Compare SFM estimated using robust estimators with that estimated by OLS

This function for single factor models (SFM’s) with a slope and intercept allows the user to easily make a scatter plot of asset returns versus benchmark returns, such as the SP500, with two overlaid straight-line fits, one obtained using least squares (LS), which can be very adversely influenced by outliers, and one obtained using a highly robust regression estimate that is not much influenced by outliers. The plot allows the user to see immediately whether or not any outliers result in a distorted LS fit that does not fit the bulk of the data, while the robust estimator results In a good fit to the bulk of the data. The plot contains a legend with LS slope estimate and the robust slope estimate, with estimate standard errors in parentheses.

Usage

chart.SFM(
  Ra,
  Rb,
  Rf = 0,
  main = NULL,
  ylim = NULL,
  xlim = NULL,
  family = "mopt",
  xlab = NULL,
  ylab = NULL,
  legend.loc = "topleft",
  makePct = FALSE
)

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

main

Title of the generated plot. Defaults to "lm vs lmRobdetMM"

ylim

Limits on the y-axis of the plots. Defaults to min-max

xlim

Limits on the x-axis of the plots. Defaults to min-max

family

(Optional): 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".

xlab

Title of the x-axis of the plots. Defaults to "Benchmark Returns"

ylab

Title of the y-axis of the plots. Defaults to "Asset Returns"

legend.loc

Position of legends. See plot() function for more info.

makePct

If Returns should be converted to percentage. Defaults to False

Details

The function chart.SFM computes the robust fit with the function lmrobdetMM contained in the package RobStatTM available at CRAN. The function lmrobdetMM has a default robust regression estimate called the mopt estimate, which is used by chart.SFM. For details on lmrobdetMM, see reference [1]. The plot made by chart.SFM has two parallel dotted lines that define a strip in the asset returns versus benchmark returns space, and data points that fall outside that strip are defined as outliers, and as such are rejected, i.e., deleted by the lmrobdetMM estimator.

References

Martin, R. D. and Xia, D. Z. (2021). Robust Time Series Factor Models, SSRN: https://www.ssrn.com/abstract=3905345. To appear in the Journal of Asset Management in 2022
Ruppert, David. Statistics and Finance, an Introduction. Springer. 2004.
Sharpe, W.F. Capital Asset Prices: A theory of market equilibrium under conditions of risk. Journal of finance, vol 19, 1964, 425-442.

Author

Dhairya Jain, Doug Martin, Dan Xia

Examples

 # CRAN tests if Suggested packages are loaded
   data(managers)
   
    mgrs <- managers["2002/"]  # So that all have managers have complete history
   names(mgrs)[7:10] <- c("LSEQ","SP500","Bond10Yr","RF") # Short names for last 3
   plot.zoo(mgrs)

   
   chart.SFM(mgrs$HAM1, mgrs$SP500, Rf=mgrs$RF)  

              
   for(k in 1:7){
        chart.SFM(mgrs[,k],mgrs$SP500,mgrs$RF,makePct = TRUE,
                       main = names(mgrs[,k]))
   }