A Simple Mathematical Model of Mutual Fund Outperformance and Persistence in Terms of Information Ratios
9 Pages Posted: 7 Mar 2020
Date Written: February 11, 2020
I present a simple mathematical model of mutual fund outperformance in terms of the information ratio (IR), that is, a Sharpe ratio in active space. The strength of the model is that it can be used to deduce the likelihood of K-year persistence as a function of IR, either in time series for a single fund, or in pooled data for a group of funds with an assumed distribution of IR. In this model, "K-year persistence" is a mutual fund's outperformance of its benchmark over K years conditional upon its outperformance of the benchmark for the previous K years.
The model provides an intuitive translation from IR to likelihood of K-year persistence, and vice versa.
Interesting findings are: a manager with a very good IR can still have a low probability of K-year persistence for high K; a manager with a low (or even negative) IR can have a moderate probability of K-year persistence for low K; and with extreme cross-sectional volatility in IR, both the expected value and the standard deviation of the likelihood of K-year persistence tend to one half for any K.
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