## Fama French Factor Model Help

#### Quantitative Model

I run a regression of a hedge fund's returns vs Fama French 3 factors. If I want to look at the distribution of idiosyncratic returns of a hedge fund, should I only use the residuals or the residuals+intercept?
it seems like an assignment question

What do you mean by distribution of residuals+intercept? The distribution of residuals is normal by assumption. It tells you how inaccurate your model is.

According to the Gauss-Markov Theorem, betas are BLUE if you fit using OLS. Since you don’t know the true population mean or variance, you use T distribution. But I don’t get how this will help in modeling idiosyncratic returns.

Original Posted by - b'Ivan':

What do you mean by distribution of residuals+intercept? The distribution of residuals is normal by assumption. It tells you how inaccurate your model is.

According to the Gauss-Markov Theorem, betas are BLUE if you fit using OLS. Since you don’t know the true population mean or variance, you use T distribution. But I don’t get how this will help in modeling idiosyncratic returns.

Sorry for the confusion. I'm looking at an equities-only hedge fund that says it looks for idiosyncratic returns while remaining neutral toward common factos. Is it possible to test that using the factor returns vs. the returns of the HF regression? Check not just for neutrality but also for ability to generate unique returns.

Original Posted by - b'Tommy':

Sorry for the confusion. I'm looking at an equities-only hedge fund that says it looks for idiosyncratic returns while remaining neutral toward common factos. Is it possible to test that using the factor returns vs. the returns of the HF regression? Check not just for neutrality but also for ability to generate unique returns.

After fitting a regression, run a F test (ANOVA) on the parameters to see if they are non-zero. If the null hypothesis is rejected, then at least one of the parameters (factors) affects the returns on hedge funds; otherwise, these factors have no effect on the returns on hedge funds. If you reject the null based on the F test, then use an individual t test to ascertain which component affects the returns. The answer will tell you whether the component contributes to idiosyncratic risk of the hedge fund results. Don't conduct use the intercept for testing.