| Title: | Cross-Section Factor Models |
|---|---|
| Description: | Linear cross-section factor model fitting with least-squares and robust fitting the 'lmrobdetMM()' function from 'RobStatTM'; related volatility, Value at Risk and Expected Shortfall risk and performance attribution (factor-contributed vs idiosyncratic returns); tabular displays of risk and performance reports; factor model Monte Carlo. The package authors would like to thank Chicago Research on Security Prices,LLC for the cross-section of about 300 CRSP stocks data (in the data.table object 'stocksCRSP', and S&P GLOBAL MARKET INTELLIGENCE for contributing 14 factor scores (a.k.a "alpha factors".and "factor exposures") fundamental data on the 300 companies in the data.table object 'factorSPGMI'. The 'stocksCRSP' and 'factorsSPGMI' data are not covered by the GPL-2 license, are not provided as open source of any kind, and they are not to be redistributed in any form. |
| Authors: | Mido Shammaa [aut, cre], Doug Martin [ctb, aut], Kirk Li [aut, ctb], Avinash Acharya [ctb], Lingjie Yi [ctb] |
| Maintainer: | Mido Shammaa <midoshammaa@yahoo.com> |
| License: | GPL-2 |
| Version: | 1.0.1 |
| Built: | 2025-03-10 03:04:17 UTC |
| Source: | https://github.com/robustport/facmodcs |
function to calculate fundamental law of active management
calcFLAM( specObj, modelStats, fitResults, analysis = c("ISM", "NEW"), targetedVol = 0.06, ... )calcFLAM( specObj, modelStats, fitResults, analysis = c("ISM", "NEW"), targetedVol = 0.06, ... )
specObj |
an object as the output from specFfm function |
modelStats |
output of the extractRegressionStats functions. Contains fit statistics of the factor model. |
fitResults |
output from fitFfmDT |
analysis |
type character, choice of c("none", "ISM","NEW"). Default = "none". Corresponds to methods used in the analysis of fundamental law of active management. |
targetedVol |
numeric; the targeted portfolio volatility in the analysis. Default is 0.06. |
... |
additional arguments |
function to convert the new ffm spec object to ffm object to make it easier in plotting and reporting
convert(SpecObj, FitObj, RegStatsObj, ...)convert(SpecObj, FitObj, RegStatsObj, ...)
SpecObj |
an object as the output from specFfm function |
FitObj |
an object as the output from fitFfmDT function |
RegStatsObj |
an object as the output from extractRegressionStats function |
... |
additional arguments |
returns an object of class ffm
Function to convert to current class # mido to change to retroFit
## S3 method for class 'ffmSpec' convert(SpecObj, FitObj, RegStatsObj, ...)## S3 method for class 'ffmSpec' convert(SpecObj, FitObj, RegStatsObj, ...)
SpecObj |
an object as the output from specFfm function |
FitObj |
an object as the output from fitFfmDT function |
RegStatsObj |
an object as the output from extractRegressionStats function |
... |
additional arguments |
returns an object of class ffm
Density, distribution function, quantile function and random generation using Cornish-Fisher approximation.
dCornishFisher(x, n, skew, ekurt) pCornishFisher(q, n, skew, ekurt) qCornishFisher(p, n, skew, ekurt) rCornishFisher(n, sigma, skew, ekurt, dp = NULL, seed = NULL)dCornishFisher(x, n, skew, ekurt) pCornishFisher(q, n, skew, ekurt) qCornishFisher(p, n, skew, ekurt) rCornishFisher(n, sigma, skew, ekurt, dp = NULL, seed = NULL)
x, q
|
vector of standardized quantiles. |
n |
scalar; number of simulated values in random simulation, sample length in density, distribution and quantile functions. |
skew |
scalar; skewness. |
ekurt |
scalar; excess kurtosis. |
p |
vector of probabilities. |
sigma |
scalar standard deviation. |
dp |
a vector of length 3, whose elements represent sigma, skew and
ekurt, respectively. If dp is specified, the individual parameters cannot be
set. Default is |
seed |
scalar; set seed. Default is |
CDF(q) = Pr(sqrt(n)*(x_bar-mu)/sigma < q)
dCornishFisher Computes Cornish-Fisher density from two term Edgeworth
expansion given mean, standard deviation, skewness and excess kurtosis.
pCornishFisher Computes Cornish-Fisher CDF from two term Edgeworth
expansion given mean, standard deviation, skewness and excess kurtosis.
qCornishFisher Computes Cornish-Fisher quantiles from two term
Edgeworth expansion given mean, standard deviation, skewness and excess
kurtosis.
rCornishFisher simulates observations based on Cornish-Fisher quantile
expansion given mean, standard deviation, skewness and excess kurtosis.
dCornishFisher gives the density, pCornishFisher gives the
distribution function, qCornishFisher gives the quantile function,
and rCornishFisher generates n random simulations.
Eric Zivot and Yi-An Chen.
DasGupta, A. (2008). Asymptotic theory of statistics and probability. Springer. Severini, T. A., (2000). Likelihood Methods in Statistics. Oxford University Press.
# generate 1000 observation from Cornish-Fisher distribution rc <- rCornishFisher(1000,1,0,5) hist(rc, breaks=100, freq=FALSE, main="simulation of Cornish Fisher Distribution", xlim=c(-10,10)) lines(seq(-10,10,0.1), dnorm(seq(-10,10,0.1), mean=0, sd=1), col=2) # compare with standard normal curve # exponential example from A.dasGupta p.188 # x is iid exp(1) distribution, sample size = 5 # then x_bar is Gamma(shape=5, scale=1/5) distribution q <- c(0,0.4,1,2) # exact cdf pgamma(q/sqrt(5)+1, shape=5, scale=1/5) # use CLT pnorm(q) # use edgeworth expansion pCornishFisher(q, n=5, skew=2, ekurt=6)# generate 1000 observation from Cornish-Fisher distribution rc <- rCornishFisher(1000,1,0,5) hist(rc, breaks=100, freq=FALSE, main="simulation of Cornish Fisher Distribution", xlim=c(-10,10)) lines(seq(-10,10,0.1), dnorm(seq(-10,10,0.1), mean=0, sd=1), col=2) # compare with standard normal curve # exponential example from A.dasGupta p.188 # x is iid exp(1) distribution, sample size = 5 # then x_bar is Gamma(shape=5, scale=1/5) distribution q <- c(0,0.4,1,2) # exact cdf pgamma(q/sqrt(5)+1, shape=5, scale=1/5) # use CLT pnorm(q) # use edgeworth expansion pCornishFisher(q, n=5, skew=2, ekurt=6)
function to compute or Extract objects to be returned
extractRegressionStats(specObj, fitResults, full.resid.cov = FALSE)extractRegressionStats(specObj, fitResults, full.resid.cov = FALSE)
specObj |
fitFM object that has been already fit |
fitResults |
output from fitFfmDT |
full.resid.cov |
an option to calculate the full residual covariance or not |
this function operates on the specObje data and the output of fitFfm to get information on the fundamental factor.
a structure of class ffm holding all the information
specFfm and fitFfmDT for information on the definition of the specFfm
object and the usage of fitFfmDT.
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"), addIntercept = FALSE, lagExposures = TRUE, resid.scaleType = "stdDev", lambda = 0.9, GARCH.params = list(omega = 0.09, alpha = 0.1, beta = 0.81), GARCH.MLE = FALSE, stdReturn = FALSE, analysis = c("none", "ISM", "NEW"), targetedVol = 0.06, ... ) ## S3 method for class 'ffm' coef(object, ...) ## S3 method for class 'ffm' fitted(object, ...) ## S3 method for class 'ffm' residuals(object, ...)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"), addIntercept = FALSE, lagExposures = TRUE, resid.scaleType = "stdDev", lambda = 0.9, GARCH.params = list(omega = 0.09, alpha = 0.1, beta = 0.81), GARCH.MLE = FALSE, stdReturn = FALSE, analysis = c("none", "ISM", "NEW"), targetedVol = 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 |
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 |
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 |
fit.method |
method for estimating factor returns; one of "LS", "WLS" "Rob" or "W-Rob". See details. Default is "LS". |
rob.stats |
logical; If |
full.resid.cov |
logical; If |
z.score |
method for exposure standardization; one of "none",
"crossSection", or "timeSeries". Default is |
addIntercept |
logical; If |
lagExposures |
logical; If |
resid.scaleType |
character; Only valid when fit.method is set to WLS or
W-Rob. The weights used in the weighted regression are estimated using
sample variance, classic EWMA, robust EWMA or GARCH model. Valid values are
|
lambda |
lambda value to be used for the EWMA estimation of residual variances. Default is 0.9 |
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 |
boolean input (TRUE|FALSE), default value = |
stdReturn |
logical; If |
analysis |
method used in the analysis of fundamental law of active management; one of "none", "ISM", or "NEW". Default is "none". |
targetedVol |
numeric; the targeted portfolio volatility in the analysis. Default is 0.06. |
... |
potentially further arguments passed. |
object |
a fit object of class |
Estimation method "LS" corresponds to ordinary least squares using
lm and "Rob" is robust regression using
lmrobdetMM. "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.scaleType argument which computes the residual variances in one of the following ways -
sample variace, 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. Make sure you have
the rugarch package installed and loaded, as is merely listed as SUGGESTS.
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.scaleType 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, corrected and expanded the functionalities and S3 methods.
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 |
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 |
covariance matrix of the g 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 |
The 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 |
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. |
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.
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. and Martin, R. D. (2016). "The Fundamental Law of Active Management Redux", SSRN 2730434.
And, the following extractor functions: coef,
fitted, residuals,
fmCov, fmSdDecomp, fmVaRDecomp
and fmEsDecomp.
library(PCRA) # load data data(stocksCRSP) data(factorsSPGMI) dateRange <- c("2006-01-31","2010-12-31") stockItems <- c("Date", "TickerLast", "CapGroupLast", "Return", "Ret13WkBill","MktIndexCRSP","Sector") factorItems <- c("BP","Beta60M","PM12M1M") stocks_factors <- selectCRSPandSPGMI("monthly", dateRange = dateRange, stockItems = stockItems, factorItems = factorItems, outputType ="data.table") # fit a fundamental factor model with style variables BP and LogMktCap fundamental_model <- fitFfm(data = stocks_factors, asset.var = "TickerLast", ret.var = "Return", date.var = "Date", exposure.vars = c("BP", "PM12M1M") ) summary(fundamental_model) # Fit a Fundamental Sector Factor Model with Intercept sector_model <- fitFfm(data = stocks_factors, asset.var = "TickerLast", ret.var = "Return", date.var = "Date", exposure.vars = c("Sector", "BP"), addIntercept = TRUE) summary(sector_model)library(PCRA) # load data data(stocksCRSP) data(factorsSPGMI) dateRange <- c("2006-01-31","2010-12-31") stockItems <- c("Date", "TickerLast", "CapGroupLast", "Return", "Ret13WkBill","MktIndexCRSP","Sector") factorItems <- c("BP","Beta60M","PM12M1M") stocks_factors <- selectCRSPandSPGMI("monthly", dateRange = dateRange, stockItems = stockItems, factorItems = factorItems, outputType ="data.table") # fit a fundamental factor model with style variables BP and LogMktCap fundamental_model <- fitFfm(data = stocks_factors, asset.var = "TickerLast", ret.var = "Return", date.var = "Date", exposure.vars = c("BP", "PM12M1M") ) summary(fundamental_model) # Fit a Fundamental Sector Factor Model with Intercept sector_model <- fitFfm(data = stocks_factors, asset.var = "TickerLast", ret.var = "Return", date.var = "Date", exposure.vars = c("Sector", "BP"), addIntercept = TRUE) summary(sector_model)
This function fits a fundamental factor model
fitFfmDT( ffMSpecObj, fit.method = c("LS", "WLS", "Rob", "W-Rob"), resid.scaleType = c("StdDev", "EWMA", "RobustEWMA", "GARCH"), lambda = 0.9, GARCH.params = list(omega = 0.09, alpha = 0.1, beta = 0.81), GARCH.MLE = FALSE, lmrobdet.control.para.list = lmrobdet.control(), ... )fitFfmDT( ffMSpecObj, fit.method = c("LS", "WLS", "Rob", "W-Rob"), resid.scaleType = c("StdDev", "EWMA", "RobustEWMA", "GARCH"), lambda = 0.9, GARCH.params = list(omega = 0.09, alpha = 0.1, beta = 0.81), GARCH.MLE = FALSE, lmrobdet.control.para.list = lmrobdet.control(), ... )
ffMSpecObj |
a specFFm object |
fit.method |
method for estimating factor returns; one of "LS", "WLS" "ROB" or "W-ROB". See details. Default is "LS". |
resid.scaleType |
one of 4 choices "StdDev","EWMA","RobustEWMA", "GARCH" |
lambda |
the ewma parameter |
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 |
boolean input (TRUE|FALSE), default value = |
lmrobdet.control.para.list |
list of parameters to pass to lmrobdet.control().
Sets tuning parameters for the MM estimator implemented in lmrobdetMM of the
RobStatTM package. See |
... |
additional pass through arguments |
this function operates on the data inside the specObj fits a fundamental factor model to the data
fitFfm returns a list with two object of class "data.table"
The first reg.listDT is object of class "data.table" is a list containing the following
components:
DATE |
length-Time vector of dates. |
id |
length-N vector of asset id's for each date. |
reg.list |
list of fitted objects that estimate factor returns in each
time period. Each fitted object is of class |
The second betasDT is object of class "data.table" is a list containing the following
components:
DATE |
length-Time vector of dates. |
R_matrix |
The K+1 by K restriction matrix where K is the number of categorical variables for each date. |
specFfm for information on the definition of the specFfm object.
Computes the covariance matrix for assets' returns based on a
fitted factor model. This is a generic function with methods for classes
tsfm, sfm and ffm.
fmCov(object, factor.cov, ...) ## S3 method for class 'ffm' fmCov(object, factor.cov, use = "pairwise.complete.obs", ...)fmCov(object, factor.cov, ...) ## S3 method for class 'ffm' fmCov(object, factor.cov, use = "pairwise.complete.obs", ...)
object |
fit object of class |
factor.cov |
factor covariance matrix (optional); defaults to the sample covariance matrix. |
... |
optional arguments passed to |
use |
method for computing covariances in the presence of missing values; one of "everything", "all.obs", "complete.obs", "na.or.complete", or "pairwise.complete.obs". Default is "pairwise.complete.obs". |
R(i, t), the return on asset i at time t,
is assumed to follow a factor model of the form, R(i,t) = alpha(i) + beta(i)*f(t) + e(i,t),
where, alpha(i) is the intercept, f(t) is a K x 1 vector of
factor returns at time t, beta(i) is a 1 x K vector of
factor exposures and the error terms e(i,t) are serially
uncorrelated across time and contemporaneously uncorrelated across assets
so that e(i,t) ~ iid(0,sig(i)^2). Thus, the variance of asset
i's return is given by var(R(i)) = beta(i)*cov(F)*tr(beta(i)) + sig(i)^2.
And, the N x N covariance matrix of asset returns is var(R) = B*cov(F)*tr(B) + D,
where, B is the N x K matrix of factor betas and D is a
diagonal matrix with sig(i)^2 along the diagonal.
The method for computing covariance can be specified via the ...
argument. Note that the default of use="pairwise.complete.obs" for
handling NAs restricts the method to "pearson".
The computed N x N covariance matrix for asset returns based
on the fitted factor model.
Eric Zivot, Yi-An Chen and Sangeetha Srinivasan.
Zivot, E., & Jia-hui, W. A. N. G. (2006). Modeling Financial Time Series with S-Plus Springer-Verlag.
cov for more details on arguments use and
method.
Compute the factor contributions to Expected Tail Loss or Expected Shortfall (ES) of assets' returns based on Euler's theorem, given the fitted factor model. The partial derivative of ES with respect to factor beta is computed as the expected factor return given fund return is less than or equal to its value-at-risk (VaR). Option to choose between non-parametric and Normal.
fmEsDecomp(object, ...) ## S3 method for class 'ffm' fmEsDecomp( object, factor.cov, p = 0.05, type = c("np", "normal"), use = "pairwise.complete.obs", ... )fmEsDecomp(object, ...) ## S3 method for class 'ffm' fmEsDecomp( object, factor.cov, p = 0.05, type = c("np", "normal"), use = "pairwise.complete.obs", ... )
object |
fit object of class |
... |
other optional arguments passed to |
factor.cov |
optional user specified factor covariance matrix with named columns; defaults to the sample covariance matrix. |
p |
tail probability for calculation. Default is 0.05. |
type |
one of "np" (non-parametric) or "normal" for calculating VaR. Default is "np". |
use |
method for computing covariances in the presence of missing values; one of "everything", "all.obs", "complete.obs", "na.or.complete", or "pairwise.complete.obs". Default is "pairwise.complete.obs". |
The factor model for an asset's return at time t has the
form R(t) = beta'f(t) + e(t) = beta.star'f.star(t)
where, beta.star=(beta,sig.e) and f.star(t)=[f(t)',z(t)]'. By
Euler's theorem, the ES of the asset's return is given by:
ES.fm = sum(cES_k) = sum(beta.star_k*mES_k)
where, summation is across the K factors and the residual,
cES and mES are the component and marginal
contributions to ES respectively. The marginal contribution to ES is
defined as the expected value of F.star, conditional on the loss
being less than or equal to VaR.fm. This is estimated as a sample
average of the observations in that data window.
Refer to Eric Zivot's slides (referenced) for formulas pertaining to the calculation of Normal ES (adapted from a portfolio context to factor models).
A list containing
ES.fm |
length-N vector of factor model ES of N-asset returns. |
mES |
N x (K+1) matrix of marginal contributions to VaR. |
cES |
N x (K+1) matrix of component contributions to VaR. |
pcES |
N x (K+1) matrix of percentage component contributions to VaR. |
Where, K is the number of factors and N is the number of assets.
Eric Zviot, Sangeetha Srinivasan and Yi-An Chen
Epperlein, E., & Smillie, A. (2006). Portfolio risk analysis Cracking VAR with kernels. RISK-LONDON-RISK MAGAZINE LIMITED-, 19(8), 70.
Hallerback (2003). Decomposing Portfolio Value-at-Risk: A General Analysis. The Journal of Risk, 5(2), 1-18.
Meucci, A. (2007). Risk contributions from generic user-defined factors. RISK-LONDON-RISK MAGAZINE LIMITED-, 20(6), 84.
Yamai, Y., & Yoshiba, T. (2002). Comparative analyses of expected shortfall and value-at-risk: their estimation error, decomposition, and optimization. Monetary and economic studies, 20(1), 87-121.
fitFfm
for the different factor model fitting functions.
fmSdDecomp for factor model SD decomposition.
fmVaRDecomp for factor model VaR decomposition.
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.
fmmcSemiParam( B = 1000, factor.ret, beta, alpha, resid.par, resid.dist = c("normal", "Cornish-Fisher", "skew-t", "empirical"), boot.method = c("random", "block"), seed = 123 )fmmcSemiParam( B = 1000, factor.ret, beta, alpha, resid.par, resid.dist = c("normal", "Cornish-Fisher", "skew-t", "empirical"), boot.method = c("random", "block"), seed = 123 )
B |
number of bootstrap samples. Default is 1000. |
factor.ret |
|
beta |
|
alpha |
|
resid.par |
matrix of parameters for the residual
distribution. See |
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. If resid.dist = "empirical", resid.par should be the TxN residuals
retunred by the ffm object. 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 |
|
boot.factor.ret |
|
sim.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
## Not run: #Empirical deistribution data("factorDataSetDjia5Yrs") exposure.vars <- fit.ffm <- fitFfm(data = factorDataSetDjia5Yrs, asset.var = "TICKER", ret.var = "RETURN", date.var = "DATE", exposure.vars = c("P2B", "MKTCAP", "SECTOR"), addIntercept = FALSE) resid.par <- fit.ffm$residuals fmmc.returns.ffm <- fmmcSemiParam(factor.ret = fit.ffm$factor.returns, beta = fit.ffm$beta, resid.par = resid.par, resid.dist = "empirical", boot.method = "block") ## End(Not run)## Not run: #Empirical deistribution data("factorDataSetDjia5Yrs") exposure.vars <- fit.ffm <- fitFfm(data = factorDataSetDjia5Yrs, asset.var = "TICKER", ret.var = "RETURN", date.var = "DATE", exposure.vars = c("P2B", "MKTCAP", "SECTOR"), addIntercept = FALSE) resid.par <- fit.ffm$residuals fmmc.returns.ffm <- fmmcSemiParam(factor.ret = fit.ffm$factor.returns, beta = fit.ffm$beta, resid.par = resid.par, resid.dist = "empirical", boot.method = "block") ## End(Not run)
Calcluate and plot the Factor Model R-Squared, Adjusted R-Squared for a portfolio of assets
fmRsq( ffmObj, rsq = TRUE, rsqAdj = FALSE, plt.type = 2, digits = 2, isPrint = TRUE, isPlot = TRUE, lwd = 2, stripText.cex = 1, axis.cex = 1, title = TRUE, ... )fmRsq( ffmObj, rsq = TRUE, rsqAdj = FALSE, plt.type = 2, digits = 2, isPrint = TRUE, isPlot = TRUE, lwd = 2, stripText.cex = 1, axis.cex = 1, title = TRUE, ... )
ffmObj |
an object of class |
rsq |
logical; if |
rsqAdj |
logical; if |
plt.type |
a number to indicate the type of plot for plotting Factor Model R-squared/Adj. R-squared values. 1 indicates barplot, 2 indicates time series xy plot. Default is 2. |
digits |
an integer indicating the number of decimal places to be used for rounding. Default is 2. |
isPrint |
logical. if |
isPlot |
logical. if |
lwd |
line width relative to the default. Default is 2. |
stripText.cex |
a number indicating the amount by which strip text in the plot(s) should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, etc. |
axis.cex |
a number indicating the amount by which axis in the plot(s) should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, etc. |
title |
logical. if |
... |
potentially further arguments passed. |
fmRsq returns the sample mean values and plots the time series of corresponding R squared values
and the Variance Inflation factors depending on the values of rsq, rsqAdj and VIF.
The time series of the output values are also printed if isPrint is TRUE
Avinash Acharya and Doug Martin
#Load the data # Fundamental Factor Model library(PCRA) dateRange <- c("2006-01-31","2010-12-31") stockItems <- c("Date", "TickerLast", "Return","Sector") factorItems <- c("BP","Beta60M","PM12M1M") facDatIT <- selectCRSPandSPGMI("monthly", dateRange = dateRange, stockItems = stockItems, factorItems = factorItems, outputType = "data.table") asset.var="TickerLast" ret.var="Return" date.var = "Date" exposure.vars= factorItems asset.var="TickerLast" ret.var="Return" date.var = "Date" spec1 <- specFfm(data = facDatIT,asset.var = asset.var, ret.var = ret.var, date.var = date.var, exposure.vars = exposure.vars,weight.var = NULL, addIntercept = TRUE, rob.stats = FALSE) # fit a fundamental factor model mdlFit <- fitFfmDT(spec1) mdlRes <- extractRegressionStats(spec1,mdlFit) fit.cross <- convert(SpecObj = spec1,FitObj = mdlFit, RegStatsObj = mdlRes) #Calculate and plot the portfolio R-squared values fmRsq(fit.cross) #Plot and print the time series of Adj R-squared and VIF values fmRsq(fit.cross, rsqAdj=TRUE, isPrint=TRUE, plt.type = 2)#Load the data # Fundamental Factor Model library(PCRA) dateRange <- c("2006-01-31","2010-12-31") stockItems <- c("Date", "TickerLast", "Return","Sector") factorItems <- c("BP","Beta60M","PM12M1M") facDatIT <- selectCRSPandSPGMI("monthly", dateRange = dateRange, stockItems = stockItems, factorItems = factorItems, outputType = "data.table") asset.var="TickerLast" ret.var="Return" date.var = "Date" exposure.vars= factorItems asset.var="TickerLast" ret.var="Return" date.var = "Date" spec1 <- specFfm(data = facDatIT,asset.var = asset.var, ret.var = ret.var, date.var = date.var, exposure.vars = exposure.vars,weight.var = NULL, addIntercept = TRUE, rob.stats = FALSE) # fit a fundamental factor model mdlFit <- fitFfmDT(spec1) mdlRes <- extractRegressionStats(spec1,mdlFit) fit.cross <- convert(SpecObj = spec1,FitObj = mdlFit, RegStatsObj = mdlRes) #Calculate and plot the portfolio R-squared values fmRsq(fit.cross) #Plot and print the time series of Adj R-squared and VIF values fmRsq(fit.cross, rsqAdj=TRUE, isPrint=TRUE, plt.type = 2)
Compute the factor contributions to standard deviation (SD) of assets' returns based on Euler's theorem, given the fitted factor model.
fmSdDecomp(object, factor.cov, ...) ## S3 method for class 'ffm' fmSdDecomp(object, factor.cov, ...)fmSdDecomp(object, factor.cov, ...) ## S3 method for class 'ffm' fmSdDecomp(object, factor.cov, ...)
object |
fit object of class |
factor.cov |
optional user specified factor covariance matrix with named columns; defaults to the sample covariance matrix. |
... |
optional arguments passed to |
The factor model for an asset's return at time t has the
form R(t) = beta'f(t) + e(t) = beta.star'f.star(t)
where, beta.star=(beta,sig.e) and f.star(t)=[f(t)',z(t)]'.
By Euler's theorem, the standard deviation of the asset's return
is given as: Sd.fm = sum(cSd_k) = sum(beta.star_k*mSd_k)
where, summation is across the K factors and the residual,
cSd and mSd are the component and marginal
contributions to SD respectively. Computing Sd.fm and
mSd is very straight forward. The formulas are given below and
details are in the references. The covariance term is approximated by the
sample covariance. Sd.fm = sqrt(beta.star''cov(F.star)beta.star) mSd = cov(F.star)beta.star / Sd.fm
A list containing
Sd.fm |
length-N vector of factor model SDs of N-asset returns. |
mSd |
N x (K+1) matrix of marginal contributions to SD. |
cSd |
N x (K+1) matrix of component contributions to SD. |
pcSd |
N x (K+1) matrix of percentage component contributions to SD. |
Where, K is the number of factors and N is the number of assets.
Eric Zivot, Yi-An Chen and Sangeetha Srinivasan
Hallerback (2003). Decomposing Portfolio Value-at-Risk: A General Analysis. The Journal of Risk, 5(2), 1-18.
Meucci, A. (2007). Risk contributions from generic user-defined factors. RISK-LONDON-RISK MAGAZINE LIMITED-, 20(6), 84.
Yamai, Y., & Yoshiba, T. (2002). Comparative analyses of expected shortfall and value-at-risk: their estimation error, decomposition, and optimization. Monetary and economic studies, 20(1), 87-121.
fitFfm
for the different factor model fitting functions.
fmCov for factor model covariance.
fmVaRDecomp for factor model VaR decomposition.
fmEsDecomp for factor model ES decomposition.
Calculate and plot the time series of t-statistic values and the
number of risk indices with significant t-stats for a fundamental factor
model of class ffm produced by fitFfm or fitFfmDT
fmTstats( ffmObj, isPlot = TRUE, isPrint = FALSE, whichPlot = "tStats", color = c("black", "cyan"), lwd = 2, digits = 2, z.alpha = 1.96, layout = c(2, 3), type = "h", scale = "free", stripText.cex = 1, axis.cex = 1, title = TRUE, ... )fmTstats( ffmObj, isPlot = TRUE, isPrint = FALSE, whichPlot = "tStats", color = c("black", "cyan"), lwd = 2, digits = 2, z.alpha = 1.96, layout = c(2, 3), type = "h", scale = "free", stripText.cex = 1, axis.cex = 1, title = TRUE, ... )
ffmObj |
an object of class |
isPlot |
logical. If |
isPrint |
logical. if |
whichPlot |
string indicating the plot(s) to be plotted. Choose from
("all", "tStats", "significantTstatsV", "significantTstatsH", "significantTstatsLikert").
Three variants of significantTstats stand for vertical, horizontal and likert barplots.
Default is |
color |
length 2 vector specifying the plotting color for t-stats plot
and for barplot respectively. default is |
lwd |
line width relative to the default. default is 2. |
digits |
an integer indicating the number of decimal places to be used for rounding. default is 2. |
z.alpha |
critical value corresponding to the confidence interval. Default is 1.96 i.e 95% C.I |
layout |
numeric vector of length 2 or 3 giving the number of columns, rows, and pages (optional) in the xyplot of t-statistics. default is c(2,3). |
type |
type character. Type of the xyplot of t-statistics; |
scale |
character. It determines how axis limits are calculated for each panel. Possible values are "same" , "free" (default) and "sliced". |
stripText.cex |
a number indicating the amount by which strip text in the plot(s) should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, etc. |
axis.cex |
a number indicating the amount by which axis in the plot(s) should be scaled relative to the default. Default = 1. 1.5 is 50% larger, 0.5 is 50% smaller, etc. |
title |
logical. if |
... |
potentially further arguments passed. |
fmTstats plots the t-stats and significant t-stats values
if isPlot is TRUE and returns a list with following components:
tstats |
an xts object of t-stats values. |
z.alpha |
critical value corresponding to the confidence interval. |
Avinash Acharya and Doug Martin
library(PCRA) # load data data(stocksCRSP) data(factorsSPGMI) dateRange <- c("2006-01-31","2010-12-31") stockItems <- c("Date", "TickerLast", "CapGroupLast", "Return", "Ret13WkBill","MktIndexCRSP","Sector") factorItems <- c("BP","Beta60M","PM12M1M") stocks_factors <- selectCRSPandSPGMI("monthly", dateRange = dateRange, stockItems = stockItems, factorItems = factorItems, outputType ="data.table") # fit a fundamental factor model with style variables BP and LogMktCap fundamental_model <- fitFfm(data = stocks_factors, asset.var = "TickerLast", ret.var = "Return", date.var = "Date", exposure.vars = c("BP", "PM12M1M") ) #Compute time series of t-stats and number of significant t-stats stats = fmTstats(fundamental_model, isPlot = TRUE, lwd = 2, color = c("blue", "blue"), z.alpha = 1.96) # Fit a SECTOR+COUNTRY+Style model with Intercept # Create a COUNTRY column with just 3 countries # # factorDataSetDjia5Yrs$COUNTRY = rep(rep(c(rep("US", 1 ), rep("GERMANY", 1 )), 11), 60) # # fit.MICM <- fitFfm(data = factorDataSetDjia5Yrs, # asset.var = "TICKER", # exposure.vars = c("SECTOR", "COUNTRY","P2B", "MKTCAP"), # ret.var = "RETURN", # date.var = "DATE", # addIntercept = FALSE) # # Load library 'HH' to access the Likert option # library("HH") # stats = fmTstats(fit.MICM, isPlot = TRUE, z.alpha =1.96, # whichPlot = "significantTstatsLikert")library(PCRA) # load data data(stocksCRSP) data(factorsSPGMI) dateRange <- c("2006-01-31","2010-12-31") stockItems <- c("Date", "TickerLast", "CapGroupLast", "Return", "Ret13WkBill","MktIndexCRSP","Sector") factorItems <- c("BP","Beta60M","PM12M1M") stocks_factors <- selectCRSPandSPGMI("monthly", dateRange = dateRange, stockItems = stockItems, factorItems = factorItems, outputType ="data.table") # fit a fundamental factor model with style variables BP and LogMktCap fundamental_model <- fitFfm(data = stocks_factors, asset.var = "TickerLast", ret.var = "Return", date.var = "Date", exposure.vars = c("BP", "PM12M1M") ) #Compute time series of t-stats and number of significant t-stats stats = fmTstats(fundamental_model, isPlot = TRUE, lwd = 2, color = c("blue", "blue"), z.alpha = 1.96) # Fit a SECTOR+COUNTRY+Style model with Intercept # Create a COUNTRY column with just 3 countries # # factorDataSetDjia5Yrs$COUNTRY = rep(rep(c(rep("US", 1 ), rep("GERMANY", 1 )), 11), 60) # # fit.MICM <- fitFfm(data = factorDataSetDjia5Yrs, # asset.var = "TICKER", # exposure.vars = c("SECTOR", "COUNTRY","P2B", "MKTCAP"), # ret.var = "RETURN", # date.var = "DATE", # addIntercept = FALSE) # # Load library 'HH' to access the Likert option # library("HH") # stats = fmTstats(fit.MICM, isPlot = TRUE, z.alpha =1.96, # whichPlot = "significantTstatsLikert")
Compute the factor contributions to Value-at-Risk (VaR) of assets' returns based on Euler's theorem, given the fitted factor model. The partial derivative of VaR w.r.t. factor beta is computed as the expected factor return given fund return is equal to its VaR and approximated by a kernel estimator. Option to choose between non-parametric and Normal.
fmVaRDecomp(object, ...) ## S3 method for class 'ffm' fmVaRDecomp( object, factor.cov, p = 0.05, type = c("np", "normal"), use = "pairwise.complete.obs", ... )fmVaRDecomp(object, ...) ## S3 method for class 'ffm' fmVaRDecomp( object, factor.cov, p = 0.05, type = c("np", "normal"), use = "pairwise.complete.obs", ... )
object |
fit object of class |
... |
other optional arguments passed to |
factor.cov |
optional user specified factor covariance matrix with named columns; defaults to the sample covariance matrix. |
p |
tail probability for calculation. Default is 0.05. |
type |
one of "np" (non-parametric) or "normal" for calculating VaR. Default is "np". |
use |
method for computing covariances in the presence of missing values; one of "everything", "all.obs", "complete.obs", "na.or.complete", or "pairwise.complete.obs". Default is "pairwise.complete.obs". |
The factor model for an asset's return at time t has the
form R(t) = beta'f(t) + e(t) = beta.star'f.star(t)
where, beta.star=(beta,sig.e) and f.star(t)=[f(t)',z(t)]'. By
Euler's theorem, the VaR of the asset's return is given by:
VaR.fm = sum(cVaR_k) = sum(beta.star_k*mVaR_k)
where, summation is across the K factors and the residual,
cVaR and mVaR are the component and marginal
contributions to VaR respectively. The marginal contribution to VaR
is defined as the expectation of F.star, conditional on the loss
being equal to VaR.fm. This is approximated as described in
Epperlein & Smillie (2006); a triangular smoothing kernel is used here.
Refer to Eric Zivot's slides (referenced) for formulas pertaining to the calculation of Normal VaR (adapted from a portfolio context to factor models)
A list containing
VaR.fm |
length-N vector of factor model VaRs of N-asset returns. |
n.exceed |
length-N vector of number of observations beyond VaR for each asset. |
idx.exceed |
list of numeric vector of index values of exceedances. |
mVaR |
N x (K+1) matrix of marginal contributions to VaR. |
cVaR |
N x (K+1) matrix of component contributions to VaR. |
pcVaR |
N x (K+1) matrix of percentage component contributions to VaR. |
Where, K is the number of factors and N is the number of assets.
Eric Zivot, Yi-An Chen and Sangeetha Srinivasan
Hallerback (2003). Decomposing Portfolio Value-at-Risk: A General Analysis. The Journal of Risk, 5(2), 1-18.
Meucci, A. (2007). Risk contributions from generic user-defined factors. RISK-LONDON-RISK MAGAZINE LIMITED-, 20(6), 84.
Yamai, Y., & Yoshiba, T. (2002). Comparative analyses of expected shortfall and value-at-risk: their estimation error, decomposition, and optimization. Monetary and economic studies, 20(1), 87-121.
fitFfm
for the different factor model fitting functions.
fmSdDecomp for factor model SD decomposition.
fmEsDecomp for factor model ES decomposition.
Function lag the style exposures in the exposure matrix by one time period.
lagExposures(specObj)lagExposures(specObj)
specObj |
an ffm specification object of of class |
this function operates on the data inside the specObj and applies a lag to it
specObj an ffm spec Object that has been lagged
specFfm for information on the definition of the specFfm object.
Generic plot method for object of class ffm.
Plots chosen characteristic(s) for one or more assets.
## S3 method for class 'ffm' plot( x, which = NULL, f.sub = 1:2, a.sub = 1:6, plot.single = FALSE, asset.name, asset.variable, colorset = c("royalblue", "dimgray", "olivedrab", "firebrick", "goldenrod", "mediumorchid", "deepskyblue", "chocolate", "darkslategray"), legend.loc = "topleft", las = 1, lwd = 2, maxlag = 15, ... )## S3 method for class 'ffm' plot( x, which = NULL, f.sub = 1:2, a.sub = 1:6, plot.single = FALSE, asset.name, asset.variable, colorset = c("royalblue", "dimgray", "olivedrab", "firebrick", "goldenrod", "mediumorchid", "deepskyblue", "chocolate", "darkslategray"), legend.loc = "topleft", las = 1, lwd = 2, maxlag = 15, ... )
x |
an object of class |
which |
a number to indicate the type of plot. If multiple plots are
required, specify a subset from 1:12 for group plots and 1:13 for individual
plots. If |
f.sub |
numeric/character vector; subset of indexes/names of factors to include for group plots. Default is 1:2. |
a.sub |
numeric/character vector; subset of indexes/names of assets to include for group plots. At least 2 assets must be selected. Default is 1:6. |
plot.single |
logical; If |
asset.name |
name of the individual asset to be plotted. Is necessary
if |
asset.variable |
the name of asset variable. |
colorset |
color palette to use for all the plots. The 1st element will be used for individual time series plots or the 1st object plotted, the 2nd element for the 2nd object in the plot and so on. |
legend.loc |
places a legend into one of nine locations on the chart:
"bottomright", "bottom", "bottomleft", "left", "topleft", "top", "topright",
"right", or "center". Default is "bottomright". Use |
las |
one of 0, 1, 2, 3 to set the direction of axis labels, same as
in |
lwd |
set the line width, same as in |
maxlag |
optional number of lags to be calculated for ACF. Default is 15. |
... |
further arguments to be passed to other plotting functions. |
The function can be used for group plots and individual plots. User can
select the type of plot either from the menu prompt (default) or directly
via argument which.
In case multiple plots are needed, the menu is repeated after each plot
(enter 0 to exit). User can also input a numeric vector of plot options via
which.
Group plots are the default. The selected assets in a.sub and
selected factors in f.sub are plotted depending on the
characteristic chosen. The default is to show the first 2 factors and first
6 assets.
Setting plot.single=TRUE enables individual plots. If there is more
than one asset fit by x, asset.name should be specified.
In case the ffm object x contains only a single asset fit,
plot.ffm can infer asset.name without user input.
Does not return a value, used for plotting
Eric Zivot, Sangeetha Srinivasan and Yi-An Chen
fitFfm, residuals.ffm,
fitted.ffm, fmCov.ffm and
summary.ffm for time series factor model fitting and related
S3 methods. Refer to fmSdDecomp, fmEsDecomp,
fmVaRDecomp for factor model risk measures.
Here is a list of plotting functions used. (I=individual, G=Group)
I(1,5,6,7), G(3,4,12) - chart.TimeSeries,
I(2,3,4,19), G(12) - plot.default,
I(3,4) - panel.smooth,
I(8,9,10) - chart.ACFplus,
I(11,12) - plot.density,
I(13) - chart.Histogram,
I(14) - chart.QQPlot,
I(15,16,17) - plot.efp (requires strucchange package),
I(18) - plot.zoo,
G(1) - chart.Boxplot,
G(2,5,9,10,11) - barchart,
G(6) - chart.Correlation and
G(7,8) - corrplot.mixed (requires corrplot package).
Compute the factor contributions to Expected Tail Loss or Expected Shortfall (ES) of portfolio returns based on Euler's theorem, given the fitted factor model. The partial derivative of ES with respect to factor beta is computed as the expected factor return given portfolio return is less than or equal to its value-at-risk (VaR). Option to choose between non-parametric and Normal.
portEsDecomp(object, ...) ## S3 method for class 'ffm' portEsDecomp( object, weights = NULL, factor.cov, p = 0.05, type = c("np", "normal"), invert = FALSE, ... )portEsDecomp(object, ...) ## S3 method for class 'ffm' portEsDecomp( object, weights = NULL, factor.cov, p = 0.05, type = c("np", "normal"), invert = FALSE, ... )
object |
fit object of class |
... |
other optional arguments passed to |
weights |
a vector of weights of the assets in the portfolio, names of the vector should match with asset names. Default is NULL, in which case an equal weights will be used. |
factor.cov |
optional user specified factor covariance matrix with named columns; defaults to the sample covariance matrix. |
p |
tail probability for calculation. Default is 0.05. |
type |
one of "np" (non-parametric) or "normal" for calculating Es. Default is "np". |
invert |
a logical variable to choose if change ES to positive number, default is False |
The factor model for a portfolio's return at time t has the
form R(t) = beta'f(t) + e(t) = beta.star'f.star(t)
where, beta.star=(beta,sig.e) and f.star(t)=[f(t)',z(t)]'. By
Euler's theorem, the ES of the portfolio's return is given by:
ES.fm = sum(cES_k) = sum(beta.star_k*mES_k)
where, summation is across the K factors and the residual,
cES and mES are the component and marginal
contributions to ES respectively. The marginal contribution to ES is
defined as the expected value of F.star, conditional on the loss
being less than or equal to portVaR. This is estimated as a sample
average of the observations in that data window.
A list containing
portES |
factor model ES of portfolio returns. |
mES |
length-(K + 1) vector of marginal contributions to Es. |
cES |
length-(K + 1) vector of component contributions to Es. |
pcES |
length-(K + 1) vector of percentage component contributions to Es. |
Where, K is the number of factors.
Douglas Martin, Lingjie Yi
fitFfm
for the different factor model fitting functions.
portSdDecomp for factor model Sd decomposition.
portVaRDecomp for factor model VaR decomposition.
Compute the factor contributions to standard deviation (Sd) of portfolio returns based on Euler's theorem, given the fitted factor model.
portSdDecomp(object, ...) ## S3 method for class 'ffm' portSdDecomp(object, weights = NULL, factor.cov, ...)portSdDecomp(object, ...) ## S3 method for class 'ffm' portSdDecomp(object, weights = NULL, factor.cov, ...)
object |
fit object of class |
... |
optional arguments passed to |
weights |
a vector of weights of the assets in the portfolio. Default is NULL, in which case an equal weights will be used. |
factor.cov |
optional user specified factor covariance matrix with named columns; defaults to the sample covariance matrix. |
The factor model for a portfolio's return at time t has the
form R(t) = beta'f(t) + e(t) = beta.star'f.star(t)
where, beta.star=(beta,sig.e) and f.star(t)=[f(t)',z(t)]'.
By Euler's theorem, the standard deviation of the portfolio's return
is given as: portSd = sum(cSd_k) = sum(beta.star_k*mSd_k)
where, summation is across the K factors and the residual,
cSd and mSd are the component and marginal
contributions to Sd respectively. Computing portSd and
mSd is very straight forward. The formulas are given below and
details are in the references. The covariance term is approximated by the
sample covariance. portSd = sqrt(beta.star''cov(F.star)beta.star) mSd = cov(F.star)beta.star / portSd
A list containing
portSd |
factor model Sd of portfolio return. |
mSd |
length-(K + 1) vector of marginal contributions to Sd. |
cSd |
length-(K + 1) vector of component contributions to Sd. |
pcSd |
length-(K + 1) vector of percentage component contributions to Sd. |
Where, K is the number of factors.
Douglas Martin, Lingjie Yi
fitFfm
for the different factor model fitting functions.
portVaRDecomp for portfolio factor model VaR decomposition.
portEsDecomp for portfolio factor model ES decomposition.
Compute the factor contributions to Value-at-Risk (VaR) of portfolio returns based on Euler's theorem, given the fitted factor model. The partial derivative of VaR w.r.t. factor beta is computed as the expected factor return given portfolio return is equal to its VaR and approximated by a kernel estimator. Option to choose between non-parametric and Normal.
portVaRDecomp(object, ...) ## S3 method for class 'ffm' portVaRDecomp( object, weights = NULL, factor.cov, p = 0.05, type = c("np", "normal"), invert = FALSE, ... )portVaRDecomp(object, ...) ## S3 method for class 'ffm' portVaRDecomp( object, weights = NULL, factor.cov, p = 0.05, type = c("np", "normal"), invert = FALSE, ... )
object |
fit object of class |
... |
other optional arguments passed to |
weights |
a vector of weights of the assets in the portfolio. Default is NULL, in which case an equal weights will be used. |
factor.cov |
optional user specified factor covariance matrix with named columns; defaults to the sample covariance matrix. |
p |
tail probability for calculation. Default is 0.05. |
type |
one of "np" (non-parametric) or "normal" for calculating VaR. Default is "np". |
invert |
a logical variable to choose if change VaR to positive number, default is False |
The factor model for a portfolio's return at time t has the
form R(t) = beta'f(t) + e(t) = beta.star'f.star(t)
where, beta.star=(beta,sig.e) and f.star(t)=[f(t)',z(t)]'. By
Euler's theorem, the VaR of the asset's return is given by:
VaR.fm = sum(cVaR_k) = sum(beta.star_k*mVaR_k)
where, summation is across the K factors and the residual,
cVaR and mVaR are the component and marginal
contributions to VaR respectively. The marginal contribution to VaR
is defined as the expectation of F.star, conditional on the loss
being equal to portVaR. This is approximated as described in
Epperlein & Smillie (2006); a triangular smoothing kernel is used here.
A list containing
portVaR |
factor model VaR of portfolio return. |
n.exceed |
number of observations beyond VaR. |
idx.exceed |
a numeric vector of index values of exceedances. |
mVaR |
length-(K + 1) vector of marginal contributions to VaR. |
cVaR |
length-(K + 1) vector of component contributions to VaR. |
pcVaR |
length-(K + 1) vector of percentage component contributions to VaR. |
Where, K is the number of factors.
Douglas Martin, Lingjie Yi
fitFfm
for the different factor model fitting functions.
portSdDecomp for factor model Sd decomposition.
portEsDecomp for factor model ES decomposition.
S3 predict method for object of class ffm.
## S3 method for class 'ffm' predict(object, newdata = NULL, pred.date = NULL, ...)## S3 method for class 'ffm' predict(object, newdata = NULL, pred.date = NULL, ...)
object |
an object of class |
newdata |
data.frame containing the variables |
pred.date |
character; unique date used to base the predictions. Should
be coercible to class |
... |
optional arguments passed to |
The estimated factor returns and potentially new factor exposures
are used to predict the asset returns during all dates from the fitted
ffm object. For predictions based on estimated factor returns from a
specific period use the pred.date argument.
predict.ffm produces a N x T matrix of predicted asset returns, where
T is the number of time periods and N is the number of assets. T=1 if
pred.date is specified.
Sangeetha Srinivasan
fitFfm, summary.ffm,
predict.lm, predict.lmrob
S3 print method for object of class ffm. Prints
the call, factor model dimension and summary statistics for the estimated
factor returns, cross-sectional r-squared values and residual variances
from the fitted object.
Refer to summary.ffm for a more detailed summary of the fit at
each time period.
## S3 method for class 'ffm' print(x, digits = max(3, .Options$digits - 3), ...)## S3 method for class 'ffm' print(x, digits = max(3, .Options$digits - 3), ...)
x |
an object of class |
digits |
an integer value, to indicate the required number of significant digits. Default is 3. |
... |
optional arguments passed to the |
Returns an object of class print.ffm.
Yi-An Chen and Sangeetha Srinivasan
## Not run: library(PCRA) data(stocksCRSP) data("factorDataSetDjia5Yrs") # fit a fundamental factor model fit.style.sector <- fitFfm(data=factorDataSetDjia5Yrs, asset.var="TICKER", ret.var="RETURN", date.var="DATE", exposure.vars = c("P2B", "MKTCAP")) print(fit.style.sector) ## End(Not run)## Not run: library(PCRA) data(stocksCRSP) data("factorDataSetDjia5Yrs") # fit a fundamental factor model fit.style.sector <- fitFfm(data=factorDataSetDjia5Yrs, asset.var="TICKER", ret.var="RETURN", date.var="DATE", exposure.vars = c("P2B", "MKTCAP")) print(fit.style.sector) ## End(Not run)
print.ffmSpec
## S3 method for class 'ffmSpec' print(x, ...)## S3 method for class 'ffmSpec' print(x, ...)
x |
an object of class ffmSpec |
... |
any other option |
No return value, called for displaying attributes
Calculate k factor time series based on fundamental factor model. This method takes fundamental factor model fit, 'ffm' object, and portfolio weight as inputs and generates numeric summary and plot visualization.
repExposures( ffmObj, weights = NULL, isPlot = TRUE, isPrint = TRUE, scaleType = "free", stripText.cex = 1, axis.cex = 1, stripLeft = TRUE, layout = NULL, color = "blue", notch = FALSE, digits = 1, titleText = TRUE, which = NULL, type = "b", ... )repExposures( ffmObj, weights = NULL, isPlot = TRUE, isPrint = TRUE, scaleType = "free", stripText.cex = 1, axis.cex = 1, stripLeft = TRUE, layout = NULL, color = "blue", notch = FALSE, digits = 1, titleText = TRUE, which = NULL, type = "b", ... )
ffmObj |
an object of class ffm returned by fitFfm. |
weights |
a vector of weights of the assets in the portfolio. Default is NULL. |
isPlot |
logical variable to generate plot or not. |
isPrint |
logical variable to print numeric summary or not. |
scaleType |
scaleType controls if use a same scale of y-axis, choose from c('same', 'free') |
stripText.cex |
a number indicating the amount by which strip text in the plot(s) should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, etc. |
axis.cex |
a number indicating the amount by which axis in the plot(s) should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, etc. |
stripLeft |
logical variable to choose the position of strip, 'TRUE' for drawing strips on the left of each panel, 'FALSE' for drawing strips on the top of each panel. Used only when isPlot = 'TRUE' |
layout |
layout is a numeric vector of length 2 or 3 giving the number of columns, rows, and pages (optional) in a multipanel display. Used only when isPlot = 'TRUE' |
color |
character specifying the plotting color for all the plots |
notch |
logical. if notch is |
digits |
digits of printout numeric summary. Used only when isPrint = 'TRUE' |
titleText |
logical varible to choose display plot title or not. Default is 'TRUE', and used only when isPlot = 'TRUE'. |
which |
a number to indicate the type of plot. If a subset of the plots
is required, specify a subset of the numbers 1:3 for plots. If |
type |
character. type of lattice plot when which=1; 'l' denotes a line, 'p' denotes a point, and 'b' and 'o' both denote both together.deafault is 'b'. |
... |
other graphics parameters available in tsPlotMP(time series plot only) can be passed in through the ellipses |
A list containing mean and standard deviation of all the factors
Douglas Martin, Lingjie Yi, Avinash
Decompostite return of portfolio into return of different factors based on fundamental factor model. This method takes fundamental factor model fit, "ffm" object, and portfolio weight as inputs and generates numeric summary and plot visualization.
repReturn( ffmObj, weights = NULL, isPlot = TRUE, isPrint = TRUE, layout = NULL, scaleType = "free", stripLeft = TRUE, stripText.cex = 1, axis.cex = 1, digits = 1, titleText = TRUE, which = NULL, ... )repReturn( ffmObj, weights = NULL, isPlot = TRUE, isPrint = TRUE, layout = NULL, scaleType = "free", stripLeft = TRUE, stripText.cex = 1, axis.cex = 1, digits = 1, titleText = TRUE, which = NULL, ... )
ffmObj |
an object of class ffm returned by fitFfm. |
weights |
a vector of weights of the assets in the portfolio. Default is NULL. |
isPlot |
logical variable to generate plot or not. |
isPrint |
logical variable to print numeric summary or not. |
layout |
layout is a numeric vector of length 2 or 3 giving the number of columns, rows, and pages (optional) in a multipanel display. |
scaleType |
scaleType controls if use a same scale of y-axis, choose from c('same', 'free') |
stripLeft |
logical variable to choose the position of strip, "TRUE" for drawing strips on the left of each panel, "FALSE" for drawing strips on the top of each panel. Used only when isPlot = 'TRUE' |
stripText.cex |
a number indicating the amount by which strip text in the plot(s) should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, etc. |
axis.cex |
a number indicating the amount by which axis in the plot(s) should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, etc. |
digits |
digits of printout numeric summary. Used only when isPrint = 'TRUE' |
titleText |
logical varible to choose display plot title or not. Default is 'TRUE', and used only when isPlot = 'TRUE'. |
which |
a number to indicate the type of plot. If a subset of the plots
is required, specify a subset of the numbers 1:4 for plots. If |
... |
other graphics parameters available in tsPlotMP(time series plot only) can be passed in through the ellipses |
A K x 2 matrix containing mean and standard deviation of K factors
Douglas Martin, Lingjie Yi
args(repReturn)args(repReturn)
Compute the factor contributions to standard deviation (SD), Value-at-Risk (VaR), Expected Tail Loss or Expected Shortfall (ES) of the return of individual asset within a portfolio return of a portfolio based on Euler's theorem, given the fitted factor model.
repRisk(object, ...) ## S3 method for class 'ffm' repRisk( object, weights = NULL, risk = c("Sd", "VaR", "ES"), decomp = c("FMCR", "FCR", "FPCR"), digits = NULL, invert = FALSE, nrowPrint = 20, p = 0.05, type = c("np", "normal"), sliceby = c("factor", "asset", "riskType"), isPrint = TRUE, isPlot = FALSE, layout = NULL, stripText.cex = 1, axis.cex = 1, portfolio.only = FALSE, ... )repRisk(object, ...) ## S3 method for class 'ffm' repRisk( object, weights = NULL, risk = c("Sd", "VaR", "ES"), decomp = c("FMCR", "FCR", "FPCR"), digits = NULL, invert = FALSE, nrowPrint = 20, p = 0.05, type = c("np", "normal"), sliceby = c("factor", "asset", "riskType"), isPrint = TRUE, isPlot = FALSE, layout = NULL, stripText.cex = 1, axis.cex = 1, portfolio.only = FALSE, ... )
object |
fit object of class |
... |
other optional arguments passed to |
weights |
a vector of weights of the assets in the portfolio, names of the vector should match with asset names. Default is NULL, in which case an equal weights will be used. |
risk |
one of 'Sd' (standard deviation), 'VaR' (Value-at-Risk) or 'ES' (Expected Tail Loss or Expected Shortfall for calculating risk decompositon. Default is 'Sd' |
decomp |
one of 'FMCR' (factor marginal contribution to risk), 'FCR' 'factor contribution to risk' or 'FPCR' (factor percent contribution to risk). |
digits |
digits of number in the resulting table. Default is NULL, in which case digtis = 3 will be used for decomp = ( 'FMCR', 'FCR'), digits = 1 will be used for decomp = 'FPCR'. Used only when isPrint = 'TRUE' |
invert |
a logical variable to change VaR/ES to positive number, default is False and will return positive values. |
nrowPrint |
a numerical value deciding number of assets/portfolio in result vector/table to print or plot |
p |
tail probability for calculation. Default is 0.05. |
type |
one of "np" (non-parametric) or "normal" for calculating VaR & Es. Default is "np". |
sliceby |
one of 'factor' (slice/condition by factor) or 'asset' (slice/condition by asset) or 'riskType' Used only when isPlot = 'TRUE' |
isPrint |
logical variable to print numeric output or not. |
isPlot |
logical variable to generate plot or not. |
layout |
layout is a numeric vector of length 2 or 3 giving the number of columns, rows, and pages (optional) in a multipanel display. |
stripText.cex |
a number indicating the amount by which strip text in the plot(s) should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, etc. |
axis.cex |
a number indicating the amount by which axis in the plot(s) should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, etc. |
portfolio.only |
logical variable to choose if to calculate portfolio only decomposition, in which case multiple risk measures are allowed. |
A table containing
decomp = 'FMCR' |
(N + 1) * (K + 1) matrix of marginal contributions to risk of portfolio return as well assets return, with first row of values for the portfolio and the remaining rows for the assets in the portfolio, with (K + 1) columns containing values for the K risk factors and the residual respectively |
decomp = 'FCR' |
(N + 1) * (K + 2) matrix of component contributions to risk of portfolio return as well assets return, with first row of values for the portfolio and the remaining rows for the assets in the portfolio, with first column containing portfolio and asset risk values and remaining (K + 1) columns containing values for the K risk factors and the residual respectively |
decomp = 'FPCR' |
(N + 1) * (K + 1) matrix of percentage component contributions to risk of portfolio return as well assets return, with first row of values for the portfolio and the remaining rows for the assets in the portfolio, with (K + 1) columns containing values for the K risk factors and the residual respectively |
Where, K is the number of factors, N is the number of assets.
Douglas Martin, Lingjie Yi
fitFfm
for the different factor model fitting functions.
# Fundamental Factor Model library(PCRA) dateRange <- c("2006-01-31","2010-12-31") stockItems <- c("Date", "TickerLast", "Return","Sector") factorItems <- c("BP","Beta60M","PM12M1M") facDatIT <- selectCRSPandSPGMI("monthly", dateRange = dateRange, stockItems = stockItems, factorItems = factorItems, outputType = "data.table") asset.var="TickerLast" ret.var="Return" date.var = "Date" exposure.vars= factorItems asset.var="TickerLast" ret.var="Return" date.var = "Date" spec1 <- specFfm(data = facDatIT,asset.var = asset.var, ret.var = ret.var, date.var = date.var, exposure.vars = exposure.vars,weight.var = NULL, addIntercept = TRUE, rob.stats = FALSE) # fit a fundamental factor model mdlFit <- fitFfmDT(spec1) mdlRes <- extractRegressionStats(spec1,mdlFit) fit.cross <- convert(SpecObj = spec1,FitObj = mdlFit, RegStatsObj = mdlRes) repRisk(fit.cross, risk = "Sd", decomp = 'FCR', nrowPrint = 10, digits = 4) # get the factor contributions of risk repRisk(fit.cross, risk = "Sd", decomp = 'FPCR', nrowPrint = 10) # portfolio only decomposition repRisk(fit.cross, risk = c("VaR", "ES"), decomp = 'FPCR', portfolio.only = TRUE) # plot repRisk(fit.cross, risk = "Sd", decomp = 'FPCR', isPrint = FALSE, nrowPrint = 15, isPlot = TRUE, layout = c(4,2))# Fundamental Factor Model library(PCRA) dateRange <- c("2006-01-31","2010-12-31") stockItems <- c("Date", "TickerLast", "Return","Sector") factorItems <- c("BP","Beta60M","PM12M1M") facDatIT <- selectCRSPandSPGMI("monthly", dateRange = dateRange, stockItems = stockItems, factorItems = factorItems, outputType = "data.table") asset.var="TickerLast" ret.var="Return" date.var = "Date" exposure.vars= factorItems asset.var="TickerLast" ret.var="Return" date.var = "Date" spec1 <- specFfm(data = facDatIT,asset.var = asset.var, ret.var = ret.var, date.var = date.var, exposure.vars = exposure.vars,weight.var = NULL, addIntercept = TRUE, rob.stats = FALSE) # fit a fundamental factor model mdlFit <- fitFfmDT(spec1) mdlRes <- extractRegressionStats(spec1,mdlFit) fit.cross <- convert(SpecObj = spec1,FitObj = mdlFit, RegStatsObj = mdlRes) repRisk(fit.cross, risk = "Sd", decomp = 'FCR', nrowPrint = 10, digits = 4) # get the factor contributions of risk repRisk(fit.cross, risk = "Sd", decomp = 'FPCR', nrowPrint = 10) # portfolio only decomposition repRisk(fit.cross, risk = c("VaR", "ES"), decomp = 'FPCR', portfolio.only = TRUE) # plot repRisk(fit.cross, risk = "Sd", decomp = 'FPCR', isPrint = FALSE, nrowPrint = 15, isPlot = TRUE, layout = c(4,2))
#' function to Residualize the returns via regressions
residualizeReturns(specObj, benchmark, rfRate, isBenchExcess = FALSE)residualizeReturns(specObj, benchmark, rfRate, isBenchExcess = FALSE)
specObj |
specObj is a ffmSpec object, |
benchmark |
we might need market returns |
rfRate |
risk free rate |
isBenchExcess |
toggle to select whether to calculate excess returns |
this function operates on the data inside the specObj and residualizes the returns to create residual return using regressions of returns on a benchmark.
the ffmSpec object with resturns residualized
specFfm for information on the definition of the specFfm object.
Compute the factor contributions to Sd, VaR and ES of returns based on Euler's theorem, given the fitted factor model.
riskDecomp.ffm( object, risk, weights = NULL, portDecomp = TRUE, factor.cov, p = 0.05, type = c("np", "normal"), invert = FALSE, ... )riskDecomp.ffm( object, risk, weights = NULL, portDecomp = TRUE, factor.cov, p = 0.05, type = c("np", "normal"), invert = FALSE, ... )
object |
fit object of class |
risk |
one of "Sd" (Standard Deviation) or "VaR" (Value at Risk) or "ES" (Expected Shortfall) |
weights |
a vector of weights of the assets in the portfolio, names of the vector should match with asset names. Default is NULL, in which case an equal weights will be used. |
portDecomp |
logical. If |
factor.cov |
optional user specified factor covariance matrix with named columns; defaults to the sample covariance matrix. |
p |
tail probability for calculation. Default is 0.05. |
type |
one of "np" (non-parametric) or "normal" for calculating Es. Default is "np". |
invert |
a logical variable to choose if change ES to positive number, default is False |
... |
other optional arguments passed to |
A list containing
portES |
factor model ES of portfolio returns. |
mES |
length-(K + 1) vector of marginal contributions to Es. |
cES |
length-(K + 1) vector of component contributions to Es. |
pcES |
length-(K + 1) vector of percentage component contributions to Es. |
Where, K is the number of factors.
Eric Zivot, Yi-An Chen, Sangeetha Srinivasan, Lingjie Yi and Avinash Acharya
fitFfm
for the different factor model fitting functions.
portSdDecomp for factor model Sd decomposition.
portVaRDecomp for factor model VaR decomposition.
roll.fitFfmDT rolls the fundamental factor model
roll.fitFfmDT( ffMSpecObj, windowSize = 60, refitEvery = 1, refitWindow = c("Expanding", "Rolling"), stdExposuresControl = list(Std.Type = "timeSeries", lambda = 0.9), stdReturnControl = list(GARCH.params = list(omega = 0.09, alpha = 0.1, beta = 0.81)), fitControl = list(fit.method = c("LS", "WLS", "Rob", "W-Rob"), resid.scaleType = c("STDDEV", "EWMA", "ROBEWMA", "GARCH"), lambda = 0.9, GARCH.params = list(omega = 0.09, alpha = 0.1, beta = 0.81), GARCH.MLE = FALSE), full.resid.cov = TRUE, analysis = c("ISM", "NEW") )roll.fitFfmDT( ffMSpecObj, windowSize = 60, refitEvery = 1, refitWindow = c("Expanding", "Rolling"), stdExposuresControl = list(Std.Type = "timeSeries", lambda = 0.9), stdReturnControl = list(GARCH.params = list(omega = 0.09, alpha = 0.1, beta = 0.81)), fitControl = list(fit.method = c("LS", "WLS", "Rob", "W-Rob"), resid.scaleType = c("STDDEV", "EWMA", "ROBEWMA", "GARCH"), lambda = 0.9, GARCH.params = list(omega = 0.09, alpha = 0.1, beta = 0.81), GARCH.MLE = FALSE), full.resid.cov = TRUE, analysis = c("ISM", "NEW") )
ffMSpecObj |
a specFFm object |
windowSize |
the size of the fit window |
refitEvery |
the frequency of fitting |
refitWindow |
choice of expanding or rolling |
stdExposuresControl |
for exposure standardization; (give the Std.Type and lambda) |
stdReturnControl |
choices to standardize the returns using GARCH controls |
fitControl |
list of options for fitting the ffm |
full.resid.cov |
True or False toggle |
analysis |
choice of "ISM" or "NEW" |
a list object containing a list of objects describing the fitted analysis.
Factor models have a few parameters that describe how the
fitting is done. This function summarizes them and returns a spec object for
cross-sectional regressions. It also preps the data. An object of class
"ffmSpec" is returned.
specFfm( data, asset.var, ret.var, date.var, exposure.vars, weight.var = NULL, addIntercept = FALSE, rob.stats = FALSE )specFfm( data, asset.var, ret.var, date.var, exposure.vars, weight.var = NULL, addIntercept = FALSE, rob.stats = FALSE )
data |
data.frame of the balanced panel data containing the variables
|
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 |
exposure.vars |
vector; names of the variables containing the fundamental factor exposures. |
weight.var |
character; name of the variable containing the weights
used when standardizing style factor exposures. Default is |
addIntercept |
logical; If |
rob.stats |
logical; If |
an object of class ffmSpec holding the details of the analysis
library(PCRA) dateRange <- c("2006-01-31","2010-12-31") stockItems <- c("Date", "TickerLast", "Return","Sector") factorItems <- c("BP","Beta60M","PM12M1M") facDatIT <- selectCRSPandSPGMI("monthly", dateRange = dateRange, stockItems = stockItems, factorItems = factorItems, outputType = "data.table") asset.var="TickerLast" ret.var="Return" date.var = "Date" exposure.vars= c("BP","Beta60M","PM12M1M") spec1 <- specFfm(data = facDatIT,asset.var = asset.var, ret.var = ret.var, date.var = date.var, exposure.vars = exposure.vars,weight.var = NULL, addIntercept = TRUE, rob.stats = FALSE) spec1$exposure.vars #lag the exposures spec1 <- lagExposures(spec1) # standardize the exposures Cross-Sectionally spec1 <- standardizeExposures(spec1, Std.Type = "CrossSection") # fit the model mdlFit <- fitFfmDT(spec1) class(mdlFit) class(mdlFit$reg.listDT)library(PCRA) dateRange <- c("2006-01-31","2010-12-31") stockItems <- c("Date", "TickerLast", "Return","Sector") factorItems <- c("BP","Beta60M","PM12M1M") facDatIT <- selectCRSPandSPGMI("monthly", dateRange = dateRange, stockItems = stockItems, factorItems = factorItems, outputType = "data.table") asset.var="TickerLast" ret.var="Return" date.var = "Date" exposure.vars= c("BP","Beta60M","PM12M1M") spec1 <- specFfm(data = facDatIT,asset.var = asset.var, ret.var = ret.var, date.var = date.var, exposure.vars = exposure.vars,weight.var = NULL, addIntercept = TRUE, rob.stats = FALSE) spec1$exposure.vars #lag the exposures spec1 <- lagExposures(spec1) # standardize the exposures Cross-Sectionally spec1 <- standardizeExposures(spec1, Std.Type = "CrossSection") # fit the model mdlFit <- fitFfmDT(spec1) class(mdlFit) class(mdlFit$reg.listDT)
function to calculate z-scores for numeric exposure using weights weight.var
standardizeExposures( specObj, Std.Type = c("None", "CrossSection", "TimeSeries"), Ts.Std.Type = c("EWMA", "RobustEWMA"), lambda = 0.9 )standardizeExposures( specObj, Std.Type = c("None", "CrossSection", "TimeSeries"), Ts.Std.Type = c("EWMA", "RobustEWMA"), lambda = 0.9 )
specObj |
is a ffmSpec object, |
Std.Type |
method for exposure standardization; one of "none", "CrossSection", or "TimeSeries". |
Ts.Std.Type |
Default is |
lambda |
lambda value to be used for the EWMA estimation of residual variances. Default is 0.9 |
this function operates on the data inside the specObj and applies a standardization to it. The user can choose CrossSectional or timeSeries standardization
the ffmSpec object with exposures z-scored
specFfm for information on the definition of the specFfm object.
Standardize the returns using GARCH(1,1) volatilities.
standardizeReturns( specObj, GARCH.params = list(omega = 0.09, alpha = 0.1, beta = 0.81) )standardizeReturns( specObj, GARCH.params = list(omega = 0.09, alpha = 0.1, beta = 0.81) )
specObj |
is a ffmSpec object |
GARCH.params |
fixed Garch(1,1) parameters |
this function operates on the data inside the specObj and standardizes the returns to create scaled return.
an ffmSpec Object with the standardized returns added
specFfm for information on the definition of the specFfm object.
summary method for object of class ffm.
Returned object is of class summary.ffm.
## S3 method for class 'ffm' summary(object, ...) ## S3 method for class 'summary.ffm' print(x, digits = 3, labels = TRUE, ...)## S3 method for class 'ffm' summary(object, ...) ## S3 method for class 'summary.ffm' print(x, digits = 3, labels = TRUE, ...)
object |
an object of class |
... |
futher arguments passed to or from other methods. |
x |
an object of class |
digits |
number of significant digits to use when printing. Default is 3. |
labels |
option to print labels and legend in the summary. Default is
|
The default summary method for a fitted lm object
computes the standard errors and t-statistics under the assumption of
homoscedasticity.
Note: This gives a summary of the fitted factor returns at each time period.
If T is large, you might prefer the more succinct summary produced by
print.ffm.
Returns an object of class summary.ffm.
The print method for class summary.ffm outputs the call,
coefficients (with standard errors and t-statistics), r-squared and
residual volatilty (under the homoskedasticity assumption) for all assets.
Object of class summary.ffm is a list of length N + 2 containing:
call |
the function call to |
sum.list |
list of summaries of the T fit objects (of class |
Sangeetha Srinivasan & Yi-An Chen.
Plot time series with specific plotting parameters
tsPlotMP( ret, add.grid = FALSE, layout = NULL, type = "l", yname = "RETURNS (%)", Pct = FALSE, scaleType = "free", stripLeft = TRUE, main = NULL, lwd = 1, stripText.cex = 1, axis.cex = 1, color = "black", zeroLine = TRUE, panel = NULL )tsPlotMP( ret, add.grid = FALSE, layout = NULL, type = "l", yname = "RETURNS (%)", Pct = FALSE, scaleType = "free", stripLeft = TRUE, main = NULL, lwd = 1, stripText.cex = 1, axis.cex = 1, color = "black", zeroLine = TRUE, panel = NULL )
ret |
an time series exposure/return object |
add.grid |
logical variable.If 'TRUE', type = c('l', 'g'); If 'FALSE', type = c('l') |
layout |
layout is a numeric vector of length 2 or 3 giving the number of columns, rows, and pages (optional) in a multipanel display. |
type |
character. type of the plot; 'l' denotes a line, 'p' denotes a point, and 'b' and 'o' both denote both together.deafault is 'l'. |
yname |
character or expression giving label(s) for the y-axis |
Pct |
Pct controls if use the percentage value. |
scaleType |
scaleType controls if use a same scale of y-axis, choose from c('same', 'free') |
stripLeft |
logical variable to choose the position of strip, 'TRUE' for drawing strips on the left of each panel, 'FALSE' for drawing strips on the top of each panel |
main |
Typically a character string or expression describing the main title. |
lwd |
The line width, a positive number, defaulting to 1 |
stripText.cex |
a number indicating the amount by which strip text in the plot(s) should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, etc. |
axis.cex |
a number indicating the amount by which axis in the plot(s) should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, etc. |
color |
A specification for the default plotting color. Default is black. |
zeroLine |
logical varible to choose add a dotted horizontal line at the zero vertical distance |
panel |
function to add customized lines to the lattice plot. See examples. |
No return value, called for plotting
Douglas Martin, Lingjie Yi
Calculate and plot the Factor Model Variance Inflaction Factor Values for a fitted model.
A VIF for a single explanatory variable (style factor) is obtained using the time series of R-squared values obtained from
the regression of that variable against all other explanatory variables.
So, at least 2 explanatory variables are required in exposure.vars of fitted model to find the VIF.
vif( ffmObj, digits = 2, isPrint = TRUE, isPlot = TRUE, lwd = 2, stripText.cex = 1, axis.cex = 1, title = TRUE, ... )vif( ffmObj, digits = 2, isPrint = TRUE, isPlot = TRUE, lwd = 2, stripText.cex = 1, axis.cex = 1, title = TRUE, ... )
ffmObj |
an object of class |
digits |
an integer indicating the number of decimal places to be used for rounding. Default is 2. |
isPrint |
logical. if |
isPlot |
logical. if |
lwd |
line width relative to the default. Default is 2. |
stripText.cex |
a number indicating the amount by which strip text in the plot(s) should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, etc. |
axis.cex |
a number indicating the amount by which axis in the plot(s) should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, etc. |
title |
logical. This argument is mainly used for the documentation purpose when you need a plot without any title.
If |
... |
potentially further arguments passed. |
ffmRsq returns the sample mean values and plots the time series of corresponding R squared values
and the Variance Inflation factors depending on the values of rsq, rsqAdj and VIF.
The time series of the output values are also printed if isPrint is TRUE
Avinash Acharya
library(PCRA) # load data data(stocksCRSP) data(factorsSPGMI) dateRange <- c("2006-01-31","2010-12-31") stockItems <- c("Date", "TickerLast", "CapGroupLast", "Return", "Ret13WkBill","MktIndexCRSP","Sector") factorItems <- c("BP","Beta60M","PM12M1M") stocks_factors <- selectCRSPandSPGMI("monthly", dateRange = dateRange, stockItems = stockItems, factorItems = factorItems, outputType ="data.table") # fit a fundamental factor model with style variables BP and LogMktCap fundamental_model <- fitFfm(data = stocks_factors, asset.var = "TickerLast", ret.var = "Return", date.var = "Date", exposure.vars = c("BP", "PM12M1M") ) #Plot and print the time series of VIF values vif(fundamental_model,isPrint=TRUE)library(PCRA) # load data data(stocksCRSP) data(factorsSPGMI) dateRange <- c("2006-01-31","2010-12-31") stockItems <- c("Date", "TickerLast", "CapGroupLast", "Return", "Ret13WkBill","MktIndexCRSP","Sector") factorItems <- c("BP","Beta60M","PM12M1M") stocks_factors <- selectCRSPandSPGMI("monthly", dateRange = dateRange, stockItems = stockItems, factorItems = factorItems, outputType ="data.table") # fit a fundamental factor model with style variables BP and LogMktCap fundamental_model <- fitFfm(data = stocks_factors, asset.var = "TickerLast", ret.var = "Return", date.var = "Date", exposure.vars = c("BP", "PM12M1M") ) #Plot and print the time series of VIF values vif(fundamental_model,isPrint=TRUE)