The Sharpe ratio and the Treynor ratio are fundamental tools in the world of investment. They help investors evaluate the risk-adjusted returns of their portfolios. Understanding these ratios can significantly influence investment decisions, guiding investors toward more informed decisions.
This short article explores how each ratio works and how they differ.
Key takeaways
- Both the Sharpe and Treynor ratios are used to understand the risk-adjusted return of an investment.
- The Sharpe ratio divides the excess return by the standard deviation of the investment.
- Instead, the Treynor Ratio divides the excess return by the Beta of the investment.
What is the Sharpe ratio?
The Sharpe ratio measures the performance of an investment compared to a risk-free asset, after adjusting for its risk. Basically, it tells you how much excess return you are receiving for the additional volatility of a riskier asset.
Formula to calculate Sharpe ratio:
Sharpe Ratio = Portfolio Standard Deviation / Portfolio Return – Risk Free Rate
The risk-free rate often refers to the yield on Treasury bills, since they are considered free of credit risk.
What is the Treynor relationship?
The American economist Jack Treynor developed this relationship. The Treynor Ratio also measures risk-adjusted returns, but uses portfolio beta as a measure of risk. Beta evaluates the sensitivity of an investment's returns to the market as a whole.
What is a good Treynor ratio?
There is no set level at which an investment is good or bad. A lower Treynor ratio one year could become very good the next if volatility decreases or returns increase, or a high ratio could worsen.
Treynor Calculus
The formula is the following:
Treynor Ratio = Portfolio Beta / Portfolio Return – Risk Free Rate
Comparison of Sharpe and Treynor
Both ratios aim to provide information about the returns obtained by investments beyond what Treasury bills offer, considering the risk inherent to the investment. The Sharpe ratio uses standard deviation to measure volatility. On the other hand, the Treynor Ratio is based on beta and focuses on market risk.
The main difference
The main difference lies in their risk measures. Sharpe Ratio uses standard deviation, making it suitable for diversified portfolios. While the Treynor Ratio uses beta, it focuses on market risk and is more applicable to well-diversified portfolios.
Limitations
Both proportions have their limitations. The Sharpe ratio does not fully consider risk in portfolios with abnormal return patterns.
The Treynor Ratio assumes that investors have diversified portfolios. And that beta is a complete measure of risk. However, this may not always be the case, especially when investments have a negative beta.
What proportion is best?
Deciding whether Sharpe or Treynor is better depends on context. For diversified portfolios where market risk is a primary concern, the Treynor Index could provide more relevant information.
However, to evaluate individual securities or not fully diversified portfolios, the broader risk measure of the Sharpe Ratio may be more informative.
What is better than the Sharpe ratio?
Some investors turn to the reporting index for a different perspective, comparing earned returns to a benchmark, rather than a risk-free rate, to assess the ability to generate excess returns from active management.
Sharpe ratio versus information ratio?
The choice between the Sharpe Ratio and the Information Ratio depends on the investment objective. If the goal is to evaluate the reward for taking on additional volatility, the Sharpe Ratio is appropriate.
If the focus is on the excess returns generated relative to a benchmark index, reflecting the skill of the portfolio manager, the information index becomes more relevant.
Is a higher Sharpe ratio good?
A higher Sharpe ratio is good because it indicates that the investment offers a higher excess return per unit of risk, making it a preferable option for investors looking to maximize their reward-volatility ratio.
Jensen's alpha vs. Sharpe vs. Treynor?
Jensen's Alpha measures the excess return of an investment over what the Capital Asset Pricing Model (CAPM) predicts it should earn, based on its inherent risk. The Sharpe ratio evaluates excess return per unit of total risk (volatility), while the Treynor ratio evaluates excess return per unit of market risk (beta). Essentially, Jensen's Alpha focuses on performance relative to expected returns based on CAPM, the Sharpe Ratio of Total Risk, and the Treynor Ratio of Market Risk.
How do Treynor's ratios compare?
When comparing Treynor ratios, look at the excess return per unit of market risk for different investments. A higher Treynor ratio indicates a more favorable investment decision, suggesting a better reward for each unit of market risk assumed.
Calculating the Treynor ratio involves using the portfolio's beta measure as a risk measure, similar to Sharpe but specifically for market risk.
Differences between Sharpe and Treynor and Jensen's Alpha?
The differences between Sharpe and Treynor indices and Jensen's Alpha lie mainly in their measures of risk and performance.
The Sharpe ratio uses standard deviation to measure total risk, making it suitable for analyzing overall risk-adjusted performance.
The Treynor Index uses beta to focus on market risk, making it ideal for diversified portfolios. Jensen's Alpha assesses an investment's ability to generate excess returns compared to those predicted by CAPM, highlighting the performance of the portfolio manager.
Bottom line
Both the Sharpe and Treynor ratios provide valuable information about risk-adjusted investment performance. But its applicability varies depending on the nature of the investment and the investor's objectives. Understanding these nuances can significantly improve investment decisions.
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