What is Sharpe’s index?

Sharpe’s index or ratio was developed by Nobel laureate William F. Sharpe and is used to help investors understand the return on an investment relative to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Volatility is a measure of the price fluctuations of an asset or portfolio.

How is Sharpe’s ratio calculated?

It is calculated as follows:

• Subtract the risk-free rate from the portfolio return. The risk-free rate could be a U.S. Treasury rate or yield, such as the one- or two-year Treasury yield.
• Divide the result by the standard deviation of the portfolio excess return. The standard deviation helps show how much the portfolio return deviates from the expected return. The standard deviation also sheds light on the volatility of the portfolio.

$Sharpe Ratio = \frac{R_p-R_f}{\sigma_p}$

Where:

• $R_p$ represents the portfolio return.
• $R_f$ is the risk-free rate
• $\sigma_p$ is the standard deviation of the portfolio.

What can Sharpe’s index tell you?

Subtracting the risk-free rate from the average return allows an investor to better isolate the returns associated with risk assets. The risk-free rate of return is the return on an investment with zero risk, that is, it is the return that investors might expect to take no risk at all. The return on a U.S. Treasury bond, for example, could be used as the risk-free rate.

Sharpe’s ratio is one of the most widely used methods of calculating risk-adjusted return. Modern portfolio theory (MPT) states that adding assets to a diversified portfolio that has low correlations can decrease portfolio risk without sacrificing return. Adding diversification should increase the Sharpe ratio relative to similar portfolios with a lower level of diversification. For this to be true, investors must also accept the assumption that risk equals volatility, which is not unreasonable but may be too narrow to apply to all investments.

Sharpe’s ratio can be used to evaluate the past performance of a portfolio (ex-post) where real returns are used in the formula. Alternatively, an investor could use the expected performance of the portfolio and the expected risk-free rate to calculate an estimated Sharpe ratio (ex-ante).

The Sharpe ratio can also help explain whether a portfolio’s excessive returns are due to smart investment decisions or the result of excessive risk. Although a portfolio or fund may enjoy higher returns than its peers, it is only a good investment if these higher returns are not accompanied by excess additional risk.

The higher the Sharpe ratio of a portfolio, the better its risk-adjusted performance. If the analysis results in a negative Sharpe ratio, it means that the risk-free rate is greater than the portfolio return, or that the portfolio return is expected to be negative. In either case, a negative Sharpe ratio conveys no useful meaning.

Example of how to use Sharpe’s ratio.

Sharpe’s ratio is often used to compare the change in overall risk-return characteristics when a new asset or asset class is added to a portfolio.

For example, an investor is considering adding a hedge fund allocation to his existing portfolio that is currently split between stocks and bonds and has returned 15 percent over the past year. The current risk-free rate is 3.5 percent and the volatility of the portfolio’s returns has been 12 percent, making the Sharpe ratio 95.8 percent, or (15 percent - 3.5 percent) divided by 12 percent.

The investor believes that the addition of the hedge fund to the portfolio will lower the expected return to 11% for next year, but they also expect the portfolio volatility to drop to 7%. They assume that the risk-free rate will remain the same for next year.

Using the same formula, with estimated future numbers, the investor finds that the portfolio has an expected Sharpe ratio of 107%, or (11% - 3.5%) divided by 7%.

Here, the investor has shown that although the hedge fund investment is lowering the absolute return of the portfolio, it has improved its performance on a risk-adjusted basis. If adding the new investment would lower the Sharpe ratio, it should not be added to the portfolio. This example assumes that the Sharpe ratio based on past performance can be properly compared to expected future performance.

Limitations of using Sharpe’s ratio.

Sharpe’s ratio uses the standard deviation of returns in the denominator as a proxy for total portfolio risk, which assumes that returns are normally distributed. A normal distribution of the data is like rolling a pair of dice. We know that on many throws, the most common outcome of the dice will be seven, and the least common outcomes will be two and twelve.

However, returns in financial markets are skewed from the mean because of a large number of surprising drops or spikes in prices. In addition, the standard deviation assumes that price movements in both directions are equally risky.

Sharpe’s ratio can be manipulated by portfolio managers seeking to increase their history of seemingly risk-adjusted returns. This can be done by lengthening the measurement interval. This will result in a lower estimate of volatility. For example, the annualized standard deviation of daily returns is generally higher than that of weekly returns, which is, in turn, higher than that of monthly returns.

Choosing a period for analysis with the best potential Sharpe ratio, rather than a neutral look-back period, is another way to select data that will skew risk-adjusted returns.

What is a good Sharpe ratio?

Sharpe ratios above 1.0 are generally considered “good,” as this suggests that the portfolio is delivering returns in excess of its volatility. That said, investors often compare the Sharpe ratio of a portfolio against its peers. Thus, a portfolio with a Sharpe ratio of 1.0 might be considered inadequate if competitors in its peer group have an average Sharpe ratio above 1.0.

Key Conclusions.

• The Sharpe ratio adjusts a portfolio’s past performance-or expected future performance-for the excess risk that has been assumed by the investor.
• A high Sharpe ratio is good when compared with similar portfolios or funds with lower returns.
• The Sharpe ratio has several weaknesses, including the assumption that investment returns are normally distributed.

Original source for this article: www.investopedia.com