# Thread: How to test significance of the mean of multiple OLS regressions (Jensen's Alpha).

1. ## How to test significance of the mean of multiple OLS regressions (Jensen's Alpha).

Hi.
Im working on a paper on mutual fund performance, using Jensen's Alpha to measure performance.

Ri-Rf=a+b(Rm-rf)+ei

Time series regression, i let out the subscript t on all variables (except a and b).
Where Ri is the return on fund i, Rf is the return on a riskfree asset, a is the intercept of the regression, b is the "market beta", Rm is market return and e is the error term.

I will run this regression for each fund, getting an estimate of the alpha (a), and use newey-west standard errors.

Based on the estimated alpha's i subdivide the funds into 5 portfolios by performance (high alpha=high risk adjusted performance), i need to calculate an average alpha (a) for each portfolio and test the significance of this estimate. The lenght of the series in the regressions will differ (from 12 to 160 observations per fund).

Any suggestions how to do this ?

2. ## Re: How to test significance of the mean of multiple OLS regressions (Jensen's Alpha)

I have found a Chi^2 test, but this requires equal lenght of the samples, which i would like to avoid in order to fully utilize my dataset.
Another alternative would be to sort the funds based on the alpha estimates, and then create eg. 5 equal weighted return series by sorting by past alpha, or weighted by alpha (adding the eg. 5 best performing series into an equal weighted high return fund, equivalent of "going long" in the high performance funds, above average funds, average funds etc.). By this method i would get a single time series of returns for each pf., and could then estimate a single alpha for the portfolio and test the significance of this alpha by standard t-test with robust errors (HAC).

Anyone who can think of an alternative method?

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