Mutual Fund Performance
Risk-to-Return

Mutual fund performance must be evaluated on a risk-to-return basis, as neither risk or return alone is provides a sufficient means of evaluation. Together they describe the tradeoffs you need to make to assemble a portfolio that is at least relatively efficient and is consistent with your level of risk aversion. The following three statistics can be used to screen mutual funds on a risk-to-return basis and the latter two can be used to evaluate the risk-return characteristics of your portfolio.

The coefficient of variation (CV) is a fund's standard deviation divided by its return. This gives you a risk-to-return ratio, i.e., units of risk per unit of return, that can be used to compare mutual fund performance on a level basis.

The Coefficient of Variation (CV)

CV = s_i ÷ r_i

Where:
s_i = thestandard deviation of asset i
r_i =the mean return of asset i

Sharpe Ratio, named after William Sharpe, is a very useful measure of performance that is especially relevant when comparing mutual funds within a category. The Sharpe Ratio is a mutual fund's excess return divided by its standard deviation, where excess return is the actual return less the risk-free rate of return. Although the Sharpe Ratio is computed from historical data, it is the same formula as the slope of the Capital Allocation Line, which is forward-looking. If you read that subsection, you should recall that the optimal risky portfolio was at the point of tangency of the CAL with the efficient frontier, thus making that CAL the Capital Market Line and that the slope of the CML was the maximum feasible slope for that universe. Needless to say, the higher the Sharpe Ratio, the better. The Sharpe Ratio is a measure of excess return per unit of total risk.

The Sharpe Ratio

SR = (r_i - r*)÷ s_i

Where:
r_{i= return on asset i}
r*= risk-free rate of return
s_{i= standard deviation of asset i's returns}

Treynor Ratio, named after Jack Treynor, is another useful measure of performance that is also relevant when comparing mutual funds within a category. The Treynor Ratio is a mutual fund's excess return divided by its beta, where excess return is the actual return less the risk-free rate of return. The Treynor Ratio is a measure of excess return per unit of systematic risk.

The Treynor Ratio

TR = (r_i - r*)÷ Beta_i

Where:
r_i =return on asset i
r*= risk-free rate of return
Beta_i= asset i's beta

You'll find these measures of mutual fund performance in some, but not all, online sources of mutual fund performance data.

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