The plight of Sears Canada pensioners has been in the news lately. After reading about the hardships created by pension cuts, it’s natural to think about what we should do to prevent this in the future.

Some, like Jen Gerson, question whether pension plans should have higher priority than they do now when divvying up the assets of a bankrupt business like Sears Canada. However, the side effect of doing this is that suppliers would be less willing to extend credit to any business with an underfunded pension, and this would drive struggling businesses into bankruptcy sooner. This is a difficult choice to make when you’re still hoping that a weak business can get back on its feet.

However, the Sears Canada case looks far different from a plucky business doing all it can to survive. “While Sears’ shareholders pocketed payouts of $3.5 billion, the chain’s pension plans remained underfunded to the tune of $270 million.” Why are owners allowed to pull assets out of a business that owes money to its pension plan?

I can see where a company with a regular modest-sized dividend might be harmed if it’s forced to suspend the dividend. However, in this case, Sears Canada paid special large dividends. It seems appropriate to me to limit a company’s ability to pay dividends while its pension plan is underfunded. By itself this won’t prevent all cases of pension cuts, but it would make it harder to drain assets from a business at the expense of pensioners.

## Tuesday, January 16, 2018

### Underfunded Pensions

## Friday, January 12, 2018

### Measuring Stock-Picking Skill

Deciding whether someone has skill in picking stocks that will give higher than average returns is a tricky business. You’d think that having a long-term track record of beating the market would be proof. However, some have found ways to argue that such records aren’t proof at all. I have my doubts about the arguments.

When investment managers have the ability to pick superior stocks, we call this

Complicating the situation is the existence of types of stocks that give superior returns. It’s well known that stock in small businesses and low-priced businesses have given superior returns over the long run. Such categories of stocks are called

In the first chapter of their book

Swedroe and Berkin go on to use factors to show that investors with strong long-term investment records did it with various types of factor-based beta rather than using alpha. I have concerns about this type of argument.

My main concern is best illustrated by taking factors to an extreme. Suppose we invent so many fine-grained factors that each factor actually represents just a single stock instead of a broad class of stocks. Then by definition, alpha is impossible. Whatever stocks you pick, there are corresponding factors saying your returns are the due to beta rather than alpha.

Now, I’m not saying that factor research has gone this far, but there is no guarantee that any given factor will persist into the future. Suppose that in the next 50 years a given factor disappears because we were guilty of data mining or for some other reason. Past investors should be given credit for alpha when they recognized stocks covered by this phantom factor as undervalued.

Factor researchers work hard to avoid data-mining. They look for sensible reasons why a factor should exist in addition to just observing it’s outperformance in returns data. However, even 100 years of stock returns is only a modest amount of data. We can’t eliminate the possibility of data mining. There are a few factors that seem fairly solid, but a great many others are not.

When we examine investment records during periods of time long before the existence of a given factor was widely-known, declaring an investor’s performance to be “merely beta” seems like 20/20 hindsight. On the other hand, if a modern era investment manager used well-known factors to increase returns, we’re justified in saying any outperformance is the result of beta, not alpha.

Of course, the main point of the book that it’s not worth it to pursue alpha still stands. Alpha is scarce and trying to get it can be very expensive. I’m not a fan of venturing too far into the world of factors either. Pursuing factors increases investment costs. If the factors don’t outperform by as much as we hope, the net effect may be lower returns.

When investment managers have the ability to pick superior stocks, we call this

*alpha*. If they beat the market averages by 2% per year, we say that they have an alpha of 2%. When we just invest in market index funds, we call the source of these returns*beta*. These returns come from putting your money at risk, but they don’t come from investment skill.Complicating the situation is the existence of types of stocks that give superior returns. It’s well known that stock in small businesses and low-priced businesses have given superior returns over the long run. Such categories of stocks are called

*factors*. These two examples are called the*size factor*and*value factor*. There are other lesser-known factors (e.g.,*momentum*). Researchers are finding new possible factors all the time.In the first chapter of their book

*The Incredible Shrinking Alpha*, Larry Swedroe and Andrew Berkin argue that if we invest in factor stocks rather than just a regular index, the outperformance we get isn’t really alpha; it’s just another kind of beta. By this they mean that we’re not showing stock-picking skill; we’re just invested in a category of stocks know to perform better than others.Swedroe and Berkin go on to use factors to show that investors with strong long-term investment records did it with various types of factor-based beta rather than using alpha. I have concerns about this type of argument.

My main concern is best illustrated by taking factors to an extreme. Suppose we invent so many fine-grained factors that each factor actually represents just a single stock instead of a broad class of stocks. Then by definition, alpha is impossible. Whatever stocks you pick, there are corresponding factors saying your returns are the due to beta rather than alpha.

Now, I’m not saying that factor research has gone this far, but there is no guarantee that any given factor will persist into the future. Suppose that in the next 50 years a given factor disappears because we were guilty of data mining or for some other reason. Past investors should be given credit for alpha when they recognized stocks covered by this phantom factor as undervalued.

Factor researchers work hard to avoid data-mining. They look for sensible reasons why a factor should exist in addition to just observing it’s outperformance in returns data. However, even 100 years of stock returns is only a modest amount of data. We can’t eliminate the possibility of data mining. There are a few factors that seem fairly solid, but a great many others are not.

When we examine investment records during periods of time long before the existence of a given factor was widely-known, declaring an investor’s performance to be “merely beta” seems like 20/20 hindsight. On the other hand, if a modern era investment manager used well-known factors to increase returns, we’re justified in saying any outperformance is the result of beta, not alpha.

Of course, the main point of the book that it’s not worth it to pursue alpha still stands. Alpha is scarce and trying to get it can be very expensive. I’m not a fan of venturing too far into the world of factors either. Pursuing factors increases investment costs. If the factors don’t outperform by as much as we hope, the net effect may be lower returns.

## Wednesday, January 10, 2018

### Dollars and Sense

If you think you spend money rationally and that businesses can’t manipulate you into spending more than you should, you probably haven’t read a recent book by Dan Ariely and Jeff Kreisler,

One of our common errors is to make spending decisions based on irrelevant comparisons. A good example is sale prices. Just because a crappy shirt has a $100 price tag on it and is marked down to $60 doesn’t mean it’s worth $100 or that anyone ever paid that price. It may still be a terrible deal at $60, and you definitely aren’t saving $40 by buying it.

The comparison we really should be making is whether owning the shirt is better than the other things we could buy for $60. But that’s harder than looking at the $100 “regular price” and deciding we’re getting a deal. “When we can’t evaluate something directly, as is often the case, we associate price with value.”

Some other mistakes we make are spending more when the method of payment is easier, overvaluing things because we own them, and giving in to the temptations of the present. The authors explain each of these and more with entertaining examples.

In an example of mental accounting, the authors explain that “people who feel guilty about how they got money will often donate part of it to charity.” This means that “How we spend money depends upon how we

The authors make an observation that I think applies far more generally than just financial decisions: “There is no limit to the effort people will make just to avoid thinking.”

The genius of credit cards is that because the real payment will be made at some point in the future, “they lessen our current pain of paying.” But then when the credit card bill comes, “we feel like we already paid at the restaurant.”

In an interesting experiment, employees in a company savings program were given the company matching amount up front each month, and then if the employee didn’t make a full contribution, they were given a statement saying “We prefunded the account with $500, you contributed $100, and the company took back $400.” This is an interesting way to harness loss aversion to get people to save more.

Over very short time periods, stocks are down almost as often as they are up. But we feel losses about twice as strongly as gains, so watching your portfolio daily will make you feel bad. The authors’ remedy is to look at your investments infrequently because the longer the time period, the more likely it is that stocks are up. Of course, this works best if you have a portfolio that doesn’t require monitoring, such as indexed investments.

We have a tendency of overvalue effort over experience. We’re happy to pay a tradesperson who takes a long time and seems to work hard. But if a highly skilled person finishes a job quickly and with high quality, we balk at paying what seems like a high price for the (apparently) low effort required.

“If we have a root canal coming in a week, it can ruin every day leading up to it.” Anticipation can multiply the impact of both positive and negative experiences. This is why when my son was having surgery and the hospital called to offer a nearer date, I jumped at the chance to end the family misery sooner.

An unfortunate example of expectations affecting performance is that “When you remind women that they are women, they expect to perform worse on mathematics tasks and they actually do perform worse on those tasks.”

In experiments involving brain scanning, researchers found that “branding doesn’t just make people

In the shake-your-head department, a survey found that “46 percent of

When it comes to big financial decisions, it’s hard to decide based on some big numbers. The authors suggest working out what you’re giving up in non-financial terms. For example, when deciding whether to buy a bigger house, we might think “the bigger house costs me the same as the smaller house plus one yearly vacation, a semester of college for each of my children, and an additional three years of working before retirement.”

On the importance of understanding the issues discussed in this book: “the struggle to improve our financial decision-making isn’t just a struggle against our personal flaws; it’s also against systems designed to exacerbate those flaws and take advantage of our shortcomings.” So, businesses know how to push our buttons and get us to spend more.

In conclusion, this book explains our many decision-making flaws and offers suggestions for making better choices in realistic ways. I find the writing clear and entertaining. It’s definitely worth a read.

*Dollars and Sense: How We Misthink Money and How to Spend Smarter*. The authors explain many of our financial “quirks” and offer ways to compensate for or even harness our irrational tendencies.One of our common errors is to make spending decisions based on irrelevant comparisons. A good example is sale prices. Just because a crappy shirt has a $100 price tag on it and is marked down to $60 doesn’t mean it’s worth $100 or that anyone ever paid that price. It may still be a terrible deal at $60, and you definitely aren’t saving $40 by buying it.

The comparison we really should be making is whether owning the shirt is better than the other things we could buy for $60. But that’s harder than looking at the $100 “regular price” and deciding we’re getting a deal. “When we can’t evaluate something directly, as is often the case, we associate price with value.”

Some other mistakes we make are spending more when the method of payment is easier, overvaluing things because we own them, and giving in to the temptations of the present. The authors explain each of these and more with entertaining examples.

In an example of mental accounting, the authors explain that “people who feel guilty about how they got money will often donate part of it to charity.” This means that “How we spend money depends upon how we

*feel*about the money.” Presumably, donating some of the money somehow cleans the rest of it in our minds.The authors make an observation that I think applies far more generally than just financial decisions: “There is no limit to the effort people will make just to avoid thinking.”

The genius of credit cards is that because the real payment will be made at some point in the future, “they lessen our current pain of paying.” But then when the credit card bill comes, “we feel like we already paid at the restaurant.”

In an interesting experiment, employees in a company savings program were given the company matching amount up front each month, and then if the employee didn’t make a full contribution, they were given a statement saying “We prefunded the account with $500, you contributed $100, and the company took back $400.” This is an interesting way to harness loss aversion to get people to save more.

Over very short time periods, stocks are down almost as often as they are up. But we feel losses about twice as strongly as gains, so watching your portfolio daily will make you feel bad. The authors’ remedy is to look at your investments infrequently because the longer the time period, the more likely it is that stocks are up. Of course, this works best if you have a portfolio that doesn’t require monitoring, such as indexed investments.

We have a tendency of overvalue effort over experience. We’re happy to pay a tradesperson who takes a long time and seems to work hard. But if a highly skilled person finishes a job quickly and with high quality, we balk at paying what seems like a high price for the (apparently) low effort required.

“If we have a root canal coming in a week, it can ruin every day leading up to it.” Anticipation can multiply the impact of both positive and negative experiences. This is why when my son was having surgery and the hospital called to offer a nearer date, I jumped at the chance to end the family misery sooner.

An unfortunate example of expectations affecting performance is that “When you remind women that they are women, they expect to perform worse on mathematics tasks and they actually do perform worse on those tasks.”

In experiments involving brain scanning, researchers found that “branding doesn’t just make people

*say*they enjoyed things more; it actually makes these things more enjoyable inside their brains.”In the shake-your-head department, a survey found that “46 percent of

*financial planners*didn’t have financial plans themselves.”When it comes to big financial decisions, it’s hard to decide based on some big numbers. The authors suggest working out what you’re giving up in non-financial terms. For example, when deciding whether to buy a bigger house, we might think “the bigger house costs me the same as the smaller house plus one yearly vacation, a semester of college for each of my children, and an additional three years of working before retirement.”

On the importance of understanding the issues discussed in this book: “the struggle to improve our financial decision-making isn’t just a struggle against our personal flaws; it’s also against systems designed to exacerbate those flaws and take advantage of our shortcomings.” So, businesses know how to push our buttons and get us to spend more.

In conclusion, this book explains our many decision-making flaws and offers suggestions for making better choices in realistic ways. I find the writing clear and entertaining. It’s definitely worth a read.

## Friday, January 5, 2018

### Short Takes: Optimism, CPP Changes, and more

*I wrote one post over the holidays:*

Dalbar’s Measure of Investor Underperformance is Wrong

*Here are some short takes and some weekend reading:*

Warren Buffett says “most American children are going to live far better than their parents did.” His sensibly optimistic essay is a good antidote to the pessimistic hand-wringing over lost jobs due to automation. However, he does warn that we have to make sure people at all economic levels share in the gains that are certainly coming.

Doug Runchey at Retire Happy explains the 5 proposed changes to CPP agreed to by the federal and provincial Ministers of Finance.

Mr. Money Mustache explains why you shouldn’t invest in bitcoin. He shows that he understands the issues very well.

The Blunt Bean Counter looks at the revised rules on taxing income sprinkling.

Big Cajun Man makes some financial predictions for 2018. I find it interesting that Canadians love to predict that the Canadian dollar will rise against the U.S. dollar. Of course, nobody knows what will happen to the dollar.

## Wednesday, January 3, 2018

### Dalbar’s Measure of Investor Underperformance is Wrong

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,

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.

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.

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.

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:

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.

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.

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.

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.

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.

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.

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