Sharpe Ratio vs. Treynor Ratio

Attribute	Sharpe Ratio	Treynor Ratio
Risk measure	Considers total risk (standard deviation of returns)	Considers systematic risk (beta)
Formula	(Return of portfolio - Risk-free rate) / Standard deviation of portfolio	(Return of portfolio - Risk-free rate) / Beta of portfolio
Interpretation	Measures risk-adjusted return per unit of total risk	Measures risk-adjusted return per unit of systematic risk
Usefulness	Useful for evaluating all types of investments	Useful for evaluating only systematic risk of investments

Definition

The Sharpe Ratio and Treynor Ratio are both widely used metrics in the world of finance to evaluate the performance of investment portfolios. The Sharpe Ratio measures the risk-adjusted return of an investment by taking into account the volatility of its returns. On the other hand, the Treynor Ratio evaluates the risk-adjusted return of a portfolio by considering only the systematic risk, which is the risk that cannot be diversified away.

Calculation

The Sharpe Ratio is calculated by subtracting the risk-free rate of return from the portfolio's return and dividing the result by the standard deviation of the portfolio's returns. This ratio gives investors an idea of how much excess return they are receiving for the level of risk they are taking. In contrast, the Treynor Ratio is calculated by dividing the excess return of the portfolio over the risk-free rate by the portfolio's beta, which measures its systematic risk relative to the market.

Interpretation

When comparing the Sharpe Ratio and Treynor Ratio, it is important to understand how to interpret the results. A higher Sharpe Ratio indicates that the portfolio is generating more return per unit of risk, while a higher Treynor Ratio suggests that the portfolio is generating more return per unit of systematic risk. Investors should consider both ratios when evaluating a portfolio, as they provide different perspectives on risk-adjusted performance.

Applicability

While the Sharpe Ratio is more commonly used in practice due to its simplicity and ease of calculation, the Treynor Ratio can be particularly useful for investors who are concerned with systematic risk. By focusing on the relationship between returns and systematic risk, the Treynor Ratio can help investors determine whether a portfolio is adequately compensated for the level of market risk it is exposed to.

Limitations

Both the Sharpe Ratio and Treynor Ratio have their limitations. The Sharpe Ratio may not be suitable for portfolios with non-normal return distributions, as it assumes that returns are normally distributed. On the other hand, the Treynor Ratio may not be appropriate for portfolios with low beta values, as it relies on the beta coefficient to measure systematic risk.

Conclusion

In conclusion, the Sharpe Ratio and Treynor Ratio are valuable tools for evaluating the risk-adjusted performance of investment portfolios. While the Sharpe Ratio considers total risk, the Treynor Ratio focuses on systematic risk. Investors should consider both ratios when making investment decisions, as they provide complementary information about the relationship between returns and risk.