Evaluating the performance of managed funds involves measuring risk-adjusted returns to determine how effectively a fund has generated returns relative to its risk exposure. The three key measures used are:
1. Sharpe Ratio
Developed by William F. Sharpe, this ratio measures the fund’s return per unit of total risk (standard deviation).
Sharpe Ratio = (Rp−Rf) / σp
Where:
- Rp = Portfolio return
- Rf = Risk-free rate
- σp = Portfolio standard deviation
A higher Sharpe ratio indicates better risk-adjusted performance. It is useful when comparing funds with different volatility levels.
2. Treynor Ratio
Developed by Jack Treynor, this measure evaluates return per unit of systematic risk (beta).
Treynor Ratio = (Rp−Rf) / βp
Where:
- βp = Portfolio beta (systematic risk)
It is useful for diversified portfolios, as it considers only market risk rather than total risk. A higher Treynor ratio suggests superior performance.
3. Jensen’s Alpha
Developed by Michael Jensen, this measure evaluates a fund’s performance relative to the CAPM-expected return.
Jensen′s Alpha = Rp − [Rf + βp(Rm−Rf)]
Where:
- Rm = Market return
A positive alpha indicates the portfolio has outperformed the market, while a negative alpha suggests underperformance.
Conclusion
- Sharpe Ratio is best for evaluating total risk-adjusted returns.
- Treynor Ratio is ideal for diversified portfolios focusing on systematic risk.
- Jensen’s Alpha measures a manager’s ability to generate excess returns beyond market expectations.