The Sharpe ratio is a way to determine how much return is achieved per unit of risk. It is useful for, and can be calculated by, all forms of capital market participants to evaluate their performance, from day traders to buy-and-long-term investors.
Indeed, when evaluating the performance of traders and investors, it is not simply a matter of determining their overall return, but their return relative to their risk.
A 20% annual gain is a very strong performance. However, if this is due to annual volatility of 60% due to over-leveraging or trading highly speculative instruments, this is actually a relatively modest performance when adjusted for risk. The Sharpe ratio will be considered as 0.3. This is calculated as follows:
Sharpe Ratio = (Portfolio Return – Risk Free Return) / Std Dev Portfolio
The risk-free rate of return is a user-based input. This is usually equivalent to a safe risk-free bond. These may be yields on US Treasuries, UK Gilts, German bunds, or other safe instruments. The duration depends on your time horizon.
For long-term investors or position traders who hold positions over a long period of time, they may choose long-term bonds. Short-term investors or day traders who may hold positions only during the day may use shorter bond durations, or nearly one equivalent to the countries overnight rate set by its central bank. This is usually estimated by one-month or three-month government bonds or simply by looking at the central bank’s own overnight policy rate.
In the case of the 20% / 60% volatility portfolio mentioned above, if one were to use the 10-year US Treasury (assuming a 3% yield), the Sharpe ratio would be around 0.283. If one were to use 3-month US Treasuries (assuming a 2% yield), the Sharpe ratio would be around 0.300.
If the risk-free rate used is higher, this means the “excess return” is lower – i.e. a 17% return over the risk-free rate is not necessarily an 18% excess return. Therefore, a higher risk-free rate will result in a lower Sharpe ratio, holding everything else equal.
Ex-Ante vs. Ex-Post Sharpe Ratio
The Sharpe ratio can be considered either ex-ante (expected) or ex-post (backward-looking to evaluate past performance).
The ratios considered above are ex-post, because the performance has already happened. The former Sharpe ratio takes into account account expectations. From the return and volatility of the portfolio, the calculation is the expected values of those things, which are marked with “E” before the conditions.
Sharpe Ratio = E (Portfolio Return – Risk Free Return) / E (Std Dev Portfolio)
Therefore, if the S & P 500 is expected to generate a nominal annual return of 7% from an annual volatility of 15%, with a risk-return rate of 3% (based on future US Treasury yields), that results in a Sharpe ratio of 0.27.
Ex-post ratios can vary, especially among shorter time periods. For example, the Sharpe ratio of the S&P 500 for 2017, due to higher returns on lower volatility, was 4.78. For the 2018 share, it has become 0.23.
Financial Application
The Sharpe ratio is often used to determine the relative performance of portfolios, traders, and fund managers over time. The Sharpe ratio for each asset class is generally around 0.2 to 0.3 over the long term.
A value between 0 and 1 indicates that the return obtained is better than the risk-free rate, but the excess risk exceeds their excess balance. Values above 1 indicate that returns are not only better than the risk-free rate, but that excess returns exceed their excess risk.
A negative Sharpe ratio means that the performance of the manager or portfolio is below the risk-free rate. For financial assets, a negative Sharpe ratio will not persist for an indefinite period of time. A capitalist economy would cease to function if this were true.
A negative Sharpe ratio can persist for a long period of time for a particular asset class, manager, or portfolio due to the timing or idiosyncratic risk associated with trading a particular asset.
However, a negative Sharpe ratio is problematic to evaluate because excessively negative returns with a lot of volatility will make the Sharpe ratio less negative (because the denominator is larger), thus confirming that the performance is not as expected. Likewise, a portfolio with a small negative excess return can be penalized if its associated volatility is large, giving it a smaller denominator and thus amplifying the negative value.
Therefore, a negative Sharpe ratio can be very difficult to evaluate.
Advantages and Disadvantages of the Sharpe Ratio
As with any statistical measure, it’s only as good as your assumptions. In studies on financial risk assessment, it is often assumed that volatility is equal to risk or its best proxy. However, not all fluctuations are dangerous and some are necessary to catch back.
Trading and investing is essentially about maximizing return per unit of risk. This is the main goal of the Sharpe ratio, but it does it modestly.
A trading or investment strategy that balances risk or can accurately identify strong risk-reward opportunities will experience high volatility. But since all volatility is penalized equally under the Sharpe ratio, the metric may not be the best for identifying the risks associated with a portfolio.
Other risk-adjusted metrics, such as the Sortino ratio, may be more appropriate for these types of portfolios and will generally be a more accurate reflection of their risk.
However, the Sharpe ratio is easy to use and can be applied to any series of returns without the need for additional information about the source of volatility or profitability.
Return volatility is also assumed to be normally distributed. In general, financial variables tend to be more fat-tailed than those associated with a normal distribution and generally exhibit higher skewness and/or kurtosis.
And because the Sharpe ratio is commonly used in ex-post indices – to evaluate past performance – it can be flawed because past performance is not necessarily any prediction of what will happen in the future or in the shorter term.
Furthermore, since the Sharpe ratio is not expressed in terms of a percentage or return, but as a simple number, its use is only valuable in comparison to other performance evaluated through the Sharpe ratio.
As a rule of thumb, a Sharpe ratio above 0.5 is a market beating performance if achieved over the long term. A ratio of 1 is great and difficult to achieve over a long period of time. A ratio of 0.2-0.3 is in line with the broader market. A negative Sharpe ratio, as mentioned above, is difficult to evaluate.