SQM Research Newsletter and Ratings Update - May 2022

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Sorting Out The Sortino Ratio

by Rob da Silva, Head of Research

I recently read an interesting treatise on the Sortino ratio and its merits as a measure of risk-adjusted return. This month we will pop down that rabbit hole and take a little look.
The Sortino Ratio is a variation on its much better known and more widely used cousin, the Sharpe Ratio.
Sharpe Ratio =                      (Fund Return minus Risk-free Rate)
                                               Standard Deviation of Fund Returns
Sortino Ratio =                       (Fund Return minus Risk-free Rate)
                                               Downside Deviation of Fund Returns
As Wikipedia describes it:
“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—downside deviation—instead of the total standard deviation of portfolio returns. The Sortino ratio takes an asset or portfolio's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.”
The discussion below is informed by analysis of 411 managed funds across the following markets – Australian Equities (Large and Small Cap), International Equities (Large and Small Cap), Emerging Market Equities, A-REITs, G-REITs and Global Infrastructure.
The Sortino Ratio is often described as a superior measure of risk-adjusted return because it focuses on downside risk rather than total risk (or volatility). The field of behavioural finance research has convincingly established the principle that investors feel the pain of loss more keenly than the joy of gain. This is the basis of the Sortino Ratio’s advantage because it focuses on downside (i.e., loss) volatility which is what investors care about.
Since the top lines of the Sharpe and Sortino ratios are the same, the difference really comes down to the merits of the denominator risk measures i.e., total volatility versus downside volatility.
Let’s look at those differences:
Sample Size
For any time frame (but particularly for shorter time frames) downside volatility is going to be statistically less robust and reliable as an estimate of risk. Why? Because it uses only about a third of the data points that is used for total volatility.
By their very nature any market that provides positive long-term returns (i.e., just about all of them) will have many fewer instances of negative returns than positive returns. For risk markets, our data shows about 30 to 35% of all monthly returns are negative. So, calculating a three-year Sortino Ratio only uses around 11-13 months of data for the downside deviation estimate while a Sharpe Ratio uses 36 months of data for total volatility. Statistically speaking when it comes to the robustness and accuracy of any estimate, the general rule is “more data is better than less data”
The table below shows this data difference using 20 years of history for the ASX 300 Index.
The Volatility of the Downside is not the Same as the Size of the Downside
Volatility measures the amount of variation in a variable, not the average size of a variable. Investors likely care more about how much they lose than they care about how volatile those losses are.
A constant loss of 3% per month should be more ‘painful’ than a volatile loss that averages 1% per month.
Ok, that seems reasonable – but shouldn’t the volatility of the downside be closely linked to its size? Won’t one be a good proxy or representation of the other?
The answer is – not so much.
Take a look at the chart below. It plots our 411 funds with Downside Volatility (x-axis) versus Downside Capture, i.e., size of losses (y-axis)
There is basically no relationship – the R^2 is virtually zero. The volatility of the downside (used in Sortino) does not appear to tell you anything about the size of the downside, which is what should really matter.
Ranking the Risk – Downside Volatility versus Total Volatility
If you rank our 411 funds by both these risk measures, the two lists are not the same, but there sure is a strong relationship between the two. See the chart below where D.Vol-Rank = risk ranked by downside volatility (Sortino) and Vol-Rank = risk ranked by total volatility (Sharpe). You can see that they are closely related, with an R^2 of over 81%
How much Difference is There between Sharpe and Sortino?
Answer – it depends, but mostly, not a huge difference.
If you rank the 411 Funds by Sortino Ratio and look at the Top 10, you will see 6 of those Funds also appear in the Top 10 when ranked by Sharpe Ratio. So, there is a 60% overlap!
The table below shows the average characteristics of the Top 10 funds sorted by A. Sortino Ratio and B. Sharpe Ratio,
There are some interesting observations to be made from this table:
  • The volatility of the Sortino list is higher than the Sharpe list
  • The betas are virtually the same
  • The worst month and downside volatility are better for the Sortino list….BUT
  • The downside capture is actually higher for the Sortino list – not what you’d expect
In summary, the Sortino Ratio has some additional information and merit as a risk measure when compared with the Sharpe ratio. BUT the marginal utility of that additional information is somewhat limited. It appears there are not huge gains to be had from using the Sortino Ratio.
Don’t look for the Sharpe Ratio to be usurped from its widely-used popularity anytime soon.
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