Sortino ratio explained
You can compare the Sortino ratio for different portfolios to find out which delivered the greatest downside risk-adjusted return over a given timeframe.
What is the Sortino ratio?
The Sortino ratio is similar to the Sharpe ratio but with a twist. If you want to calculate a portfolio’s risk-adjusted return, but only want to consider its downside risk (by excluding upside risk), then the Sortino ratio is the more suitable measure to use.
The more widely known Sharpe ratio takes a portfolio return, subtracts the risk-free rate and divides the difference by the investment’s total volatility. This allows for comparability across different portfolios to see which rewarded investors the most per unit of risk taken.
But why would you want to exclude upside volatility by using the Sortino ratio? Many financial analysts believe that the Sortino ratio is a better measure of risk-adjusted returns since upside volatility is what investors should look to target, and so this type of volatility shouldn’t be seen as negative and therefore be excluded from the equation.
Going back to basics, when we speak about risk or volatility, we are talking about the variance of a portfolios returns. The further a share price fluctuates, the riskier it is deemed to be. The volatility of a portfolio’s returns is measured taking the standard deviation of the returns over a certain period.
The Sortino ratio is calculated by taking the difference between portfolio return and the risk-free rate and dividing this by the standard deviation of the negative returns.
Sortino ratio formula
The formula for the Sortino ratio is:
Or in plain English:
The portfolio’s return is measured over a certain time period. This can be the actual returns for the portfolio or the expected return in the future.
The risk-free rate is the return that you can expect from taking on zero risk. Many investors use a short-term government bond, such as the yield on US Treasury bill or UK gilts.
A portfolio’s downside deviations is measured by taking the standard deviation of only the negative returns witnessed over the time period.
How to calculate the Sortino ratio
The numerator of the Sortino ratio equation is simply your portfolio’s return minus the risk-free rate. This is also known as Jensen’s alpha.
To calculate the denominator, there are some calculations that you’ll need to make in Excel. Below contains a step by step guide using last year’s returns on the FTSE 100 index. The cell ranges in the formulas below reference the table below. For instance, 'Month' in the top left of the table lies in cell A1.
Table 1: Monthly return data
|A1: month||B1: index||C1: return||D1: downside returns|
Step 1: calculate your portfolios monthly returns
This is the end value for month t divided by end value of month t-1. In the table below, the return for February in cell C3 = 6175.04 / 6392.10 – 1 = -3.40%
Step 2: calculate the total return over the period
This is the product of your monthly returns. In Excel, the formula is an array function, so you will need to press Ctrl + Shift + Enter to calculate it. The formula based on the cell positions for the table above is =PRODUCT(1+(C2:C13))–1
The total return for the FTSE 100 over the year was -8.73%. This was a particularly poor year for global stock markets after a ten year bull market.
Step 3: find standard deviation of negative returns:
In column D, copy the return in column C but replace any positive returns with zeros.
Then use the standard deviation function in Excel on the downside returns in column D. The formula is =STDEV(D2:D13)*(12^0.5)
Multiplying the standard deviations by (12^0.5) annualises the output, which is important for calculating for the Sortino ratio. The standard deviation of the negative returns in this example is 5.95%.
Step 4: choose your risk-free rate
In our example below, we used a rate of 0.5%, which is the annual return you may expect if you held cash in the bank. You could have also used the yield on a short-term government bond, a minimum acceptable rate of return or even just 0%, which implies you are happy as long as your returns are positive.
Step 5: calculate the Sortino ratio
Using your total return, the risk-free rate and the standard deviation of downside returns, as calculated above, we can now compute the Sortino ratio.
What is a good Sortino ratio?
A higher Sortino ratio is better than a lower one as it indicates that the portfolio is operating efficiently by not taking on unnecessary risk that is not being rewarded in the form of higher returns. A low, or negative, Sortino ratio may suggest that the investor is not being rewarded for taking on additional risk.
In the case above, the FTSE 100 underperformed the risk-free rate in the year. But it is important to look at risk and returns over multiple years to get a true reflection of a portfolio’s risk and return profile.
Sortino ratio vs Sharpe ratio
Whether you use the Sortino or Sharpe ratio to calculate an investment’s risk-adjusted return is solely based on if you want to consider total volatility using the standard deviation or the downside volatility using the downside deviations (excluding the deviations on upside returns). Financial analysis is not a strict science, and analysts are free to use their own judgement to decide which calculation best supports their investigation.
Sortino ratio example
As discussed above, it is important to calculate risk-adjusted returns over multiple years. The table below gives actual data for the Sharpe and Sortino ratios for the FTSE 100 index and four of our IG Smart Portfolios. The risk-free rate we’ve used in the calculations is an annual return of 0.5%, similar to what you can expect to receive on the average cash ISA account.
Figure 1: FTSE 100 versus IG Smart Portfolios: 29 August 2014 to 29 March 2019
|FTSE 100 index||Conservative||Moderate||Balanced||Growth|
|Downside stantard deviation||5.5%||1.0%||2.4%||3.5%||4.5%|
*As of 18 April 2018
Our range of Smart Portfolios are actively managed and investment decisions are based on research from BlackRock. IG Smart Portfolios were launched in February 2017 and return data before this date excludes fees. As the data shows, all four of these portfolios have Sharpe and Sortino ratios that are above those for the FTSE 100 index. This is because the portfolios invest in a mix of equities and bonds from across the world. This diversification across asset classes and regions of the global economy helps to reduce portfolio risk, as shown by lower standard deviations and downside deviations compared to the FTSE 100.
Since the portfolios were first launched by BlackRock in August 2014, the bond market has outperformed equities on a risk-adjusted return basis. This is shown in the table above with our more fixed income focused portfolios (Conservative, Moderate) displaying higher Sharpe and Sortino ratios than our other portfolios with higher weights in equities (Balanced, Growth).
We have not included our aggressive portfolio in this analysis since as it was created in 2017 by BlackRock for IG clients, and so does not have a long enough track record to compare Sharpe and Sortino ratios with the other portfolios. But since it holds a higher proportion of equities, over the longer term it would be reasonable to expect greater volatility and higher returns compared to the other portfolios.
What can impact a portfolio’s Sortino Ratio?
A key consideration is the timeframe used to analyse portfolio returns. The period used should be multiple years and ideally cover a complete business cycle. Covering only a period of positive stock returns will hide the true risk of your investment and consequently inflate the Sortino ratio.
Another factor that needs to be considered is the liquidity of the underlying holdings in a portfolio. A portfolio may appear to have low risk statistics, but this could be due to the underlying investments that it holds being illiquid. Small cap stocks or investments in privately held companies which do not price regularly are examples of potentially illiquid investments. If these are included in a portfolio, they could artificially improve its Sortino ratio, making your risk-adjusted returns appear better than they actually are.
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