The Sharpe ratio can also help explain whether a portfolio's excess returns are due to smart investment decisions or a result of too much risk. Although one portfolio or fund can enjoy higher returns than its peers, it is only a good investment if those higher returns do not come with an excess of additional risk.
The current risk-free rate is 3.5%, and the volatility of the portfolio’s returns was 12%, which makes the Sharpe ratio of 95.8%, or (15% - 3.5%) divided by 12%. The investor believes that adding the hedge fund to the portfolio will lower the expected return to 11% for the coming year, but also expects the portfolio’s volatility to drop to 7%.
Any Sharpe Ratio less than 1.0 is not acceptable. It means that the risk is greater than the excess return, so the return does not justify the risk you are taking. A greater than 1.0 is considered acceptable, and the higher the better.
The Treynor ratio formula is the return of the portfolio, minus the risk-free rate, divided by the portfolio’s beta. The Sharpe ratio uses the standard deviation of returns in the denominator as its proxy of total portfolio risk, which assumes that returns are normally distributed. A normal distribution of data is like rolling a pair of dice.
But if the return far outweighs the risk, the Sharpe Ratio will be high, making the investment attractive, as there is enough return to justify the extra risk. Thus, the higher the Sharpe Ratio, the better the risk-adjusted return from the investment — which means that the ratio can be used to compare funds.
The ratio shows the extra return you are getting per unit extra risk you’re taking. So, you can use it to determine whether the higher risk associated with some investments, such as stocks and currency trading, is justified. A portfolio with higher returns may not be justified if the risk outweighs the excess return.
So here, you are checking whether the new asset does that effectively. For instance, let’s say your portfolio returns 15% with a volatility of 10%, while the risk-free rate is 5%. Your portfolio’s Sharpe Ratio is (15-5)/10 = 1
Checking your portfolio diversification: The Sharpe Ratio can help you to determine whether the new fund you want to invest in would be of benefit to your existing portfolio. If the fund increases your portfolio’s Sharpe Ratio, it is a good addition. But if it reduces the ratio, it’s either that it’s not reducing your overall risk or not boosting your returns, so it adds no value to your investment portfolio.
It only requires you to compute the expected return on the asset or portfolio under review and then subtract the risk-free rate of return — here, you can use the yield of the short-term U.S. Treasury bills. Then, you divide the difference, which is called the excess return, by the standard deviation of the expected return of the investment or portfolio. Alternatively, you can calculate the Sharpe Ratio after the returns have been realized, in which case you use the actual returns instead of the expected.
By using a standard deviation as a measure of volatility (risk), the ratio assumes that the returns are normally distributed, but this is not the case in the financial markets, as violent price spikes occur in the market from time to time. Also, it assumes that the maximum price movement is the same in either direction — up or down. But we know that the stocks are limited on the downside to zero while the upside is potentially limitless.
When the Sharpe Ratio is negative, it means that the portfolio’s return is less than the risk-free rate, or that it has a negative value. In this case, the ratio offers very little information, but whichever way, you are better off investing in the risk-free asset.