# CFA Level I: Portfolio Performance Evaluation Measures

There are various ways to assess portfolio performance, especially when just knowing the return may not tell us much about the true performance of a manager. The measures below are four commonly used methods to evaluate portfolio performance.

• Sharpe Ratio = (Rp – Rf)/σp

The Sharpe Ratio is a measure of risk premium gained per unit of risk in the portfolio. The goal is to have a good risk to reward return on the portfolio.

• Treynor Ratio = (Rp – Rf)/ßp

A limitation of the Sharpe ratio is that it uses a measure of total risk instead of allowing us to measure return per unit of systematic risk. This is a limitation because under the CAPM, we assume that the non-systematic risk has been diversified away. The Treynor ratio overcomes this risk by using the beta of the portfolio as the standard unit of risk instead of the standard deviation of the portfolio.

• M-squared = (Rp – Rf)(σmp) – (Rm – Rf)

The M-squared measure compares our portfolio return to a market portfolio’s total risk. A M-squared value of 0 means that our portfolio matches market performance in terms of risk considered returns. The M-squared value outputs a rank-able percentage, unlike the Sharpe and Treynor Ratios.

• Jensen’s Alpha = Rp – [Rf + ßp(Rm – Rf)]

Like the Treynor ratio, Jensen’s Alpha also only models the return compared to systematic risk only. Like the M-squared value, this is done by comparing our return to the market return, this time using the CAPM equation as the market portfolio.

• Sortino Ratio = (E(r) – R)­fd
• Where σ = std of downside risk

The Sortino ratio is another modification of the Sharpe ratio which focuses on return compared to downside risk mostly. A large Sortino ratio means that there is low probability of large losses. This is a good ratio to use for portfolios and ratio which display a negative distribution skew.