Sortino Ratio: Formula, Calculator, and Definition
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.
Named after Frank A. Sortino, the economist who created it, the Sortino Ratio is another performance metric for measuring an investment’s performance relative to the amount of risk involved.
The ratio is considered a variation of the Sharpe Ratio, but what exactly is it? One of the ratios for measuring risk-adjusted returns of a particular investment scheme, such as a mutual fund, the Sortino Ratio is a variation of the Sharpe Ratio that differentiates harmful market fluctuations 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.
What is the Sortino Ratio Definition?
The Sortino ratio is a financial metric used to evaluate the risk-adjusted return of an investment, portfolio, or trading strategy. It enhances the widely-used Sharpe ratio, focusing on downside risk rather than overall volatility.
The Sortino ratio is calculated by dividing the excess return (i.e., the return above the target) by the downside deviation, which measures the volatility of returns below the target. A higher Sortino ratio indicates a better risk-adjusted return, as it implies a higher return per unit of downside risk.
Sortino Ratio Calculator
How do you calculate Sortino Ratio?
To calculate the Sortino Ratio, you first determine the investment’s average return. Then, you subtract the risk-free rate of return. Finally, divide this result by the standard deviation of the negative returns.
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). Still, 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, often called downside deviation.
The standard Sortino Ratio formula is given as:
S = (R – T) / DR
Where:
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 ]
Where:
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 can be the yield on U.S. Treasury Bills or U.K. gilts depending on the market you are invested in. This simplified version is given as follows: To determine your investment portfolio’s target returns, you must consider the monthly returns and additional returns that may be obtained.
Sortino Ratio = (Rp – Rf)/σd
Where:
Rp = Actual or expected portfolio return
Rf = Risk-free rate of return
σd = Standard deviation of the downside returns
What is the Interpretation of the Sortino ratio?
The Sortino ratio measures an investment’s risk-adjusted return by focusing solely on downside volatility. It provides a more insightful interpretation of performance than the traditional Sharpe ratio.
By definition and interpretation, the Sortino ratio is a statistical tool that measures the performance of a mutual fund relative to the downward deviation. Unlike Sharpe, it doesn’t consider the upside volatility. It is obtained by subtracting the target rate of return or the risk-free rate of return from a fund’s expected or actual return and dividing it by the standard deviation of the downside returns. So, it is the extra return over and above the target or risk-free rate of return per unit downward risk for investors.
But why does the Sortino Ratio achieve by excluding the upside volatility? Well, upside volatility is what investors aim 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 investors, you already know that the risk in an investment scheme means the variation in the scheme’s returns. The more the returns fluctuate, the riskier the investment scheme is deemed to be. This volatility of an investment scheme’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.
What is a good Sortino Ratio?
A good Sortino Ratio indicates higher returns per unit of downside risk, typically above 1.0, signaling efficient risk-adjusted performance. Unlike the Sharpe Ratio where a score of one and above is considered very good, 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 Sortino ratio is particularly useful in assessing a portfolio’s acceptable return, as it considers the bad risk. It measures the excess return an investment earns relative to the minimum acceptable return.
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, the investment is not rewarded for taking on additional risk.
What is the significance of Sortino Ratio?
The Significance of the Sortino Ratio lies in its ability to measure the risk-adjusted return of an investment, specifically focusing on downside risk. It helps investors evaluate an investment’s performance relative to the volatility of its downside movements, providing a more targeted assessment compared to other ratios like the Sharpe 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. Additionally, it helps to determine the amount of additional returns an investment generates in relation to its downside risk.
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 is 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 the 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 produces 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 despite the bad risk associated with sell options.
What are some uses of Sortino Ratio?
The Sortino Ratio is used to evaluate the risk-adjusted return of an investment, particularly focusing on downside risk. It helps investors assess how well an investment performs relative to the downside volatility.
You can compare the Sortino Ratio for different portfolios to determine which delivered the greatest downside risk-adjusted return over a given period since the ratio measures excess return per unit of downside risk. The Sortino Ratio has been found very useful in finance 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 risk-free rate of return are given in the table below:
| Fund G | Fund H | |
| Average return last 4 years % | 28 | 18 |
| Downside deviation % | 18 | 10 |
| 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 has limited upside or downside potential, it is better to analyze it with the Sortino Ratio because, unlike 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. In contrast, a strategy with limited downside risk and unlimited upside potential is rightly favored with a high score.
What is the difference between the Sortino Ratio and Sharpe Ratio?
The difference between the Sortino Ratio and the Sharpe Ratio is that the Sortino Ratio only considers downside risk, while the Sharpe Ratio considers total volatility.
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. However, some people still use the risk-free rate of return to simplify the formula.
The Sharpe Ratio and the Sortino Ratio are both risk-adjusted evaluations of return on investment that are relevant to mutual fund investors. These ratios use a 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 (rf), which is important for investors who want to assess the performance of their scheme. Meanwhile, the Sharpe Ratio penalizes both upside and downside volatility equally, which may not be suitable for some investors.
What are the factors that can impact a portfolio’s Sortino Ratio?
Several factors can impact a portfolio’s Sortino Ratio. These include the choice of assets in the portfolio, their risk-adjusted returns, the frequency of returns, and the investor’s risk tolerance.
A few factors 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.
What is the Sortino Ratio and how does it differ from the Sharpe Ratio?
The Sortino Ratio, like the Sharpe Ratio, measures risk-adjusted return. However, unlike the Sharpe Ratio, which considers total volatility, the Sortino Ratio only factors in downside volatility, making it particularly useful for assessing investments with asymmetric risk profiles.
The Sortino Ratio is a performance metric named after economist Frank A. Sortino. It measures the risk-adjusted return of an investment, focusing solely on downside risk by using the standard deviation of negative returns. Unlike the Sharpe Ratio, which penalizes both upside and downside volatility equally, the Sortino Ratio specifically targets negative returns.
Why exclude upside volatility in the Sortino Ratio calculation?
Excluding upside volatility in the Sortino Ratio calculation focuses specifically on measuring an investment’s downside risk, providing a more accurate assessment of risk-adjusted returns by only considering downside deviation from the target return.
Upside volatility is excluded from the Sortino Ratio because it represents positive returns that investors aim to achieve. By focusing solely on downside risk, the Sortino Ratio provides a more accurate measure of risk-adjusted returns, making it a preferred choice over the Sharpe Ratio for many financial analysts.