# Sharpe and Sortino Ratios

What is the best way to quantify an investment’s risk? The answer is still open to debate, and the Sharpe and Sortino Ratios reflect two separate camps of thought.

One of the most commonly used measurements of risk is variance, the dispersion of an investment’s returns from their mean. In the calculation of this value, no distinction is made between upside and downside deviation. For this reason, a hedge fund with monthly returns of -5% and +5% will have the same variance as another investment that is flat one month and +10% the next.

The formula for the Sharpe Ratio is return minus the risk free rate divided by standard deviation. It is important to note that standard deviation is simply the square root of variance. In accordance with the description above, the Sharpe Ratio is therefore using a non directionally-biased measurement of volatility to adjust for risk. This concept has been criticized, as it may actually punish a fund for a month of exceptionally high performance. For many individuals, this type of deviation is not only acceptable, but also desirable. It is for this reason that the Sortino Ratio was developed. Instead of using standard deviation in the denominator, the Sortino Ratio uses downside semi-variance. This is a measurement of return deviation below a minimal acceptable rate. By utilizing this value, the Sortino Ratio only penalizes for “harmful” volatility. It is a measurement of return per unit of risk on the downside.

Although there are arguments in favor of both ratios, the use of the Sharpe has been more mainstream. In some cases, this may reflect a certain comfort level associated with its use of standard deviation, which is a more traditional measurement of volatility. Funds that cite their Sortino Ratio have traditionally been those with the least tolerance for risk. In these cases, the Sortino may be presented as a compliment to an investment thesis that stresses the containment of losses to a minimum.

Although both the ratios are measurements of return-to-risk, understanding the distinctions of each may provide insight into their unique drawbacks. It is important to note that thorough interpretation of their values requires attention to each of these considerations

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