The Treynor ratio and the Sharpe ratio are financial metrics that use different approaches to evaluate the risk-adjusted returns of an investment portfolio. The Treynor ratio employs beta and measures returns relative to the amount of systematic risk the portfolio carries. The Sharpe ratio looks at standard deviation and accounts for unsystematic risk. Both these risk-adjusted metrics provide a more complete look at investment performance than assessing only absolute investment returns.
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What Is the Treynor Ratio and How Is it Used?
The Treynor ratio is a tool in portfolio analysis that helps investors assess how well a portfolio compensates them for taking on market risk, also known as systematic risk. The Treynor ratio of a portfolio shows how much return an investor can expect for each unit of market risk. It offers insight into how efficiently a portfolio’s manager is balancing risk and return, and can be useful for comparing portfolios or funds that might have different risk levels.
Named after American economist Jack Treynor, this ratio is calculated by dividing the excess return of a portfolio over the risk-free rate by its beta. A high Treynor ratio figure suggests that the portfolio is delivering strong returns for its level of risk, while a lower ratio may indicate underperformance relative to market volatility.
For example, imagine a portfolio with an annual return of 9%, a risk-free rate of 3% and a beta of 1.2. The Treynor ratio would be calculated as follows: Treynor ratio = (9 – 3) / 1.2 = 0.5. This indicates the portfolio is earning 0.5 points of excess return.
What Is the Sharpe Ratio and How Is It Used?
The Sharpe ratio, named after Nobel-winning economist William F. Sharpe, also assesses performance relative to risk. It uses standard deviation, which measures how much an asset’s rate of return varies from its historical average. This ratio includes both systematic and unsystematic risk, while the Treynor ratio uses beta and focuses exclusively on systematic risk.
To see how the Sharpe ratio can be used, let's use the example of an investor holding a portfolio that has an annual return of 8%, while the risk-free rate is 2%. The portfolio’s standard deviation, which measures its volatility, is 10%. The calculation for the Sharpe ratio would look like this: Sharpe ratio = (8 – 2) / 10 = 0.6.
This means that for every unit of risk taken, the investor is earning 0.6 units of excess return, helping them assess whether the portfolio's return justifies the level of volatility.
Treynor Ratio vs. Sharpe Ratio: Key Differences
Although both the Treynor ratio and Sharpe ratio assess risk-adjusted returns, they differ in their approach to measuring risk and their ideal uses. Here are four major distinctions:
- Type of risk measured: The Sharpe ratio accounts for total risk, which includes both market-wide (systematic) and stock or sector-specific (unsystematic) risks. In contrast, the Treynor ratio concentrates solely on systematic risk associated with broader market fluctuations.
- Risk measure used: The Sharpe ratio uses standard deviation to measure the overall volatility of an investment, while the Treynor ratio relies on beta, which gauges an investment’s sensitivity to market changes.
- Application: The Sharpe ratio is ideal for comparing investments across different asset classes or individual securities, while the Treynor ratio is best suited for evaluating the performance of portfolios, particularly those benchmarked against market indices.
- Diversification consideration: The Sharpe ratio is useful for assessing diversified portfolios where unsystematic risk is minimized. The Treynor ratio, on the other hand, is more relevant for portfolios where systematic risk is the primary concern.
For portfolios that are not well-diversified, the Sharpe ratio may be more appropriate since it accounts for total risk, including the portion that can be diversified away. On the other hand, for investors dealing with well-diversified portfolios, the Treynor ratio can be more useful because it focuses on market-related risk.
Bottom Line
The Treynor ratio offers a lens through which investors can evaluate the performance of a portfolio relative to the risk it assumes from broader market movements. When compared with the Sharpe ratio, another risk-adjusted performance metric, the Treynor ratio differs primarily in the use of systematic risk or market risk rather than unsystematic risk. By focusing on systematic risk, it allows for a more refined comparison of returns between different portfolios or strategies. But, you should also consider its limitations, such as its exclusion of unsystematic risk and sensitivity to changes in the risk-free rate.
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