Sharpe Ratio: Risk-Adjusted Returns Tell a Different Story than Absolute Returns

The Sharpe ratio, developed by Nobel laureate William F. Sharpe, quantifies the return of an investment relative to its risk. The ratio represents how much excess return you receive for the extra volatility of holding an asset.

The Sharpe ratio is most commonly calculated for portfolios and funds. It's an important metric to consider when selecting which funds to invest in. Top hedge funds that use highly sophisticated tactics can often achieve Sharpe ratios above 1. On the other hand, passive funds and indexes (e.g. S&P 500) often have Sharpe ratios closer to 0.

Sharpe Ratio Formula

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In the above formula, the compound annual growth rate (CAGR) is most commonly used for the average rate of return on investment x. The best available rate of return on a risk-free security, such as a T-bill, as most often used for the risk-free rate.

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Understanding the Sharpe Ratio

As previously mentioned, the Sharpe ratio is often use to compare the performance of investment managers by adjusting for risk.

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For example, let's say you are deciding between two funds. Fund A has returned an average of 10% over the last three years, while Fund B has returned an average of 15% over the last three years. At first glance, it may seem that Fund B is the better investment due to its higher absolute return. However, let's say that Fund A has a Sharpe ratio of 1.5 while Fund B has a Sharpe ratio of 0.2. In this case, Fund A is a significantly better risk-adjusted investment than Fund B. In other words, Fund B took significantly more risks than Fund A, but did not achieve the returns to show for it. If it were me deciding, I would go with Fund A.

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Now let's say you discover Fund C, which has averaged a 15% return with a Sharpe ratio of 1.2. Even though Fund C has a slightly lower Sharpe ratio than Fund A, you might still want to consider Fund C given its superior absolute return and the fact that its Sharpe ratio is in a comparable range to Fund A. So as you can see, while the Sharpe ratio gives a good idea of risk-adjusted return, it is not the only metric to consider.

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Why the Sharpe Ratio Matters

The Sharpe ratio is essential because it adjusts for risk, allowing investors to compare the performance of different investments on a level playing field. A higher Sharpe ratio indicates a more favorable risk-adjusted return, making it a valuable metric for evaluating investment funds.

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For example, consider two funds: Fund A and Fund B. Fund A has an average return of 10% with a standard deviation of 5%, while Fund B has an average return of 15% with a standard deviation of 12%. At first glance, Fund B appears more attractive due to its higher return. However, when we calculate the Sharpe ratio, we might find that Fund A has a higher Sharpe ratio, indicating it offers a better risk-adjusted return.

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Limitations

The biggest limitation of the Sharpe ratio is that it assumes returns are normally distributed, which, of course, we know is not the case. Nevertheless, the Sharpe ratio is still commonly used in the investment community to quantify risk-adjusted returns.

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Another limitation is that the Sharpe ratio can be somewhat manipulated by fund managers to look better. Since the denominator of the Sharpe ratio is portfolio volatility, a fund manager can simply select the time interval (e.g. daily, weekly, monthly, annually) with the lowest volatility, which will then inflate their Sharpe ratio. That's why it's important to look at Sharpe ratios on the same time interval when comparing different managers with each other and/or benchmarks. This way, you can be certain everything is on an apples to apples basis.

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