Modigliani-Modigliani measure
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.
MMp = SRp * sigmab + E[Rf]
where SRp - Sharpe ratio, sigmab - benchmark standard deviation
Modigliani(Ra, Rb, Rf = 0, ...)
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 |
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.
Andrii Babii, Brian G. Peterson
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
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])
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