Sortino Ratio | Definition and Formula easily explained
What is the Sortino Ratio? How does it work? When should you use it?
The Sortino Ratio is a value that measures the performance of a financial instrument, or rather, the relationship between the downside risk and return. The higher the Sortino Ratio, the better the performance of the financial instrument.
How does the Sortino Ratio work? How is it calculated? What are the advantages and disadvantages of this ratio?

What is the Sortino Ratio

In finance, the Sortino Ratio (also called the Sortino index) measures the performance of a single financial instrument (stocks, mutual funds, etc.) or of a portfolio compared to a target return, normalized with respect to volatility.
This means that the Sortino Ratio represents the additional amount of return an investor receives per unit of increased risk.

Difference between Sortino Ratio and Sharpe Ratio

If you have read our article on the Sharpe Ratio, you probably noticed that conceptually the Sortino Ratio is very similar to the Shape Ratio.
The main difference between Sharpe Ratio and Sortino Ratio lies in the definition of volatility.
In the Sharpe Ratio volatility is measured through the standard deviation of the returns of the financial instrument. This means that both positive and negative swings are included in the volatility.
However, does it make sense to consider positive swings in risk? In some cases yes, in others no.
Generally speaking, when we talk about risk we are talking about drawdowns, price drops. Since the Sharpe Ratio is unable to capture the difference between positive and negative fluctuations, the Sortino Ratio was introduced.
Contrary to what happens for the Shape Ratio, in which both positive and negative fluctuations are included in the term “risk”, for Sortino Ratio risk is measured by taking into account only negative fluctuations. This makes the Sortino Ratio more suitable for determining the actual risk and, consequently, evaluating the risk-return ratio.
But how does the Sortino Ratio work specifically? How is it calculated?

How to calculate the Sortino Ratio

The Sortino Ratio is defined as the difference between the investment returns and a set target return, divided by the “negative deviation”.
In more scientific terms, the "negative deviation" is defined as the square root of the semi-variance calculated with respect to a target return.
In formulas the Sortino Ratio is:

S = ( R - T ) / ( DR )
Where:
S = the Sortino Ratio of the financial instrument under analysis
R = the annual return of the financial instrument under analysis
T = the target annual return
DR = downward deviation or "downside risk"

When to use the Sortino Ratio

The Sortino Ratio tries to characterize how efficiently the return of an asset compensates the investor for the risk taken. For example, when comparing two assets, the one with the highest Sortino Ratio generally provides a better return for the same risk and is therefore more attractive to investors.
However, as we will see in the following chapters, it is not always so easy to evaluate the quality of an investment just by looking at the Sortino Ratio.

How to interpret the Sortino Ratio

The Sortino Ratio measures the risk-adjusted return of an asset, portfolio or investment strategy.
The Sortino Ratio is also used as a method to compare the risk-adjusted performance of financial instruments with different risk and reward profiles. Thanks to the normalization with respect to the “downside risk”, it helps to identify which instruments and which strategies have the best performance at the same risk level.
However, the Sortino Ratio is highly dependent on the conditions imposed for the calculation. This makes it almost impossible to define which are "good" or "excellent" values ​​for the Sortino Ratio. In fact, the Sortino Ratio is highly dependent on: the target return, the length of the "monitoring" period and the monitoring frequency.
For example, if we wanted to measure the Sortino Ratio of the S&P500, we could analyze the price action of the last 6 months or of the last 5 years; using the daily or weekly prices; setting a target return of 2% or 5%. The results would be completely different with the different timelines.
Hence the Sortino Ratio should be used only for comparisons, not as an absolute value.

Limits of the Sortino Ratio

The limits of the Sortino Ratio are:
  • Does not take into account the temporal distribution of gains and losses (having a completely negative or a completely positive period has a different psychological impact than continuous fluctuations)
  • Assumes returns have a normal distribution, which is unrealistic
  • The result depends a lot on the way the ratio is calculated (the target return, the observation period, the length of the observation period and the frequency of measurement of the returns)

Alternatives to the Sortino Ratio

Given the limits of the Sortino Ratio, in many cases it is easier and more convenient to use the Sharpe Ratio. As already discussed, the Sharpe Ratio does not take into account the difference between “positive volatility” and “negative volatility”. This is why the Sharpe Ratio represents a more general measure of the risk-return ratio.
Another variation of the Sortino Ratio is the Treynor Ratio. This indicator uses the Beta (a measure of the volatility and risk of an investment relative to the general market) of a portfolio as a benchmark for risk.
The Treynor Ratio is particularly useful in determining whether an investor is compensated for taking a higher risk than "market risk"