Sortino Ratio: How to Measure the Downside Risk of your Portfolio?

What is the Sortino Ratio?

This ratio was developed by Frank Sortino and featured in a 1981 paper published in the Journal of Risk Management. Sortino relied on Modern Portfolio Theory (MPT), which suggests that downside price deviations are of interest to investors for risk management —positive fluctuations are of benefit to investors.

This contrasts with the ratio developed by William Sharpe in 1966, named after him, which is based on the standard deviation of price movements, whether upside or downside. Therefore, the Sortino ratio is an evolution of the Sharpe ratio.

In principle, the Sortino ratio weights downside price deviations. That is, it is based on the principle that downside risk requires higher returns to compensate.

How to Calculate the Sortino Ratio

The Sortino ratio is calculated based on the average realized return, the target return, and the downside deviation of returns, according to the following equation:

Where:

R represents the average return recorded during the study period or the expected return.

T is the target return, or it may be the risk-free return—usually the rate or yield of return on US Treasury bonds.

DD is the downside deviation of returns, calculated using a modified method of calculating the standard deviation, also according to the following equation:

Where:

N represents the study period (or sample size).

ri is the realized return in period i.

Note that the previous equation is based only on returns less than zero and, in a simple principle, calculates the extent of their deviation from the target return. While the traditional method for calculating standard deviation is based on essentially measuring the deviation of returns, whether positive or negative, from their mean.

An Example of Calculating the Sortino Ratio

The following example demonstrates step-by-step how to calculate the Sortino ratio for the returns of an investment portfolio over a seven-year period, assuming a target return (T) of 2%.

To begin, the following table illustrates how to calculate the negative deviation of returns (DD):

Therefore, the Sortino ratio is calculated as follows:

Interpreting Sortino Ratio Values and What are the Factors Affecting It?

As we saw in the example above, the Sortino ratio focuses exclusively on negative return volatility and those below a predetermined level. This approach allows for more specific risk analysis, especially in cases where the investor's primary objective is to minimize losses rather than dealing with returns that are generally on either side of zero.

In general, a high Sortino ratio indicates the ability of an investment manager or portfolio to generate higher returns relative to the level of risk they are exposed to.

While there is no threshold that separates a good or bad Sortino ratio reading, the ratio's calculation must be within a specific framework. Based on this, the Sortino ratio readings of a group of portfolios managed by asset managers can be compared to determine which one is better at managing risk, or the ratio's evolution over time can be monitored to track the effectiveness of risk management.

Interpreting Sortino ratio values may depend largely on the choice of target return. A target return that is too ambitious may exaggerate the surrounding downside risk, while a target that is too moderate may mask underlying downside volatility, as the ratio may rise if the target return rises.

Advantages and limitations of the Sortino ratio

Advantages

• Risk-adjusted return metric: Simple metrics for calculating return are often misleading and present an incomplete picture for the investor. The Sortino ratio weights this return based on the risk tolerance of the investor. The higher the risk, the higher the required rate of return.

• Focusing on downside risk: By focusing on negative returns, the investor can eliminate the distortion that sudden price spikes can cause in their risk assessment.

• Adapting investor needs: By focusing exclusively on returns below a predetermined threshold, it aligns with the needs of an investor who wants to determine their desired profitability or with an investor with a limited risk tolerance.

Limitations

• Subjective factors in selecting the target return: One of the main limitations of the Sortino ratio lies in the selection of the minimum target return. An investor may overestimate the target return, which could lead to an underestimation of the Sortino ratio and an unrealistic assessment of risk management. Underestimating the target return may also underestimate the surrounding risk, especially when the investor sees the Sortino ratio rising, especially during a bull market.

• Ignoring the hidden aspects of positive returns: While it is true that ignoring the volatility resulting from positive returns may provide a clearer perception of risk, high volatility resulting from a series of relatively high returns may indicate the possibility of a market reversal in the coming period, correcting previous gains and turning them into huge losses. This is not reflected in the Sortino ratio calculation.

• Sensitivity to extreme returns: Sudden market flash crashes may occur, lasting for a short period but of enormous magnitude, ultimately leading to the Sortino ratio reading being lower than it should be.

What are the Advantages of Sortino over the Sharpe Ratio?

First, remember that the Sharpe ratio is also a risk-adjusted measure of return. Unlike the Sortino ratio, it uses the volatility of positive and negative returns—the overall standard deviation of returns—into account for risk. While measuring risk by the standard deviation of returns makes the impact of positive and negative returns of the same absolute value equivalent, this may not seem acceptable or realistic to some investors.

Even though the Sharpe ratio appears to be a more comprehensive measure—and as we have argued, ignoring positive returns can sometimes give an incomplete the perception of the surrounding risk—treating positive and negative deviations may not be in the best interests of investors whose primary goal is to preserve their capital.

At the same time, the Sharpe ratio’s symmetrical treatment of positive and negative returns may leave an asset manager’s evaluation vulnerable to distortion if extreme positive abnormal returns, substantially higher than the average, are recorded, even when accompanied by acceptable negative returns (whether preceding or following them). Therefore, accounting for the detrimental effects of volatility may sometimes provide a more realistic measure of risk management effectiveness.

The two ratios also share similar negative aspects in some respects. Both risk measurement methods are affected by extreme returns, which can lead to a misaligned and less realistic assessment of the effectiveness of risk management strategies.

Using the Sortino Ratio in Portfolio Management and Trading

The Sortino ratio can be used in several ways to assess returns in a risk-weighted manner that is consistent with investor needs, as follows:

• Evaluating hedge fund performance: Hedge funds typically generate attractive returns, especially during periods of bull market. However, above-average returns are difficult to sustain, and they may underestimate downside risks. The Sortino ratio's focus on negative return volatility provides a more conservative assessment of risk management, free from the noise that may be generated by extremely high positive returns.

• Using Sortino ratio in portfolio management: More conservative investors can track the performance of their portfolio, which may include a range of stocks or other asset classes on a risk-adjusted basis. Comparing the Sortino ratio readings across multiple portfolios can give a clearer picture of the risk associated with each portfolio.

• Evaluating trading strategies: In trading, you are essentially managing your risk. The downside risks of a strategy may be more important than the potential gains. By focusing on negative performance volatility, the Sortino ratio (as calculated in the example above) can be used to evaluate the effectiveness of any trading strategy in managing your risk.

Conclusion

The Sortino ratio is a prominent risk management tool used to evaluate the performance of asset managers, hedge funds, investment portfolios, and trading strategies. What distinguishes the Sortino ratio is its focus on the downside of return volatility, which represents the damage that investors seek to avoid, as opposed to positive return volatility. The Sortino ratio is a risk-weighted return metric. It is calculated based on the actual return minus the target return, both of which are adjusted for negative return volatility. This distinguishes it from the similar Sharpe ratio, which is calculated based on the deviation of total returns, whether positive or negative.