Investors invest in actively managed mutual fund schemes in a hope to generate superior returns as compared to overall returns provided by market i.e. an index. While choosing a fund, investors generally compare, on an average how much alpha fund has generated over its benchmark. Yes, actively managed funds are beating its benchmark.

**But are these funds appropriately benchmarked ? Is the alpha really significant ? Analysis of T-Statistics, help in checking whether the alpha is significant or it is by chance?**

You may like to read this article to know more about how T-Statistic is calculated and what it revels. We also encourage you to read these two articles to know more about T-statistic – Article 1, Article 2 & its application in mutual fund performance analysis.

Broadly, T-statistic is calculated considering alpha generated and standard deviation of alpha for a given period. T-statistic of 2 indicates that the average is statistically significant and that one can be 95% confident that the average alpha did not occur by chance. With a T-statistic of 2 or more, there is still 5% probability that the true value of the average is zero. In simple terms, if T-statistic is 2 or higher one can be 95% confident that average alpha did not occur by chance, however still there can be 5% probability that alpha is due to luck or chance.

We have tried to analyse performance and significance of alpha generated by 83 funds i.e. 21 large cap funds and 62 multi cap funds. We compared these 83 funds with ICICI Prudential Nifty Next 50 Index Fund, as it is well diversified large cap fund. As on October 31, 2016 this fund has 91% exposure to large cap stocks and 9% to mid cap stocks. As ICICI Prudential Nifty Next 50 Index Fund was launched in June 2010, we have selected 83 funds out of 355 funds which have its daily NAV published since June 2010. For all the funds we have considered Growth Option of Regular Plans.

Yearly returns of each of these funds are calculated, being first period from July 1, 2010 to June 30, 2011 second period from 2011 to 2012 up to 2015 to 2016. Thus we have 6 yearly return data points for each of these funds. Further, we calculated alpha of each of these funds over ICICI Prudential Nifty Next 50 Index Fund for each of these periods. Finally T-Statistics is calculated considering average alpha, slandered deviation of alpha and number of data points using the formula **( Average Alpha x Square Root of Number of observations ) / Slandered Deviation of Alpha.**

**Example:** In this example on an average Franklin India Bluechip fund has generated 1.17% of alpha over ICICI Prudential Nifty Next 50 Index Fund i.e. actively managed fund has beaten passively managed fund by 1.17%. The fluctuation of beating up index fund i.e. standard deviation is 7.36%. Basis 0.39 of T-Statistic of these alpha, one can conclude that alpha might be due to sheer luck or chance.

**T-Statistic Comparison of 21 are large cap and 62 are multi cap funds**

Out of 21 large cap funds only 1 fund has T-Stat above 2, and out of 62 multi cap funds only 5 funds has T-Stat above 2. Further, 11 large cap & 22 multi cap funds has negative alpha. Balance 9 large cap & 35 multi cap funds has generated postive alpha but that alpha is NOT significant i.e. alpha is generated by chance.

Summary is provided below.

Click here to download full calculation

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Nice study quantum long term is not in the list

Why quantum long term equity fund is not in the list.

Thanks Sadashiv for pointing. Quantum Long Term Equity Fund got excluded as we have considered only Regular Plans of all the funds and Quantum only has direct plans. However I have included it now. On an average it has generated 3.06% of alpha with standard deviation of 7.92% and T-Stat of 0.95.

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Please include a few balanced funds (hybrid-equity oriented) in this study as some of them have given better returns than pure equity funds, whether it be large cap, multi-cap or mid-caps too over the long term.

Good study.Can you please tell the difference between The statistic and Sharpe/ Sortino ratios.

Also L&T India Value fund & ICICI Value discovery not included. Similarly ELSS funds and balanced funds

The Sharpe ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk.

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 asset returns, called downside deviation

T-Statistics is use for null-hypothesis. E.g. in Mutual Funds it is used to know if the alpha generated is due to skill or luck. I have provided two links in the article if you wish to understand it in more detail.

Have not included ELSS and Balanced funds, as these are used for different purpose and can not be compared with Pure Equity Funds.

L&T India Value fund & ICICI Value discovery was not included as it did not met the selection criteria at that point of time.

Thank you for the reply