Last Updated on December 18, 2021 at 10:41 pm
Mutual fund star ratings are supposed to rate funds on a risk adjusted basis. That is, more the number of stars, better the risk-adjusted performance. If you look at some of the metrics they use to award star ratings, you might agree with me that this is not as easy as it sounds and that the ‘best’ funds need not necessarily carry five stars.
First some simple definitions
1. Beta is a volatility measure and tell us how much the fund changes for a given change in the index. A beta of 1 implies the fund movement is identical to the index movement. A beta of 0.9 implies the fund is 10% less volatile than the index.
Lower the beta, lower the volatility
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2. Standard deviation is a volatility measure and tell us, for a given set of returns (daily returns in this case), how much do individual returns deviate from the average. This is calculated for both the fund and the benchmark.
Lower the standard deviation, lower the volatility
3. Alpha is a risk adjusted performance measure. It takes into account, the average return of the fund and its benchmark, a risk-free rate defined by the user and how the fund responds to swing in the benchmark (Beta)
Higher the alpha, higher the outperformance of the fund.
4. Sharpe ratio is a risk adjusted performance measure. We calculate the excess returns of the fund wrt a risk-free rate. The ratio is the average of the excess return and the standard deviation of the excess return. This is calculated for both the fund and the benchmark.
Higher the Sharpe ratio, better is the performance (higher returns + low deviation from average return)
5. Sortino Ratio is a risk adjusted performance measure. The Sharpe ratio considers both positive and negative excess returns (wrt risk free rate). The Sortino ratio considers only the negative excess returns while calculating the standard deviation. There should be enough negative excess return data points to justify the use of the Sortino ratio. To take care of this, daily returns are used (instead of monthly returns as done by AMCs/fund portals).
Higher the Sortino ratio, better is the performance (higher returns + low negative deviation from average return)
The next step is to understand that these metrics are not independent
The following is based on data for all equity funds, except sector funds from Value Research online. The metrics are computed over a 3 year period.
Higher the standard deviation, higher the beta, typically.
Higher the Sharpe ratio, higher the Sortino ratio, typically.
Higher the Sharpe ratio, higher the alpha, again typically.
Now let us look at these metrics wrt star ratings
Standard deviation vs. Star Ratings
Try to ignore the red box first! Notice that several one star funds have comparable standard deviation with 5 star funds.
The red box is a filter. It aims to filter funds that have a standard deviation no higher than 5 star funds. About 20%. All funds above this box are eliminated for risk vs. reward analysis (see below).
Sharpe Ratio vs. Star Ratings
About 50% of two star funds have comparable Sharpe ratios with five star funds. The red box this time eliminates all funds which have Sharpe ratio below five star funds. That is, all points below the box are eliminated for risk-vs. reward analysis.
3-year return vs. Star ratings (filtered)
After applying both red box filters mentioned above, the 3-year return vs. star ratings is shown below.
There is one 1-star fund and several 2-star funds that have a risk-adjusted profile similar to 5 star funds!
3-year Alpha vs. Star ratings (filtered)
After applying both red box filters mentioned above, the 3-year alpha vs. star ratings is shown below.
Again, the conclusions are the same as the above graph.
Risk vs. Reward (full data set)
Return (reward) vs. risk (standard deviation) for the full data set. There is no correlation. Higher risk does not mean higher reward!
Risk vs. Reward (filtered)
Return (reward) vs. risk (standard deviation) for the data set filtered with two red boxes (no standard deviation more than 5 star funds, no Sharpe ratio less than a 5 star fund). Now the correlation has improved (the data bunch slopes up) but it is still quite poor.
Risk vs. Reward (3,4 and 5 star funds only)
Return (reward) vs. risk (standard deviation) for all funds except 1-star and 2-star funds. The correlation is still poor. More stars does not necessarily mean better risk adjusted performance.
Sharpe Ratio vs. Star Ratings (a new filter)
Let us now try another kind of filer. Let us now push the red box up and eliminate all funds which have a Sharpe ratio lower than the highest value observed for a 2-star fund. That is all points below the box are eliminated. This means eliminating most 3-star funds, many 4-star funds and a handful of 5-star funds.
Risk vs. Reward (with the new filter)
Notice now that the correlation between risk and reward has improved after eliminating some 3,4 and 5 star funds. This is only 28% of the full data set!
I am not proposing a method of correlating risk and reward. The indisputable truth is that they cannot be correlated.
The point I am trying to make is,
do not assume, higher star rating implies better risk adjusted performance.
So I choose to not depend on star ratings at all. I prefer to focus on long-term consistent performance.
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