Sortino ratioThe Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy.[1] It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.[2] DefinitionThe ratio is calculated as
where is the asset or portfolio average realized return, is the target or required rate of return for the investment strategy under consideration (originally called the minimum acceptable return MAR), and is the target semi-deviation (the square root of target semi-variance), termed downside deviation. is expressed in percentages and therefore allows for rankings in the same way as standard deviation. An intuitive way to view downside risk is the annualized standard deviation of returns below the target. Another is the square root of the probability-weighted squared below-target returns. The squaring of the below-target returns has the effect of penalizing failures at a quadratic rate. This is consistent with observations made on the behavior of individual decision making under uncertainty. Here = downside deviation or (commonly known in the financial community) "downside risk" (by extension, = downside variance), = the annual target return, originally termed the minimum acceptable return MAR, = the random variable representing the return for the distribution of annual returns , and = the distribution for the annual returns, e.g., the log-normal distribution. For the reasons provided below, this continuous formula is preferred over a simpler discrete version that determines the standard deviation of below-target periodic returns taken from the return series.
Using the observed points to create a distribution is a staple of conventional performance measurement. For example, monthly returns are used to calculate a fund's mean and standard deviation. Using these values and the properties of the normal distribution, we can make statements such as the likelihood of losing money (even though no negative returns may actually have been observed) or the range within which two-thirds of all returns lies (even though the specific returns identifying this range have not necessarily occurred). Our ability to make these statements comes from the process of assuming the continuous form of the normal distribution and certain of its well-known properties. In post-modern portfolio theory an analogous process is followed.
As a caveat, some practitioners have fallen into the habit of using discrete periodic returns to compute downside risk. This method is conceptually and operationally incorrect and negates the foundational statistic of post-modern portfolio theory as developed by Brian M. Rom and Frank A. Sortino. UsageThe Sortino ratio is used to score a portfolio's risk-adjusted returns relative to an investment target using downside risk. This is analogous to the Sharpe ratio, which scores risk-adjusted returns relative to the risk-free rate using standard deviation. When return distributions are near symmetrical and the target return is close to the distribution median, these two measure will produce similar results. As skewness increases and targets vary from the median, results can be expected to show dramatic differences. The Sortino ratio can also be used in trading. For example, whenever you want to get a performance metric for your trading strategy in an asset, you can compute the Sortino ratio to compare your strategy performance with any other strategy. [3] Practitioners who use a lower partial Standard Deviation (LPSD) instead of a standard deviation also tend to use the Sortino ratio instead of the Sharpe ratio. [4] See also
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