Package 'GCPM'

Description

The package helps to analyze the default risk of credit portfolios. Commonly known models, like CreditRisk+ or the CreditMetrics model are implemented in their very basic settings. The portfolio loss distribution can be achieved either by simulation or analytically in case of the classic CreditRisk+ model. Models are only implemented to respect losses caused by defaults, i.e. migration risk is not included. The package structure is kept flexible especially with respect to distributional assumptions in order to quantify the sensitivity of risk figures with respect to several assumptions. Therefore the package can be used to determine the credit risk of a given portfolio as well as to quantify model sensitivities.

Details

Author(s)

Kevin Jakob

Maintainer: Kevin Jakob <[email protected]>

References

Jakob, K. & Fischer, M. "GCPM: A flexible package to explore credit portfolio risk" Austrian Journal of Statistics 45.1 (2016): 25:44
Morgan, J. P. "CreditMetrics-technical document." JP Morgan, New York, 1997
First Boston Financial Products, "CreditRisk+", 1997
Gundlach & Lehrbass, "CreditRisk+ in the Banking Industry", Springer, 2003

See Also

GCPM-class, init, analyze

Examples

#create a random portfolio with NC counterparties
NC=100
#assign business lines and countries randomly
business.lines=c("A","B","C")
CP.business=business.lines[ceiling(runif(NC,0,length(business.lines)))] 
countries=c("A","B","C","D","E")
CP.country=countries[ceiling(runif(NC,0,length(countries)))]

#create matrix with sector weights (CreditRisk+ setting)
#according to business lines
NS=length(business.lines)
W=matrix(0,nrow = NC,ncol = length(business.lines),
dimnames = list(1:NC,business.lines)) 
for(i in 1:NC){W[i,CP.business[i]]=1}

#create portfolio data frame
portfolio=data.frame(Number=1:NC,Name=paste("Name ",1:NC),Business=CP.business,
                     Country=CP.country,EAD=runif(NC,1e3,1e6),LGD=runif(NC),
                     PD=runif(NC,0,0.3),Default=rep("Bernoulli",NC),W)

#draw sector variances randomly
sec.var=runif(NS,0.5,1.5)
names(sec.var)=business.lines

#draw N sector realizations (independent gamma distributed sectors)
N=5e4
random.numbers=matrix(NA,ncol=NS,nrow=N,dimnames=list(1:N,business.lines))
for(i in 1:NS){
random.numbers[,i]=rgamma(N,shape = 1/sec.var[i],scale=sec.var[i])}

#create a portfolio model and analyze the portfolio
TestModel=init(model.type = "simulative",link.function = "CRP",N = N,
loss.unit = 1e3, random.numbers = random.numbers,LHR=rep(1,N),loss.thr=5e6,
max.entries=2e4)
TestModel=analyze(TestModel,portfolio)

#plot of pdf of portfolio loss (in million) with indicators for EL, VaR and ES
alpha=c(0.995,0.999)
plot(TestModel,1e6,alpha=alpha)

#calculate portfolio VaR and ES
VaR=VaR(TestModel,alpha)
ES=ES(TestModel,alpha)

#Calculate risk contributions to VaR and ES 
risk.cont=cbind(VaR.cont(TestModel,alpha = alpha),
ES.cont(TestModel,alpha = alpha))

Description

Get the maximum value of the model's CDF. For simulative models, the value should be equal to 1. For an analytical model, the value depends on the value specified during initiation of the model (see init).

Usage

alpha.max(this)

Arguments

Value

numeric of length 1

See Also

init

Description

The method analyzes a given portfolio with a predefined portfolio model (i.e. a GCPM object). Portfolio key numbers such as the number of portfolio positions, sum of EAD and PL or the expected loss are calculated. Afterwards the loss distribution is estimated according to model.type.

Usage

analyze(this,portfolio,alpha,Ncores)

Arguments

Details

In case of an analytical CreditRisk+ model, a modified version of the algorithm described in Gundlach & Lehrbass (2003) is used. For a simulative model, the loss distribution is estimated based on N simulations with sector drawings specified by random.numbers (see init). The sector names (column names) should not include any white spaces. In case of a CreditMetrics type model, the values of R (not R^2) have to be provided as sector weights. In the standard CreditMetrics or CreditRisk+ framework a counterparty can be assigned to more than one sector. Within a analytical CreditRisk+ model, the sector names have to match the names of sec.var or in a simulative model the column names of random.numbers (see init)

Value

object of class GCPM.

Methods

signature(this = "GCPM", portfolio = "data.frame", alpha = "missing")

If loss levels alpha are not provided, risk measures such as economic capital, value at risk and expected shortfall are not calculated by default. However, they can be calculated afterwards by calling the corresponding methods (see VaR, ES, EC)

signature(this = "GCPM", portfolio = "data.frame", alpha = "numeric")

If loss levels alpha are provided, risk measures such as economic capital, value at risk and expected shortfall are calculated and printed. To extract these risk measures into a separate variable you can use the corresponding methods.

References

Jakob, K. & Fischer, M. "GCPM: A flexible package to explore credit portfolio risk" Austrian Journal of Statistics 45.1 (2016): 25:44
Morgan, J. P. "CreditMetrics-technical document." JP Morgan, New York, 1997
First Boston Financial Products, "CreditRisk+", 1997
Gundlach & Lehrbass, "CreditRisk+ in the Banking Industry", Springer, 2003

See Also

init

Examples

#create a random portfolio with NC counterparties
NC=100
#assign business lines and countries randomly
business.lines=c("A","B","C")
CP.business=business.lines[ceiling(runif(NC,0,length(business.lines)))]
countries=c("A","B","C","D","E")
CP.country=countries[ceiling(runif(NC,0,length(countries)))]

#create matrix with sector weights (CreditRisk+ setting)
#according to business lines
NS=length(business.lines)
W=matrix(0,nrow = NC,ncol = length(business.lines),
dimnames = list(1:NC,business.lines))
for(i in 1:NC){W[i,CP.business[i]]=1}

#create portfolio data frame
portfolio=data.frame(Number=1:NC,Name=paste("Name ",1:NC),Business=CP.business,
                     Country=CP.country,EAD=runif(NC,1e3,1e6),LGD=runif(NC),
                     PD=runif(NC,0,0.3),Default=rep("Bernoulli",NC),W)

#draw sector variances randomly
sec.var=runif(NS,0.5,1.5)
names(sec.var)=business.lines

#draw N sector realizations (independent gamma distributed sectors)
N=5e4
random.numbers=matrix(NA,ncol=NS,nrow=N,dimnames=list(1:N,business.lines))
for(i in 1:NS){
random.numbers[,i]=rgamma(N,shape = 1/sec.var[i],scale=sec.var[i])}

#create a portfolio model and analyze the portfolio
TestModel=init(model.type = "simulative",link.function = "CRP",N = N,
loss.unit = 1e3, random.numbers = random.numbers,LHR=rep(1,N),loss.thr=5e6,
max.entries=2e4)
TestModel=analyze(TestModel,portfolio)

#plot of pdf of portfolio loss (in million) with indicators for EL, VaR and ES
alpha=c(0.995,0.999)
plot(TestModel,1e6,alpha=alpha)

#calculate portfolio VaR and ES
VaR=VaR(TestModel,alpha)
ES=ES(TestModel,alpha)

#Calculate risk contributions to VaR and ES
risk.cont=cbind(VaR.cont(TestModel,alpha = alpha),
ES.cont(TestModel,alpha = alpha))

#Use parallel computing for Monte Carlo simulation
TestModel=analyze(TestModel,portfolio,Ncores=2)

Description

Get the business information for each counterparty defined in the portfolio.

Usage

business(this)

Arguments

Value

factor of length equal to number of portfolio positions

See Also

portfolio.pois

Description

Get the CDF of the portfolio loss, available after execution of analyze.

Usage

CDF(this)

Arguments

Value

numeric vector

See Also

analyze

Description

Get the country information of each counterparty defined in the portfolio.

Usage

country(this)

Arguments

Value

factor of length equal to number of portfolio positions

See Also

portfolio.pois

Description

Get the default distribution of each portfolio position. Using “Poisson” as default distribution one can simulate the standard CR+ model or group smaller counterparties into a pool and simulate their defaults.

Usage

default(this)

Arguments

Value

character of length equal to number of portfolio positions

See Also

portfolio.pois

Description

Get the counterparties' exposure at default defined in the portfolio data.

Usage

EAD(this)

Arguments

Value

numeric value of length equal to the number of counterparties

See Also

portfolio.pois

Description

Get the value of economic capital for the portfolio on level(s) alpha

Usage

EC(this,alpha)

Arguments

Value

numeric vector of length equal to length(alpha).

Description

Calculate contributions to the economic capital on portfolio level for each portfolio position. In case of a simulative model, the risk contributions are calculated as contributions to expected shortfall on a lower loss level $\tau$, such that ES($\tau$) is as close as possible to EC($\alpha$). Furthermore, in case of a simulative model, loss scenarios above a predefined threshold (loss.thr) are analyzed in order to calculate the risk contributions. If loss.thr is too high (depending on value of alpha) the calculation will be not possible.

Usage

EC.cont(this,alpha)

Arguments

Value

numeric matrix with number of rows equal to number of counterparties within the portfolio and number of columns equal to length(alpha)

See Also

loss.thr

Description

Get the expected loss (EL) calculated from the portfolio loss distribution. Because of the discretization and/or simulation errors, this is not equal to the analytical EL (see EL.analyt). Please also note, that in case of a simulative model (with Bernoulli default distribution) of the CreditRisk+ type the simulated EL tends to be smaller than the analytical one because the conditional PD $\overline{PD}=PD\cdot (w^Tx)$ has to be truncated (if $\overline{PD}>1$).

Usage

EL(this)

Arguments

Value

numeric value of length 1

See Also

EL.analyt

Description

Get the expected loss (EL) calculated from the portfolio data. Because of the discretization and/or simulation errors, this is not equal to the EL calculated from the portfolio loss distribution (see EL).

Usage

EL.analyt(this)

Arguments

Value

numeric value of length 1

See Also

EL

Description

Get the value of the expected shortfall for the portfolio on level(s) alpha

Usage

ES(this,alpha)

Arguments

Value

numeric vector of length equal to length(alpha).

Description

Calculate contributions to the expected shortfall on portfolio level for each portfolio position. In case of a simulative model, loss scenarios above a predefined threshold (loss.thr) are analyzed in order to calculate the risk contributions. If loss.thr is too high, calculation may be not possible (depending on value of alpha).

Usage

ES.cont(this,alpha)

Arguments

Value

numeric matrix with number of rows equal to number of counterparties within the portfolio and number of columns equal to length(alpha)

See Also

loss.thr

Description

This method provides an easy way to export the main results of the portfolio (i.e. after running analyze). A summary file and the portfolio loss distribution (PDF and CDF) are exported to path.out. With the help of file.format one can specify the csv format (“csv1” or “csv2”). If a vector alpha of loss levels is specified, risk contributions to EC, VaR and ES are also exported according to level(s) alpha.

Usage

export(this,path.out,file.format,alpha)

Arguments

Description

The class represents a generalized credit portfolio framework. Users which are not familiar with credit portfolio models in general and the CreditRisk+ model as well as the CreditMetrics model in particular should refer to the references given below. Models can be simulative or analytical (in case of a CreditRisk+ type model). The link function can be chosen to be either of the CreditRisk+ or the CreditMetrics type. Counterparties' default distribution can be specified to be either Bernoulli or Poisson, which is the default distribution in the basic CreditRisk+ framework.

Objects from the Class

Objects can be created via the init function (see init)

Slots

model.type:

Character value, specifying the model type. One can choose between “simulative” and “CRP” which corresponds to the analytical version of the CreditRisk+ model (see First Boston Financial Products, 1997)

default:

Character vector specifying the counterparties' default distribution (either “Bernoulli” or “Poisson”)

link.function:

character value, specifying the type of the link function. One can choose between “CRP”, which corresponds to $\overline{PD}=PD\cdot (w^Tx)$ and “CM” which corresponds to $\overline{PD}=\Phi\left(\frac{\Phi^{-1}PD-w^Tx}{\sqrt{1-w^T\Sigma w}}\right)$, where PD is the original PD from portfolio data, x is the vector of sector drawings, $\Phi$ is the CDF of the standard normal distribution, w is the vector of sector weights given in the portfolio data and $\Sigma$ is the correlation matrix of the sector variables estimated from random.numbers. “CRP” will be used automatically if model.type == "CRP".

loss.unit:

numeric value used to discretize potential losses.

NS:

number of sectors

NC:

number of counterparties

name:

counterparties' names defined in the portfolio

NR:

counterparties' identification numbers defined in the portfolio

EAD:

counterparties' exposure at default defined in the portfolio

LGD:

counterparties' loss given default defined in the portfolio

PL:

counterparties' potential loss ($EAD*LGD$)

PD:

counterparties' probability of default defined in the portfolio

business:

counterparties' business line defined in the portfolio

country:

counterparties' country defined in the portfolio

EL.analyt:

Expected loss calculated from portfolio data (without discretization)

EL:

Expected loss derived from loss distribution

nu:

multiples of loss unit representing discretized potential losses within an analytical CreditRisk+ type model

PL.disc:

counterparties' potential loss ($EAD*LGD$) after discretization

PD.disc:

counterparties' probability of default defined in the portfolio after discretization

sec.var:

sector variances within an analytical CreditRisk+ type model

sector.names:

sector names

SD.div:

diversifiable part of portfolio risk (measured by standard deviation) in case of a CreditRisk+ type model

SD.syst:

Non-diversifiable part of portfolio risk (measured by standard deviation) in case of a CreditRisk+ type model

SD.analyt:

portfolio standard deviation derived from portfolio data in case of a CreditRisk+ type model

SD:

portfolio standard deviation derived from loss distribution

W:

counterparties' sector weights

idiosyncr:

counterparties idiosyncratic weight in case of a CreditRisk+ type model

alpha.max:

maximum level of CDF of the loss distribution within an analytical CreditRisk+ type model

a:

internal parameter used to calculate risk contributions in case of an analytical CreditRisk+ type model

PDF:

probability density function of portfolio losses

CDF:

cumulative distribution function of portfolio losses

B:

internal parameter used to calculate risk contributions in case of an analytical CreditRisk+ type model

loss:

portfolio losses corresponding to PDF and CDF

random.numbers:

sector drawing in case of a simulative model

LHR:

likelihood ration of sector drawing in case of a simulative model

max.entries

numeric value defining the maximum number of loss scenarios stored to calculate risk contributions.

N:

number of simulations in case of a simulative model

scenarios:

scenarios (rows) of random.numbers used within the simulation of portfolio losses

seed:

parameter used to initialize the random number generator. If seed is not provided a value based on current system time will be used.

loss.thr:

specifies a lower bound for portfolio losses to be stored in order to derive risk contributions on counterparty level. Using a lower value needs a lot of memory but will be necessary in order to calculate risk contributions on lower CDF levels. This parameter is used only if model.type == "simulative".

sim.losses:

simulated portfolio losses in case of a simulative model

CP.sim.losses:

simulated losses on counterparty level when the overall portfolio loss is greater or equal to loss.thr

Author(s)

Kevin Jakob

References

Jakob, K. & Fischer, M. "GCPM: A flexible package to explore credit portfolio risk" Austrian Journal of Statistics 45.1 (2016): 25:44
Morgan, J. P. "CreditMetrics-technical document." JP Morgan, New York, 1997
First Boston Financial Products, "CreditRisk+", 1997
Gundlach & Lehrbass, "CreditRisk+ in the Banking Industry", Springer, 2003

See Also

GCPM-package, init, analyze

Description

Get the idiosyncratic risk weights (i.e. risk weights which are not assigned to any sector). Currently only available if model.type == "CRP".

Usage

idiosyncr(this)

Arguments

Value

numeric vector of length equal to number of counterparties

Description

The function helps to create a new object of class GCPM. The arguments of the function are passed to the object after performing some plausibility checks.

Usage

init(model.type = "CRP", link.function = "CRP", N, seed,
loss.unit, alpha.max = 0.9999, loss.thr = Inf, sec.var,
random.numbers = matrix(), LHR, max.entries=1e3)

Arguments

Value

object of class GCPM

Author(s)

Kevin Jakob

References

Jakob, K. & Fischer, M. "GCPM: A flexible package to explore credit portfolio risk" Austrian Journal of Statistics 45.1 (2016): 25:44
Morgan, J. P. "CreditMetrics-technical document." JP Morgan, New York, 1997
First Boston Financial Products, "CreditRisk+", 1997
Gundlach & Lehrbass, "CreditRisk+ in the Banking Industry", Springer, 2003

See Also

GCPM, GCPM-class, analyze

Examples

#create a random portfolio with NC counterparties
NC=100
#assign business lines and countries randomly
business.lines=c("A","B","C")
CP.business=business.lines[ceiling(runif(NC,0,length(business.lines)))] 
countries=c("A","B","C","D","E")
CP.country=countries[ceiling(runif(NC,0,length(countries)))]

#create matrix with sector weights (CreditRisk+ setting)
#according to business lines
NS=length(business.lines)
W=matrix(0,nrow = NC,ncol = length(business.lines),
dimnames = list(1:NC,business.lines)) 
for(i in 1:NC){W[i,CP.business[i]]=1}

#create portfolio data frame
portfolio=data.frame(Number=1:NC,Name=paste("Name ",1:NC),Business=CP.business,
                     Country=CP.country,EAD=runif(NC,1e3,1e6),LGD=runif(NC),
                     PD=runif(NC,0,0.3),Default=rep("Bernoulli",NC),W)

#draw sector variances randomly
sec.var=runif(NS,0.5,1.5)
names(sec.var)=business.lines

#draw N sector realizations (independent gamma distributed sectors)
N=5e4
random.numbers=matrix(NA,ncol=NS,nrow=N,dimnames=list(1:N,business.lines))
for(i in 1:NS){
random.numbers[,i]=rgamma(N,shape = 1/sec.var[i],scale=sec.var[i])}

#create a portfolio model and analyze the portfolio
TestModel=init(model.type = "simulative",link.function = "CRP",N = N,
loss.unit = 1e3, random.numbers = random.numbers,LHR=rep(1,N),loss.thr=5e6,
max.entries=2e4)
TestModel=analyze(TestModel,portfolio)

#plot of pdf of portfolio loss (in million) with indicators for EL, VaR and ES
alpha=c(0.995,0.999)
plot(TestModel,1e6,alpha=alpha)

#calculate portfolio VaR and ES
VaR=VaR(TestModel,alpha)
ES=ES(TestModel,alpha)

#Calculate risk contributions to VaR and ES 
risk.cont=cbind(VaR.cont(TestModel,alpha = alpha),
ES.cont(TestModel,alpha = alpha))

Description

Get the values of LGD, defined within the portfolio

Usage

LGD(this)

Arguments

Value

numeric vector of length equal to number of counterparties

See Also

portfolio.pois

Description

Get the likelihood ratio for each scenario defined in random.numbers (see init)

Usage

LHR(this)

Arguments

Value

numeric vector of length equal to nrow(random.numbers)

Description

Get the models link function (see init)

Usage

link.function(this)

Arguments

Value

character value of length 1

See Also

init

Description

Get the loss levels of the portfolio loss distribution.

Usage

loss(this)

Arguments

Value

numeric vector

Description

Get the value of loss.thr (see init)

Usage

loss.thr(this)

Arguments

Value

numeric value of length 1

See Also

init

Description

Get the loss unit used for potential loss discretization of the model

Usage

loss.unit(this)

Arguments

Value

numeric value of length 1

See Also

init

Description

Get the value of model.type (see init)

Usage

model.type(this)

Arguments

Value

character value of length 1

See Also

init

Description

Get the value of N (number of simulations, see init)

Usage

N(this)

Arguments

Value

numeric value of length 1

See Also

init

Description

Get the value of name, i.e. the counterparties' names, defined in the portfolio (see analyze)

Usage

name(this)

Arguments

Value

character value of length equal to number of counterparties

See Also

portfolio.pois

Description

Get the value of NC, representing the number of counterparties within the portfolio (see analyze)

Usage

NC(this)

Arguments

Value

numeric value of length 1

See Also

analyze

Description

Get the value of NR, the counterparties' identification numbers within the portfolio (see analyze)

Usage

NR(this)

Arguments

Value

numeric value of length equal to number of counterparties

See Also

portfolio.pois

Description

Get the value of NS, the number of sectors within the model (see init)

Usage

NS(this)

Arguments

Value

numeric value of length 1

See Also

init

Description

Get the value of PD, the counterparties default probabilities within the portfolio (see analyze. Please note, that these PDs are adjusted because of discretization in order to preserve the expected loss.)

Usage

PD(this)

Arguments

Value

numeric value of length equal to the number of counterparties

See Also

portfolio.pois

Description

Get the value of PDF, representing the pdf of the estimated portfolio loss distribution.

Usage

PDF(this)

Arguments

Value

numeric vector

Description

Get the value of PL, the potential losses of counterparties (see GCPM-class). Please note, that the potential losses are discretized according to loss.unit (see init).

Usage

PL(this)

Arguments

Value

numeric value of length equal to the number of counterparties

See Also

portfolio.pois,init

Description

Plot of the estimated pdf of the portfolio loss distribution.

Usage

plot(x,y,...)

Arguments

Description

The dataset contains an example portfolio in the structure needed by the analyze function.

Usage

data("portfolio.pois")

Format

A data frame with 3000 counterparties and the following variables.

Number

Counterparty ID (numeric)

Name

Counterparty name (character)

Business

Business line (character)

Country

Country (character)

EAD

Exposure at default (numeric)

LGD

Loss given dafault (numeric)

PD

Probability of default (numeric)

Default

Default mode (‘Poisson’ or ‘Benroulli’)

A

sector weights for sector A

B

sector weights for sector B

C

sector weights for sector C

Description

In order to speed up calculations, counterparties of portfolio.pois with EAD*LGD < 200,000 are grouped together (pooled).

Usage

data("portfolio.pool")

Format

A data frame with 1400 counterparties and 3 pools (each per sector) and the following variables.

Number

Counterparty ID (numeric)

Name

Counterparty name (character)

Business

Business line (character)

Country

Country (character)

EAD

Exposure at default (numeric); pool: average EAD per counterparty

LGD

Loss given dafault (numeric); pool: EAD-weighted average LGD per counterparty

PD

Probability of default (numeric); pool: expectation of number of defaults

Default

Default mode (‘Poisson’ for pools or ‘Benroulli’)

A

sector weights for sector A

B

sector weights for sector B

C

sector weights for sector C

Description

The workspace contain the example portfolio (with Poisson default mode) in the structure needed by the analyze function as well as a pooled version.

Usage

data("portfolios")

Format

Two data frames containing the portfolios.

See Also

portfolio.pois, portfolio.pool, analyze

Description

Get the content of random.numbers, representing the sector drawings (see init)

Usage

random.numbers(this)

Arguments

Value

numeric matrix

See Also

init

Description

Get the value of SD, the portfolio standard deviation derived from the loss distribution.

Usage

SD(this)

Arguments

Value

numeric value of length 1

Description

Get the value of SD.analyt, the portfolio standard deviation derived from the portfolio data (see GCPM-class). This value is only available in case of an analytical model.

Usage

SD.analyt(this)

Arguments

Value

numeric value of length 1

Description

Get the counterparties' contributions to portfolio standard deviation (see GCPM-class). These values are only available in case of an analytical model.

Usage

SD.cont(this)

Arguments

Value

numeric value of length equal to number of counterparties

Description

Get the value of SD.div, the diversifiable part of portfolio standard deviation (see GCPM-class)

Usage

SD.div(this)

Arguments

Value

numeric value of length 1

Description

Get the value of SD.syst, the non-diversifiable part of portfolio standard deviation.

Usage

SD.syst(this)

Arguments

Value

numeric value of length 1

Description

Get the value of sec.var, the sector variances in case of an analytical CreditRisk+ like model (see init)

Usage

sec.var(this)

Arguments

Value

numeric value of length equal to number of sectors

See Also

init

Description

Get the value of sector.names, the sector names (see init)

Usage

sector.names(this)

Arguments

Value

factor of length equal to number of sectors

See Also

init

Description

Get the value of seed (see init)

Usage

seed(this)

Arguments

Value

numeric value of length 1

See Also

init

Description

Displays the most important parameters and portfolio statistics (if available).

Description

Create a Summary List with Model Parameters.

Usage

summary(object,...)

Arguments

Value

list

Description

Calculate the portfolio value at risk on level(s) alpha.

Usage

VaR(this,alpha)

Arguments

Value

numeric value of length equal to length of alpha

Description

Get the counterparties' contributions to portfolio value at risk (see GCPM-class). In case of a simulative model, these values are calculated from individual losses greater or equal loss.thr (see init). Contributions are not available if loss.thr is too high.

Usage

VaR.cont(this,alpha)

Arguments

Value

numeric matrix

See Also

init,loss.thr

Description

Get the value of W, the matrix of counterparties' sector weights defined within the portfolio (see analyze)

Usage

W(this)

Arguments

Value

numeric matrix

See Also

init