29 Jul 2015
Sharpe Ratio; Risk vs. Reward

by veristrat

According to the behavioural portfolio theory an investor is risk averse and will always choose an investment that provides higher return compared to the risk of the investment. One of the most widely relied upon measure of risk and return is Sharpe Ratio, the ratio of expected excess return of an investment to its standard deviation .

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Sharpe ratio was derived in 1966 by William Sharpe; it is very simple and uses only three inputs namely asset return, risk-free return and standard deviation of return. This simplicity has been its biggest advantage and the reason for its popularity. From a risk-return perspective, when analysing an investment, the higher the Sharpe ratio, the more desirable is the investment.

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Consider two hypothetical shares with similar returns. Share X gained an average of 15% a year over the past two years, but had a standard deviation of 40%, giving it a Sharpe ratio of 0.375. Share Y returned an average of 12% over that same period but had a standard deviation of 20%, giving it a Sharpe ratio of 0.6. (Considering short-term Treasury yields or risk free rate near zero.)

While Share X had better return than share Y, share Y returned more in terms of one unit of risk it had. In spite of its wide applicability Sharpe ratio has a number of limitations which sometimes leads to a false conclusion.

The Sharpe ratio is time dependent; that is, the overall Sharpe ratio increases proportionally with the square root of time.

When an investment has an asymmetrical return distribution, with either positive or negative skewness, Sharpe ratio is not an appropriate measure of risk adjusted return.

The Sharpe ratio is primarily a risk-adjusted performance measure for stand-alone investments and does not take into consideration the correlations with other assets in a portfolio. The Sharpe ratio can be gamed; that is the reported Sharpe ratio can be increased without the investment really delivering higher risk-adjusted returns in the following ways:

Lengthening the measurement interval, compounding the monthly returns but calculating the standard deviation from non-compounded monthly returns.

Despite of many faults Sharpe ratio is still relevant and has been the base of many alternatively developed risk and return measures lie RoMAD and Sortino ratio. The popularity of Sharpe ratio can never be undermine till we develop another risk return measure that takes into account the drawbacks of Sharpe ratio.

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