I have optimised a set of portfolio and subsequently regressed the returns against the fama-french-Carhart factors. I have two portfolio, one in which short sales are allowed (the portfolio can take on leverage) and the other limits short sales (so that the leverage is zero). Now my question is: How are the alpha and beta of the levered portfolio affected by the ability to assume leverage??
For the levered portfolio I find a beta close to 1.5. The non-levered portfolio displays a beta of 0.5. As beta is the coefficient explaining the variance of the returns, I would think that this difference is due to leverage as it naturally leads to a higher risk in similar proportion to the return. However, I am not completely sure as I read that levering up the portfolio (simply taking larger positions) would not affect the beta as the exposure remains similar.
I expect the alpha not to be affected by the leverage as it involves no specific skill and therefore will not improve the risk adjusted returns.
However could it also be that establishing long short positions allows the the manager to add alpha?? (as it can short stocks it would normally not be able to do so? i.e. short side alpha)
Looking forward to your thoughts!