Sharpe Ratio
The Sharpe Ratio is a formula used to measure risk/return. The ratio describes the amount of extra return received for the extra volatility of a more risky asset. The higher the Sharpe Ratio, the greater returns are for each unit of risk. The Sharpe Ratio is calculated by subtracting the risk free rate or return from the return of the portfolio and then dividing by the portfolio’s standard deviation. By using the Sharpe Ratio, investors can theoretically compare risk adjusted returns of investments or portfolios that have different returns and risk levels. The higher the ratio is the better.
Formula
E = Expected Value
R = Expected Portfolio Return
Rf = Risk Free Rate
The numerator of the ratio is the expected return that an asset is expected to provide above the risk free rate.
The denominator is the portfolio’s standard deviation. Standard deviation is the square root of the variance of the portfolio. Possible outcomes fall within standard deviations. Possible returns are most likely within one standard deviation. Two standard deviations covers about 95% of observations. Three standard deviations account for over 99% of observations.
Note:Images and historic Sharpe Ratios reported from second hand source. Discussion about these and other figures can be viewed here.
Sharpe Ratio Problems or Limitations
The Sharpe Ratio is a very useful statistic for portfolio or investment comparison. However, like many aspects of finance and investing the ratio has problems and limitations.
The Sharpe Ratio uses standard deviation as a measure of volatility. Some argue, however, that standard deviation is not a proper measure of volatility. Standard deviation is only a rough proxy for a non definite concepts such as risk.
The Portfolio return component of the Sharpe Ratio assumes or requires that returns are normally distributed. However, the markets are subject to many abnormalities, such as fatter tails, that can skew this normal distribution, thus limiting the Sharpe Ratio’s accuracy.
Future market uncertainty also limits the Sharpe Ratio. Historic Sharpe Ratios are calculated using returns and standard deviations over previous periods. While historic data can provide a good general idea of trends and values, past performance is no guarantee of future results. Forward-looking Sharpe Ratios are based on projections which also are limited by future uncertainty.
Sharpe Ratio calculation needs to be adjusted for portfolio analysis. Using the Sharpe Ratio to directly compare two investments as the basis for adding one to a portfolio is not entirely correct. The Sharpe Ratio may be inaccurate if one or more of the investments is highly correlated with other investments in the portfolio. The solution to this problem is to construct different Sharpe Ratios for different portfolios.
Conclusion
The Sharpe Ratio is an important statistic for measuring risk adjusted returns, comparing alternative portfolios, and comparing similar investments. Although the ratio has limitations, the Sharpe Ratio is still a very important tool for investment comparison and analysis.
Read John Bogle’s Opinion of the Sharpe Ratio in this excerpt from Common Sense on Mutual funds.
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