Why can’t we use Jensen’s alpha for measuring the over/under-performance of un-diversified portfolios? I can’t seem to find a good explanation for this anywhere
Jensen’s alpha is derived from CAPM which assumes that all expected returns can be explained by systematic risk (market beta). Therefore, Jensen’s alpha might give a misleading measure of an un-diversified portfolio as it does not reward unsystematic risk.
yes but according to the theory, you get no returns for assuming unsystematic risk so I don’t see how this is an issue.
Since it’s based on the CAPM, which only accounts for systematic risk, any return generated from unsystematic risk can incorrectly appear as alpha, even though it’s just uncompensated, diversifiable risk. A better measure would be the sharpe ratio which includes total risk, and not just systematic risk.
So as a summary. You say in theory you get no returns from unsystematic risk. This is true statistically, but can happen occasionally. So with an undiversified portfolio you can according to Jensen’s Alpha generate abnormal returns, but this might be due to occasional returns coming from the unsystematic risk you hold. If we talk about true alpha it will be consistent over time, not random like you would get from unsystematic risk.
Ye, that makes sense to me. In practice, you might get returns for unsystematic risk temporarily as theory might not always hold. Thanks for clearing that up!