Sharpe ratio is the measure of the risk-adjusted return of a financial portfolio. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.
Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for the risk-free rate.
The formula for calculating the Sharpe ratio is {R (p) – R (f)} /s (p)
Where
R (p): Portfolio return
R (f): Risk-free rate of return
s (p): Standard deviation of the portfolio
Realized historical return is used to calculate the ex-post Sharpe ratio while the ex-ante Sharpe ratio employs expected return.
If two funds offer similar returns, the one with a higher standard deviation will have a lower Sharpe ratio. In order to compensate for the higher standard deviation, the fund needs to generate a higher return to maintain a higher Sharpe ratio. In simple terms, it shows how much additional return an investor earns by taking additional risk. Intuitively, it can be inferred that the Sharpe ratio of a risk-free asset is zero.
Portfolio diversification with assets having low to negative correlation tends to reduce the overall portfolio risk and consequently increases the Sharpe ratio. For instance, let’s take a portfolio that comprises 50 percent equity and 50 percent bonds with a portfolio return of 20 percent and a standard deviation of 10 percent. Let’s take the risk-free rate to be 5 percent. In this case, the Sharpe ratio will be 1.5 [(20%-5%)/10%]. Let’s add another asset class to the portfolio, namely a hedge fund, and tweak the portfolio allocation to 50 percent in equity, 40 percent in bonds, and 10 percent in the hedge fund. After the addition, the portfolio return becomes 25 percent and the standard deviation remains at 10 percent. If the risk-free rate is taken as 5 percent, the new Sharpe ratio will be 2 [(25%-5%)/10%].
This shows that the addition of a new asset can give a fillip to the overall portfolio return without adding any undue risk. This has the effect of augmenting the Sharpe ratio.
The Sharpe ratio, however, is a relative measure of risk-adjusted return. If considered in isolation, it does not provide much information about the fund’s performance. Moreover, the measure considers standard deviation, which assumes asymmetrical distribution of returns. For asymmetrical return distribution with a Skewness greater or lesser than zero and Kurtosis greater or lesser than 3, the Sharpe ratio may not be a good measure of performance.
Considering standard deviation as a proxy for risk has its pitfalls. Standard deviation takes into account both the positive as well as the negative deviation in returns from the mean, hence it doesn’t accurately measure the downside risk. Measures like Sortino, which only considers negative deviation from the mean return, can remove the limitation of the Sharpe ratio to some extent.
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