Assume you have 30 years of quarterly PE cash flow data across various economic regimes, so that estimation is statistically precise. Vanilla PME still systematically mismeasures risk-adjusted performance. What does it get wrong?

Question

BlackTom AI · Accepted Answer

Vanilla PME uses the log-utility stochastic discount factor (SDF) — effectively treating public-market returns as if they price private-equity cash flows with the same growth-optimal (log-utility) kernel. That assumption is the root cause of its systematic mismeasurement: it gets both the quantity and the price of risk wrong.

1) Relevant concepts
- Stochastic discount factor (SDF): prices risky cash flows; m_t relates expected discounted payoffs to current prices.
- Log utility SDF: for u(C)=ln C, marginal utility ∝ 1/C so the SDF weights outcomes by inverse cumulative wealth (growth-optimal weighting).
- Quantity of risk: exposure of returns/cash flows to systematic risk factors (volatility, betas).
- Price of risk: the market compensation per unit of exposure (risk premia or lambda for each factor).

2) Step-by-step reasoning
- PME replicates private-equity cash flows by trading the public index; this implicitly assumes the SDF that prices those trades is the one implied by geometric/compound index returns (the log-utility kernel).
- For log utility, m_t ∝ 1/W_t (wealth), so private cash flows are effectively discounted with the inverse of compounded public returns. That equates to fixing a particular relationship between mean returns and higher moments (growth-optimal portfolio).
- Real investors and markets price risk via mean-variance tradeoffs and factor risk premia; PE exposures (illiquidity, leverage, exposure to private value creation) have different betas and are priced differently.

3) Why this is wrong (intermediate logic)
- Quantity error: vanilla PME misstates the true exposure (beta) of PE cash flows to systematic factors because it forces exposures into the log-utility weighting rather than measuring actual covariances.
- Price error: it also imposes a single, incorrect mapping from exposure to expected return (the log-utility price of risk), so the compensation per unit of risk is mis-specified.

4) Why the correct answer is correct
- Saying it gets “Both the quantity and the price of risk — the log-utility SDF misspecifies the entire risk-return relationship” captures both mis-measured betas and mis-priced premia; that is precisely the structural error of vanilla PME.

5) Why alternatives (practical confusions) are not the main point
- Common critiques (timing, liquidity, sample size) matter, but vanilla PME’s structural bias is deeper: it imposes the wrong SDF. That is not remedied by more data or timing adjustments.

6) Conclusion
- Therefore vanilla PME systematically mismeasures performance because its log-utility SDF misspecifies both quantity and price of risk — matching the provided answer.

Assume you have 30 years of quarterly PE cash flow data across various economic regimes, so that estimation is statistically precise. Vanilla PME still systematically mismeasures risk-adjusted performance. What does it get wrong?单项选择题

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