Investor returns versus fund returns

Posted by on May 18, 2011 @ 1:04 pm in investing

There’s been a lot of back and forth about the differences between the posted performance of a mutual fund or exchange-traded fund (ETF) and the returns actually realized by investors taking into account cash flow.

Reading the discussion around this, you might come away with the impression that differences in these two ways of measuring returns are entirely the result of the timing (good or poor) of investors in terms of buying and selling. But what is often being ignored in such analyses is that differences between standard fund returns (so-called time weighted or lump-sum returns) and investor returns (a.k.a. internal rates of return or dollar-weighted returns) can be as much a function of the timing of returns as it is the timing of investors’ purchases or redemptions.

For example, let’s take a “fund” investment that provides the following 12-month sequence of returns (these data are made-up, totally random, and hypothetical, and have nothing to do with any particular fund or investment):

Hypothetical fund returns

If you compound these returns, you’ll find that over the whole period, the (time-weighted) total return averages 1.28% per month, or 16.6% over the whole period. This is the standard “fund performance” calculation that effectively assumes a lump-sum deposit up-front that is held over the period.

Now let’s suppose that instead of depositing their money all at once at the beginning of the period, investors did so in equal installments over a 12-month period, and let’s calculate the “investor return.” This pattern of systematic deposits over time is actually quite typical, and reflects something like the regular paycheck deductions used by millions of investors in 401(k) plans.

So, how does taking into account periodic cash flows change our assessment of performance, and how does it compare to “fund performance”?

Well, if you do that calculation, you’d expect it to tend to underweight returns early in the series and overweight those in the recent past. More dollars are invested at the end of the period than were at the beginning, given the returns, thus pushing up measured performance. And in fact, the internal rate of return on equal purchases of this hypothetical investment is 1.81% per month, or 24.0% when annualized over the whole period—a huge, positive performance difference relative to the standard performance metric. But the point is that this result isn’t due to good timing or poor timing, just the randomness of returns: The deposits are equal in every period.

To see this point more clearly, let’s suppose instead the return sequence looked like this:

Hypothetical fund returns

Note that this is exactly the same set of returns, just in reverse order. Obviously, this does not change the total “fund return” over the period one iota. It’s still 1.28% per month, or 16.6% over the whole period.

But what about our investor returns? The same phenomenon occurs in the investor return calculation as before: More cash is invested by the end than the beginning. But now what is overweighted is the relatively poor performance at the end of the period. The IRR for an investor making 12 equal monthly purchases here is only 0.8% per month, or 9.8% over the whole period—more than 6 percentage points less over the full period than the “lump-sum”/”fund return”.

So, does the fact that “investor returns” are below or above the time-weighted return tell you anything about investor timing ability or the goodness or badness of investor behavior? Not in the above example. What it tells you has much more to do with what has happened recently in the market, given gradual investments. The takeaway is that in doing this kind of analysis, we need to be much more careful than just comparing investor returns with time-weighted returns, and concluding that if one is less than the other it’s because of investors’ “poor timing” or “bad choices.”

I’m not saying that I think investors have great timing. My read of the thorough analysis I’ve seen on this is that they tend to have poor timing (though it bears saying that by investors, I mean everyone: including institutions and advisors, not just individuals). What I am saying here is that simple comparisons of investor-versus-fund-return calculations aren’t necessarily a reliable way to measure timing quality. At a minimum, for such comparisons to be useful, we need to take a stand on what investor flows and investment choices would look like absent any poor timing to compute an investor return benchmark. Once that is done, we can get at the real issue of how much difference there is in returns as a result of poor timing, as opposed to just timing in general.

This little example also suggests each of us needs to be very circumspect in comparing our own reports of personalized performance, which use dollar-weighted returns, relative to standard reported fund performance. Particularly poor—or particularly good—comparisons of our own IRRs versus a fund’s reported return depends on the sequence of both returns and cash flows.

For most of us, who have gradually accumulated assets, what’s happened most recently in the markets will tend to matter most in the IRR calculations. Unfortunately, the fact that your IRR may be radically ahead of a fund’s return now doesn’t mean you’re any more an investment genius today than being well behind that fund’s return meant you were a goat at the end of 2008.

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