Many traders and investment managers require a means to measure and evaluate portfolio managers and trading systems. Riskadjusted metrics play a pivotal role in this evaluation. It’s because more returns can always be achieved from taking more risks, inherent in the leverage nature of the futures markets. While Sharpe ratio is the most widely used riskadjusted measure since its introduction in 1966, Sortino ratio offers an alternative perspective and improves Sharpe ratio in specific aspects.
Sortino ratio, developed by Frank A. Sortino in the 1980s, is a riskadjusted performance measure of a portfolio. It’s similar to Sharpe Ratio, which was named after William Sharpe. The key difference is that the Sortino ratio differentiates harmful volatility from overall volatility. It can be viewed as a modification of Sharpe Ratio, but it only considers the standard deviation of the downside risk, rather than that of the entire upside plus downside risks.
Formula and Calculation
Sortino ratio penalizes those returns failing a specific target, or minimum acceptable return. On the other hand, Sharpe ratio penalizes any upside or downside difference. The formula and calculation of Sortino is as follows:
where:

R_{p} is the actual portfolio return,

T is the target return or the minimum acceptable return, and

DR is the downside risk.
The downside risk from a data sample over N periods is calculated as follows:
where R_{i} is the portfolio return in time period i and T is the minimum acceptable return.
In postmodern portfolio theory, another way to view the downside risk is the squareroot of the probabilityweighted squared belowtarget return:
where r is the random variable representing the return and f(r) is its probability function.
Both forms have their values in practice. Some practitioners use the discrete calculation due to its simplicity, while others use the continuous form in postmodern portfolio theory.
It’s interesting to note that in 1959, Nobel laureate Harry Markowitz recognized that investors primarily care about downside deviation when developing Modern Portfolio Theory. Hence using the downside deviation would be more appropriate than using the standard deviation. However, Markowitz used variance (the square of deviation) in his Modern Portfolio Theory since downside deviation was computationally impractical at the time.
Key Features
Sharpe ratio penalizes both upside and downside deviation, which means one can achieve higher Sharpe ratio by removing the largest positive return. This is undesirable as investors certainly welcome large positive returns. Additionally, for a positivelyskewed investment strategy (e.g. trend following), the performance is often achieved with lower risk than Sharpe ratio suggests. Indeed, for a skewed/nonnormal distribution of returns, Sharpe ratio often falls short and becomes a poor performance measure.
The Sortino ratio focuses only on the negative deviation from the minimum acceptable return, which is thought to give a better view of riskadjusted performance since positive deviation is indeed a benefit. It is also a useful way for investors, analysts, and portfolio managers to evaluate a portfolio for a given level of bad risk.
Similar to Sharpe ratio, a higher Sortino ratio is better. When looking at two portfolios, a rational investor would prefer the one with a higher Sortino ratio as it yields higher return per every unit of bad risk. The following table shows the recommended range:
Example
In this example, we will calculate the annual Sortino ratio for the following set of annual returns:

Annual returns: 19%, 12%, 23%, 5%, 15%, 6%, 13%, 4%,

Target return: 7%.
We calculate the excess return and the downside difference with the min function:
The numerator in Sortino ratio is the average of excess return:
The denominator DR in Sortino ratio is calculated as follows:
The Sortino ratio is then:
Conclusion
The Sortino ratio provides a more nuanced view of risk compared to other riskadjusted performance measures. By focusing on downside risk, it offers valuable insights for investors to optimize their portfolios against potential losses. As with any financial metrics, it’s better to use Sortino ratio in conjunction with other measures and not in isolation.