# What is Sharpe ratio and its usage?

Sharpe ratio is the measure of risk-adjusted return of a financial portfolio.

What does it tell us?

Sharpe ratio is a computation of excess portfolio return over the risk-free rate relative to its standard deviation. It’s very useful for calculating the risk-adjusted returns potential of a mutual fund. Usually, risk-adjusted return happens to be the returns earned over and above the returns generated by a risk-free asset just like a fixed deposit or a government bond. The excessive returns are seen in the light of the “extra risk” which an investor takes upon investing in a risky asset like equity funds. The risk inherent in an investment is determined by using the standard deviation. Therefore, a higher Sharpe ratio proves to give better return yielding capacity of a fund for every additional unit of risk taken by it. It becomes justifiable for the underlying volatility of the fund. We can use this ratio to compare the funds. Generally, we take a 90-day Treasury bill rate as the proxy for the risk-free rate. This measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University. Usually, Sharpe Ratio represents a trade-off between risk and return on investment.

Calculation of Sharpe Ratio

We can quickly find the Sharpe ratio in the fact sheet of a mutual fund. It is easily calculated by subtracting the risk-free return from the portfolio return which is known as the excess return. Eventually, the excess return is divided by the standard deviation of the portfolio returns. Generally, it is calculated every month and annualized for easy understanding.

It is calculated by using the formula given below:

Sharpe Ratio = (Average fund returns – Risk-free Rate) / Standard Deviation of fund returns

It means that if the Sharpe ratio of a fund is 2 per annum, then the fund generates a 2% extra return on every 1% of additional annual volatility. A higher standard deviation should earn higher returns to keep its Sharpe ratio at higher levels. On the contrary, the funds with a lower standard deviation may achieve a higher Sharpe ratio by earning moderate returns consistently.

Importance of Sharpe Ratio?

Sharpe ratio shows investors’ desire to earn returns which are higher than are provided by risk-free instruments like treasury bills. As this ratio is formed based on standard deviation which in turn is a measure of total risk inherent in an investment, it indicates the degree of returns generated by an investment after considering all kinds of risks. It is the handiest ratio to ascertain the performance of a fund and we need to know its importance.

It is a detailed mechanism to determine the performance of a fund against a given level of risk. The higher the Sharpe ratio of a portfolio, the better is its risk-adjusted-performance. However, if we obtain a negative Sharpe ratio, then it means that it proves to be a profitable one we would be better off investing in a risk-free asset than the one in which we are invested right now.

• Measure for Fund Comparison:

It may be used as a tool to compare funds that are placed in the same category to analyze the funds’ performance of Fund A and Fund B which are large-cap equity funds. In this way, we will make sure that both the funds are facing a similar level of risk. On the contrary, we might compare funds that give the same returns but which are at different levels of risk.

• Measure for Comparison Against the Benchmark:

It can tell us whether our preferred fund is suitable for an investment perspective as compared to peer funds in the selected category. We may even broaden our horizon by comparing the fund’s Sharpe ratio with that of the underlying benchmark. In this way, we get to know whether our fund is outperforming/underperforming the benchmark. Ultimately, we get to know how well are we being compensated for the risk that we have taken in the investment.

Example

A portfolio that consists of 50 percent equity and 50 percent bonds with a portfolio return of 30 percent and a standard deviation of 10 percent. Taking the risk-free rate to be 5 percent. In this case, the Sharpe ratio will be 2.5 [(30%-5%)/10%]. Adding 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 35 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 3 [(35%-5%)/10%].

This shows that the addition of a new asset gives a stimulus to the overall portfolio return without adding any undue risk. It leads to the effect of elevating the Sharpe ratio.

The Sharpe ratio is a relative estimation of risk-adjusted return. I assumed in isolation, it does not provide much information about the fund’s performance. Furthermore, the measure considers standard deviation which assumes the 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. Standard deviation takes into report both the positive as well as the negative deviation in returns from the mean, hence it doesn’t accurately compute the downside risk. Measures like the Sortino ratio which only assumes negative deviation from the mean return which removes the limitation of Sharpe ratio to some extent.

Author: Yash Tanwar