factorModelMonteCarlo: Simulate returns using factor model Monte Carlo method.

In R-Finance/FactorAnalytics: factor analysis

Description

Simulate returns using factor model Monte Carlo method. Parametric method like normal distribution, Cornish-Fisher and skew-t distribution for residuals can be selected. Resampling method such as non-parametric bootstrap or stationary bootstrap can be selected.

Usage

  factorModelMonteCarlo(n.boot = 1000, factorData,
    Beta.mat, Alpha.mat = NULL, residualData,
    residual.dist = c("normal", "Cornish-Fisher", "skew-t"),
    boot.method = c("random", "block"), seed = 123,
    return.factors = FALSE, return.residuals = FALSE)

Arguments

n.boot	Integer number of bootstrap samples.
factorData	n.months x n.funds matrix or data.frame of factor returns.
Beta.mat	n.funds x n.factors matrix of factor betas.
Alpha.mat	n.funds x 1 matrix of factor alphas (intercepts). If NULL then assume that all alphas are zero.
residualData	n.funds x n.parms matrix of residual distribution parameters. The columns of residualData depend on the value of residual.dist. If residual.dist = "normal", then residualData has one column containing variance values; if residual.dist = "Cornish-Fisher", then residualData has three columns containing variance, skewness and excess kurtosis values; if residual.dist="skew-t", then residualData has four columns containing location, scale, shape, and df values.
residual.dist	character vector specifying the residual distribution. Choices are "normal" for the normal distribution; "Cornish-Fisher" for the Cornish-Fisher distribution based on the Cornish-Fisher expansion of the normal distribution quantile; "skew-t" for the skewed Student's t distribution of Azzalini and Captiano.
boot.method	character vector specifying the resampling method. Choices are "random" for random sampling with replacement (non-parametric bootstrap); "block" for stationary block bootstrapping.
seed	integer random number seed used for resampling the factor returns.
return.factors	logical; if TRUE then return resampled factors in output list object.
return.residuals	logical; if TRUE then return simulated residuals in output list object.

Details

The factor model Monte Carlo method is described in Jiang (2009).

Value

A list with the following components:

• returns n.boot x n.funds matrix of simulated fund returns.

• factors n.boot x n.factors matrix of resampled factor returns. Returned only if return.factors = TRUE.

• residuals n.boot x n.funds matrix of simulated fund residuals. Returned only if return.residuals = TRUE.

Author(s)

Eric Zivot and Yi-An Chen.

References

Jiang, Y. (2009). UW PhD Thesis.

Examples

# load data from the database
data(managers.df)
fit <- fitTimeSeriesFactorModel(assets.names=colnames(managers.df[,(1:6)]),
                                factors.names=c("EDHEC.LS.EQ","SP500.TR"),
                                data=managers.df,fit.method="OLS")
factorData= managers.df[,c("EDHEC.LS.EQ","SP500.TR")]
Beta.mat=fit$beta
residualData=as.matrix(fit$resid.variance,1,6)
n.boot=1000
# bootstrap returns data from factor model with residuals sample from normal distribution
bootData <- factorModelMonteCarlo(n.boot, factorData,Beta.mat, residual.dist="normal",
                                  residualData, Alpha.mat=NULL, boot.method="random",
                                  seed = 123, return.factors = "TRUE", return.residuals =
                                  "TRUE")
# Cornish-Fisher distribution
# build different residualData matrix
residualData <- cbind(c(1,2,1,3,0.1,0.5),rnorm(6),c(2,3,1,2,1,0))
colnames(residualData) <- c("var","skew","ekurt")
rownames(residualData) <- colnames(managers.df[,(1:6)])
bootData <- factorModelMonteCarlo(n.boot, factorData,Beta.mat, residual.dist="Cornish-Fisher",
                                  residualData, Alpha.mat=NULL, boot.method="random",
                                  seed = 123, return.factors = "TRUE", return.residuals =
                                  "TRUE")


# skew-t distribution
# build residualData matrix
residualData <- cbind(rnorm(6),c(1,2,1,3,0.1,0.5),rnorm(6),c(2,3,1,6,10,100))
colnames(residualData) <- c("location","scale","shape","df")
rownames(residualData) <- colnames(managers.df[,(1:6)])
bootData <- factorModelMonteCarlo(n.boot, factorData,Beta.mat, residual.dist="skew-t",
                                  residualData, Alpha.mat=NULL, boot.method="random",
                                  seed = 123, return.factors = "TRUE", return.residuals =
                                  "TRUE")

R-Finance/FactorAnalytics documentation built on May 8, 2019, 3:51 a.m.