Prasad,
Nice write up. The problem with PME and this new variant - they all assume that the beta of the private equity fund to the reference index is 1. This is most likely not the case. Venture has been shown by many researchers to to have a beta closer to 2, for example. Private equity also can include many other factor loadings, such as small cap and illiquidity. Without estimating these betas, this isn't really a measure of alpha, instead it only measures excess return.

There is another paper by Ang, Chen, Goetzmann, and Phalippou from 2014 available on SSRN titled "Estimating Private Equity Returns form Limited Partner Cash Flows" that provides a more robust way to estimate the alpha and betas simultaneously, thus removing the beta = 1 assumption of PME. The betas they estimate include the market, size, value, and illiquidity. I would recommend your readers take a look.

All the best,
Ross