
weights |
vector of asset weights |
Ross Bennett
The diversification constraint specifies a target diversification value.
This function is called by add.constraint when type="diversification" is
specified, see add.constraint. Diversification is computed
as 1 - sum(weights^2).
diversification_constraint( type = "diversification", div_target = NULL, enabled = TRUE, message = FALSE, ... )diversification_constraint( type = "diversification", div_target = NULL, enabled = TRUE, message = FALSE, ... )
type |
character type of the constraint |
div_target |
diversification target value |
enabled |
TRUE/FALSE |
message |
TRUE/FALSE. The default is message=FALSE. Display messages if TRUE. |
... |
any other passthru parameters to specify diversification constraint an object of class 'diversification_constraint' |
Ross Bennett
data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) pspec <- add.constraint(portfolio=pspec, type="diversification", div_target=0.7)data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) pspec <- add.constraint(portfolio=pspec, type="diversification", div_target=0.7)
Entropy program will change the initial predictive distribution 'p' to a new set 'p_' that satisfies specified moment conditions but changes other propoerties of the new distribution the least by minimizing the relative entropy between the two distributions. Theoretical note: Relative Entropy (Kullback-Leibler information criterion KLIC) is an asymmetric measure.
EntropyProg(p, A = NULL, b = NULL, Aeq, beq, verbose = FALSE)EntropyProg(p, A = NULL, b = NULL, Aeq, beq, verbose = FALSE)
p |
a vector of initial probabilities based on prior (reference model, empirical distribution, etc.). Sum of 'p' must be 1 |
A |
matrix consisting of inequality constraints (paired with argument 'b'). Denoted as 'F' in the Meucci paper |
b |
vector consisting of inequality constraints (paired with matrix A). Denoted as 'f' in the Meucci paper |
Aeq |
matrix consisting of equality constraints (paired with argument 'beq'). Denoted as 'H' in the Meucci paper. (denoted as 'H' in the "Meucci - Flexible Views Theory & Practice" paper formlua 86 on page 22) |
beq |
vector corresponding to the matrix of equality constraints (paired with argument 'Aeq'). Denoted as 'h' in the Meucci paper |
verbose |
If TRUE, prints out additional information. Default FALSE. '
|
We retrieve a new set of probabilities for the joint-scenarios using the Entropy pooling method Of the many choices of 'p' that satisfy the views, we choose 'p' that minimize the entropy or distance of the new probability distribution to the prior joint-scenario probabilities.
We use Kullback-Leibler divergence or relative entropy dist(p,q): Sum across all scenarios [ p-t * ln( p-t / q-t ) ] Therefore we define solution as p* = argmin (choice of p ) [ sum across all scenarios: p-t * ln( p-t / q-t) ], such that 'p' satisfies views. The views modify the prior in a cohrent manner (minimizing distortion) We forumulate the stress tests of the baseline scenarios as linear constraints on yet-to-be defined probabilities Note that the numerical optimization acts on a very limited number of variables equal to the number of views. It does not act directly on the very large number of variables of interest, namely the probabilities of the Monte Carlo scenarios. This feature guarantees the numerical feasability of entropy optimization.
Note that new probabilities are generated in much the same way that the state-price density modifies objective probabilities of pay-offs to risk-neutral probabilities in contingent-claims asset pricing
Compute posterior (=change of measure) with Entropy Pooling, as described in
a list with
p_:revised probabilities based on entropy pooling
optimizationPerformance:a list with status of optimization, value, number of iterations, and sum of probabilities
Ram Ahluwalia [email protected]
A. Meucci - "Fully Flexible Views: Theory and Practice". See page 22 for illustration of numerical implementation Symmys site containing original MATLAB source code https://www.arpm.co/ NLOPT open-source optimization site containing background on algorithms https://nlopt.readthedocs.io/en/latest/ We use the information-theoretic estimator of Kitamur and Stutzer (1997). Reversing 'p' and 'p_' leads to the empirical likelihood" estimator of Qin and Lawless (1994). See Robertson et al, "Forecasting Using Relative Entropy" (2002) for more theory
This function calculates objective measures for an equal weight portfolio.
equal.weight(R, portfolio, ...)equal.weight(R, portfolio, ...)
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
portfolio |
an object of type "portfolio" specifying the constraints and objectives for the optimization |
... |
any other passthru parameters to |
This function is simply a wrapper around constrained_objective
to calculate the objective measures in the given portfolio object of
an equal weight portfolio. The portfolio object should include all objectives
to be calculated.
a list containing the returns, weights, objective measures, call, and portfolio object
Ross Bennett
This function is called by optimize.portfolio to solve minimum ETL problems via mixed integer linear programming.
etl_milp_opt( R, constraints, moments, target, alpha, solver = "glpk", control = NULL )etl_milp_opt( R, constraints, moments, target, alpha, solver = "glpk", control = NULL )
R |
xts object of asset returns |
constraints |
object of constraints in the portfolio object extracted with |
moments |
object of moments computed based on objective functions |
target |
target return value |
alpha |
alpha value for ETL/ES/CVaR |
solver |
solver to use |
control |
list of solver control parameters |
Ross Bennett
This function is called by optimize.portfolio to solve minimum ETL problems.
etl_opt( R, constraints, moments, target, alpha, solver = "glpk", control = NULL )etl_opt( R, constraints, moments, target, alpha, solver = "glpk", control = NULL )
R |
xts object of asset returns |
constraints |
object of constraints in the portfolio object extracted with |
moments |
object of moments computed based on objective functions |
target |
target return value |
alpha |
alpha value for ETL/ES/CVaR |
solver |
solver to use |
control |
list of solver control parameters |
Ross Bennett
extract the risk value when knowing the weights
extract_risk(R, w, ES_alpha = 0.05, CSM_alpha = 0.05, moment_setting = NULL)extract_risk(R, w, ES_alpha = 0.05, CSM_alpha = 0.05, moment_setting = NULL)
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
w |
the weight of the portfolio |
ES_alpha |
the default value is 0.05, but could be specified as any value between 0 and 1 |
CSM_alpha |
the default value is 0.05, but could be specified as any value between 0 and 1 |
moment_setting |
the default is NULL, should provide moment_setting=list(mu=, sigma=) if customize momentFUN |
Extract the cokurtosis matrix estimate from a statistical factor model
extractCokurtosis(model, ...)extractCokurtosis(model, ...)
model |
statistical factor model estimated via
|
... |
not currently used |
cokurtosis matrix estimate
Ross Bennett
Extract the coskewness matrix estimate from a statistical factor model
extractCoskewness(model, ...)extractCoskewness(model, ...)
model |
statistical factor model estimated via
|
... |
not currently used |
coskewness matrix estimate
Ross Bennett
Extract the covariance matrix estimate from a statistical factor model
extractCovariance(model, ...)extractCovariance(model, ...)
model |
statistical factor model estimated via
|
... |
not currently used |
covariance matrix estimate
Ross Bennett
This function extracts the efficient frontier from an object created by
optimize.portfolio.
extractEfficientFrontier( object, match.col = "ES", n.portfolios = 25, risk_aversion = NULL )extractEfficientFrontier( object, match.col = "ES", n.portfolios = 25, risk_aversion = NULL )
object |
an optimal portfolio object created by |
match.col |
string name of column to use for risk (horizontal axis).
|
n.portfolios |
number of portfolios to use to plot the efficient frontier |
risk_aversion |
vector of risk_aversion values to construct the efficient frontier.
|
If the object is an optimize.portfolio.ROI object and match.col
is "ES", "ETL", or "CVaR", then the mean-ETL efficient frontier will be
created via meanetl.efficient.frontier.
If the object is an optimize.portfolio.ROI object and match.col
is "StdDev", then the mean-StdDev efficient frontier will be created via
meanvar.efficient.frontier. Note that if 'var' is specified as the
name of an objective, the value returned will be 'StdDev'.
For objects created by optimize.portfolo with the DEoptim, random, or
pso solvers, the efficient frontier will be extracted from the object via
extract.efficient.frontier. This means that optimize.portfolio must
be run with trace=TRUE.
an efficient.frontier object with weights and other metrics along the efficient frontier
Ross Bennett
This function extracts the weights by group and/or category from an object
of class optimize.portfolio. Group constraints or category_labels must
be specified for this to return group constraints.
extractGroups(object, ...)extractGroups(object, ...)
object |
object of class |
... |
passthrough parameters. Not currently used |
a list with two elements
Optimal set of weights from the optimize.portfolio object
Weights by category if category_labels are supplied in the portfolio object
Weights by group if group is a constraint type
Ross Bennett
This function will extract the objective measures from the optimal portfolio
run via optimize.portfolio
extractObjectiveMeasures(object)extractObjectiveMeasures(object)
object |
list returned by optimize.portfolio |
list of objective measures
Ross Bennett
optimize.portfolio
This function will dispatch to the appropriate class handler based on the input class of the optimize.portfolio output object.
extractStats(object, prefix = NULL, ...)extractStats(object, prefix = NULL, ...)
object |
list returned by optimize.portfolio |
prefix |
prefix to add to output row names |
... |
any other passthru parameters |
For optimize.portfolio objects:
In general, extractStats will extract the values objective measures
and weights at each iteration of a set of weights. This is the case for the
DEoptim, random portfolios, and pso solvers that return trace information.
Note that trace=TRUE must be specified in optimize.portfolio
to return the trace information.
For optimize.portfolio.pso objects, this function will extract the
weights (swarm positions) from the PSO output and the out values
(swarm fitness values) for each iteration of the optimization.
This function can be slow because we need to run constrained_objective
to calculate the objective measures on the transformed weights.
For optimize.portfolio.rebalancing objects:
The extractStats function will return a list of the objective measures
and weights at each rebalance date for optimize.portfolio.rebalancing
objects. The objective measures and weights of each iteration or permutation
will be returned if the optimization was done with DEoptim, random portfolios,
or pso. This could potentially result in a very large list object where each
list element has thousands of rows of at each rebalance period.
The output from the GenSA solver does not store weights evaluated at each iteration The GenSA output for trace.mat contains nb.steps, temperature, function.value, and current.minimum
optimize.portfolio or optimize.portfolio.rebalancing
This function will dispatch to the appropriate class handler based on the input class of the optimize.portfolio or optimize.portfolio.rebalancing output object
extractWeights(object, ...)extractWeights(object, ...)
object |
list returned by optimize.portfolio |
... |
any other passthru parameters |
optimize.portfolio, optimize.portfolio.rebalancing
The factor exposure constraint sets upper and lower bounds on exposures to risk factors.
This function is called by add.constraint when type="factor_exposure" is specified, see add.constraint
factor_exposure_constraint( type = "factor_exposure", assets, B, lower, upper, enabled = TRUE, message = FALSE, ... )factor_exposure_constraint( type = "factor_exposure", assets, B, lower, upper, enabled = TRUE, message = FALSE, ... )
type |
character type of the constraint |
assets |
named vector of assets specifying initial weights |
B |
vector or matrix of risk factor exposures |
lower |
vector of lower bounds of constraints for risk factor exposures |
upper |
vector of upper bounds of constraints for risk factor exposures |
enabled |
TRUE/FALSE |
message |
TRUE/FALSE. The default is message=FALSE. Display messages if TRUE. |
... |
any other passthru parameters to specify risk factor exposure constraints |
B can be either a vector or matrix of risk factor exposures (i.e. betas).
If B is a vector, the length of B must be equal to the number of
assets and lower and upper must be scalars. If B is passed in as a vector,
it will be converted to a matrix with one column.
If B is a matrix, the number of rows must be equal to the number
of assets and the number of columns represent the number of factors. The length
of lower and upper must be equal to the number of factors. The B matrix should
have column names specifying the factors and row names specifying the assets.
Default column names and row names will be assigned if the user passes in a
B matrix without column names or row names.
an object of class 'factor_exposure_constraint'
Ross Bennett
The purpose of the mapping function is to transform a weights vector that does not meet all the constraints into a weights vector that does meet the constraints, if one exists, hopefully with a minimum of transformation.
fn_map(weights, portfolio, relax = FALSE, verbose = FALSE, ...)fn_map(weights, portfolio, relax = FALSE, verbose = FALSE, ...)
weights |
vector of weights |
portfolio |
object of class |
relax |
TRUE/FALSE, default FALSE. Enable constraints to be relaxed. |
verbose |
print error messages for debuggin purposes |
... |
any other passthru parameters |
The first step is to test for violation of the constraint. If the constraint is violated, we will apply a transformation such that the weights vector satisfies the constraints. The following constraint types are tested in the mapping function: leverage, box, group, and position limit. The transformation logic is based on code from the random portfolio sample method.
If relax=TRUE, we will attempt to relax the constraints if a feasible
portfolio could not be formed with an initial call to rp_transform.
We will attempt to relax the constraints up to 5 times. If we do not have a
feasible portfolio after attempting to relax the constraints, then we will
default to returning the weights vector that violates the constraints.
vector of transformed weights meeting constraints.
vector of min box constraints that may have been modified if relax=TRUE.
vector of max box constraints that may have been modified if relax=TRUE.
vector of lower bound group constraints that may have been modified if relax=TRUE.
vector of upper bound group constraints that may have been modified if relax=TRUE.
Ross Bennett
This function creates the sequence of min<->max weights for use by random or brute force optimization engines.
generatesequence(min = 0.01, max = 1, by = min/max, rounding = 3)generatesequence(min = 0.01, max = 1, by = min/max, rounding = 3)
min |
minimum value of the sequence |
max |
maximum value of the sequence |
by |
number to increment the sequence by |
rounding |
integrer how many decimals should we round to |
The sequence created is not constrained by asset.
Peter Carl, Brian G. Peterson
optimize.portfolio and constrained_objective . This function
will check that these variables are in the portfolio object in the
constraints list. We will default to min_sum=1 and max_sum=1
if leverage constraints are not specified. We will default to min=-Inf
and max=Inf if box constraints are not specified.
This function is used at the beginning of optimize.portfolio and other
functions to extract the constraints from the portfolio object. We Use the
same naming as the v1_constraint object.Helper function to get the enabled constraints out of the portfolio object
When the v1_constraint object is instantiated via constraint, the arguments
min_sum, max_sum, min, and max are either specified by the user or default
values are assigned. These are required by other functions such as
optimize.portfolio and constrained_objective . This function
will check that these variables are in the portfolio object in the
constraints list. We will default to min_sum=1 and max_sum=1
if leverage constraints are not specified. We will default to min=-Inf
and max=Inf if box constraints are not specified.
This function is used at the beginning of optimize.portfolio and other
functions to extract the constraints from the portfolio object. We Use the
same naming as the v1_constraint object.
get_constraints(portfolio)get_constraints(portfolio)
portfolio |
an object of class 'portfolio' |
an object of class 'constraint' which is a flattened list of enabled constraints
Ross Bennett
This function is called by optimize.portfolio to solve minimum variance or maximum quadratic utility problems
gmv_opt( R, constraints, moments, lambda, target, lambda_hhi, conc_groups, solver = "quadprog", control = NULL )gmv_opt( R, constraints, moments, lambda, target, lambda_hhi, conc_groups, solver = "quadprog", control = NULL )
R |
xts object of asset returns |
constraints |
object of constraints in the portfolio object extracted with |
moments |
object of moments computed based on objective functions |
lambda |
risk_aversion parameter |
target |
target return value |
lambda_hhi |
concentration aversion parameter |
conc_groups |
list of vectors specifying the groups of the assets. |
solver |
solver to use |
control |
list of solver control parameters |
Ross Bennett
This function is called by optimize.portfolio to solve minimum variance or maximum quadratic utility problems with a leverage constraint
gmv_opt_leverage( R, constraints, moments, lambda, target, solver = "quadprog", control = NULL )gmv_opt_leverage( R, constraints, moments, lambda, target, solver = "quadprog", control = NULL )
R |
xts object of asset returns |
constraints |
object of constraints in the portfolio object extracted with |
moments |
object of moments computed based on objective functions |
lambda |
risk_aversion parameter |
target |
target return value |
solver |
solver to use |
control |
list of solver control parameters |
Ross Bennett
This function is called by optimize.portfolio to solve minimum variance or maximum quadratic utility problems with proportional transaction cost constraint
gmv_opt_ptc( R, constraints, moments, lambda, target, init_weights, solver = "quadprog", control = NULL )gmv_opt_ptc( R, constraints, moments, lambda, target, init_weights, solver = "quadprog", control = NULL )
R |
xts object of asset returns |
constraints |
object of constraints in the portfolio object extracted with |
moments |
object of moments computed based on objective functions |
lambda |
risk_aversion parameter |
target |
target return value |
init_weights |
initial weights to compute turnover |
solver |
solver to use |
control |
list of solver control parameters |
Ross Bennett
This function is called by optimize.portfolio to solve minimum variance or maximum quadratic utility problems with turnover constraint
gmv_opt_toc( R, constraints, moments, lambda, target, init_weights, solver = "quadprog", control = NULL )gmv_opt_toc( R, constraints, moments, lambda, target, init_weights, solver = "quadprog", control = NULL )
R |
xts object of asset returns |
constraints |
object of constraints in the portfolio object extracted with |
moments |
object of moments computed based on objective functions |
lambda |
risk_aversion parameter |
target |
target return value |
init_weights |
initial weights to compute turnover |
solver |
solver to use |
control |
list of solver control parameters |
Ross Bennett
Group constraints specify the grouping of the assets, weights of the groups, and number of postions (i.e. non-zero weights) iof the groups.
This function is called by add.constraint when type="group" is specified. see add.constraint
group_constraint( type = "group", assets, groups, group_labels = NULL, group_min, group_max, group_pos = NULL, enabled = TRUE, message = FALSE, ... )group_constraint( type = "group", assets, groups, group_labels = NULL, group_min, group_max, group_pos = NULL, enabled = TRUE, message = FALSE, ... )
type |
character type of the constraint |
assets |
number of assets, or optionally a named vector of assets specifying initial weights |
groups |
list of vectors specifying the groups of the assets |
group_labels |
character vector to label the groups (e.g. size, asset class, style, etc.) |
group_min |
numeric or vector specifying minimum weight group constraints |
group_max |
numeric or vector specifying minimum weight group constraints |
group_pos |
vector specifying the number of non-zero weights per group |
enabled |
TRUE/FALSE |
message |
TRUE/FALSE. The default is message=FALSE. Display messages if TRUE. |
... |
any other passthru parameters to specify group constraints |
an object of class 'group_constraint'
Ross Bennett
data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) # Assets 1 and 3 are groupA # Assets 2 and 4 are groupB pspec <- add.constraint(portfolio=pspec, type="group", groups=list(groupA=c(1, 3), groupB=c(2, 4)), group_min=c(0.15, 0.25), group_max=c(0.65, 0.55)) # 2 levels of grouping (e.g. by sector and geography) pspec <- portfolio.spec(assets=5) # Assets 1, 3, and 5 are Tech # Assets 2 and 4 are Oil # Assets 2, 4, and 5 are UK # Assets 1 and are are US group_list <- list(group1=c(1, 3, 5), group2=c(2, 4), groupA=c(2, 4, 5), groupB=c(1, 3)) pspec <- add.constraint(portfolio=pspec, type="group", groups=group_list, group_min=c(0.15, 0.25, 0.2, 0.1), group_max=c(0.65, 0.55, 0.5, 0.4))data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) # Assets 1 and 3 are groupA # Assets 2 and 4 are groupB pspec <- add.constraint(portfolio=pspec, type="group", groups=list(groupA=c(1, 3), groupB=c(2, 4)), group_min=c(0.15, 0.25), group_max=c(0.65, 0.55)) # 2 levels of grouping (e.g. by sector and geography) pspec <- portfolio.spec(assets=5) # Assets 1, 3, and 5 are Tech # Assets 2 and 4 are Oil # Assets 2, 4, and 5 are UK # Assets 1 and are are US group_list <- list(group1=c(1, 3, 5), group2=c(2, 4), groupA=c(2, 4, 5), groupB=c(1, 3)) pspec <- add.constraint(portfolio=pspec, type="group", groups=group_list, group_min=c(0.15, 0.25, 0.2, 0.1), group_max=c(0.65, 0.55, 0.5, 0.4))
The function loops through each group and tests if cLO or cUP have been violated
for the given group. This is a helper function for rp_transform.
group_fail(weights, groups, cLO, cUP, group_pos = NULL)group_fail(weights, groups, cLO, cUP, group_pos = NULL)
weights |
weights vector to test |
groups |
list of vectors specifying the groups of the assets |
cLO |
numeric or vector specifying minimum weight group constraints |
cUP |
numeric or vector specifying minimum weight group constraints |
group_pos |
vector specifying the number of non-zero weights per group |
logical vector: TRUE if group constraints are violated for a given group
Ross Bennett
This function computes the concentration of weights using the Herfindahl Hirschman Index
HHI(weights, groups = NULL)HHI(weights, groups = NULL)
weights |
set of portfolio weights |
groups |
list of vectors of grouping |
Ross Bennett
Monthly data of five indexes beginning on 1980-01-31 and ending 2009-12-31. The indexes are: US Bonds, US Equities, International Equities, Commodities, US T-Bills, and Inflation
data(indexes)data(indexes)
CSV converted into xts object with montly observations
data(indexes) #preview the data head(indexes) #summary period statistics summary(indexes)data(indexes) #preview the data head(indexes) #summary period statistics summary(indexes)
This is a helper function primarily for backwards compatibility to insert constraints from a 'v1_constraint' object into the v2 'portfolio' object.
insert_constraints(portfolio, constraints)insert_constraints(portfolio, constraints)
portfolio |
object of class 'portfolio' |
constraints |
list of constraint objects |
Ross Bennett
This is a helper function primarily for backwards compatibility to insert objectives from a 'v1_constraint' object into the v2 'portfolio' object.
insert_objectives(portfolio, objectives)insert_objectives(portfolio, objectives)
portfolio |
object of class 'portfolio' |
objectives |
list of objective objects |
Ross Bennett
This function calculates objective measures for an equal weight portfolio.
inverse.volatility.weight(R, portfolio, ...)inverse.volatility.weight(R, portfolio, ...)
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
portfolio |
an object of type "portfolio" specifying the constraints and objectives for the optimization |
... |
any other passthru parameters to |
This function is simply a wrapper around constrained_objective
to calculate the objective measures in the given portfolio object of
an inverse volatility weight portfolio. The portfolio object should include all objectives
to be calculated.
a list containing the returns, weights, objective measures, call, and portfolio object
Peter Carl
check function for constraints
is.constraint(x)is.constraint(x)
x |
object to test for type |
Brian G. Peterson
check class of an objective object
is.objective(x)is.objective(x)
x |
an object potentially of type 'objective' to test |
Brian G. Peterson
check function for portfolio
is.portfolio(x)is.portfolio(x)
x |
object to test for type |
Ross Bennett
The leverage_exposure constraint specifies a maximum leverage where
leverage is defined as the sum of the absolute value of the weights.
Leverage exposure is computed as the sum of the absolute value of the
weights, sum(abs(weights)).
leverage_exposure_constraint( type = "leverage_exposure", leverage = NULL, enabled = TRUE, message = FALSE, ... )leverage_exposure_constraint( type = "leverage_exposure", leverage = NULL, enabled = TRUE, message = FALSE, ... )
type |
character type of the constraint |
leverage |
maximum leverage value |
enabled |
TRUE/FALSE |
message |
TRUE/FALSE. The default is message=FALSE. Display messages if TRUE. |
... |
any other passthru parameters to specify diversification constraint an object of class 'diversification_constraint' |
This should be used for constructing, for example, 130/30 portfolios or dollar neutral portfolios with 2:1 leverage. For the ROI solvers, this is implemented as a MILP problem and is not supported for problems formulated as a quadratic programming problem. This may change in the future if a MIQP solver is added.
This function is called by add.constraint when type="leverage_exposure"
is specified, see add.constraint.
Ross Bennett
data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) pspec <- add.constraint(portfolio=pspec, type="leverage_exposure", leverage=1.6)data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) pspec <- add.constraint(portfolio=pspec, type="leverage_exposure", leverage=1.6)
This function is called by optimize.portfolio to solve maximum return problems via mixed integer linear programming.
maxret_milp_opt( R, constraints, moments, target, solver = "glpk", control = NULL )maxret_milp_opt( R, constraints, moments, target, solver = "glpk", control = NULL )
R |
xts object of asset returns |
constraints |
object of constraints in the portfolio object extracted with |
moments |
object of moments computed based on objective functions |
target |
target return value |
solver |
solver to use |
control |
list of solver control parameters |
Ross Bennett
This function is called by optimize.portfolio to solve maximum return
maxret_opt(R, moments, constraints, target, solver = "glpk", control = NULL)maxret_opt(R, moments, constraints, target, solver = "glpk", control = NULL)
R |
xts object of asset returns |
moments |
object of moments computed based on objective functions |
constraints |
object of constraints in the portfolio object extracted with |
target |
target return value |
solver |
solver to use |
control |
list of solver control parameters |
Ross Bennett
This function generates the mean-CSM efficient frontier of a portfolio
specifying the constraints and objectives. The portfolio object
should have two objectives: 1) mean and 2) CSM. If the
portfolio object does not contain these objectives, they will be added
using default parameters.
meancsm.efficient.frontier( portfolio, R, optimize_method = "CVXR", n.portfolios = 25, ... )meancsm.efficient.frontier( portfolio, R, optimize_method = "CVXR", n.portfolios = 25, ... )
portfolio |
a portfolio object with constraints and objectives created via |
R |
an xts or matrix of asset returns |
optimize_method |
the optimize method to get the efficient frontier, default is CVXR |
n.portfolios |
number of portfolios to generate the efficient frontier |
... |
passthru parameters to |
a matrix of objective measure values and weights along the efficient frontier
Xinran Zhao
This function generates the mean-ETL efficient frontier of a portfolio
specifying the constraints and objectives. The portfolio object
should have two objectives: 1) mean and 2) ES (or ETL or cVaR). If the
portfolio object does not contain these objectives, they will be added
using default parameters.
meanetl.efficient.frontier( portfolio, R, optimize_method = "ROI", n.portfolios = 25, ... )meanetl.efficient.frontier( portfolio, R, optimize_method = "ROI", n.portfolios = 25, ... )
portfolio |
a portfolio object with constraints and objectives created via |
R |
an xts or matrix of asset returns |
optimize_method |
the optimize method to get the efficient frontier, default is ROI |
n.portfolios |
number of portfolios to generate the efficient frontier |
... |
passthru parameters to |
a matrix of objective measure values and weights along the efficient frontier
Ross Bennett
This function generates the mean-risk efficient frontier of a portfolio
specifying the constraints and objectives. The risk_type object
is for the basic mean-risk efficient frontier, other efficient frontiers
will be generated with the same target returns. All mean-StdDev, mean-ES
and mean-CSM efficient frontiers will be generated.
meanrisk.efficient.frontier( portfolio, R, optimize_method = "CVXR", n.portfolios = 25, risk_type = "StdDev", compare_port = c("StdDev", "ES"), ... )meanrisk.efficient.frontier( portfolio, R, optimize_method = "CVXR", n.portfolios = 25, risk_type = "StdDev", compare_port = c("StdDev", "ES"), ... )
portfolio |
a portfolio object with constraints and objectives created via |
R |
an xts or matrix of asset returns |
optimize_method |
the optimize method to get the efficient frontier, default is CVXR |
n.portfolios |
number of portfolios to generate the efficient frontier |
risk_type |
one of "StdDev", "ES" and "CSM", which determines the type of basic efficient frontier. |
compare_port |
vector composed of any risk "StdDev", "ES", "CSM", for example, compare_port=c("StdDev", "ES") |
... |
passthru parameters to |
a matrix of objective measure values and weights along the efficient frontier
Xinran Zhao
This function generates the mean-variance efficient frontier of a portfolio
specifying the constraints and objectives. The portfolio object
should have two objectives: 1) mean and 2) var (or sd or StdDev). If the
portfolio object does not contain these objectives, they will be added
using default parameters.
meanvar.efficient.frontier( portfolio, R, optimize_method = "ROI", n.portfolios = 25, risk_aversion = NULL, ... )meanvar.efficient.frontier( portfolio, R, optimize_method = "ROI", n.portfolios = 25, risk_aversion = NULL, ... )
portfolio |
a portfolio object with constraints created via |
R |
an xts or matrix of asset returns |
optimize_method |
the optimize method to get the efficient frontier, default is ROI |
n.portfolios |
number of portfolios to plot along the efficient frontier |
risk_aversion |
vector of risk_aversion values to construct the efficient frontier.
|
... |
passthru parameters to |
a matrix of objective measure values and weights along the efficient frontier
Ross Bennett
Compute the first and second moments using the Fully Flexible Views framework as described in A. Meucci - "Fully Flexible Views: Theory and Practice".
meucci.moments(R, posterior_p)meucci.moments(R, posterior_p)
R |
xts object of asset returns |
posterior_p |
vector of posterior probabilities |
a list with the first and second moments
mu: vector of expected returns
sigma: covariance matrix
Ross Bennett
A. Meucci - "Fully Flexible Views: Theory and Practice".
Express views on the relative expected asset returns as in A. Meucci, "Fully Flexible Views: Theory and Practice" and compute the first and second moments.
meucci.ranking(R, p, order)meucci.ranking(R, p, order)
R |
xts object of asset returns |
p |
a vector of the prior probability values |
order |
a vector of indexes of the relative ranking of expected asset
returns in ascending order. For example, |
The estimated moments based on ranking views
This function is based on the ViewRanking function written by
Ram Ahluwalia in the Meucci package.
A. Meucci, "Fully Flexible Views: Theory and Practice" https://www.arpm.co/articles/fully-flexible-views-theory-and-practice/ See Meucci script for "RankingInformation/ViewRanking.m"
data(edhec) R <- edhec[,1:4] p <- rep(1 / nrow(R), nrow(R)) meucci.ranking(R, p, c(2, 3, 1, 4))data(edhec) R <- edhec[,1:4] p <- rep(1 / nrow(R), nrow(R)) meucci.ranking(R, p, c(2, 3, 1, 4))
This objective allows for min and max targets to be specified.
minmax_objective( name, target = NULL, arguments = NULL, multiplier = 1, enabled = TRUE, ..., min, max )minmax_objective( name, target = NULL, arguments = NULL, multiplier = 1, enabled = TRUE, ..., min, max )
name |
name of the objective, should correspond to a function, though we will try to make allowances |
target |
univariate target for the objective |
arguments |
default arguments to be passed to an objective function when executed |
multiplier |
multiplier to apply to the objective, usually 1 or -1 |
enabled |
TRUE/FALSE |
... |
any other passthru parameters |
min |
minimum value |
max |
maximum value |
If target is set, we'll try to meet the metric
If target is NULL and min and max are specified, then do the following:
If max is violated to the upside, penalize the metric. If min is violated to the downside, penalize the metric. The purpose of this objective is to try to meet the range between min and max
object of class 'minmax_objective'
Ross Bennett
Create and specify a multiple layer portfolio
mult.portfolio.spec(portfolio, levels = 2, ...)mult.portfolio.spec(portfolio, levels = 2, ...)
portfolio |
the "top level" portfolio |
levels |
number of levels of sub-portfolios |
... |
any additional parameters |
The sub.portfolios slot is a list where each element contains the
portfolio object and rebalancing parameters for the optimization of the
sub portfolio.
This allows, for example, each sub portfolio to have different rebalancing
frequencies (i.e. monthly or quarterly), optimization methods, etc.
Each sub portfolio is optimized with optimize.portfolio.rebalancing
to create a time series of proxy returns.
The "top level" portfolio is used to specify the constraints and objectives to control the optimization given the proxy returns of each sub portfolio.
a mult.portfolio.spec object with the top level portfolio
and sub portfolios with optimization parameters for each sub portfolio
Ross Bennett
Auxiliary function for passing the estimation options as parameters to the estimation function MCD.robust.moment
MycovRobMcd( alpha = 1/2, nsamp = 500, nmini = 300, kmini = 5, scalefn = "hrv2012", maxcsteps = 200, seed = NULL, tolSolve = 1e-14, wgtFUN = "01.original", beta, use.correction = TRUE )MycovRobMcd( alpha = 1/2, nsamp = 500, nmini = 300, kmini = 5, scalefn = "hrv2012", maxcsteps = 200, seed = NULL, tolSolve = 1e-14, wgtFUN = "01.original", beta, use.correction = TRUE )
alpha |
numeric parameter controlling the size of the subsets over which the determinant is minimized. Allowed values are between 0.5 and 1 and the default is 0.5. |
nsamp |
number of subsets used for initial estimates or "best", "exact", or "deterministic". Default is nsamp = 500. For nsamp = "best" exhaustive enumeration is done, as long as the number of trials does not exceed 100'000, which is the value of nlarge. For "exact", exhaustive enumeration will be attempted however many samples are needed. In this case a warning message may be displayed saying that the computation can take a very long time. For "deterministic", the deterministic MCD is computed; as proposed by Hubert et al. (2012) it starts from the h most central observations of six (deterministic) estimators. |
nmini, kmini
|
for n >= 2*n0, n0 := nmini, the algorithm splits the data into maximally kmini (by default 5) subsets, of size approximately, but at least nmini. When nmini*kmini < n, the initial search uses only a subsample of size nmini*kmini. The original algorithm had nmini = 300 and kmini = 5 hard coded. |
scalefn |
function to compute a robust scale estimate or character string specifying a rule determining such a function for the deterministic MCD. The default is "hrv2012". Another option value is "v2014". |
maxcsteps |
maximal number of concentration steps in the deterministic MCD |
seed |
initial seed for random generator |
tolSolve |
numeric tolerance to be used for inversion of the covariance matrix |
wgtFUN |
a character string or function, specifying how the weights for the reweighting step should be computed. Default is "01.originalz". |
beta |
a quantile, experimentally used for some of the prespecified wgtFUNs. For our MCD method, the default is 0.975. |
use.correction |
whether to use finite sample correction factors; defaults to TRUE. |
a list of passed parameters
Auxiliary function for passing the estimation options as parameters to the estimation function custom.TSGS
MycovRobTSGS( filter = c("UBF-DDC", "UBF", "DDC", "UF"), partial.impute = FALSE, tol = 1e-04, maxiter = 150, loss = c("bisquare", "rocke"), init = c("emve", "qc", "huber", "imputed", "emve_c") )MycovRobTSGS( filter = c("UBF-DDC", "UBF", "DDC", "UF"), partial.impute = FALSE, tol = 1e-04, maxiter = 150, loss = c("bisquare", "rocke"), init = c("emve", "qc", "huber", "imputed", "emve_c") )
filter |
the filter to be used in the first step. Available choices are "UBF-DDC","UBF","DDC","UF". The default one is "UBF-DDC". |
partial.impute |
whether partial imputation is used prior to estimation. The default is FALSE. |
tol |
tolerance for the convergence criterion. Default is 1e-4. |
maxiter |
maximum number of iterations. Default is 150. |
loss |
loss function to use, "bisquare" or "rocke". Default is "bisquare" |
init |
type of initial estimator. Options include "emve", "qc", "huber","imputed","emve_c" |
a list of passed parameters
utility function to replace awkward named from unlist
name.replace(rnames)name.replace(rnames)
rnames |
character vector of names to check for cleanup |
Typically called as a sub-function by the user function add.objective.
See main documentation there.
objective( name, target = NULL, arguments, enabled = TRUE, ..., multiplier = 1, objclass = "objective" )objective( name, target = NULL, arguments, enabled = TRUE, ..., multiplier = 1, objclass = "objective" )
name |
name of the objective which will be used to call a function, like 'ES', 'VaR', 'mean' |
target |
univariate target for the objective, default NULL |
arguments |
default arguments to be passed to an objective function when executed |
enabled |
TRUE/FALSE |
... |
any other passthrough parameters |
multiplier |
multiplier to apply to the objective, usually 1 or -1 |
objclass |
string class to apply, default 'objective' |
Brian G. Peterson
Converts output of 'optimize.portfolio' to a list of the portfolio weights, mean, volatility and Sharpe Ratio.
opt.outputMvo( opt, returns, digits = NULL, annualize = TRUE, frequency = "monthly", rf = 0 )opt.outputMvo( opt, returns, digits = NULL, annualize = TRUE, frequency = "monthly", rf = 0 )
opt |
List output of 'optimize.portfolio' |
returns |
Multivariate xts object of portfolio assets returns |
digits |
Integer number of significant digits with default NULL |
annualize |
Logical with default TRUE |
frequency |
Returns frequency: "monthly", "weekly" or "daily" |
rf |
Numeric value with default 0.0 |
This function uses the weights returned by optimize.portfolio, along with the portfolio assets returns, and a risk-free rate, to to compute the portfolio mean return, volatility, and Sharpe Ratio.
A list containing the portfolio numeric weights, mean value, volatility and Sharpe Ratio.
R. Douglas Martin
args(opt.outputMvo)args(opt.outputMvo)
This function aims to provide a wrapper for constrained optimization of portfolios that specify constraints and objectives.
optimize.portfolio_v1( R, constraints, optimize_method = c("DEoptim", "random", "ROI", "ROI_old", "pso", "GenSA"), search_size = 20000, trace = FALSE, ..., rp = NULL, momentFUN = "set.portfolio.moments_v1" ) optimize.portfolio( R, portfolio = NULL, constraints = NULL, objectives = NULL, optimize_method = c("DEoptim", "random", "ROI", "pso", "GenSA", "Rglpk", "osqp", "mco", "CVXR", ...), search_size = 20000, trace = FALSE, ..., rp = NULL, momentFUN = "set.portfolio.moments", message = FALSE )optimize.portfolio_v1( R, constraints, optimize_method = c("DEoptim", "random", "ROI", "ROI_old", "pso", "GenSA"), search_size = 20000, trace = FALSE, ..., rp = NULL, momentFUN = "set.portfolio.moments_v1" ) optimize.portfolio( R, portfolio = NULL, constraints = NULL, objectives = NULL, optimize_method = c("DEoptim", "random", "ROI", "pso", "GenSA", "Rglpk", "osqp", "mco", "CVXR", ...), search_size = 20000, trace = FALSE, ..., rp = NULL, momentFUN = "set.portfolio.moments", message = FALSE )
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
constraints |
default=NULL, a list of constraint objects. An object of class 'v1_constraint' can be passed in here. |
optimize_method |
one of "DEoptim", "random", "ROI", "pso", "GenSA", "osqp", "Rglpk", "mco", "CVXR", or a vector to specify CVXR solver. A solver of ROI or CVXR can also be specified and will be solved via ROI or CVXR. See details. |
search_size |
integer, how many portfolios to test, default 20,000 |
trace |
TRUE/FALSE if TRUE will attempt to return additional information on the path or portfolios searched |
... |
any other passthru parameters |
rp |
matrix of random portfolio weights, default NULL, mostly for automated use by rebalancing optimization or repeated tests on same portfolios |
momentFUN |
the name of a function to call to set portfolio moments, default |
portfolio |
an object of type "portfolio" specifying the constraints and objectives for the optimization |
objectives |
default=NULL, a list of objective objects. |
message |
TRUE/FALSE. The default is message=FALSE. Display messages if TRUE. |
This function currently supports DEoptim, random portfolios, pso, GenSA, ROI, osqp, Rglpk, mco, and CVXR solvers as back ends. Additional back end contributions for Rmetrics, ghyp, etc. would be welcome.
When using random portfolios, search_size is precisely that, how many portfolios to test. You need to make sure to set your feasible weights in generatesequence to make sure you have search_size unique portfolios to test, typically by manipulating the 'by' parameter to select something smaller than .01 (I often use .002, as .001 seems like overkill)
When using DE, search_size is decomposed into two other parameters which it interacts with, NP and itermax.
NP, the number of members in each population, is set to cap at 2000 in DEoptim, and by default is the number of parameters (assets/weights) * 10.
itermax, if not passed in dots, defaults to the number of parameters (assets/weights) * 50.
When using GenSA and want to set verbose=TRUE, instead use trace.
If optimize_method="ROI" is specified, a default solver will be
selected based on the optimization problem. The glpk solver is the
default solver for LP and MILP optimization problems. The quadprog
solver is the default solver for QP optimization problems. For example,
optimize_method = "quadprog" can be specified and the optimization
problem will be solved via ROI using the quadprog solver.
The extension to ROI solves a limited type of convex optimization problems:
Maxmimize portfolio return subject leverage, box, group, position limit, target mean return, and/or factor exposure constraints on weights.
Minimize portfolio variance subject to leverage, box, group, turnover, and/or factor exposure constraints (otherwise known as global minimum variance portfolio).
Minimize portfolio variance subject to leverage, box, group, and/or factor exposure constraints and a desired portfolio return.
Maximize quadratic utility subject to leverage, box, group, target mean return, turnover, and/or factor exposure constraints and risk aversion parameter.
(The risk aversion parameter is passed into optimize.portfolio as an added argument to the portfolio object).
Maximize portfolio mean return per unit standard deviation (i.e. the Sharpe Ratio) can be done by specifying maxSR=TRUE in optimize.portfolio.
If both mean and StdDev are specified as objective names, the default action is to maximize quadratic utility, therefore maxSR=TRUE must be specified to maximize Sharpe Ratio.
Minimize portfolio ES/ETL/CVaR optimization subject to leverage, box, group, position limit, target mean return, and/or factor exposure constraints and target portfolio return.
Maximize portfolio mean return per unit ES/ETL/CVaR (i.e. the STARR Ratio) can be done by specifying maxSTARR=TRUE in optimize.portfolio.
If both mean and ES/ETL/CVaR are specified as objective names, the default action is to maximize mean return per unit ES/ETL/CVaR.
These problems also support a weight_concentration objective where concentration of weights as measured by HHI is added as a penalty term to the quadratic objective.
Because these convex optimization problem are standardized, there is no need for a penalty term.
The multiplier argument in add.objective passed into the complete constraint object are ignored by the ROI solver.
If optimize_method="CVXR" is specified, a default solver will be selected based on the optimization problem.
The default solver for Quadratic Programming will be OSQP,
and the default solver for Linear Problem and Second-Order Cone Programming will be SCS.
Specified CVXR solver can be given by using optimize_method=c("CVXR", "CVXRsolver").
CVXR supports some commercial solvers, including CBC, CPLEX, GUROBI and MOSEK, and some open source solvers, including GLPK, GLPK_MI, OSQP, SCS and ECOS.
For example, optimize_method = c("CVXR", "ECOS") can be specified and the optimization problem will be solved via CVXR using the ECOS solver.
The extension to CVXR solves a limited type of convex optimization problems:
Maxmimize portfolio mean return subject leverage, box, group, and/or target mean return constraints
Minimize portfolio variance subject to leverage, box, group, and/or target mean return constraints (otherwise known as global minimum variance portfolio).
Maximize quadratic utility subject to leverage, box, group, and/or target mean return constraints and risk aversion parameter.
(The default risk aversion is 1, and specified risk aversion could be given by risk_aversion = 1.
The risk aversion parameter is passed into optimize.portfolio as an added argument to the portfolio object.)
Minimize portfolio ES/ETL/CVaR optimization subject to leverage, box, group, and/or target mean return constraints and tail probability parameter.
(The default tail probability is 0.05, and specified tail probability could be given by arguments = list(p=0.95).
The tail probability parameter is passed into optimize.portfolio as an added argument to the portfolio object.)
Minimize portfolio CSM optimization subject to leverage, box, group, and/or target mean return constraints and tail probability parameter.
(The default tail probability is 0.05, and specified tail probability could be given by arguments = list(p=0.95).
The tail probability parameter is passed into optimize.portfolio as an added argument to the portfolio object.)
Maximize portfolio mean return per unit standard deviation (i.e. the Sharpe Ratio) subject to leverage, box, group, and/or target mean return constraints.
It should be specified by maxSR=TRUE in optimize.portfolio with both mean and var/StdDev objectives.
Otherwise, the default action is to maximize quadratic utility.
Maximize portfolio mean return per unit ES (i.e. the ES ratio/STARR) subject to leverage, box, group, and/or target mean return constraints.
It could be specified by maxSTARR=TRUE or ESratio=TRUE in optimize.portfolio with both mean and ES objectives.
The default action is to maximize ES ratio. If maxSTARR=FALSE or ESratio=FALSE is given, the action will be minimizing ES.
Maximize portfolio mean return per unit CSM (i.e. the CSM ratio) subject to leverage, box, group, and/or target mean return constraints.
It could be specified by CSMratio=TRUE in optimize.portfolio with both mean and CSM objectives.
The default action is to maximize CSM ratio. If CSMratio=FALSE is given, the action will be minimizing CSM.
Because these convex optimization problem are standardized, there is no need for a penalty term.
The multiplier argument in add.objective passed into the complete constraint object are ignored by the CVXR solver.
a list containing the following elements
weights:The optimal set weights.
objective_measures:A list containing the value of each objective corresponding to the optimal weights.
opt_values:A list containing the value of each objective corresponding to the optimal weights.
out:The output of the solver.
call:The function call.
portfolio:The portfolio object.
R:The asset returns.
data summary: The first row and last row of R.
elapsed_time:The amount of time that elapses while the optimization is run.
end_t:The date and time the optimization completed.
When Trace=TRUE is specified, the following elements will be returned in addition to the elements above. The output depends on the optimization method and is specific to each solver. Refer to the documentation of the desired solver for more information.
optimize_method="random"
random_portfolios:A matrix of the random portfolios.
random_portfolio_objective_results:A list of the following elements for each random portfolio.
out:The output value of the solver corresponding to the random portfolio weights.
weights:The weights of the random portfolio.
objective_measures:A list of each objective measure corresponding to the random portfolio weights.
optimize_method="DEoptim"
DEoutput:A list (of length 2) containing the following elements:
optim
member
DEoptim_objective_results:A list containing the following elements for each intermediate population.
out: The output of the solver.
weights: Population weights.
init_weights: Initial population weights.
objective_measures: A list of each objective measure corresponding to the weights
optimize_method="pso"
PSOoutput: A list containing the following elements:
par
value
counts
convergence
message
stats
optimize_method="GenSA"
GenSAoutput: A list containing the following elements:
value
par
trace.mat
counts
An object of class v1_constraint can be passed in for the constraints argument.
The v1_constraint object was used in the previous 'v1' specification to specify the
constraints and objectives for the optimization problem, see constraint.
We will attempt to detect if the object passed into the constraints argument
is a v1_constraint object and update to the 'v2' specification by adding the
constraints and objectives to the portfolio object.
Kris Boudt, Peter Carl, Brian G. Peterson, Ross Bennett, Xiaokang Feng, Xinran Zhao
This function will not speed up optimization!
optimize.portfolio.parallel( R, portfolio, optimize_method = c("DEoptim", "random", "ROI", "pso", "GenSA", "CVXR"), search_size = 20000, trace = FALSE, ..., rp = NULL, momentFUN = "set.portfolio.moments", message = FALSE, nodes = 4 )optimize.portfolio.parallel( R, portfolio, optimize_method = c("DEoptim", "random", "ROI", "pso", "GenSA", "CVXR"), search_size = 20000, trace = FALSE, ..., rp = NULL, momentFUN = "set.portfolio.moments", message = FALSE, nodes = 4 )
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
portfolio |
an object of type "portfolio" specifying the constraints and objectives for the optimization |
optimize_method |
one of "DEoptim", "random", "pso", "GenSA". |
search_size |
integer, how many portfolios to test, default 20,000 |
trace |
TRUE/FALSE if TRUE will attempt to return additional information on the path or portfolios searched |
... |
any other passthru parameters |
rp |
matrix of random portfolio weights, default NULL, mostly for automated use by rebalancing optimization or repeated tests on same portfolios |
momentFUN |
the name of a function to call to set portfolio moments, default |
message |
TRUE/FALSE. The default is message=FALSE. Display messages if TRUE. |
nodes |
how many processes to run in the foreach loop, default 4 |
This function exists to run multiple copies of optimize.portfolio, presumabley in parallel using foreach.
This is typically done to test your parameter settings, specifically total population size, but also possibly to help tune your convergence settings, number of generations, stopping criteria, etc.
If you want to use all the cores on your multi-core computer, use the parallel version of the apppropriate optimization engine, not this function.
a list containing the optimal weights, some summary statistics, the function call, and optionally trace information
Kris Boudt, Peter Carl, Brian G. Peterson
Portfolio optimization with support for rebalancing periods for out-of-sample testing (i.e. backtesting)
optimize.portfolio.rebalancing_v1( R, constraints, optimize_method = c("DEoptim", "random", "ROI"), search_size = 20000, trace = FALSE, ..., rp = NULL, rebalance_on = NULL, training_period = NULL, rolling_window = NULL ) optimize.portfolio.rebalancing( R, portfolio = NULL, constraints = NULL, objectives = NULL, optimize_method = c("DEoptim", "random", "ROI", "CVXR"), search_size = 20000, trace = FALSE, ..., rp = NULL, rebalance_on = NULL, training_period = NULL, rolling_window = NULL )optimize.portfolio.rebalancing_v1( R, constraints, optimize_method = c("DEoptim", "random", "ROI"), search_size = 20000, trace = FALSE, ..., rp = NULL, rebalance_on = NULL, training_period = NULL, rolling_window = NULL ) optimize.portfolio.rebalancing( R, portfolio = NULL, constraints = NULL, objectives = NULL, optimize_method = c("DEoptim", "random", "ROI", "CVXR"), search_size = 20000, trace = FALSE, ..., rp = NULL, rebalance_on = NULL, training_period = NULL, rolling_window = NULL )
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
constraints |
default NULL, a list of constraint objects |
optimize_method |
one of "DEoptim", "random", "pso", "GenSA", or "ROI" |
search_size |
integer, how many portfolios to test, default 20,000 |
trace |
TRUE/FALSE if TRUE will attempt to return additional information on the path or portfolios searched |
... |
any other passthru parameters to |
rp |
a set of random portfolios passed into the function to prevent recalculation |
rebalance_on |
character string of period to rebalance on. See
|
training_period |
an integer of the number of periods to use as a training data in the front of the returns data |
rolling_window |
an integer of the width (i.e. number of periods) of the rolling window, the default of NULL will run the optimization using the data from inception. |
portfolio |
an object of type "portfolio" specifying the constraints and objectives for the optimization |
objectives |
default NULL, a list of objective objects |
Run portfolio optimization with periodic rebalancing at specified time periods. Running the portfolio optimization with periodic rebalancing can help refine the constraints and objectives by evaluating the out of sample performance of the portfolio based on historical data.
If both training_period and rolling_window are NULL,
then training_period is set to a default value of 36.
If training_period is NULL and a rolling_window is
specified, then training_period is set to the value of
rolling_window.
The user should be aware of the following behavior when both
training_period and rolling_window are specified and have
different values
training_period < rolling_window: For example, if you have
rolling_window=60, training_period=50, and the periodicity
of the data is the same as the rebalance frequency (i.e. monthly data with
rebalance_on="months") then the returns data used in the optimization
at each iteration are as follows:
1: R[1:50,]
2: R[1:51,]
...
11: R[1:60,]
12: R[1:61,]
13: R[2:62,]
...
This results in a growing window for several optimizations initially while
the endpoint iterator (i.e. [50, 51, ...]) is less than the
rolling window width.
training_period > rolling_window: The data used in the initial
optimization is R[(training_period - rolling_window):training_period,].
This results in some of the data being "thrown away", i.e. periods 1 to
(training_period - rolling_window - 1) are not used in the optimization.
This function is a essentially a wrapper around optimize.portfolio
and thus the discussion in the Details section of the
optimize.portfolio help file is valid here as well.
This function is massively parallel and requires the 'foreach' package. It is suggested to register a parallel backend.
a list containing the following elements
portfolio:The portfolio object.
R:The asset returns.
call:The function call.
elapsed_time:The amount of time that elapses while the optimization is run.
opt_rebalancing: A list of optimize.portfolio
objects computed at each rebalancing period.
Kris Boudt, Peter Carl, Brian G. Peterson
portfolio.spec optimize.portfolio
## Not run: data(edhec) R <- edhec[,1:4] funds <- colnames(R) portf <- portfolio.spec(funds) portf <- add.constraint(portf, type="full_investment") portf <- add.constraint(portf, type="long_only") portf <- add.objective(portf, type="risk", name="StdDev") # Quarterly rebalancing with 5 year training period bt.opt1 <- optimize.portfolio.rebalancing(R, portf, optimize_method="ROI", rebalance_on="quarters", training_period=60) # Monthly rebalancing with 5 year training period and 4 year rolling window bt.opt2 <- optimize.portfolio.rebalancing(R, portf, optimize_method="ROI", rebalance_on="months", training_period=60, rolling_window=48) ## End(Not run)## Not run: data(edhec) R <- edhec[,1:4] funds <- colnames(R) portf <- portfolio.spec(funds) portf <- add.constraint(portf, type="full_investment") portf <- add.constraint(portf, type="long_only") portf <- add.objective(portf, type="risk", name="StdDev") # Quarterly rebalancing with 5 year training period bt.opt1 <- optimize.portfolio.rebalancing(R, portf, optimize_method="ROI", rebalance_on="quarters", training_period=60) # Monthly rebalancing with 5 year training period and 4 year rolling window bt.opt2 <- optimize.portfolio.rebalancing(R, portf, optimize_method="ROI", rebalance_on="months", training_period=60, rolling_window=48) ## End(Not run)
Generates histogram
pHist(X, p, nBins, freq = FALSE)pHist(X, p, nBins, freq = FALSE)
X |
a vector containing the data points |
p |
a vector containing the probabilities for each of the data points in X |
nBins |
expected number of Bins the data set is to be broken down into |
freq |
a boolean variable to indicate whether the graphic is a representation of frequencies |
a list with f the frequency for each midpoint x the midpoints of the nBins intervals
Ram Ahluwalia [email protected] and Xavier Valls [email protected]
https://www.arpm.co/ See Meucci script pHist.m used for plotting
optimize.portfolio
Scatter and weights chart for portfolio optimizations run with trace=TRUE
## S3 method for class 'optimize.portfolio.DEoptim' plot( x, ..., return.col = "mean", risk.col = "ES", chart.assets = FALSE, neighbors = NULL, main = "optimized portfolio plot", xlim = NULL, ylim = NULL ) ## S3 method for class 'optimize.portfolio.GenSA' plot( x, ..., rp = FALSE, return.col = "mean", risk.col = "ES", chart.assets = FALSE, cex.axis = 0.8, element.color = "darkgray", neighbors = NULL, main = "GenSA.Portfolios", xlim = NULL, ylim = NULL ) ## S3 method for class 'optimize.portfolio.pso' plot( x, ..., return.col = "mean", risk.col = "ES", chart.assets = FALSE, cex.axis = 0.8, element.color = "darkgray", neighbors = NULL, main = "PSO.Portfolios", xlim = NULL, ylim = NULL ) ## S3 method for class 'optimize.portfolio.ROI' plot( x, ..., rp = FALSE, risk.col = "ES", return.col = "mean", chart.assets = FALSE, element.color = "darkgray", neighbors = NULL, main = "ROI.Portfolios", xlim = NULL, ylim = NULL ) ## S3 method for class 'optimize.portfolio.random' plot( x, ..., return.col = "mean", risk.col = "ES", chart.assets = FALSE, neighbors = NULL, xlim = NULL, ylim = NULL, main = "optimized portfolio plot" ) ## S3 method for class 'optimize.portfolio' plot( x, ..., return.col = "mean", risk.col = "ES", chart.assets = FALSE, neighbors = NULL, xlim = NULL, ylim = NULL, main = "optimized portfolio plot" )## S3 method for class 'optimize.portfolio.DEoptim' plot( x, ..., return.col = "mean", risk.col = "ES", chart.assets = FALSE, neighbors = NULL, main = "optimized portfolio plot", xlim = NULL, ylim = NULL ) ## S3 method for class 'optimize.portfolio.GenSA' plot( x, ..., rp = FALSE, return.col = "mean", risk.col = "ES", chart.assets = FALSE, cex.axis = 0.8, element.color = "darkgray", neighbors = NULL, main = "GenSA.Portfolios", xlim = NULL, ylim = NULL ) ## S3 method for class 'optimize.portfolio.pso' plot( x, ..., return.col = "mean", risk.col = "ES", chart.assets = FALSE, cex.axis = 0.8, element.color = "darkgray", neighbors = NULL, main = "PSO.Portfolios", xlim = NULL, ylim = NULL ) ## S3 method for class 'optimize.portfolio.ROI' plot( x, ..., rp = FALSE, risk.col = "ES", return.col = "mean", chart.assets = FALSE, element.color = "darkgray", neighbors = NULL, main = "ROI.Portfolios", xlim = NULL, ylim = NULL ) ## S3 method for class 'optimize.portfolio.random' plot( x, ..., return.col = "mean", risk.col = "ES", chart.assets = FALSE, neighbors = NULL, xlim = NULL, ylim = NULL, main = "optimized portfolio plot" ) ## S3 method for class 'optimize.portfolio' plot( x, ..., return.col = "mean", risk.col = "ES", chart.assets = FALSE, neighbors = NULL, xlim = NULL, ylim = NULL, main = "optimized portfolio plot" )
x |
set of portfolios created by |
... |
any other passthru parameters |
return.col |
string name of column to use for returns (vertical axis) |
risk.col |
string name of column to use for risk (horizontal axis) |
chart.assets |
TRUE/FALSE to include risk-return scatter of assets |
neighbors |
set of 'neighbor portfolios to overplot |
main |
an overall title for the plot: see |
xlim |
set the limit on coordinates for the x-axis |
ylim |
set the limit on coordinates for the y-axis |
rp |
TRUE/FALSE to plot feasible portfolios generated by |
cex.axis |
the magnification to be used for axis annotation relative to the current setting of |
element.color |
provides the color for drawing less-important chart elements, such as the box lines, axis lines, etc. |
return.col must be the name of a function used to compute the return metric on the random portfolio weights
risk.col must be the name of a function used to compute the risk metric on the random portfolio weights
neighbors may be specified in three ways.
The first is as a single number of neighbors. This will extract the neighbors closest
portfolios in terms of the out numerical statistic.
The second method consists of a numeric vector for neighbors.
This will extract the neighbors with portfolio index numbers that correspond to the vector contents.
The third method for specifying neighbors is to pass in a matrix.
This matrix should look like the output of extractStats, and should contain
risk.col,return.col, and weights columns all properly named.
The ROI and GenSA solvers do not store the portfolio weights like DEoptim or random
portfolios, random portfolios can be generated for the scatter plot with the
rp argument.
Generate efficient frontiers plot by providing frontiers.
plotFrontiers( R, frontiers, risk, ES_alpha = 0.05, CSM_alpha = 0.05, moment_setting = NULL, main = "Efficient Frontiers", plot_type = "l", cex.axis = 0.5, element.color = "darkgray", legend.loc = NULL, legend.labels = NULL, cex.legend = 0.8, xlim = NULL, ylim = NULL, ..., labels.assets = TRUE, pch.assets = 21, cex.assets = 0.8, col = NULL, lty = NULL, lwd = NULL )plotFrontiers( R, frontiers, risk, ES_alpha = 0.05, CSM_alpha = 0.05, moment_setting = NULL, main = "Efficient Frontiers", plot_type = "l", cex.axis = 0.5, element.color = "darkgray", legend.loc = NULL, legend.labels = NULL, cex.legend = 0.8, xlim = NULL, ylim = NULL, ..., labels.assets = TRUE, pch.assets = 21, cex.assets = 0.8, col = NULL, lty = NULL, lwd = NULL )
R |
an xts object of asset returns |
frontiers |
a list of frontiers, for example, list(ef1=meanvar.efficient.frontier(), ef2=meanvar.efficient.frontier()) |
risk |
type of risk that you want to compare, could be 'StdDev', 'ES', 'CSM' |
ES_alpha |
the default value is 0.05, but could be specified as any value between 0 and 1 |
CSM_alpha |
the default value is 0.05, but could be specified as any value between 0 and 1 |
moment_setting |
the default is NULL, if customize momentFUN please provide moment_setting=list(mu=, sigma=) |
main |
title used in the plot. |
plot_type |
define the plot_type, default is "l" |
cex.axis |
the magnification to be used for sizing the axis text relative to the current setting of 'cex', similar to |
element.color |
provides the color for drawing less-important chart elements, such as the box lines, axis lines, etc. |
legend.loc |
location of the legend; NULL, "bottomright", "bottom", "bottomleft", "left", "topleft", "top", "topright", "right" and "center". |
legend.labels |
character vector to use for the legend labels. |
cex.legend |
The magnification to be used for sizing the legend relative to the current setting of 'cex', similar to |
xlim |
set the x-axis limit, same as in |
ylim |
set the y-axis limit, same as in |
... |
passthrough parameters to |
labels.assets |
TRUE/FALSE to include the asset names in the plot. |
pch.assets |
plotting character of the assets, same as in |
cex.assets |
A numerical value giving the amount by which the asset points and labels should be magnified relative to the default. |
col |
vector of colors with length equal to the number of portfolios in |
lty |
vector of line types with length equal to the number of portfolios in |
lwd |
vector of line widths with length equal to the number of portfolios in |
This function provides the ability to plot frontiers based on the result of 'meanvar.efficient.frontier', 'meanetl.efficient.frontier' or 'meancsm.efficient.frontier'.
When using meanvar.efficient.frontier, meanetl.efficient.frontier
and meancsm.efficient.frontier, the result will be frontiers data,
including the weights for each point on the mean-risk efficient frontiers.
Before using this function, user should declare which risk that they want to
compare, and what parameters that they want to use to calculate the risk,
e.g. ES_alpha for ES, moment_setting for var. Then this function
will calculate back mean and risk based on the weight, and draw a plot.
Default settings use colors and line types to differentiate portfolios, and set the portfolio name as 'Portfolio 1' and so on. Users could customize col, lty, lwd and legend.labels to better the plot.
Xinran Zhao
if target is null, we'll try to minimize the risk metric
portfolio_risk_objective( name, target = NULL, arguments = NULL, multiplier = 1, enabled = TRUE, ... )portfolio_risk_objective( name, target = NULL, arguments = NULL, multiplier = 1, enabled = TRUE, ... )
name |
name of the objective, should correspond to a function, though we will try to make allowances |
target |
univariate target for the objective |
arguments |
default arguments to be passed to an objective function when executed |
multiplier |
multiplier to apply to the objective, usually 1 or -1 |
enabled |
TRUE/FALSE |
... |
any other passthru parameters |
object of class 'portfolio_risk_objective'
Brian G. Peterson
Set portfolio moments for use by lower level optimization functions using a basic Black Litterman model.
portfolio.moments.bl( R, portfolio, momentargs = NULL, P, Mu = NULL, Sigma = NULL, ... )portfolio.moments.bl( R, portfolio, momentargs = NULL, P, Mu = NULL, Sigma = NULL, ... )
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
portfolio |
an object of type |
momentargs |
list containing arguments to be passed down to lower level functions, default NULL |
P |
a K x N pick matrix representing views |
Mu |
vector of length N of the prior expected values. The sample mean
is used if |
Sigma |
an N x N matrix of the prior covariance matrix. The sample
covariance is used if |
... |
any other passthru parameters |
If any of the objectives in the portfolio object have
clean as an argument, the cleaned returns are used to fit the model.
Set portfolio moments for use by lower level optimization functions using a statistical factor model based on the work of Kris Boudt.
portfolio.moments.boudt(R, portfolio, momentargs = NULL, k = 1, ...)portfolio.moments.boudt(R, portfolio, momentargs = NULL, k = 1, ...)
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
portfolio |
an object of type |
momentargs |
list containing arguments to be passed down to lower level functions, default NULL |
k |
number of factors used for fitting statistical factor model |
... |
any other passthru parameters |
If any of the objectives in the portfolio object have
clean as an argument, the cleaned returns are used to fit the model.
The portfolio object is created with portfolio.spec. The portfolio
object is an S3 object of class 'portfolio' used to hold the initial asset weights,
constraints, objectives, and other information about the portfolio. The only
required argument to portfolio.spec is assets.
portfolio.spec( assets = NULL, name = "portfolio", category_labels = NULL, weight_seq = NULL, message = FALSE )portfolio.spec( assets = NULL, name = "portfolio", category_labels = NULL, weight_seq = NULL, message = FALSE )
assets |
number of assets, or optionally a named vector of assets specifying seed weights. If seed weights are not specified, an equal weight portfolio will be assumed. |
name |
give the portfolio a name, the default name will be 'portfolio' |
category_labels |
character vector to categorize assets by sector, industry, geography, market-cap, currency, etc. Default NULL |
weight_seq |
seed sequence of weights, see |
message |
TRUE/FALSE. The default is message=FALSE. Display messages if TRUE. |
The portfolio object contains the following elements:
assetsnamed vector of the seed weights
category_labelscharacter vector to categorize the assets by sector, geography, etc.
weight_seq sequence of weights used by random_portfolios. See generatesequence
constraints a list of constraints added to the portfolio object with add.constraint
objectives a list of objectives added to the portfolio object with add.objective
call the call to portfolio.spec with all of the specified arguments
an object of class portfolio
Ross Bennett, Brian G. Peterson
add.constraint,
add.objective,
optimize.portfolio
data(edhec) pspec <- portfolio.spec(assets=colnames(edhec)) pspec <- portfolio.spec(assets=10, weight_seq=generatesequence())data(edhec) pspec <- portfolio.spec(assets=colnames(edhec)) pspec <- portfolio.spec(assets=10, weight_seq=generatesequence())
This is used as a helper function for rp_transform to check
for violation of position limit constraints. The position limit constraints
checked are max_pos, max_pos_long, and max_pos_short.
pos_limit_fail(weights, max_pos, max_pos_long, max_pos_short)pos_limit_fail(weights, max_pos, max_pos_long, max_pos_short)
weights |
vector of weights to test |
max_pos |
maximum number of assets with non-zero weights |
max_pos_long |
maximum number of assets with long (i.e. buy) positions |
max_pos_short |
maximum number of assets with short (i.e. sell) positions |
TRUE if any position_limit is violated. FALSE if all position limits are satisfied
This function is called by add.constraint when type="filter" is specified, add.constraint
position_limit_constraint( type = "position_limit", filter_name = NULL, enabled = TRUE, message = FALSE, ... )position_limit_constraint( type = "position_limit", filter_name = NULL, enabled = TRUE, message = FALSE, ... )
type |
character type of the constraint |
filter_name |
either a function to apply, or a name of a function to apply |
enabled |
TRUE/FALSE |
message |
TRUE/FALSE. The default is message=FALSE. Display messages if TRUE. |
... |
any other passthru parameters to specify position limit constraints |
Allows the user to specify a filter function which will take returns, weights, and constraints as inputs, and can return a modified weights vector as output.
Fundamentally, it could be used to filter out certain assets, or to ensure that they must be long or short.
Typically, filter functions will be called by the random portfolio simulation function or via the fn_map function.
an object of class 'position_limit_constraint'
Ross Bennett
data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) pspec <- add.constraint(portfolio=pspec, type="position_limit", max_pos=3) pspec <- add.constraint(portfolio=pspec, type="position_limit", max_pos_long=3, max_pos_short=1)data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) pspec <- add.constraint(portfolio=pspec, type="position_limit", max_pos=3) pspec <- add.constraint(portfolio=pspec, type="position_limit", max_pos_long=3, max_pos_short=1)
print method for constraint objects
## S3 method for class 'constraint' print(x, ...)## S3 method for class 'constraint' print(x, ...)
x |
object of class |
... |
any other passthru parameters |
Ross Bennett
Print method for efficient frontier objects. Display the call to create or extract the efficient frontier object and the portfolio from which the efficient frontier was created or extracted.
## S3 method for class 'efficient.frontier' print(x, ...)## S3 method for class 'efficient.frontier' print(x, ...)
x |
objective of class |
... |
any other passthru parameters |
Ross Bennett
print method for optimize.portfolio.rebalancing objects
## S3 method for class 'optimize.portfolio.rebalancing' print(x, ..., digits = 4)## S3 method for class 'optimize.portfolio.rebalancing' print(x, ..., digits = 4)
x |
an object used to select a method |
... |
any other passthru parameters |
digits |
the number of significant digits to use when printing. |
Ross Bennett
optimize.portfolio.rebalancing
print method for optimize.portfolio objects
## S3 method for class 'optimize.portfolio.ROI' print(x, ..., digits = 4) ## S3 method for class 'optimize.portfolio.CVXR' print(x, ..., digits = 4) ## S3 method for class 'optimize.portfolio.random' print(x, ..., digits = 4) ## S3 method for class 'optimize.portfolio.DEoptim' print(x, ..., digits = 4) ## S3 method for class 'optimize.portfolio.GenSA' print(x, ..., digits = 4) ## S3 method for class 'optimize.portfolio.pso' print(x, ..., digits = 4)## S3 method for class 'optimize.portfolio.ROI' print(x, ..., digits = 4) ## S3 method for class 'optimize.portfolio.CVXR' print(x, ..., digits = 4) ## S3 method for class 'optimize.portfolio.random' print(x, ..., digits = 4) ## S3 method for class 'optimize.portfolio.DEoptim' print(x, ..., digits = 4) ## S3 method for class 'optimize.portfolio.GenSA' print(x, ..., digits = 4) ## S3 method for class 'optimize.portfolio.pso' print(x, ..., digits = 4)
x |
an object used to select a method |
... |
any other passthru parameters |
digits |
the number of significant digits to use when printing. |
Ross Bennett
Print method for objects of class portfolio created with portfolio.spec
## S3 method for class 'portfolio' print(x, ...)## S3 method for class 'portfolio' print(x, ...)
x |
an object of class |
... |
any other passthru parameters |
Ross Bennett
print method for objects of class summary.optimize.portfolio
## S3 method for class 'summary.optimize.portfolio' print(x, ...)## S3 method for class 'summary.optimize.portfolio' print(x, ...)
x |
an object of class |
... |
any other passthru parameters. Currently not used. |
Ross Bennett
print method for objects of class summary.optimize.portfolio.rebalancing
## S3 method for class 'summary.optimize.portfolio.rebalancing' print(x, ..., digits = 4)## S3 method for class 'summary.optimize.portfolio.rebalancing' print(x, ..., digits = 4)
x |
an object of class |
... |
any other passthru parameters |
digits |
number of digits used for printing |
Ross Bennett
summary.optimize.portfolio.rebalancing
This function calls return_objective and portfolio_risk_objective
to create a list of the objectives to be added to the portfolio.
quadratic_utility_objective(risk_aversion = 1, target = NULL, enabled = TRUE)quadratic_utility_objective(risk_aversion = 1, target = NULL, enabled = TRUE)
risk_aversion |
risk_aversion (i.e. lambda) parameter to penalize variance |
target |
target mean return value |
enabled |
TRUE/FALSE, default enabled=TRUE |
a list of two elements
return_objective
portfolio_risk_objective
Ross Bennett
Generate random portfolios using the 'sample', 'simplex', or 'grid' method. See details.
random_portfolios( portfolio, permutations = 100, rp_method = "sample", eliminate = TRUE, ... )random_portfolios( portfolio, permutations = 100, rp_method = "sample", eliminate = TRUE, ... )
portfolio |
an object of class 'portfolio' specifying the constraints for the optimization, see |
permutations |
integer: number of unique constrained random portfolios to generate |
rp_method |
method to generate random portfolios. Currently "sample", "simplex", or "grid". See Details. |
eliminate |
TRUE/FALSE, eliminate portfolios that do not satisfy constraints |
... |
any other passthru parameters |
Random portfolios can be generate using one of three methods.
The 'sample' method to generate random portfolios is based on an idea pioneerd by Pat Burns. This is the most flexible method, but also the slowest, and can generate portfolios to satisfy leverage, box, group, position limit, and leverage exposure constraints.
The 'simplex' method to generate random portfolios is
based on a paper by W. T. Shaw. The simplex method is useful to generate
random portfolios with the full investment constraint, where the sum of the
weights is equal to 1, and min box constraints. Values for min_sum
and max_sum of the leverage constraint will be ignored, the sum of
weights will equal 1. All other constraints such as group and position
limit constraints will be handled by elimination. If the constraints are
very restrictive, this may result in very few feasible portfolios remaining.
The 'grid' method to generate random portfolios is based on
the gridSearch function in package 'NMOF'. The grid search method
only satisfies the min and max box constraints. The
min_sum and max_sum leverage constraints will likely be
violated and the weights in the random portfolios should be normalized.
Normalization may cause the box constraints to be violated and will be
penalized in constrained_objective.
The constraint types checked are leverage, box, group, position limit, and
leverage exposure. Any
portfolio that does not satisfy all these constraints will be eliminated. This
function is particularly sensitive to min_sum and max_sum
leverage constraints. For the sample method, there should be some
"wiggle room" between min_sum and max_sum in order to generate
a sufficient number of feasible portfolios. For example, min_sum=0.99
and max_sum=1.01 is recommended instead of min_sum=1
and max_sum=1. If min_sum=1 and max_sum=1, the number of
feasible portfolios may be 1/3 or less depending on the other constraints.
matrix of random portfolio weights
Peter Carl, Brian G. Peterson, Ross Bennett
portfolio.spec,
objective,
rp_sample,
rp_simplex,
rp_grid
repeatedly calls randomize_portfolio to generate an
arbitrary number of constrained random portfolios.
random_portfolios_v1(rpconstraints, permutations = 100, ...)random_portfolios_v1(rpconstraints, permutations = 100, ...)
rpconstraints |
an object of type "constraints" specifying the constraints for the optimization, see |
permutations |
integer: number of unique constrained random portfolios to generate |
... |
any other passthru parameters |
matrix of random portfolio weights
Peter Carl, Brian G. Peterson, (based on an idea by Pat Burns)
constraint, objective, randomize_portfolio
rpconstraint<-constraint_v1(assets=10, min_mult=-Inf, max_mult=Inf, min_sum=.99, max_sum=1.01, min=.01, max=.4, weight_seq=generatesequence()) rp<- random_portfolios_v1(rpconstraints=rpconstraint,permutations=1000) head(rp)rpconstraint<-constraint_v1(assets=10, min_mult=-Inf, max_mult=Inf, min_sum=.99, max_sum=1.01, min=.01, max=.4, weight_seq=generatesequence()) rp<- random_portfolios_v1(rpconstraints=rpconstraint,permutations=1000) head(rp)
deprecated random portfolios wrapper until we write a random trades function
random_walk_portfolios(...)random_walk_portfolios(...)
... |
any other passthru parameters |
bpeterson
version 2 generate random permutations of a portfolio seed meeting your constraints on the weights of each asset
randomize_portfolio(portfolio, max_permutations = 200)randomize_portfolio(portfolio, max_permutations = 200)
portfolio |
an object of type "portfolio" specifying the constraints for the optimization, see |
max_permutations |
integer: maximum number of iterations to try for a valid portfolio, default 200 |
named weighting vector
Peter Carl, Brian G. Peterson, (based on an idea by Pat Burns)
This function generates random permutations of a portfolio seed meeting
leverage and box constraints. The final step is to run fn_map
on the random portfolio weights to transform the weights so they satisfy
other constraints such as group or position limit constraints. This is the
'sample' method for random portfolios and is based on an idea by Pat Burns.
randomize_portfolio_v1(rpconstraints, max_permutations = 200, rounding = 3)randomize_portfolio_v1(rpconstraints, max_permutations = 200, rounding = 3)
rpconstraints |
an object of type "constraints" specifying the constraints for the optimization, see |
max_permutations |
integer: maximum number of iterations to try for a valid portfolio, default 200 |
rounding |
integer how many decimals should we round to |
named weights vector
Peter Carl, Brian G. Peterson, (based on an idea by Pat Burns)
Construct a regime.portfolios object that contains a time series of
regimes and portfolios corresponding to the regimes.
regime.portfolios(regime, portfolios)regime.portfolios(regime, portfolios)
regime |
xts or zoo object specifying the regime |
portfolios |
list of portfolios created by
|
Create a regime.portfolios object to support regime switching
optimization. This object is then passed in as the portfolio
argument in optimize.portfolio. The regime is detected and the
corresponding portfolio is selected. For example, if the current
regime is 1, then portfolio 1 will be selected and used in the
optimization.
a regime.portfolios object with the following elements
An xts object of the regime
List of portfolios corresponding to the regime
Ross Bennett
The return constraint specifes a target mean return value.
This function is called by add.constraint when type="return" is specified, add.constraint
return_constraint( type = "return", return_target, enabled = TRUE, message = FALSE, ... )return_constraint( type = "return", return_target, enabled = TRUE, message = FALSE, ... )
type |
character type of the constraint |
return_target |
return target value |
enabled |
TRUE/FALSE |
message |
TRUE/FALSE. The default is message=FALSE. Display messages if TRUE. |
... |
any other passthru parameters |
an object of class 'return_constraint'
Ross Bennett
data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) pspec <- add.constraint(portfolio=pspec, type="return", return_target=mean(colMeans(ret)))data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) pspec <- add.constraint(portfolio=pspec, type="return", return_target=mean(colMeans(ret)))
if target is null, we'll try to maximize the return metric
return_objective( name, target = NULL, arguments = NULL, multiplier = -1, enabled = TRUE, ... )return_objective( name, target = NULL, arguments = NULL, multiplier = -1, enabled = TRUE, ... )
name |
name of the objective, should correspond to a function, though we will try to make allowances |
target |
univariate target for the objective |
arguments |
default arguments to be passed to an objective function when executed |
multiplier |
multiplier to apply to the objective, usually 1 or -1 |
enabled |
TRUE/FALSE |
... |
any other passthru parameters |
if target is set, we'll try to meet or exceed the metric, penalizing a shortfall
object of class 'return_objective'
Brian G. Peterson
constructor for class risk_budget_objective
risk_budget_objective( assets, name, target = NULL, arguments = NULL, multiplier = 1, enabled = TRUE, ..., min_prisk, max_prisk, min_concentration = FALSE, min_difference = FALSE )risk_budget_objective( assets, name, target = NULL, arguments = NULL, multiplier = 1, enabled = TRUE, ..., min_prisk, max_prisk, min_concentration = FALSE, min_difference = FALSE )
assets |
vector of assets to use, should come from constraints object |
name |
name of the objective, should correspond to a function, though we will try to make allowances |
target |
univariate target for the objective |
arguments |
default arguments to be passed to an objective function when executed |
multiplier |
multiplier to apply to the objective, usually 1 or -1 |
enabled |
TRUE/FALSE |
... |
any other passthru parameters |
min_prisk |
minimum percentage contribution to risk |
max_prisk |
maximum percentage contribution to risk |
min_concentration |
TRUE/FALSE whether to minimize concentration, default FALSE, always TRUE if min_prisk and max_prisk are NULL |
min_difference |
TRUE/FALSE whether to minimize difference between concentration, default FALSE |
object of class 'risk_budget_objective'
Brian G. Peterson
This function generates random portfolios based on the gridSearch
function from the 'NMOF' package.
rp_grid(portfolio, permutations = 2000, normalize = TRUE)rp_grid(portfolio, permutations = 2000, normalize = TRUE)
portfolio |
an object of class 'portfolio' specifying the constraints for the optimization, see |
permutations |
integer: number of unique constrained random portfolios to generate |
normalize |
TRUE/FALSE to normalize the weghts to satisfy min_sum or max_sum |
The number of levels is calculated based on permutations and number of assets. The number of levels must be an integer and may not result in the exact number of permutations. We round up to the nearest integer for the levels so the number of portfolios generated will be greater than or equal to permutations.
The grid search method only satisfies the min and max box
constraints. The min_sum and max_sum leverage constraints will
likely be violated and the weights in the random portfolios should be
normalized. Normalization may cause the box constraints to be violated and
will be penalized in constrained_objective.
matrix of random portfolio weights
This function generates random portfolios based on an idea by Pat Burns.
rp_sample(portfolio, permutations, max_permutations = 200)rp_sample(portfolio, permutations, max_permutations = 200)
portfolio |
an object of type "portfolio" specifying the constraints for the optimization, see |
permutations |
integer: number of unique constrained random portfolios to generate |
max_permutations |
integer: maximum number of iterations to try for a valid portfolio, default 200 |
The 'sample' method to generate random portfolios is based on an idea pioneerd by Pat Burns. This is the most flexible method, but also the slowest, and can generate portfolios to satisfy leverage, box, group, and position limit constraints.
a matrix of random portfolio weights
This function generates random portfolios based on the method outlined in the Shaw paper. Need to add reference.
rp_simplex(portfolio, permutations, fev = 0:5)rp_simplex(portfolio, permutations, fev = 0:5)
portfolio |
an object of class 'portfolio' specifying the constraints for the optimization, see |
permutations |
integer: number of unique constrained random portfolios to generate |
fev |
scalar or vector for FEV biasing |
The simplex method is useful to generate random portfolios with the full investment constraint where the sum of the weights is equal to 1 and min box constraints with no upper bound on max constraints. Values for min_sum and max_sum will be ignored, the sum of weights will equal 1. All other constraints such as group and position limit constraints will be handled by elimination. If the constraints are very restrictive, this may result in very few feasible portfolios remaining.
The random portfolios are created by first generating a set of uniform random numbers.
The portfolio weights are then transformed to satisfy the min of the box constraints.
fev controls the Face-Edge-Vertex (FEV) biasing where
As q approaches infinity, the set of weights will be concentrated in a
single asset. To sample the interior and exterior, fev can be passed
in as a vector. The number of portfolios, permutations, and the
length of fev affect how the random portfolios are generated. For
example, if permutations=10000 and fev=0:4, 2000 portfolios will
be generated for each value of fev.
a matrix of random portfolio weights
This function uses a block of code from randomize_portfolio
to transform the weight vector if either the weight_sum (leverage)
constraints, box constraints, group constraints, position_limit constraints,
or leverage exposure constraints are violated. The logic from
randomize_portfolio is heavily utilized here with extensions to
handle more complex constraints.
The resulting weights vector might be quite different from the original weights vector.
rp_transform( w, min_sum, max_sum, min_box, max_box, groups = NULL, cLO = NULL, cUP = NULL, max_pos = NULL, group_pos = NULL, max_pos_long = NULL, max_pos_short = NULL, leverage = NULL, weight_seq = NULL, max_permutations = 200 )rp_transform( w, min_sum, max_sum, min_box, max_box, groups = NULL, cLO = NULL, cUP = NULL, max_pos = NULL, group_pos = NULL, max_pos_long = NULL, max_pos_short = NULL, leverage = NULL, weight_seq = NULL, max_permutations = 200 )
w |
weights vector to be transformed |
min_sum |
minimum sum of all asset weights, default 0.99 |
max_sum |
maximum sum of all asset weights, default 1.01 |
min_box |
numeric or named vector specifying minimum weight box constraints |
max_box |
numeric or named vector specifying maximum weight box constraints |
groups |
vector specifying the groups of the assets |
cLO |
numeric or vector specifying minimum weight group constraints |
cUP |
numeric or vector specifying minimum weight group constraints |
max_pos |
maximum assets with non-zero weights |
group_pos |
vector specifying maximum number assets with non-zero weights per group |
max_pos_long |
maximum number of assets with long (i.e. buy) positions |
max_pos_short |
maximum number of assets with short (i.e. sell) positions |
leverage |
maximum leverage exposure where leverage is defined as |
weight_seq |
vector of seed sequence of weights |
max_permutations |
integer: maximum number of iterations to try for a valid portfolio, default 200 |
named weighting vector
Peter Carl, Brian G. Peterson, Ross Bennett (based on an idea by Pat Burns)
This function is used to calculate risk or return metrics given a matrix of asset returns and will be used for a risk-reward scatter plot of the assets
scatterFUN(R, FUN, arguments = NULL)scatterFUN(R, FUN, arguments = NULL)
R |
xts object of asset returns |
FUN |
name of function |
arguments |
named list of arguments to FUN |
Ross Bennett
Set portfolio moments for use by lower level optimization functions. Currently three methods for setting the moments are available
set.portfolio.moments( R, portfolio, momentargs = NULL, method = c("sample", "boudt", "black_litterman", "meucci"), ... )set.portfolio.moments( R, portfolio, momentargs = NULL, method = c("sample", "boudt", "black_litterman", "meucci"), ... )
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
portfolio |
an object of type "portfolio" specifying the constraints and objectives for the optimization, see |
momentargs |
list containing arguments to be passed down to lower level functions, default NULL |
method |
the method used to estimate portfolio moments. Valid choices include "sample", "boudt", and "black_litterman". |
... |
any other passthru parameters |
sample estimates are used for the moments
estimate the second, third, and fourth moments using a statistical factor model based on the work of Kris Boudt.
estimate the first and second moments using the
Black Litterman Formula. See black.litterman
.
set portfolio moments for use by lower level optimization functions
set.portfolio.moments_v1(R, constraints, momentargs = NULL, ...)set.portfolio.moments_v1(R, constraints, momentargs = NULL, ...)
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
constraints |
an object of type "constraints" specifying the constraints for the optimization, see |
momentargs |
list containing arguments to be passed down to lower level functions, default NULL |
... |
any other passthru parameters FIXME NOTE: this isn't perfect as it overwrites the moments for all objectives, not just one with clean='boudt' |
Fit a statistical factor model using Principal Component Analysis (PCA)
statistical.factor.model(R, k = 1, ...)statistical.factor.model(R, k = 1, ...)
R |
xts of asset returns |
k |
number of factors to use |
... |
additional arguments passed to |
The statistical factor model is fitted using prcomp. The factor
loadings, factor realizations, and residuals are computed and returned
given the number of factors used for the model.
#'
N x k matrix of factor loadings (i.e. betas)
m x k matrix of factor realizations
m x N matrix of model residuals representing idiosyncratic risk factors
Where N is the number of assets, k is the number of factors, and m is the number of observations.
Summary method for efficient frontier objects. Display the call to create or extract the efficient frontier object as well as the weights and risk and return metrics along the efficient frontier.
## S3 method for class 'efficient.frontier' summary(object, ..., digits = 3)## S3 method for class 'efficient.frontier' summary(object, ..., digits = 3)
object |
object of class |
... |
passthrough parameters |
digits |
number of digits to round to |
Ross Bennett
summary method for class optimize.portfolio
## S3 method for class 'optimize.portfolio' summary(object, ...)## S3 method for class 'optimize.portfolio' summary(object, ...)
object |
an object of class |
... |
any other passthru parameters. Currently not used. |
Ross Bennett
summary method for optimize.portfolio.rebalancing
## S3 method for class 'optimize.portfolio.rebalancing' summary(object, ...)## S3 method for class 'optimize.portfolio.rebalancing' summary(object, ...)
object |
object of type optimize.portfolio.rebalancing |
... |
any other passthru parameters |
summary method for class portfolio created with portfolio.spec
## S3 method for class 'portfolio' summary(object, ...)## S3 method for class 'portfolio' summary(object, ...)
object |
an object of class |
... |
any other passthru parameters |
Ross Bennett
this function is primarily designed for use with portfolio functions passing 'x' or 'R' and weights, but may be usable for other things as well, see Example for a vector example.
trailingFUN(R, weights, n = 0, FUN, FUNargs = NULL, ...)trailingFUN(R, weights, n = 0, FUN, FUNargs = NULL, ...)
R |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
weights |
a vector of weights to test |
n |
numeric number of trailing periods |
FUN |
string describing the function to be called |
FUNargs |
list describing any additional arguments |
... |
any other passthru parameters |
called with e.g.
trailingFUN(seq(1:100), weights=NULL, n=12, FUN='mean',FUNargs=list())
The transaction cost constraint specifies a proportional cost value.
This function is called by add.constraint when type="transaction_cost" is specified, see add.constraint.
transaction_cost_constraint( type = "transaction_cost", assets, ptc, enabled = TRUE, message = FALSE, ... )transaction_cost_constraint( type = "transaction_cost", assets, ptc, enabled = TRUE, message = FALSE, ... )
type |
character type of the constraint |
assets |
number of assets, or optionally a named vector of assets specifying initial weights |
ptc |
proportional transaction cost value |
enabled |
TRUE/FALSE |
message |
TRUE/FALSE. The default is message=FALSE. Display messages if TRUE. |
... |
any other passthru parameters to specify box and/or group constraints |
Note that with the ROI solvers, proportional transaction cost constraint is currently only supported for the global minimum variance and quadratic utility problems with ROI quadprog plugin.
an object of class 'transaction_cost_constraint'
Ross Bennett
data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) pspec <- add.constraint(portfolio=pspec, type="transaction_cost", ptc=0.01)data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) pspec <- add.constraint(portfolio=pspec, type="transaction_cost", ptc=0.01)
add.objective
Calculates turnover given two vectors of weights.
This is used as an objective function and is called when the user adds an objective of type turnover with add.objective
turnover(weights, wts.init = NULL)turnover(weights, wts.init = NULL)
weights |
vector of weights from optimization |
wts.init |
vector of initial weights used to calculate turnover from |
Ross Bennett
The turnover constraint specifies a target turnover value.
This function is called by add.constraint when type="turnover" is specified, see add.constraint.
Turnover is calculated from a set of initial weights. Turnover is
computed as sum(abs(initial_weights - weights)) / N where N is
the number of assets.
turnover_constraint( type = "turnover", turnover_target, enabled = TRUE, message = FALSE, ... )turnover_constraint( type = "turnover", turnover_target, enabled = TRUE, message = FALSE, ... )
type |
character type of the constraint |
turnover_target |
target turnover value |
enabled |
TRUE/FALSE |
message |
TRUE/FALSE. The default is message=FALSE. Display messages if TRUE. |
... |
any other passthru parameters to specify box and/or group constraints |
Note that with the ROI solvers, turnover constraint is currently only supported for the global minimum variance and quadratic utility problems with ROI quadprog plugin.
an object of class 'turnover_constraint'
Ross Bennett
data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) pspec <- add.constraint(portfolio=pspec, type="turnover", turnover_target=0.6)data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) pspec <- add.constraint(portfolio=pspec, type="turnover", turnover_target=0.6)
if target is null, we'll try to minimize the turnover metric
turnover_objective( name, target = NULL, arguments = NULL, multiplier = 1, enabled = TRUE, ... )turnover_objective( name, target = NULL, arguments = NULL, multiplier = 1, enabled = TRUE, ... )
name |
name of the objective, should correspond to a function, though we will try to make allowances |
target |
univariate target for the objective |
arguments |
default arguments to be passed to an objective function when executed |
multiplier |
multiplier to apply to the objective, usually 1 or -1 |
enabled |
TRUE/FALSE |
... |
any other passthru parameters |
if target is set, we'll try to meet the metric
an objective of class 'turnover_objective'
Ross Bennett
The function takes the constraints and objectives specified in the v1_constraint object and updates the portfolio object with those constraints and objectives. This function is used inside optimize.portfolio to maintain backwards compatibility if the user passes in a v1_constraint object for the constraint arg in optimize.portfolio.
update_constraint_v1tov2(portfolio, v1_constraint)update_constraint_v1tov2(portfolio, v1_constraint)
portfolio |
portfolio object passed into optimize.portfolio |
v1_constraint |
object of type v1_constraint passed into optimize.portfolio |
portfolio object containing constraints and objectives from v1_constraint
Ross Bennett
portfolio.spec, add.constraint
can we use the generic update.default function?
## S3 method for class 'constraint' update(object, ...)## S3 method for class 'constraint' update(object, ...)
object |
object of type |
... |
any other passthru parameters, used to call |
bpeterson
This function is used to calculate the portfolio variance via a call to constrained_objective when var is an object for mean variance or quadratic utility optimization.
var.portfolio(R, weights)var.portfolio(R, weights)
R |
xts object of asset returns |
weights |
vector of asset weights |
numeric value of the portfolio variance
Ross Bennett
This function penalizes weight concentration using the Herfindahl-Hirschman Index as a measure of concentration.
weight_concentration_objective( name, conc_aversion, conc_groups = NULL, arguments = NULL, enabled = TRUE, ... )weight_concentration_objective( name, conc_aversion, conc_groups = NULL, arguments = NULL, enabled = TRUE, ... )
name |
name of concentration measure, currently only "HHI" is supported. |
conc_aversion |
concentration aversion value(s) |
conc_groups |
list of vectors specifying the groups of the assets. Similar
to |
arguments |
default arguments to be passed to an objective function when executed |
enabled |
TRUE/FALSE |
... |
any other passthru parameters |
The conc_aversion argument can be a scalar or vector of concentration
aversion values. If conc_aversion is a scalar and conc_groups is
NULL, then the concentration aversion value will be applied to the overall
weights.
If conc_groups is specified as an argument, then the concentration
aversion value(s) will be applied to each group.
an object of class 'weight_concentration_objective'
Ross Bennett
The constraint specifies the upper and lower bound on the sum of the weights.
This function is called by add.constraint when "weight_sum", "leverage", "full_investment", "dollar_neutral", or "active" is specified as the type. see add.constraint
weight_sum_constraint( type = "weight_sum", min_sum = 0.99, max_sum = 1.01, enabled = TRUE, ... )weight_sum_constraint( type = "weight_sum", min_sum = 0.99, max_sum = 1.01, enabled = TRUE, ... )
type |
character type of the constraint |
min_sum |
minimum sum of all asset weights, default 0.99 |
max_sum |
maximum sum of all asset weights, default 1.01 |
enabled |
TRUE/FALSE |
... |
any other passthru parameters to specify weight_sum constraints |
Special cases for the weight_sum constraint are "full_investment" and "dollar_nuetral" or "active"
If type="full_investment", min_sum=1 and max_sum=1
If type="dollar_neutral" or type="active", min_sum=0, and max_sum=0
an object of class 'weight_sum_constraint'
Ross Bennett
data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) # min_sum and max_sum can be specified with type="weight_sum" or type="leverage" pspec <- add.constraint(pspec, type="weight_sum", min_sum=1, max_sum=1) # Specify type="full_investment" to set min_sum=1 and max_sum=1 pspec <- add.constraint(pspec, type="full_investment") # Specify type="dollar_neutral" or type="active" to set min_sum=0 and max_sum=0 pspec <- add.constraint(pspec, type="dollar_neutral") pspec <- add.constraint(pspec, type="active")data(edhec) ret <- edhec[, 1:4] pspec <- portfolio.spec(assets=colnames(ret)) # min_sum and max_sum can be specified with type="weight_sum" or type="leverage" pspec <- add.constraint(pspec, type="weight_sum", min_sum=1, max_sum=1) # Specify type="full_investment" to set min_sum=1 and max_sum=1 pspec <- add.constraint(pspec, type="full_investment") # Specify type="dollar_neutral" or type="active" to set min_sum=0 and max_sum=0 pspec <- add.constraint(pspec, type="dollar_neutral") pspec <- add.constraint(pspec, type="active")