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I am exploring the wonderful library by K. Sheppard et al. on linear models applied to asset pricing. In particular, Fama Macbeth and two-step regression (leaving GMM for later)

My question is concerning the j-statistic, which is a wald test on the null that the alphas are centered around zero.

I have created a small simulator of stock returns that overlays perfect normal noise and have not been able to generate a dataset in which I accept the model. Seeing the link below from Sheppard, it doesn't seem he has neither.

What is the true importance from a practitioner point of view of this test? I understand the desire to have a model that yields normal errors centered around cero, but is it a lost cause in finance? Is it just a metric that one can just improvement upon? (ie. seeking models that reduce the j-stat even if they still firmly reject it)

Other side questions:

  • Even if it makes sense as a premise, does it still hold when one uses assets instead of portfolios? I could imagine that having a large universe of stocks (eg 200) instead 10-20 portfolios would make the test even more impossible not to reject.
  • how would you generate synthetic stock data that would yield an acceptance of the null?

Thank you so much.

Here is the link to catch up on what i am referring to: https://bashtage.github.io/linearmodels/asset-pricing/examples/examples.html

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