fmmcSemiParam: Semi-parametric factor model Monte Carlo
In factorAnalytics: Factor Analytics

Description Usage Arguments Details Value Author(s) References See Also Examples

Simulate asset returns using semi-parametric Monte Carlo, by making use of a fitted factor model. Residuals are randomly generated from a chosen parametric distribution (Normal, Cornish-Fisher or Skew-t). Factor returns are resampled through non-parametric or stationary bootstrap.

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fmmcSemiParam(B = 1000, factor.ret, beta, alpha, resid.par,
  resid.dist = c("normal", "Cornish-Fisher", "skew-t"),
  boot.method = c("random", "block"), seed = 123)

`B`	number of bootstrap samples. Default is 1000.
`factor.ret`	`T x K` matrix or data.frame of factor returns having a complete history of data.
`beta`	`N x K` matrix of factor betas.
`alpha`	`N x 1` matrix of factor alphas (intercepts). If missing, these are assumed to be 0 for all funds.
`resid.par`	`N x P` matrix of parameters for the residual distribution.
`resid.dist`	the residual distribution; one of "normal", "Cornish-Fisher" or "skew-t". Default is "normal".
`boot.method`	the resampling method for factor returns; one of "random" or "block".
`seed`	integer to set random number generator state before resampling factor returns.

Refer to Yindeng Jiang's PhD thesis referenced below for motivation and empirical results. An abstract can be found at <http://gradworks.umi.com/33/77/3377280.html>.

T is the no. of observations, K is the no. of factors, N is the no. of assets or funds, P is the no. of parameters for the residual distribution and B is the no. of bootstrap samples.

The columns in resid.par depend on the choice of resid.dist. If resid.dist = "normal", resid.par has one column for standard deviation. If resid.dist = "Cornish-Fisher", resid.par has three columns for sigma=standard deviation, skew=skewness and ekurt= excess kurtosis. If resid.dist = "skew-t", resid.par has four columns for xi=location, omega=scale, alpha=shape, and nu=degrees of freedom. Cornish-Fisher distribution is based on the Cornish-Fisher expansion of the Normal quantile. Skew-t is the skewed Student's t-distribution– Azzalini and Captiano. The parameters can differ across funds, though the type of distribution is the same.

Bootstrap method: "random" corresponds to random sampling with replacement, and "block" corresponds to stationary block bootstrap– Politis and Romano (1994).

A list containing the following components:

`sim.fund.ret`	`B x N` matrix of simulated fund returns.
`boot.factor.ret`	`B x K` matrix of resampled factor returns.
`sim.residuals`	`B x N` matrix of simulated residuals.

Eric Zivot, Yi-An Chen, Sangeetha Srinivasan.

Jiang, Y. (2009). Factor model Monte Carlo methods for general fund-of-funds portfolio management. University of Washington.

http://gradworks.umi.com/33/77/3377280.html

# fit a time series factor model for all assets
data(managers)
fit <- fitTsfm(asset.names=colnames(managers[,(1:6)]),
               factor.names=colnames(managers[,(7:9)]), data=managers)

# bootstrap returns using the fitted factor model, Normal dist. for residuals
resid.par <- as.matrix(fit$resid.sd,1,6)
fmmc.returns <- fmmcSemiParam(factor.ret=managers[,(7:9)], beta=fit$beta, 
                              alpha=fit$alpha, resid.par=resid.par)
                     
# Cornish-Fisher distribution for residuals
resid.par <- cbind(c(1,2,1,3,0.1,0.5), rnorm(6), c(2,3,1,2,1,0))
colnames(resid.par) <- c("var","skew","xskurt")
rownames(resid.par) <- colnames(managers[,(1:6)])
fmmc.returns.CF <- fmmcSemiParam(factor.ret=managers[,(7:9)], beta=fit$beta, 
                                 alpha=fit$alpha, resid.par=resid.par,
                                 resid.dist="Cornish-Fisher")

# skew-t distribution
resid.par <- cbind(rnorm(6), c(1,2,1,3,0.1,0.5), rnorm(6), c(2,3,1,6,10,100))
colnames(resid.par) <- c("xi","omega","alpha","nu")
rownames(resid.par) <- colnames(managers[,(1:6)])
fmmc.returns.skewt <- fmmcSemiParam(factor.ret=managers[,(7:9)], 
                                    beta=fit$beta, alpha=fit$alpha, 
                                    resid.dist="skew-t", resid.par=resid.par)