Modigliani: Modigliani-Modigliani measure

Description

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

Usage

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

Arguments

an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns

return vector of the benchmark asset

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

Examples

Run this code

# NOT RUN {
data(managers)
Modigliani(managers[,1,drop=FALSE], managers[,8,drop=FALSE], Rf=.035/12)
Modigliani(managers[,1:6], managers[,8,drop=FALSE], managers[,8,drop=FALSE])
Modigliani(managers[,1:6], managers[,8:7], managers[,8,drop=FALSE])

# }