Last Updated on May 18, 2022 by Quantified Trading
Named after Frank A. Sortino, the economist that created it, the Sortino Ratio is another performance metric for measuring the performance of an investment relative to the amount of risk involved. The ratio is considered a variation of the Sharpe Ratio, but what exactly is it?
Sortino Ratio is a performance metric that measures the risk-adjusted return of an investment using only the downside risk. Considered a variation of the Sharpe Ratio, Sortino Ratio uses only the standard deviation of the negative returns as its risk measure in the calculation. A good Sortino Ratio is one with a score of 2 or above.
In this post, we will discuss the following:
- What the Sortino Ratio is
- How it is calculated
- The significance of the ratio
- How the ratio is used
- The difference between the Sortino Ratio and Sharpe Ratio
- Factors that can impact a portfolio’s Sortino Ratio
What is the Sortino Ratio?
One of the ratios for measuring risk-adjusted returns of a portfolio, the Sortino Ratio is a variation of the Sharpe Ratio that differentiates harmful volatility from total overall volatility by using the asset’s standard deviation of negative portfolio returns, called downside deviation, instead of the total standard deviation of portfolio returns.
The Sharpe Ratio and the Sortino Ratio are both risk-adjusted evaluations of return on investment and make use of similar formula, so the Sortino Ratio is a variation of the Sharpe. As a modification of the Sharpe Ratio, Sortino Ratio penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe Ratio penalizes both upside and downside volatility equally.
By definition, the Sortino ratio is a statistical tool that measures the performance of an investment relative to the downward deviation. Unlike Sharpe, it doesn’t consider the upside volatility. It is gotten by subtracting the target rate of return or the risk-free rate of return from the expected or actual return of a portfolio and dividing it by the standard deviation of the downside returns. So, it is the extra return over and above the target rate of return or risk-free rate of return per unit downward risk.
But why does the Sortino Ratio achieve by excluding the upside volatility? Well, upside volatility is what investors are aiming to get when investing in a portfolio, so it should not be seen as a risk to the portfolio, which is why it is excluded from the equation. Because of this, many financial analysts believe that the Sortino Ratio is a better measure of risk-adjusted returns than the Sharpe Ratio.
As you already know, the risk in a portfolio means the variation in the portfolio’s returns. The more the returns fluctuate, the riskier the portfolio is deemed to be. This volatility of a portfolio’s returns is measured with the standard deviation of the returns over a given period. While the Sharpe Ratio considers both the upside and downside returns, the Sortino Ratio considers only the downside returns.
How to calculate Sortino Ratio
Sortino ratio is a statistical tool to measure the risk-adjusted performance of an investment portfolio relative to the standard deviation of negative asset return, also called the downward deviation. It is calculated by dividing the difference between the portfolio’s return and the risk-free rate of return or the target rate of return with the standard deviation of the negative returns. The numerator of the Sortino ratio equation is normally your portfolio’s return minus the target rate of return, previously known as the minimum acceptable return (MAR), but some analysts simply use the risk-free rate as the minimum acceptable rate of return. The denominator is the standard deviation of the negative returns, which is often referred to as downside deviation.
The standard Sortino Ratio formula is given as:
S = (R – T) / DR
S = Sortino Ratio
R = Portfolio or strategy’s average realized return
T = the required rate of return
DR = the target downside deviation / “downside risk”
And DR is given as:
DR = √[ ∫ (T – r)2 f(r) dr ]
T = the required rate of return
r = Return for the distribution of annual returns, f(r)
f(r) = Probability distribution of annual returns
However, most financial analysts simplify the calculation by using the risk-free rate of return, which depending on the market you are invested in, can be the yield on U.S. Treasury Bills or U.K. gilts. This simplified version is given as:
Sortino Ratio = (Rp – Rf)/σd
Rp = Actual or expected portfolio return
Rf = Risk-free rate of return
σd = Standard deviation of the downside returns
Grading the Sortino Ratio: What is a good Sortino Ratio?
Unlike the Sharpe Ratio where a score of one and above is considered good enough, for the Sortino ratio, most financial analysts prefer a score of two or above but some may still accept a score of one and above.
The higher the Sortino Ratio, the better because a higher value indicates that the portfolio is more efficient and does not take on unnecessary risk without being rewarded with higher returns. When the Sortino Ratio is very low or negative, it means that the investment does not get rewarded for taking on additional risk.
The Significance of Sortino Ratio
The Sortino Ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy using only the downside risk. So it is a useful way for analysts, portfolio managers, and retail investors to evaluate an investment’s return per unit of bad risk over a specified period of time.
Because the Sortino Ratio uses only the downside deviation as its risk measure, it excludes the upside volatility, which is beneficial to investors and should not be considered a risk. Hence, it addresses the problem inherent in using total risk or standard deviation of both the positive and negative returns in calculating a risk-adjusted return as it’s the case with the Sharpe Ratio.
As you would expect, the central purpose of risk management is to avoid large downside risk, and the measures used to describe risk should reflect that. So, penalizing both positive and downside risk, as it’s done in Sharpe Ratio, is flawed. With the Sortino Ratio, only the returns that fall under a user-specified target or required rate of return are considered risky. Hence, a portfolio or strategy that is producing strong upside moves and lower downside moves will have a better risk-adjusted score using the Sortino Ratio than with the Sharpe Ratio.
Therefore, it is better to use the Sortino Ratio when analyzing strategies/portfolios that have a positive skew in their performance distributions, such as buy options, since it will rightly give them better scores. On the other hand, portfolios/strategies that are capped on the upside (with negative skews), such as sell options that have streams of small, positive, and consistent returns but with potential for large, though infrequent negative returns, are duly penalized by the Sortino Ratio. If it’s the Sharpe ratio, it would treat them equally.
The uses of Sortino Ratio
You can compare the Sortino Ratio for different portfolios to find out which delivered the greatest downside risk-adjusted return over a given period since the ratio measures excess return per unit of downside risk. In finance, the Sortino Ratio has been found very useful in many ways, but here, we will only consider a few examples.
1. Comparing funds
Let’s say that you want to compare the performance of two mutual funds on a risk basis. We call the first one Fund G and the second one, Fund H. Their average returns, downside risk, and the risk-free rate of return are given in the table below:
|Fund G||Fund H|
|Average returns in the last 4 years||28% per annum||18% per annum|
|Risk-free rate of return||4%||4%|
The Sortino Ratio of each fund can be given as:
Fund G: (28% – 4%)/18% = 1.3
Fund H: (18% – 4%)/10% = 1.4
Hence, Fund H is a better investment because it earns more returns than Fund G, per unit of downside risk taken.
2. Analyzing the risk-adjusted returns of strategies that cap the upside or downside volatility
When an investment strategy is such that the upside or downside potential is limited, it is better to analyze it with the Sortino Ratio because unlike the other ratios that treat the upside and downside volatility equally, the Sortino Ratio focuses on the real risk, which is the downside volatility.
By focusing on the downside risk, a strategy that limits the upside potential but has an unlimited downside risk is rightly penalized with a low score, while a strategy with limited downside risk and unlimited upside potential is rightly favored with a high score.
The difference between the Sortino Ratio and Sharpe Ratio
The Sortino Ratio is a variation of the Sharpe Ratio, and the difference between the two is that the Sortino Ratio removes the effects of upward price movements to focus on the distribution of the negative returns. In other words, Sortino Ratio uses only the standard deviation of the negative returns, while the Sharpe Ratio includes the positive returns in its calculation, thereby punishing upside returns which is what the investors are after in the first place.
Another difference is that the main formula of the Sortino Ratio uses the target/required return, instead of the risk-free rate of return, in the numerator of the formula. However, some people still use the risk-free rate of return to simplify the formula.
Factors that can impact a portfolio’s Sortino Ratio
There are a few factors that can significantly affect a portfolio’s Sortino Ratio, giving you a false result. One of them is the timeframe used in analyzing the portfolio returns. The period for consideration must be multiple years and in fact, it should cover a complete business cycle. If you consider a short duration in your analysis, you will get a false result because the market may be in a bull phase with mostly positive returns or a bearish phase with mostly negative returns. So, it’s better to consider a full business cycle to get the real value of the Sortino ratio.
Another factor that can influence the Sortino Ratio is the liquidity of the underlying assets in a portfolio. A portfolio can seem to have a low-risk score simply because the underlying securities in the portfolio are illiquid. For example, small-cap stocks or investments in privately held companies, which are not frequently priced, tend not to fluctuate that much. So, if your portfolio has a high concentration of these type of assets, the portfolio’s Sortino Ratio can be artificially high, making you think that your risk-adjusted returns are good, while they may not be that good.