SFM.alpha: Calculate single factor model (CAPM) alpha

In PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis

Calculate single factor model (CAPM) alpha

Description

This is a wrapper for calculating a single factor model (CAPM) alpha.

Usage

SFM.alpha(
  Ra,
  Rb,
  Rf = 0,
  ...,
  digits = 3,
  benchmarkCols = T,
  method = "LS",
  family = "mopt",
  warning = T
)

Arguments

Ra	an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns
Rb	return vector of the benchmark asset
Rf	risk free rate, in same period as your returns
...	Other parameters like max.it or bb specific to lmrobdetMM regression.
digits	Number of digits to round the results to. Defaults to 3.
benchmarkCols	Boolean to show the benchmarks as columns. Defaults to TRUE.
method	string representing linear regression model, "LS" for Least Squares and "Robust" for robust. Defaults to "LS"
family	If method == "Robust": This is a string specifying the name of the family of loss function to be used (current valid options are "bisquare", "opt" and "mopt"). Incomplete entries will be matched to the current valid options. Defaults to "mopt". Else: the parameter is ignored
warning	Boolean to show warnings or not. Defaults to TRUE.

Details

"Alpha" purports to be a measure of a manager's skill by measuring the portion of the managers returns that are not attributable to "Beta", or the portion of performance attributable to a benchmark.

While the classical CAPM has been almost completely discredited by the literature, it is an example of a simple single factor model, comparing an asset to any arbitrary benchmark.

Author(s)

Dhairya Jain, Peter Carl

References

Sharpe, W.F. Capital Asset Prices: A theory of market equilibrium under conditions of risk. Journal of finance, vol 19, 1964, 425-442.
Ruppert, David. Statistics and Finance, an Introduction. Springer. 2004.

See Also

CAPM.beta CAPM.utils

Examples

# First we load the data
    data(managers)
    SFM.alpha(managers[, "HAM1"], managers[, "SP500 TR"], Rf = managers[, "US 3m TR"])
    SFM.alpha(managers[,1:3], managers[,8:10], Rf=.035/12) 
    # SFM.alpha(managers[,1], managers[,8:10], Rf=.035/12, benchmarkCols=FALSE) # other variations
if(requireNamespace("RobStatTM", quietly = TRUE)) { # CRAN requires conditional execution
   alphas <- SFM.alpha(managers[,1:6], 
		                  	managers[,8:10], 
			                  Rf=.035/12, method="Robust", 
			                  family="opt", bb=0.25, max.it=200, digits=4)
	  alphas["HAM1", ]
	  alphas[, "Alpha : SP500 TR"]
} # CRAN can have issues with RobStatTM 

PerformanceAnalytics documentation built on April 4, 2025, 12:39 a.m.