Every year market research firm Dalbar reports how investors’ mutual fund returns compare to market benchmarks. The results get reported widely and are always dismal. In one example,

Seeking Alpha says “Investors Suck at Investing.” A few people have criticized Dalbar’s methodology, which isn’t surprising given the large number of people who see their reports. What I did find surprising is that this criticism isn’t just nitpicking; Dalbar’s calculations significantly overstate investor underperformance.

According to Dalbar’s 2016 Quantitative Analysis of Investor Behavior,

In 2015, the 20-year annualized S&P return was 8.19% while the 20-year annualized return for the average equity mutual fund investor was only 4.67%, a gap of 3.52%.

So, for the 20 years from the start of 1996 to the end of 2015, equity mutual fund investors’ actual returns were supposedly 3.52% per year lower than the stock market average. Over the full 20 years, this works out to investors ending up with 48% smaller portfolios than they could have had.

This is a huge gap. To find the source of this gap, we need to start with how Dalbar calculates investors’ returns.

**Dalbar’s calculation method**
We can describe Dalbar’s calculation method quite simply. We need the following 3 quantities:

A – starting mutual fund assets at the beginning of the 20 years

B – ending mutual fund assets after 20 years

F – net flow into mutual funds from deposits and withdrawals during the 20 years

We begin by treating all the deposits and withdrawals as though they happened at the start of the 20 years. So the cost basis C is

C = A + F,

and the return over the 20 years is

R = B – C.

Then the 20-year return is

R/C,

and the annualized return is

(1 + R/C)^(1/20) – 1.

For the 20 years ending in 2015, Dalbar used this method to get the annual investor return of 4.67%. Then they compared this to the 20-year annualized S&P return of 8.19%.

Dalbar attributes this huge gap to poor choices by investors collectively: “Over and over, it emerged that the leading cause of the diminished return is the investors’ own behavior.” However, a big part of this gap has to do with the flawed way they calculate investor returns, as I’ll show after going through other criticisms of Dalbar’s methodology.

**Sequence of returns**
Harry Sit says “DALBAR’s methodology confounds the impact of investor behavior and the simple consequences of return sequences.” Because new money is added to mutual funds over time, less money is invested in early years more in later years.

Referencing Dalbar’s 2012 report, Sit says “it’s entirely possible that some or all of the low DALBAR investor returns are simply due to the fact that markets rose for the first half of their time sample (the 1990s) and were flat for the second half (the 2000s).”

There is some truth to Sit’s criticism about sequences of returns, but there’s a better explanation for the huge gap Dalbar finds that I’ll get to below.

**Where is the missing money?**
Michael Edesess, Kwok L. Tsui, Carol Fabbri, and George Peacock made a point similar to Sit’s about the effect of the sequence of returns. They also made another interesting observation:

If some investors – say, the individual investors who are the main subject of the DALBAR study – systematically underperform the market, then there must be some other group that systematically outperforms the market. The trouble is, there is no evidence of any such group. One would think that if individual investors underperform the market, then it must be professional investors who outperform the market.

But they don’t. Study after study after study shows that professional investors do not, on average and in aggregate, outperform the market. So it simply can’t be true that individual investors as a group systematically underperform the market.

This doesn’t prove there is anything wrong with Dalbar’s calculations, but it creates an apparent paradox that needs to be resolved one way or another.

**Moving cash flows to the start of the study period**
Recall that for the calculation of investor returns, Dalbar treats all mutual fund deposits and withdrawals as though they took place at the start of the 20-year period.

Wade Phau explains that this unfairly penalizes the returns of dollar-cost averaging investors.

One part of Dalbar’s report looks at the returns of investors who make regular equal-sized investments over the full 20-year period. Pfau explains that an investor who deposits a total of $10,000 steadily over the 20 years will end up with less money than an investor who deposits a lump sum of $10,000 at the beginning of the 20 years: “It is naturally less, because contributions were made more gradually over time and experienced less opportunity to grow as the market rose. On average, the contributions were invested for a much shorter period.”

Dalbar takes the dollar-cost averaging investor’s final portfolio value and calculates an annual return based on the assumption that this investor had actually deposited a lump sum of $10,000 at the beginning of the 20 years. This method gives an unfairly low return.

To fix this problem, Pfau says “the annualized investment return for this scenario requires calculating an internal rate-of-return for the ongoing cash flows that accurately reflects when the investments were made.” Instead of moving all cash flows to the start of the 20 years, Pfau says we must leave the cash flows where they are and calculate the

internal rate of return (IRR).

This criticism is clearly valid for the dollar-cost averaging investor return calculation, but it’s less clear how important it is for the calculation of the overall investor return gap where cash flows are smaller relative to total mutual fund assets.

So, this left me unsure of whether Pfau’s criticism of Dalbar’s methodology in calculating the investor return gap is important or just a nitpick. The short answer is that it’s important as I’ll show.

**A Thought Experiment**
Let’s imagine a world where stocks give the same return every month, and cash flows perfectly steadily into equity mutual funds. To match Dalbar’s 1996-2015 study period, stocks in this world will give returns of exactly 8.19% every year.

I went to the

Investment Company Institute to get information on equity mutual fund deposits and withdrawals. From 1996 to the end of 2015, net flows swelled equity mutual fund assets by a compound average of 2.12% per year. Of course, money flowed in and out at different rates from year to year, but in our hypothetical smooth world, flows will come in perfectly smoothly amounting to 2.12% each year. Investment returns then grow assets by an additional 8.19% each year.

In this smooth world, it’s not possible for investors to make good or bad choices about investment timing. After all, stock returns are perfectly steady, and investor money flows perfectly smoothly into mutual funds. Dalbar’s gap calculation should give zero in this case.

However, if we calculate investors’ return using Dalbar’s method, we get 5.90%, which gives a gap of 2.29% to the market return of 8.19%. So, the error introduced by Dalbar’s methodology can make a big difference.

If we use the internal rate of return to calculate investor return in this smooth world, the gap is zero, as it should be. This doesn’t necessarily mean that using IRR is the best way to compute investor returns, but we do know that Dalbar’s method is seriously flawed.

**Dalbar’s response to Pfau**
Pfau’s article includes responses from Dalbar defending their methodology. They say that their “study was developed to quantify the widely held view by investors that the returns they received were different from what was publicly reported.”

For an investor to judge his investments consistent with Dalbar’s return calculation method, he’d have to perform an unusual calculation. Suppose I’ve been investing in equity mutual funds for 20 years. If I look up the market return of 8.19% per year, I can calculate the full 20-year return of 383%. Suppose the total of my total contributions to mutual funds over the 20 years was $100,000. Am I really going to be confused about the fact that my portfolio value isn’t $483,000 when I know most of my money was invested for less than 20 years? The fact that my portfolio value is less than $483,000 has nothing to do with my poor market timing.

When we take my actual portfolio value and calculate my annual return as though I had invested the full $100,000 20 years ago, the gap between that return and the 8.19% market return also has nothing to do with my poor market timing.

This calculation is not a meaningful measure of my returns. We can take this to a more ridiculous extreme. Suppose that we measure my 50-year return by assuming I invested the whole $100,000 50 years ago. Now the return gap is even bigger. Dalbar encourages us to treat their calculated percentage as a meaningful measure of investor return when they say “the 20-year annualized S&P return was 8.19% while the 20-year annualized return for the average equity mutual fund investor was only 4.67%, a gap of 3.52%.” However, their calculations plainly do not give a sensible measure of investor returns.

**Conclusion**
Mutual fund investors might be poor market timers, but Dalbar fails to measure this effect correctly. As long as there are net inflows to mutual funds, Dalbar’s methodology will continue to overstate how much investors underperform their investments.