fitFfm: Fit a fundamental factor model using cross-sectional...
In sangeeuw/factorAnalytics: Factor Analytics

Description Usage Arguments Details Value Author(s) References Examples

Fit a fundamental (cross-sectional) factor model using ordinary least squares or robust regression. Fundamental factor models use observable asset specific characteristics (or) fundamentals, like industry classification, market capitalization, style classification (value, growth) etc. to calculate the common risk factors. An object of class "ffm" is returned.

fitFfm(data, asset.var, ret.var, date.var, exposure.vars, weight.var = NULL,
  fit.method = c("LS", "WLS", "Rob", "W-Rob"), rob.stats = FALSE,
  full.resid.cov = FALSE, z.score = c("none", "crossSection", "timeSeries"),
  add.intercept = FALSE, lag.exposures = TRUE,
  resid.scale.type = c("stdDev", "EWMA", "robEWMA", "GARCH"),
  GARCH.params = list(omega = 0.09, alpha = 0.1, beta = 0.81), lambda = 0.9,
  GARCH.MLE = FALSE, std.return = FALSE, analysis = c("none", "ISM",
  "NEW"), target.vol = 0.06, ...)

## S3 method for class 'ffm'
coef(object, ...)

## S3 method for class 'ffm'
fitted(object, ...)

## S3 method for class 'ffm'
residuals(object, ...)

`data`	data.frame of the balanced panel data containing the variables `asset.var`, `ret.var`, `exposure.vars`, `date.var` and optionally, `weight.var`.
`asset.var`	character; name of the variable for asset names.
`ret.var`	character; name of the variable for asset returns.
`date.var`	character; name of the variable containing the dates coercible to class `Date`.
`exposure.vars`	vector; names of the variables containing the fundamental factor exposures.
`weight.var`	character; name of the variable containing the weights used when standarizing style factor exposures. Default is `NULL`. See Details.
`fit.method`	method for estimating factor returns; one of "LS", "WLS" "Rob" or "W-Rob". See details. Default is "LS".
`rob.stats`	logical; If `TRUE`, robust estimates of covariance, correlation, location and univariate scale are computed as appropriate (see Details). Default is `FALSE`.
`full.resid.cov`	logical; If `TRUE`, a full residual covariance matrix is estimated. Otherwise, a diagonal residual covariance matrix is estimated. Default is `FALSE`.
`z.score`	method for exposure standardization; one of "none", "crossSection", or "timeSeries". Default is `"none"`.
`add.intercept`	logical; If `TRUE`, intercept is added in the exposure matrix. Default is `FALSE`.
`lag.exposures`	logical; If `TRUE`, the style exposures in the exposure matrix are lagged by one time period. Default is `TRUE`.
`resid.scale.type`	character; method for computing weights when fit.method is set to WLS or W-Rob; one of `stdDev`, `EWMA`, `robEWMA`, or `GARCH`. Default is `stdDev`. See details.
`GARCH.params`	list containing GARCH parameters omega, alpha, and beta. Default values are 0.09, 0.1, 0.81 respectively. Valid only when `GARCH.MLE` is set to `FALSE`.
`lambda`	value of lambda to be used for the EWMA estimation of residual variances. Default is 0.9.
`GARCH.MLE`	logical; If `TRUE`, GARCH parameters are estimated by maximum liklihood estimation. Default is `FALSE`.
`std.return`	logical; If `TRUE`, the returns will be standardized using GARCH(1,1) volatilities. Default is `FALSE`.
`analysis`	method used in the analysis of fundamental law of active management; one of "none", "ISM", or "NEW". Default is "none".
`target.vol`	numeric; the targeted portfolio volatility in the analysis. Default is 0.06.
`...`	potentially further arguments passed.
`object`	a fit object of class `ffm` which is returned by `fitFfm`

Estimation method "LS" corresponds to ordinary least squares using lm and "Rob" is robust regression using lmRob. "WLS" is weighted least squares using estimates of the residual variances from LS regression as weights (feasible GLS). Similarly, "W-Rob" is weighted robust regression.

The weights to be used in "WLS" or "W-Rob" can be set using resid.scale.type argument which computes the residual variances in one of the following ways - sample variance, EWMA, Robust EWMA and GARCH(1,1). The inverse of these residual variances are used as the weights. For EWMA model, lambda = 0.9 is used as default and for GARCH(1,1) omega = 0.09, alpha = 0.1, and beta = 0.81 are used as default as mentioned in Martin & Ding (2017). These default parameters can be changed using the arguments lambda, GARCH.params for EWMA and GARCH respectively. To compute GARCH parameters via MLE, set GARCH.MLE to TRUE.

Standardizing style factor exposures: The exposures can be standardized into z-scores using regular or robust (see rob.stats) measures of location and scale. Further, weight.var, a variable such as market-cap, can be used to compute the weighted mean exposure, and an equal-weighted standard deviation of the exposures about the weighted mean. This may help avoid an ill-conditioned covariance matrix. Default option equally weights exposures of different assets each period.

If rob.stats=TRUE, covRob is used to compute a robust estimate of the factor covariance/correlation matrix, and, scaleTau2 is used to compute robust tau-estimates of univariate scale for residuals during "WLS" or "W-Rob" regressions. When standardizing style exposures, the median and mad are used for location and scale respectively. When resid.scale.type is EWMA or GARCH, the residual covariance is equal to the diagonal matrix of the estimated residual variances in last time period.

The original function was designed by Doug Martin and initially implemented in S-PLUS by a number of University of Washington Ph.D. students: Christopher Green, Eric Aldrich, and Yindeng Jiang. Guy Yollin ported the function to R and Yi-An Chen modified that code. Sangeetha Srinivasan re-factored, tested, and expanded the functionalities and S3 methods. Avinash Acharya and Chindhanai Uthaisaad further added new functionalities.

fitFfm returns an object of class "ffm" for which print, plot, predict and summary methods exist.

The generic accessor functions coef, fitted and residuals extract various useful features of the fit object. Additionally, fmCov computes the covariance matrix for asset returns based on the fitted factor model.

An object of class "ffm" is a list containing the following components:

`factor.fit`	list of fitted objects that estimate factor returns in each time period. Each fitted object is of class `lm` if `fit.method="LS" or "WLS"`, or, class `lmRob` if `fit.method="Rob" or "W-Rob"`.
`beta`	N x K matrix of factor exposures for the last time period.
`factor.returns`	xts object of K-factor returns (including intercept).
`residuals`	xts object of residuals for N-assets.
`r2`	length-T vector of R-squared values.
`factor.cov`	K x K covariance matrix of the factor returns.
`g.cov`	G x G covariance matrix of the coefficients for a Sector plus Market and Sector plus Country plus Global Market models.
`resid.cov`	N x N covariance matrix of residuals.
`return.cov`	N x N return covariance estimated by the factor model, using the factor exposures from the last time period.
`restriction.mat`	restriction matrix used in the computation of f=Rg.
`resid.var`	N x T matrix of estimated residual variances. It will be a length-N vector of sample residual variances when `resid.scale.type` is set to `stdDev`
`call`	the matched function call.
`data`	data frame object as input.
`date.var`	date.var as input
`ret.var`	ret.var as input
`asset.var`	asset.var as input.
`exposure.vars`	exposure.vars as input.
`weight.var`	weight.var as input.
`fit.method`	fit.method as input.
`asset.names`	length-N vector of asset names.
`factor.names`	length-K vector of factor.names.
`time.periods`	length-T vector of dates.
`activeWeights`	active weights obtaining from the fundamental law of active management
`activeReturns`	active returns corresponding to the active weights
`IR`	the vector of Granold-K, asymptotic IR, and finite-sample IR.

Where N is the number of assets, K is the number of factors (including the intercept or dummy variables) and T is the number of unique time periods.

Sangeetha Srinivasan, Guy Yollin, Yi-An Chen, Avinash Acharya and Chindhanai Uthaisaad

Menchero, J. (2010). The Characteristics of Factor Portfolios. Journal of Performance Measurement, 15(1), 52-62.

Grinold, R. C., & Kahn, R. N. (2000). Active portfolio management (Second Ed.). New York: McGraw-Hill.

Ding, Z., & Martin, R. D. (2017). The fundamental law of active management: Redux. Journal of Empirical Finance, 43, 91-114.

And, the following extractor functions: coef, fitted, residuals, fmCov, fmSdDecomp, fmVaRDecomp and fmEsDecomp.

paFm for Performance Attribution.

# Load fundamental and return data
 data("factorDataSetDjia5Yrs")

# fit a fundamental factor model
exposure.vars <- c("P2B", "MKTCAP")
fit <- fitFfm(data=factorDataSetDjia5Yrs, asset.var="TICKER", ret.var="RETURN",
              date.var="DATE", exposure.vars=exposure.vars)
names(fit)

# fit a Industry Factor Model with Intercept
exposure.vars <- c("SECTOR","P2B")
fit1 <- fitFfm(data=factorDataSetDjia5Yrs, asset.var="TICKER", ret.var="RETURN",
               date.var="DATE", exposure.vars=exposure.vars, add.intercept=TRUE)

# Fit a SECTOR+COUNTRY+Style model with Intercept
# Create a COUNTRY column with just 3 countries

 factorDataSetDjia5Yrs$COUNTRY = rep(rep(c(rep("US",1),rep("GERMANY",1)),11),60)
 exposure.vars= c("SECTOR","COUNTRY","P2B","MKTCAP")

 fit.MICM <- fitFfm(data=factorDataSetDjia5Yrs, asset.var="TICKER", ret.var="RETURN",
                   date.var="DATE", exposure.vars=exposure.vars, add.intercept=TRUE)