How do we know markets are efficient? But before that, what is market efficiency? Market efficiency as a concept championed by Eugene Francis Fama basically states that the market absorbs all available information and incorporates it in the price. If this concept were true, all of us should stop this treasure hunt of picking undervalued stocks and invest in index funds. Index funds have been gaining popularity ever since investors realized that they could get better returns at cheaper cost. But can they? Are markets really efficient? How difficult is it to beat the market?

I decided to evaluate the performance of the top 34 multi cap equity mutual funds who have been around for 5 years and compare it to an index fund. The idea is to gauge the efficiency of India markets and also figure out the destination of your next SIP (maybe). So, let’s look at the performance of the funds in the last 5 years:

So far so good, next I observed the mean and median performance against an average nifty etf fund. The results are shown below:

For a symmetric distribution the average is a better indicator than the median but since this isn’t a symmetric distribution, we must look at the median. I then ran a regression of the median performance against the nifty etf performance.

**Regression Result:**

The R squared is more than 92 percent which indicates that market movements explain the performance of equity mutual funds 92 percent of the times. Any stock picking skills that fund managers might or might not have account for 8%. The very high t statistic indicates that the null hypothesis that there is no relation between the two is rejected. I now lead you to observe the intercept and slope of the regression given by the two coefficients.

**Jensen’s Alpha:**

The intercept indicates how well the mutual funds have done in the past and the slope gives the covariance of the mutual fund performance against the index. Hence if we compare the regression equation to the capital asset pricing model equation we get:

where,

Rj- Median multi cap equity mutual fund performance

Rm- Market Return or in this case average Nifty ETF return

Rf- Risk free rate

a- regression intercept

b- slope of the regression line

Jensen’s alpha is basically a measure performance relative to the market by subtracting Rf(1-b) from a. Any number greater than zero signifies over-performance and a value less than zero signifies under-performance with respect to the market. I estimated the risk-free rate at 5.16% using the 5 year government bond yield and computed Jensen’s alpha at -2.9%.

**Conclusion:**

With better data and advanced analytics, you would expect mutual funds to do better than simple index funds but the data indicates that this isn’t so. If you are a long term investor with little patience for statistics I leave you with this final analysis. In the last 5 years the nifty 50 index fund has given superior returns than 90% of multi-cap equity mutual funds.