The Sharpe Ratio is an asset’s average excess rate of return above the risk-free return rate per unit of volatility.
The risk-free rate of return is the rate of return on an investment that is considered to be ‘risk-free’, for which the rate of return on U.S. Treasury bills is used.
Therefore, any return on an asset that is in excess of the risk-free rate is considered to be the return for taking on the risk of holding that specific asset, while the risk-free rate of return is simply the standard return for holding any asset.
Sharpe Ratio Formula
The formula for calculating the Sharpe ratio of an asset is its average rate of return (r) minus the risk-free rate of return (rf) divided by the standard deviation of the asset’s rate of return (sd). So the formula for the Sharpe ratio would be (r-rf)/sd.
The use of standard deviation in the Sharpe ratio is to account for the variability of an asset’s rate of return. Holding an asset with a high average rate of return is ideal, but the more variable the rate of return, the less attractive the asset becomes.
For example, if the rates of return on an asset are 8%, 10% and -3%, the average rate of return of 5% may be attractive, but the fact that investors who held the asset for only the 3rd period lost 3% makes is much less so.
Sharpe Ratio Example
Suppose an asset has an average rate of return (r) of 8%, a standard deviation (sd) of 2% and the risk-free rate (rf) for Treasury bills is 4%.
The Sharpe ratio for this asset over this period would be (8-4)/2, or 2.
Sharpe Ratio Applications
The Sharpe ratio is generally used as a means of evaluating portfolios of assets, as opposed to single assets. The principle remains the same, but the entire value of the portfolio is used instead of just a single asset.
The Sharpe ratio provides a means of evaluating a portfolio’s performance relative to the risk involved in the portfolio. High returns that are gained by taking big risks are less attractive than high returns achieved with little risk.
Portfolio managers tend to aim for a balance of risk and return, and the Sharpe ratio is an essential tool in this process.
The Sharpe ratio is also very useful when a manager is re-balancing a portfolio with new assets and asset classes.
Due to the correlation, or lack thereof, between asset classes, small changes to a portfolio that have a marginal impact on the expected rate of return can have an out-sized impact on the portfolio’s risk profile.
Sharpe Ratio Shortcomings
While the Sharpe ratio’s simplicity and broad applicability are the reasons why it is such a popular analytical tool, they are also the source of its greatest shortcomings.
The formula for the Sharpe ratio tends to breakdown the more an asset or portfolio incorporates outlier returns or ‘tail risks’.
One extremely bad or good year can drastically skew the Sharpe ratio to the point that it is not representative of the risk to return profile for that asset or portfolio.
The same principle applies to portfolios that face various non-linear risks, generally as a result of containing a significant proportion of derivatives, which have a notably different return profile when compared to traditional assets, such as equities, bonds and commodities.
Sharpe Ratio Alternatives
There have been various alternatives to the Sharpe ratio proposed over the years. Most of these alternatives are focused on alternate formulations of risk that are either more sophisticated or more specific than simply the standard deviation of returns used in the traditional Sharpe ratio.
The most popular alternatives to the Sharpe ratio tend to incorporate systemic risk or ‘beta‘, which measures the risk to the market as a whole.
While most day traders tend to use all their liquid capital for their trading strategies, a comfort with general portfolio theory and key associated tools, such as the Sharpe ratio, can still be very useful.
The Sharpe ratio is an excellent tool for making quick evaluations of assets as they might be viewed by the average investor, which is essential to understanding how that asset will be treated by the market.
While few day trading strategies will be built around the Sharpe ratio, it is an excellent tool when used as part of a process of due diligence meant to gain an understanding of an asset before it is traded.