Sortino Ratio: Is it better than Sharpe in judging MF performance?

Let us understand the logic of risk adjusted measure of returns.

Aug 10, 2020 08:08 IST India Infoline News Service

Mutual Funds
For a long time, the Sharpe ratio has been the benchmark for evaluating the risk adjusted performance of mutual funds, especially equity funds. Sharpe, essentially, calculates the risk adjusted excess returns. In other words, it calculates the returns earned by the fund over and above the required rate of return and then divides this by the standard deviation of the fund returns. Let us understand the logic of risk adjusted measure of returns.

If two equity funds earn 14% and 16%, which is better? Obviously, you will say that the fund giving 16% is better. Suppose, you were also told that the first fund has 15% standard deviation while the second fund has 35% standard deviation, then you would rethink your decision. That is captured by the Sharpe ratio and it is a useful measure. However, Sharpe considers all deviations from the mean; positive and negative. However, positive deviations are not risk and only negative deviations are risk. That is captured by the Sortino Ratio. Instead of using standard deviation, the Sortino Ratio only uses the downside deviations.

What is the Sortino Ratio all about?

The Sortino ratio is a tool that measures performance of mutual fund relative to the downward deviation. Here the focus is only on downside deviation. If you bought a stock at Rs.550, then the price going to Rs.600 is not a risk but the price going to Rs.510 is a risk. That in a nutshell, is what Sortino ratio is all about.  Unlike Sharpe, the Sortino does not consider total volatility, but just the downside volatility. Therefore, the Sortino Ratio gives you a quick snapshot of how the fund balances risk and reward. It can be more precise measure of risk as it only considers the downside deviations.

Understanding the Sortino numerator and denominator

Let us first focus on the numerator of the Sortino. The numerator represents the fund's excess returns as calculated on a monthly basis, measured as the difference between the actual portfolio return and the expected return. This is what the fund is earning over and above what the investor should be ideally earning.

In the case of the Sortino, the denominator will only use the negative deviations rather than looking at all deviations. In a nutshell, the Sortino ratio's denominator aims to focus only on undesirable downside deviations. The process of calculating the downward deviation is the same as the standard deviation. The only difference in Sortino is that all positive return cases are equated to zero and only the negative deviations are summed up. That gives a much better picture of risk to the investor.

Before looking at the actual Sortino calculations, when can Sortino be used? The thumb rule is to use Sortino only when the period under consideration is too volatile or when the fund category is too volatile. In other instances, the Sharpe can give a good enough picture.

How is the Sortino ratio calculated?

Let us consider an illustration of 12 monthly return data points of a fund over a one year period. Check the table below. The investor is expecting 0.50% returns per month.

Expected Return 0.50%
Month Returns Excess Return Negative Excess Returns Square of (Negative Excess Returns)
1 0.50% 0.00% 0.00% 0.00%
2 0.40% -0.10% -0.10% 0.00%
3 0.10% -0.40% -0.40% 0.00%
4 2.30% 1.80% 0.00% 0.00%
5 -0.80% -1.30% -1.30% 0.02%
6 2.55% 2.05% 0.00% 0.00%
7 2.95% 2.45% 0.00% 0.00%
8 -2.30% -2.80% -2.80% 0.08%
9 -1.30% -1.80% -1.80% 0.03%
10 6.00% 5.50% 0.00% 0.00%
11 4.00% 3.50% 0.00% 0.00%
12 -2.30% -2.80% -2.80% 0.08%
Total 6.10% -9.20% 0.21%
Downside Risk = √(∑(Square of Negative Excess Returns) / No. of months)
Downside Risk 0.0131593
Average Excess Return = Sum of Excess Return / No of Months
Average Excess Return 0.508%
Sortino Ratio= Average Excess Return / Downside Risk
Sortino Ratio 0.386

The above sheet clearly demonstrates how the downside deviations can be separated and the Sortino can be calculated to give a more precise and granular picture of risk adjusted returns of a mutual fund portfolio.

How do Indian mutual funds rank on Sortino ratio?

Let us take the example of the top funds ranked on Sortino among multi-cap funds.

Fund Name Sharpe Ratio Sortino Ratio Alpha
Parag Parikh Long Term Equity 0.28 0.26 5.59
IIFL Focused Equity 0.21 0.22 6.13
SBI Focused Equity 0.21 0.22 5.09
Axis Focused 25 0.18 0.18 4.69
Quant Active Fund 0.14 0.18 3.88
Axis Equity Advantage 0.16 0.17 2.48
Canara Robeco Equity 0.15 0.16 3.65
  Data Source: Value Research

One reason the Sortino is yet to pick up is that the actual comparative output tends to match with Sharpe in most cases. However, in specific cases of high volatility periods or for high risk funds, the Sortino can give a smarter and more elegant analysis.

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