Calculate single factor model (CAPM) alpha

Source: R/CAPM.alpha.R

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

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.

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.

Author

Dhairya Jain, Peter Carl

Examples


# First we load the data
    data(managers)
    SFM.alpha(managers[, "HAM1"], managers[, "SP500 TR"], Rf = managers[, "US 3m TR"])
#> [1] 0.005774729
    SFM.alpha(managers[,1:3], managers[,8:10], Rf=.035/12) 
#>      Alpha : SP500 TR Alpha : US 10Y TR Alpha : US 3m TR
#> HAM1            0.006             0.009            0.008
#> HAM2            0.009             0.011            0.010
#> HAM3            0.006             0.010            0.008
    # 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 
#>   HAM1   HAM2   HAM3   HAM4   HAM5   HAM6 
#> 0.0059 0.0053 0.0048 0.0029 0.0044 0.0075