## Mutual Fund performance: luck vs skill

Robert Kosowski, Allan Timmermann, Russ Wermers, and Hal White ( usually abbreviated as KTWW) (2006) conducted an examination of mutual fund performance to know whether managers have superior stock picking skills or they just happen to perform better than others merely due to luck. They applied several different bootstrap approaches to analyze the significance of the alphas of extreme funds, that is, funds with large, positive estimated alphas. They conclude that the alphas of the top 10% of funds are more likely to be an outcome of managers’ superior skills to pick good stocks.

### Implementation of the bootstrap approach

Kosowski et al. (2006) use estimated alphas and estimated *t*-statistic in their bootstrap tests. The bootstrap procedure is applied using CAPM, the four-factor model of Carhart, the three-factor model of Fama and French, and several other models. To show the implementation of the bootstrap approach, they use the Carhart model with the following steps

1. Compute ordinary least squares (OLS)-estimated alphas, factor loadings, and residuals using the time series of monthly net returns

2. Then, for each fund, draw a sample with replacement from the fund residuals that are saved in the first step above, creating a pseudo–time series of resampled residuals

3. Next, construct a time series of pseudo–monthly excess returns for each fund, imposing the null hypothesis of zero true performance

4. Repeat the process 1000 times to create 1000 bootstrap alphas and *t*-statistics

5. If we find that the bootstrap iterations generate far fewer extreme positive values of estimated alphas and *t*-statistics compared to those observed in the actual data, then we conclude that sampling variation (luck) is not the sole source of high alphas, but rather that genuine stock-picking skills actually exist.

### Our Stata Code

We have developed easy to use yet robust codes for implementing the above steps. Usually, the bootstrap procedure is very slow due to the larger number of iterations, however, our code is specifically twitched for time efficiency. Therefore, the code is really fast. The code needs just a basic understanding of Stata. Further, our comments on each line of code will surely help you to not only apply the code but also understand the process more clearly.

### Pricing

The code is available for $ 100/model or test, plus a $50 for raw data processing (in case the data is not in Stata format and variables are not already constructed). For further details, please contact us at:

attaullah.shah@imsciences.edu.pk

Stata.Professor@gmail.com

### Reference:

Kosowski, R., Timmermann, A., Wermers, R., & White, H. (2006). Can mutual fund “stars” really pick stocks? New evidence from a bootstrap analysis. *The Journal of
*