Modigliani {PerformanceAnalytics}

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

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.

Author(s)

Andrii Babii, Brian G. Peterson

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

See Also

SharpeRatio, TreynorRatio

Examples

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])