Modigliani-Modigliani measure

Source: R/Modigliani.R

The Modigliani-Modigliani measure is the portfolio return adjusted upward or downward to match the benchmark's standard deviation. This puts the portfolio return and the benchmark return on 'equal footing' from a standard deviation perspective. $$MM_{p}=\frac{E[R_{p} - R_{f}]}{\sigma_{p}}=SR_{p} * \sigma_{b} + E[R_{f}]$$ where \(SR_{p}\) - Sharpe ratio, \(\sigma_{b}\) - benchmark standard deviation

Modigliani(Ra, Rb, Rf = 0, ...)

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

...

any other passthrough parameters

Details

This is also analogous to some approaches to 'risk parity' portfolios, which use (presumably costless) leverage to increase the portfolio standard deviation to some target.

References

J. Christopherson, D. Carino, W. Ferson. Portfolio Performance Measurement and Benchmarking. 2009. McGraw-Hill, p. 97-99.
Franco Modigliani and Leah Modigliani, "Risk-Adjusted Performance: How to Measure It and Why," Journal of Portfolio Management, vol.23, no., Winter 1997, pp.45-54

Author

Andrii Babii, Brian G. Peterson

Examples


data(managers)
Modigliani(managers[,1,drop=FALSE], managers[,8,drop=FALSE], Rf=.035/12)
#> [1] 0.01678381
Modigliani(managers[,1:6], managers[,8,drop=FALSE], managers[,8,drop=FALSE])
#>                                               HAM1       HAM2      HAM3
#> Modigliani-Modigliani measure: SP500 TR 0.01281799 0.01505458 0.0131509
#>                                               HAM4       HAM5       HAM6
#> Modigliani-Modigliani measure: SP500 TR 0.01057959 0.01053081 0.01844616
Modigliani(managers[,1:6], managers[,8:7], managers[,8,drop=FALSE])
#>                                                  HAM1       HAM2       HAM3
#> Modigliani-Modigliani measure: SP500 TR    0.01281799 0.01505458 0.01315090
#> Modigliani-Modigliani measure: EDHEC LS EQ 0.01062640 0.01168261 0.01078361
#>                                                  HAM4        HAM5       HAM6
#> Modigliani-Modigliani measure: SP500 TR    0.01057959 0.010530812 0.01844616
#> Modigliani-Modigliani measure: EDHEC LS EQ 0.00956933 0.009546295 0.01328426