Most advisers will say to dollar cost average, but I do not think this is the right answer. Dollar cost averaging has nearly universal support among financial education teachers, banker, brokers, and money advisers. And yet, there has never really been a compelling mathematical case for dollar cost averaging.

To see why, let’s take a step back and understand the reasons people suggest to use dollar cost averaging. Then, we can explore the academic and logical arguments and suggest other alternatives. This article is outlined in 5 parts.

1. The standard explanation of DCA
2. Academic papers showing why DCA is wrong
3. Why the standard explanation is wrong
4. The people who really benefit from DCA
5. Alternatives: better ways to invest

(Standard disclaimers apply: I am not a money expert and you should always consult a professional before making your own decision.)

1. The standard explanation of DCA

Dollar cost averaging is about investing a set dollar amount of money regularly. Why would anyone do this?

Here’s an explanation that comes from our own government, in an article about investing basics at the SEC:

Consider dollar cost averaging.

Through the investment strategy known as dollar “cost averaging,” you can protect yourself from the risk of investing all of your money at the wrong time by following a consistent pattern of adding new money to your investment over a long period of time. By making regular investments with the same amount of money each time, you will buy more of an investment when its price is low and less of the investment when its price is high. Individuals that typically make a lump-sum contribution to an individual retirement account either at the end of the calendar year or in early April may want to consider “dollar cost averaging” as an investment strategy, especially in today’s volatile market.

The explanation is usually accompanied by a chart along the following lines:

table from about.com

Notice how the person ends up with more shares when the price dips and fewer shares when the price rises.

This is supposed to “reduce risk” and be good for investors. It sounds nice, but is there any merit to the argument?

2. Academic papers showing why DCA is wrong

I first read about why DCA is bunk in an excellent article by Timothy Middleton on MSN Money: the costly myth of dollar cost averaging.

Middleton cites two from a handful of papers that show DCA is not a good strategy. The first paper is from 1979 called “A Note on the Suboptimality of Dollar-Cost Averaging” by George Constantinides (pdf). This paper shows why DCA is not as good as another investment strategy in a theoretical perfect market setting.

This work was further refined by a 1993 paper “Nobody Gains from Dollar-Cost Averaging” in Financial Services Review pdf. This paper did analytical and numerical analysis to show that DCA is worse than a regular buy and hold strategy or an optimal portfolio rebalancing strategy.

These papers should end matters, but it does not explain why dollar cost averaging has universal support. Let’s explore why people think it’s a good idea.

3. Why the standard explanation is wrong

The promise of dollar cost averaging is tempting, but if you think about it, the claims are hollow.

First, there is a sleight of hand about what you are really doing. Dollar cost averaging is supposed to be an averaging mechanism because you buy more as the stock price rises, and less and the stock price falls. The problem is you are not really doing any averaging at all but instead mindlessly investing. The truth is you are putting in the same dollar amount regularly, without any regard to what the market does!

Second, the discussion of risk is very unsatisfactory. Dollar cost averaging is said to lower risk when compared to investing a lump sum all at once. But notice this: there is actually no measure of risk provided, at all! This is an obvious omission. But most people are tricked because they hear the word “average,” which is associated with the middle and avoiding extremes. This is another sleight of hand in the marketing of dollar cost averaging.

(Dollar cost averaging can avoid the risk of some extreme losses if you’re planning for retirement (paper here), but this is not the same as reducing risk. The papers cited above explain why DCA is not sensible on a risk-return basis).

4. The people who really benefit from DCA

If dollar cost averaging does not make sense, then why is it taught? I suspect there are two main reasons.

The first is the financial incentives. If people buy into dollar cost averaging, then that means people will invest money regularly into banks and brokerages. In fact, people who truly buy into dollar cost averaging will mindlessly invest even when the markets are tumbling and there is cause for concern! It is therefore definitely in the interests of banks and brokerages to promote dollar cost averaging so that mindless investors will pour money into accounts on a regular basis.

The second reason is paternalism. The argument is as follows. The common person is afraid to invest in stocks because of perceived risk. This is to their detriment, as the market has tended to rise over longer periods of time. Dollar cost averaging is a way to reduce fears and get people to invest through small amounts. Therefore, even if dollar cost averaging is not technically correct, teaching it is a way to get more people to invest and that serves the common good.

You’d be surprised to learn how many advisors subscribe to the second view. The truth is that many advisers are smart, and they are aware that dollar cost averaging is not a good idea. But rather than trusting people to learn, they are happy to get a second best solution. After all, dollar cost averaging has such a good image, why not capitalize on it?

Or think about it another way. If an adviser tells you to put all your money in, and then the market falls 10 percent in a week, you end up an angry customer who probably fires the adviser and complains to others. So the adviser will happily say it’s fine to dollar cost average as a way to reduce THEIR risk of losing you as a client.

I can sympathize with advisers in this regard, but I still do not think this justifies the widespread agreement about dollar cost averaging.

Financial education should teach the truth and let people decide. And the numbers show that dollar cost averaging is just not a good idea.

5. Alternatives: better ways to invest

There are two major alternatives to DCA. One is to invest the money all at once, as a lump sum. This strategy does require some patience and nerves, but it will be the best if the market is expected to rise.

Another alternative is to invest the money at random days. This is a modified version of dollar cost averaging, as one is investing the same amount, but at random times.

Middleton’s article shows an example of how both methods can be better than DCA. The article was from 2005 so the example is from 2004 data:

Table data from this article

In this example, dollar cost averaging is the worst return. This example does not prove anything, but it is an illustration of what the academic papers cited above were claiming.

A third alternative is to do an enhanced dollar cost averaging method (EDCA). This is an idea I found in a 2011 paper from the University of Nebraska (pdf). In regular DCA, you mindlessly invest the same amount every month. In EDCA, you will invest extra money if the market falls, and invest less or hold off as the price rises. This strategy was tested to be better by 0.3 to 0.7 of a percent based on historical data.

The long and short: dollar cost averaging is a popular and tempting way to invest, but its track record does not back up its claims.

But our predictably irrational ways can get in the way. I was reading an interesting example of how something as simple as a smiling face can influence our ability to judge savings accounts.

Diagnostic sway

In the book Sway, there is a chapter about tendency to stick with an initial impression, even as more important information becomes relevant.

For example, the book explains a common trap of people who are looking for a new house. After researching several ads, imagine you read a description for a house that you decide is your dream house. You are already sure of this, even though you have never been to the house.

How does this affect your visit to the house? When you visit the house, suppose you find that it’s not as perfect as you imagined because there’s traffic noise outside and it’s dimly lit. Rather than evaluating the new information, you are likely to make excuses and rationalize how the bad parts aren’t that awful. You want to confirm your initial impression due to diagnostic sway.

Bank accounts

The book then cites an interesting study from 2005. A South African lending bank was seeking to offer loans to fifty thousand of its customers. The bank did what any good company would do and experimented in its marketing material.

In classical economic theory, the most relevant variables would have been lending rates and other bottom-line numbers. But that’s not the way it turned out.

Men who received a loan solicitation with a picture of a smiling woman instead of a smiling man were much more likely to sign up for a loan. The effect was amazingly powerful, the study says, it was “about as much as dropping the interest rate 4.5 percentage points.”

What appeared to be happening is the smiling face of a woman makes the loan seem more attractive to men, and they were thus more likely to keep to that impression as they read the rates and analyzed the offer.

Be on guard!

More and more companies are applying behavioral economics. Here’s an example I found from Citibank’s website for savings accounts.

Citibank’s savings rates are meager compared to online banks like ING or Ally. Perhaps that’s why their savings accounts are advertised with a picture of a smiling mother and daughter:

Remember to look at the bottom line because we can be influenced by irrelevant images, even for important financial decisions.

I want to explain a bit about how FSAs work, and then I’ll get into the math. Most people know you save money by paying for health expenses pre-tax.

In this article I want to explain why the benefit can be even larger to due some of the details of FSA. In an extreme, extreme example, the benefit can be in the range of a 1,000+ percent of the money used to fund the account.

How FSAs work

FSAs are financially advantaged accounts that some companies offer. This will be a specified benefit, and not all companies offer FSAs. (more details in this article)

The basic way FSAs work is this: you specify how big you want the account, say $1,000. Your employer will put up that money, and you’ll be given a card to use to pay for qualified health expenses, like hospital bills and over-the-counter drugs.

But this is not free money. You have to pay for your FSA; your employer will cut a certain amount from each paycheck. For example, if you are paid biweekly and have 26 paychecks in a year, then your employer will cut about $39 dollars ($1,000 / 26) from each paycheck.

The great part is this: you get a tax break on your contribution. The $39 from your paycheck is deducted as a pre-tax amount. The net result is that you only end up spending a net $28 per paycheck, for someone in the 28 percent marginal tax bracket.

This means your net cost is about $720 in a year to be able to spend $1,000 for health expenses. That’s almost like $280 of free money due to tax considerations.

This is an amazing deal, but there is one big catch to FSAs. The funds in the account must be used up within the calendar year. You lose any money in the account you don’t spend.

For this reason, FSA literature recommends funding a conservative amount. You want to give a reasonable estimate as you will lose money not spent.

This “use it or lose it” feature sounds scary, but keep reading and I’ll explain why the benefit is worth it.

FSA eligible items

FSAs are especially useful if you have a planned surgery or dental work. You will definitely have some idea of what you’ll spend, and you can elect a sensible amount that will get spent.

Even otherwise, you should consider funding something to your FSA if you wear contacts/glasses or visit the doctor or dentist a couple of times. Some things you can spend on, as of this writing, are (list from WageWorks FSA list):

–copays on prescriptions, doctor visits
–co-insurance on medical bills
–eyeglasses
–contact solution
–sunscreen

(always double check before you buy: the list of FSA eligible items does change year to year)

Many people easily spend $200 on these items in a year, so one might as well fund an FSA to buy the items on a pre-tax basis.

Optional part 1: FSA math

This part of the article is a bit technical, but it’s the part I find the most interesting. It was in fact one of my friends that alerted me to this peculiarity of FSA funding, so a special thanks to him.

FSAs save you money because you get to spend the money pre-tax. But there is also an additional benefit because of the exact timing of how the FSA is funded.

The thing is this: the FSA is pre-funded immediately by your employer, but your contributions are only deducted through regular, small pre-tax amounts from your paycheck. So your net investment is a bit smaller and your return a bit larger.

Here’s an example calculation. Consider someone that elects $1,000, is paid biweekly, and is in the 28 percent marginal tax bracket. A casual analysis is the person is saving 28 percent in taxes.

The real benefit is even larger. The person is really contributing a net $720 in all to the account (because contributions are deducted pre-tax), but gets access to $1,000 of funds for qualified expenses immediately. This means the individual has more like a 39 percent “return” on “investment” (that is, $1,000 to spend from $720 invested is a return of 280/720 = 38.8 percent).

In fact, the benefit is technically even larger due to the time value of money. Imagine the individual spent the $1,000 from the FSA during the month of January. This is okay as the employer pre-funds the account, and has to wait to deduct the money from the employee through each paycheck. So technically the person is getting a $1,000 benefit immediately, but then the repayment cash flows are delayed. Because of the time value of money, there is an extra benefit (this is a complicated calculation; I put the cash flows in Excel and estimated the benefit was around 47 percent).

But there’s even more!

Optional part 2: gain from FSA pre-funding

Imagine the person spends $1,000 in January for a planned surgery. For whatever reason, the individual no longer works for the company a month later in February. Now, you’ll notice the person already spent the $1,000 that was pre-funded in the FSA, but the employer only deducted a few amounts from the person’s paycheck.

If the individual was deducted for three paychecks, then he contributed about $83 pre-tax but was still able to spend $1,000 in health expenses. This ends up being a 1,100 percent “return” on the money “invested” into the FSA. I admit this is an extreme and perhaps unrealistic example, but it is meant to illustrate the possible maximum benefit one could get from an FSA.

Now it may seem strange that you can spend $1,000 immediately as in the last example. Employers have to pre-fund the account, and they occasionally lose money when employees drain their FSA and leave the company. This is a risk to the employer, and it merits a special section in the Wikipedia article on FSAs: pre-funding and risks to employers on FSAs.

Employers make up for the risk of pre-funding in one way. Remember the money you lose if you don’t spend it in a year? That money goes to the employer. This amount can partially or more than offset the pre-funding losses. So the “use it or lose it” nature is not necessarily as bad as it seems at first: it’s one way employers can limit their risk.

Here is a problem that demonstrates the value of investing at a young age.

Alice and Bob are the same age, and they both plan on saving for retirement.

Alice starts at age 25 and invests $1,000 at the beginning of each year until age 65.

Bob plans to do the same thing, but he waits until age 35 to start.

How much does Bob have to contribute each year to have the same amount as Alice at age 65?

Assume both get a fixed investment return of 6 percent each year.

I will get to how to solve this problem in a second. But let me cut to the chase about the answer.

The answer: Bob would have to invest about $1,946 per year–nearly DOUBLE the amount Alice invested each year.

Furthermore, Bob ends up having to invest more money too: he ends up contributing over $60,000 whereas Alice puts in $41,000.

The lesson is that investing at a young age eases the burden of saving for retirement considerably. Here’s a small chart of their investment totals.

(This lesson is often taught as “the power of compounding,” which I believe is missing the point. I think this is more a lesson that having a head start gives you a big lead. Note that even if markets stagnate, Alice still wins out. That is, even if Alice gets a 0 percent return for the first decade, she starts out with a $10,000 lead over Bob. If both expect a 6 percent return from then on, Bob would still need to invest a lot more ($1,635) to catch up by age 65–that’s 60 percent more than Alice contributes annually. Having to save more of his paycheck makes it harder for Bob to save.)

Optional: math

I used a numerical solver in my spreadsheet to play around with the numbers.

But I also came up with an explicit formula for fun.

The amount Alice invests can be written as a geometrical series. The first investment she makes at age 25 will compound for 41 years, then the contribution at age 26 compounds for 40 years, and so on, with the final contribution at age 65 compounding for 1 year (she invests at the beginning of each year):

$1,000(1.06)⁴¹ + $1,000(1.06)⁴⁰ + … +$1,000(1.06)

Bob will invest an amount x each year, but he starts at age 35, meaning his initial contribution compounds for 31 years, and each subsequent one for 1 year less:

$x (1.06)³¹ + $x (1.06)³⁰ + … +$x (1.06)

To make Bob’s investment catch up to Alice’s, we set these two equations equal to each other and solve for x.

The two series can be summed using the formula for the sum of a geometrical series, as follows:

This formula can be generalized for a return of r, Alice investing for T number of year, Bob investing for t years, and Alice contributing A dollars per year. This is the amount Bob would need to contribute each year to catch up at age 65:

I got an email the other day from someone who had some questions about opening a bank account. Specifically, the person was curious about how the APY was calculated and how that related to interest earned:

Presh, could you help me understand what an APY of 0.05% means? I want to start a money market account, and the bank says that their annual percentage yield is 0.05% and that the interest is compounded daily and paid monthly. The amount of interest earned is based on the daily collected balances in the account. I really don’t understand what all this means.

If I deposit $5000 into the account, how much interest can I expect? That’s all I want to know. I don’t understand how to figure out the interest using the above information that the bank has provided. Thanks

This is a very good question, and I felt it would be educational to discuss the details of the bank account.

The big picture: how much interest

Carol primarily wanted to know how much money she would earn on a $5,000 deposit.

The APY is the relevant piece of information here. APY stands for annual percentage yield, and it represents the percent interest one can expect to earn, taking into account for the effects of compounding.

In this case, the 0.05% APY means that you earn 0.05% interest on your money in a year. So if you deposit $5,000, then you can expect to earn $2.50 in interest (0.05% * $5000) by the year end.

(This is a really small sum of money. As you are probably aware, there are online savings accounts with higher APY. Banks like ING and Ally Bank are currently offering something like 0.8%, which would translate into $5,000 earning $40 in interest per year.)

The APY is the most important detail in the email. But there are a few subtle points that also merit discussion.

Payment frequency: interest paid monthly

This is a very important detail. This tells you the bank only credits the interest to your account once a month on a specified day.

It helps to know when the interest is paid, especially if you are closing the account. You can lose out on interest if you close out just before a payment. For instance, if you expect an interest payment of say $50 on the 15th of the month, but you happen to close the account on the 14th, then you would lose out on that $50.

In the account mentioned in the email, we expect to earn $2.50 a year, so that comes out to about 20 cents each month paid on a specific day.

Balance calculation: daily collected balances

This is another important detail. Unlike a CD where you invest a fixed amount of money, a money market account will change depending on withdrawals and deposits.

Because your balance can change daily, the bank has to specify which balance it uses for computing interest.

The daily collected balance is one method banks often use. The daily collected balance method says the following: you take the closing balances for each day of the month for collected funds (deposits that have not cleared are uncollected funds), and then take the average.

For example, if you started with $5,000 and then on the 15th day withdrew $1000, then you’ll have $4000 for another 15 days. So if you have $5000 for half the month, then $4000 for half the month, your average daily collected balance would be $4,500.

Compounding frequency: interest compounded daily

This is a final point that I wanted to talk about from the email, though it is not as important.

In theory, it matters whether interest is compounded on a daily or monthly basis. The shorter the compounding period, the more interest that will get accumulated over a year. Here is an article that shows how daily compounding results in slightly more interest than monthly compounding: daily vs monthly compounding.

But we don’t really need to concern ourselves with this detail. The reason is that the bank account quoted an APY, which already takes into account the effect of compounding. If you have two accounts with the same APY, they can expect to give you the same interest at the year end. The effect of monthly versus daily compounding is already accounted for in the APY.

The only time you care about the compounding frequency is when you are comparing APR (annual percentage rate) rather than APY (annual percentage yield).

Typically the APR is quoted for credit cards, and APY for savings accounts, a practice that I have explained before in this article: APR vs APY: what is the difference?.