Sortino index: how to evaluate the returns of a portfolio

What is the Sortino index

The Sortino index is a measure of financial performance that takes into account the specific risk of an investment, known as downside risk. This indicator was introduced by economist Frank Sortino and is used to assess the extra return of a portfolio relative to a minimum acceptable return, considered in relation to the possibility of negative returns.

While other performance indicators, such as the Sharpe Index, evaluate risk-adjusted return by considering overall volatility, Sortino’s index focuses only on the risk of loss, making it particularly useful for capital protection-oriented investors. The focus is on the average return of a portfolio and its ability to exceed a predetermined threshold, without including cases where positive returns are achieved above expectations.

How to calculate Sortino’s index

The calculation of this index takes the average portfolio return, denoted as \(R_p\), and compares it to a risk-free return \(S\) or minimum acceptable return, known as \(MAR\) (Minimum AcceptableReturn). The risk considered is the downside risk (\(DSR\)), which is based only on the volatility of returns below the minimum acceptable return. The formula is as follows:

Sortino Index = \({\displaystyle \frac{Rp – S}{DSR}}\)

where:

\(R_p\) represents the average return of the portfolio;

\(S\) represents the minimum acceptable return;

\(DSR\) is the measure of downside risk, calculated by considering only returns below \(S\).

\({\displaystyle DSR=\left(\int _{-\infty }^{T}(T-x)^{2}\,f(x)\,dx\right)^{1/2}}\)

Sortino’s index and comparison with other indicators

Compared with indexes such as Sharpe‘s Index or Treynor‘s Index , Sortino’s index differs in two key respects.

• First, it allows a minimum return threshold to be set, which varies according to the investor’s specific objectives.
• Second, risk is considered only for returns below the minimum return, leaving out positive returns.

For this reason, it is an attractive parameter when comparing funds or portfolios that aim to protect capital against losses, rather than to maximize growth. As with other performance indices, a higher Sortino value indicates better performance, as it means the portfolio is able to generate returns above the minimum threshold with less exposure to the risk of loss.

When to use the Sortino index

The Sortino index is particularly useful for conservative investors or those who prefer to avoid wide swings in returns. In contrast to aggressive investing, where greater volatility is accepted, a portfolio with a high Sortino index signals stability and less exposure to risk of loss. This indicator also proves effective for those comparing different investment instruments, such as mutual funds, ETFs, or diversified portfolios, to identify the one best suited for a capital protection strategy. In the context of Capital Asset Pricing Model (CAPM) theory, Sortino’s index is a viable alternative to Jensen’s alpha or Modigliani’s Index, adapting to valuations focused on downside risk management.

Benefits of the Sortino index for capital protection.

Investors who aim to avoid extreme fluctuations in returns may particularly appreciate this index for its ability to isolate downside risk from traditional indicators. This approach makes it easier to select portfolios in line with capital protection objectives, improving decision making when choosing among investment options with similar risk characteristics.

Although it is advisable to use this index in conjunction with other valuation tools such as the Sharpe Index , the Sortino Index remains one of the main tools for identifying investments that aim to minimize losses while maintaining a minimum acceptable return.

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