Whose performance matters more? The investor’s or the manager’s?

The most common approach to calculating a portfolio’s investment return is the time-weighted rate of return. This approach is dictated by the industry performance standard (“Firms must calculate time-weighted rates of return that adjust for external cash flows”[1]) and for a long time was widely taught to trainee analysts as simply being the right way to calculate performance.[2] The feature that distinguishes time-weighted returns from the alternative money-weighted approach is that time-weighted returns negate the effect of external cash flows. The argument for doing so is that the investment manager does not control those cash flows, so it would be unfair to allow them to influence the client’s assessment of the manager. To explore this argument further, we will use the following example: A portfolio has an initial value of $100, and in its first year grows by 50% to $150. Following this good run, an additional $100 is added to the portfolio, bringing the total value to $250. The second year is less successful, however, with a loss of 20% being incurred. The portfolio ends the second year worth $200. So the ending value of the portfolio is $200 and the net effect of the investment activity is neither a gain nor a loss. This outcome is captured in the money-weighted rate of return calculation, which would show a 0% return. Had the additional capital not been injected, however, the portfolio value would have gone from $100 to $150 to $120, producing a gain of $20. Hence the argument that it is unfair to the manager to say they did not add value for the portfolio: it was not their decision to inject additional money. So the time-weighted return would give the same weight to the first year’s return of 50% as to the second year’s return of -20%, and show a positive return of 9.5% a year.[3] But wait a second: who is more important here? The investor or the manager? The first question that performance measurement ought to address is to measure the experience of the investor: what was the outcome from their point of view? And that question is answered with a money-weighted return. Certainly, we also want to do the best job we can of accurately assessing how good a job the investment manager did. And it’s true that, as in the example above, the investor’s outcome can be affected by factors outside the manager’s control – including external cash flows. So the time-weighted return is a useful tool when we’re assessing a manager’s ability to generate returns, because that ability is largely independent of portfolio size.[4] But it’s really an attribution tool. The manager’s ability to add value is not the only thing that affects the investor’s outcome, and the primary thing that performance measurement should be measuring is that outcome. To the extent that money-weighted returns exceed or lag time-weighted returns, that’s an indication of the impact of the investor’s capital allocation decisions: did the decision to add to one manager’s portfolio – or to subtract from another’s – add value or subtract it?[5] That, too, is useful information – but once again is attribution. So time-weighted returns are useful in assessing manager skill, and the manager in the example above can claim that they demonstrated skill over the two-year period. But they cannot claim to have delivered a net gain for the client. The time-weighted return is not the best measure of the investment performance as experienced from the perspective that matters most: the asset owner’s. It shouldn’t be the primary number shown on the typical client performance report. Technical addendum: Time-weighted returns generally have an upward bias relative to money-weighted. This follows from the fact that assets tend to be taken away from investment portfolios that have performed poorly, and to be added to portfolios that have done well. In the example above, the manager’s time-weighted return will exceed the money-weighted return whenever the second year’s performance is below that of the first year. Similarly, for a manager from whom money is taken, time-weighted returns will be above money-weighted whenever the second year’s performance exceeds the first’s. So if there is any reversion in performance patterns – i.e. unless exceptional performance persists indefinitely – time-weighted returns will paint a more positive picture of performance than investors’ actual experience.
 
[1] CFA Institute (2010). Global Investment Performance Standards (GIPS).
[2] There is another (somewhat related) debate to be had concerning the merits of absolute vs. benchmark-relative returns. That’s a subject for another day.
[3] MWRR formula solves for 100 x (1 + mwrr)2 + 100 x (1 + mwrr) = 200. TWRR solves for (1 + twrr)2 = (150 / 100) x (200/250).
[4] “Largely” because with extremes of very small or large portfolios, practical considerations come into play. And the claim that cash flows are outside the manager’s control has its exceptions, too.
[5] It would be nice to think that some managers can provide useful input to these capital allocation decisions: to give a steer on when would be particularly good or bad times to add to the portfolio. It would be unrealistic to expect that input to be completely objective, of course.