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Using Kaplan–Schoar PME to Compare Portfolios with Cash Flows

Article Quant Q&A · Author: Topdown
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Summary

The document addresses how to compare an investor’s money-weighted return with a benchmark while separating investment selection from the timing and size of deposits and withdrawals. Applying the same dollar cash flows to both portfolios, as in the Long–Nickels public market equivalent (PME), can create an implausible benchmark account: withdrawals may exceed the benchmark value and make its theoretical invested balance negative.

It recommends the Kaplan–Schoar PME as an alternative. The measure discounts the portfolio’s cash outflows and inflows using benchmark returns, then forms a ratio; a value above one indicates outperformance, while a value below one indicates underperformance. This avoids interpreting the result as the return of a benchmark account subjected to potentially infeasible withdrawals. The brief answer points to literature for descriptions and theoretical justification but provides no worked example, data, or detailed implementation guidance. Readers should treat it as a relative performance measure for cash-flowing investments, not as a direct replacement for an ordinary time-weighted benchmark return.

Key ideas

  • Long–Nickels PME applies the investment’s cash flows to a benchmark account, which can become negative after large withdrawals.
  • Kaplan–Schoar PME discounts cash outflows and inflows using benchmark returns and compares their totals as a ratio.
  • A Kaplan–Schoar PME above one signals outperformance, while a value below one signals underperformance.
  • The document cites supporting literature but does not provide a worked calculation or implementation details.

Tags

Portfolio constructionStatisticsBacktesting
Full text
# Answer by Alex C (score 3, accepted)


# Comparing a money-weighted return of my own portfolio with a benchmark ETF/other portfolio that is subject to the same cashflows












I am able to calculate the money-weighted return (XIRR equivalent in Excel) of my portfolio. Whilst I can compare this with ‘headline’ returns of ETF’s, Mutual Funds etc, I want to isolate the timing of my cashflows from my choice of investments. In other words, I want to see if I would have been better making my investment timing decisions and investing in the benchmark rather than investing in my own choice.

The difficulty seems to be that if I apply the same cashflows to benchmark the benchmark itself can be very misrepresentative – for example, if I have outperformed the benchmark, then make a cashflow deduction from my portfolio and try and replicate this in the benchmark (with the same dollar amount) then the benchmark return itself may go negative. Is there a common approach to this?

## Answer by Alex C (score 3, accepted)

https://quant.stackexchange.com/a/21840

A similar problem arises in comparing private equity investments (which involve cash inflows and outflows) to the performance of a benchmark such as the S&P500.

The simplest method available, the Long Nickels PME, does what you say, it assumes that the same cash flows that occur in the PE investment are also made in the benchmark. The problem with this method is exactly what you mention: the amount theoretically invested in the benchmark can go negative if you withdraw a large amount of cash from your portfolio.

There are several solutions available in the literature, the one I would recommend is called the Kaplan Schoar PME. It is a ratio of discounted cash flows, such that if greater than 1 you are outperforming the benchmark, and if less than 1 you are underperforming. In the numerator you discount (using the rates of return of the benchmark) the cash outflows from your portfolio, and in the denominator you discount the cash inflows into your portfolio.

These methods are described in the Wikipedia article Public Market Equivalent PME link

A theoretical justification of the Kaplan Schoar PME method can be found in a recent article by Sorensen and Jagannathan SSRN link.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.