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The Sortino ratio is a risk-adjusted performance measure that calculates the return per unit of downside risk. It is similar to the Sharpe ratio, but it uses the standard deviation of negative returns instead of the total standard deviation.

The Sortino ratio is calculated as follows:

Sortino ratio = (Return - Risk-free rate) / Standard deviation of negative returns

The risk-free rate is the return of an investment with no risk, such as a government bond. The standard deviation of negative returns is the square root of the variance of negative returns.

A higher Sortino ratio indicates that an investment has a lower risk-adjusted return. The Sortino ratio is often used to compare the performance of different investments, or to evaluate the performance of an investment over time.

Here is an example of how to calculate the Sortino ratio:

Let’s say an investment has a return of 10%, a risk-free rate of 2%, and a standard deviation of negative returns of 5%. The Sortino ratio would be calculated as follows:

Sortino ratio = (10% – 2%) / 5% = 2

This means that the investment has a risk-adjusted return of 2. In other words, for every unit of risk (as measured by the standard deviation of negative returns), the investment generates 2 units of return.

The Sortino ratio is a useful measure of risk-adjusted performance, but it is important to note that it is not without its limitations. One limitation is that it is sensitive to the number of negative returns in the period being analyzed. For example, an investment with a few large negative returns will have a lower Sortino ratio than an investment with many small negative returns.

Another limitation is that the Sortino ratio does not take into account the distribution of returns. For example, two investments with the same Sortino ratio could have very different return distributions. One investment could have a few large positive returns and a few large negative returns, while the other investment could have many small positive returns and no negative returns.

Despite its limitations, the Sortino ratio is a useful tool for evaluating the risk-adjusted performance of investments. It is a good complement to the Sharpe ratio, and it can be used to identify investments that have high returns with relatively low downside risk.