The Sharpe ratio is a way of determining how much return is achieved per unit of risk. It is useful for and can be calculated by all types of capital market participants to evaluate their performance, from day traders to long-term buy-and-hold investors.
In assessing the performance of traders and investors, it is of course not just a question of determining their overall return, but their return relative to their risk.
An annual profit of 20% is very strong. However, if it arises from a 60% annual volatility due to excessive leverage or trading very speculative instruments, it is actually a fairly moderate performance when risk-adjusted. The Sharpe ratio will be considered 0.3. It is calculated as follows:
Sharp ratio = (Return of portfolio – Risk free return) / Std Dev of portfolio
The risk-free rate of return is a user-based input. This is usually the equivalent of a secured risk-free mortgage. This could be the yield on a US Treasury, UK gilt, German bond or other safe instrument. Its duration depends on your time horizon.
For long-term investors or position traders who hold positions over long periods of time, they can choose a mortgage with a longer duration. Short-term investors or day traders who may only hold intraday positions can use a shorter bond duration, or virtually one equivalent to the rate set by the country’s overnight rate. This is usually approximated by a one-month or three-month government bond or simply by looking at the overnight policy rate from the central bank.
In the case of the 20% volatility portfolio mentioned above, the Sharpe ratio would be 0.283 if a ten-year US Treasury was used (assuming a 3% yield). Using a three-month US Treasury (assuming 2% yield), the Sharpe ratio would be 0.300.
If the risk-free rate used is higher, it means that the ‘excess return’ is lower – ie a return of 17% above the risk-free rate is not as good as an excess return of 18%. Thus, a higher risk-free rate will lead to a lower Sharpe ratio, all things being equal.
Ex-Ante vs. Ex-Post Sharpe Ratio
The Sharpe ratio can be viewed as ex ante (expected) or ex post (looked back to evaluate past performance).
The relationship considered above is from the outside, because its performance has already taken place. The ex ante Sharpe ratio takes the expectations into account. Instead of portfolio returns and volatility, the calculation is instead the expected values of those things, denoted by ‘E’ before the terms.
Sharpness Ratio = E (Return of Portfolio – Risk Free Return) / E (Std Dev of Portfolio)
So if the S&P 500 is expected to deliver 7% nominal annualized returns against 15% annualized volatility, with a risk-free rate of return of 3% (based on future U.S. returns), it produces a Sharpe -ratio of 0.27.
Post-post ratios can vary greatly, especially between shorter time frames. For example, the Sharpe ratio of the S&P 500 for 2017, due to higher returns against low volatility, was 4.78. For the year to date of 2018, it was 0.23.
Application in Finance
The Sharpe ratio is frequently used to determine the relative performance of portfolios, traders and fund managers over time. The Sharpe ratios of individual asset classes are generally 0.2 to 0.3 over the long term.
A value between 0 and 1 indicates that the returns obtained are better than the risk-free rate, but that their excess risks exceed their excess returns. A value above 1 indicates that the returns are not only better than the risk-free rate, but that the excess returns are above their excess risks.
A negative Sharpe ratio means that the performance of a manager or portfolio is lower than the risk-free rate. For financial assets, the negative Sharpe ratios will not last indefinitely. Capitalist economies would cease to function if this were true.
Negative Sharpe ratios can exist for long periods of time for specific asset classes, managers or portfolios due to timing or the idiosyncratic risk associated with trading certain assets.
However, a negative Sharpe ratio is problematic to evaluate because a negative excess return with a large amount of volatility will make the Sharpe ratio less negative (because the denominator is larger), suggesting that the performance was not that poor. than expected. Similarly, a portfolio with a small negative excess return can be penalized if the volatility associated with it is large, giving a smaller denominator and thus amplifying the negative value.
Therefore, negative Sharpe ratios can be exceptionally difficult to judge.
Pros and cons of the Sharpe Ratio
Like any statistical measure, it is only as good as the assumptions. In studies of financial risk assessment, volatility is often assumed to be equal to risk or its best conclusion. However, not all volatility is harmful and some is absolutely necessary to bounce back.
Trading and investing is basically about maximizing returns per unit of risk. This is the central intent of the Sharpe ratio, but it is done in a simplistic way.
Trading or investment strategies that balance the risks well or can accurately identify the strong reward-to-risk opportunities will have a high improbability. But considering that all volatility is penalized equally under the Sharpe ratio, the statistic may not be the best to accurately identify the risks associated with the portfolio.
Other risk-adjusted metrics, such as the Sortino ratio, may be a better fit for these portfolios and will generally be a more accurate representation of their risk.
However, the Sharpe ratio is easy to apply and can be applied to any time series of returns without needing additional information about the sources of volatility or profitability.
Volatility of returns is assumed to be normally distributed. Financial variables are usually more fat-tailed than those associated with the normal distribution and generally exhibit higher skewness and/or kurtosis.
And because the Sharpe ratio is usually used ex-post – to evaluate past performance, it can be flawed, as past performance is not necessarily a predictor of what will happen in the future or over shorter time horizons.
Since the Sharpe ratio is not expressed in terms of a percentage or return, but rather as a simple number, its use is only valuable in comparison to other performances assessed by the Sharpe ratio.
As a rule of thumb, a Sharpe ratio of more than 0.5 is market-beating performance if achieved over the long term. A ratio of 1 is excellent and difficult to achieve over long periods. A ratio of 0.2-0.3 is consistent with the broader market. A negative Sharpe ratio, as mentioned above, is difficult to evaluate.