Interesting work and I will certainly want to learn more. One important issue you fail to mention is that investors in a PE Fund program need to have a reserve of liquid assets to then fund their PE commitments. This is hard to quantify but it further degrades the returns of PE fund program. And a related point would be that it is hard to hit your target allocation through PE fund commitments given that unpredictable nature of calls and distributions. A situation that can lead to an over allocation during a recession when PE funds may need to call significant capital while not being able to distribute capital to LPs.