Dollar Cost Averaging: A Not Very Magical or Good Investment Strategy

Professor Matthew Spiegel

May 6, 2006

The way some investment advisors talk about dollar cost averaging you would think that it is a magical strategy by which you can increase your portfolio’s overall return. If only it were so!

If you are unsure of what exactly dollar cost averaging is and what it supposed to do for you Investopedia.com offers some help. They define Dollar Cost Averaging (DCA) as:

The technique of buying a fixed dollar amount of a particular investment on a regular schedule, regardless of the share price. More shares are purchased when prices are low, and fewer shares are bought when prices are high.

If you do this, then Investopedia.com tells you that by using DCA:

Eventually the average cost per share of the security will become smaller and smaller. Dollar-cost averaging lessens the risk of investing a large amount in a single investment at the wrong time.

So clearly it must be a good idea. Right? Well, not exactly.

Fool’s Gold

The logical fallacy behind dollar cost averaging probably comes from the misconception that buying a security is like buying steaks. When steaks are cheap you buy more, and when they are expensive you buy fewer. But, with steaks you have a benchmark of some sort. You know that typically they sell for $5 per pound. Thus, if they are now $4 they are cheap as it is unlikely their price will drop any more. If they are $6 they are expensive since it is unlikely their price will increase.

But securities are not steaks. When you buy a steak you consume it. When you buy a security you hope to profit. Consider a stock that currently sells for $12. Now suppose its price drops to $6. Is it now cheap? Maybe, but maybe not. You should think of an investment in terms of its expected return and not its price. If a stock goes from $12 to $6 you lose 50% of your investment. But that does not make a price of $6 cheap. The $6 stock can go to $3, meaning you can still lose 50% of your investment. That is, unlike steaks and other goods, securities do not have a natural benchmark value you can use to determine if they are currently cheap or expensive.

Rather than thinking of stocks as bouncing from a low to a high price, it is better (and more accurate) to think of them as generating a return from period to period. As a simple example suppose a stock returns either +20% or −10% each period with equal probability and begins with a value of $10. In this case you can draw out the set of possible prices for the next two periods as follows:

From the picture you can see that $12 is not "expensive," $9 is not "cheap," and $10 is not "just right." (Where is Goldilocks when you need her?) At any of these prices the expected return on your investment is the same, 5% per period. As we will soon see this also means that dollar cost averaging cannot possibly improve your portfolio’s expected return.

Portfolio Returns and Investment Strategies

Ultimately investing is about portfolio management. So, if we are going to understand what dollar cost averaging will or will not do for us we need to understand how it influences our portfolio’s risk and return. To keep matters simple assume you will only put your money into one of two investments: a stock and a bond. The stock is the one in the example given above and has an expected return of 5% and a standard deviation of 15%. (The standard deviation is a measure of risk. So if you prefer, everywhere you see the word standard deviation replace it with risk. Better yet follow the link in the text box to the right to learn more about calculating a portfolio’s risk and return!) The bond is risk free and pays 2% with certainty.

In our example, the expected return on your portfolio will be the weighted average of the stock and the bond’s return. The weights are simply the fraction of your portfolio invested in each. Thus, if you put 30% of your money in the stock and 70% in the bond your portfolio’s expected return is .3×.05+.7×.02=.029 or 2.9%. The standard deviation (risk) of your portfolio is even easier to calculate; it just equals the fraction of your portfolio invested in the stock times the stock’s standard deviation. In our example, this comes to .3×.15=.045.

At long last we can now see what dollar cost averaging will or will not do for us. Suppose you begin with a $10,000 nest egg that is initially invested entirely in the risk free bond (perhaps you have a savings account at your local bank that plays an equivalent role). Having decided to start a dollar cost averaging plan you intend to put $1,000 from your nest egg into the stock each period. At this point you have 10% of your money in the stock and 90% in the bond. Therefore, the expected return and standard deviation of your portfolio is:

Period 0

Expected Return: .9×.02+.1×.05=.023 or 2.3%

Standard Deviation: .1×15% = 1.5%

After one period what happens next? On average the stock’s value will increase by 5% and the bond’s by 2%, leaving you with $1,050 in the stock and $9,180 in the bond, or a total of $10,230. Next, you take $1,000 out of the bond and put it into the stock since that is what DCA asks you to do. This leaves you with $2,050 in the stock and $8,180 in the bond. Your portfolio weights are therefore 2050/10230 = .2 in the stock, and .8 in the bond. We can again summarize your portfolio’s expected risk and return as:

Period 1

Expected Return: .8×.02+.2×.05=.026 or 2.6%

Standard Deviation: .2×15% = 3.0%

Continuing with these calculations you will find that over time the expected return and standard deviation of your portfolio goes up and up. Well, that is a very odd portfolio. Why would you want your investments to become riskier and riskier over time? If you thought that the right amount of risk would give you a portfolio with a standard deviation of 3% why not just begin with putting 20% of you money into the stock? Why wait? In fact, there is no reason to wait. Logically, you should decide and how much risk you wish to take and invest in a way that keeps your portfolio as close to that target as reasonably possible.

Commitment to a Savings Plan

Occasionally, you will read that the good thing about dollar cost averaging is that it can help commit you to a regular savings plan. Thus, you might decide to “dollar cost average” by putting $100 into a mutual fund each time you get paid. But this is not really dollar cost averaging; absent the jargon it is a savings plan. Savings plans are good. You should have one. It is not, however, dollar cost averaging. With a savings plan you should set up an ideal portfolio (say 80% in mutual funds that invest in stocks, and 20% in mutual funds that invest in bonds) and then allocate your periodic savings accordingly. If this 80-20 split is what you want then the ideal thing for you to do is allocate your savings in those proportions. Then each month you should invest however much you can in a way moves your portfolio back towards this ratio. For example, if stocks have done well and thus now constitute more than 80% of your investments, put more money into the bond funds. On the other hand if stocks have done poorly, put more money into the stock funds. This, by the way, is not easy. I know from personal experience, that when stocks take a nose dive it is very hard to get yourself to buy more of them. Nevertheless, it is the right way to manage your portfolio.

If you need help either setting up an investment plan or advice concerning how much risk is associated with various choices feel free to contact us Alpha Investment Opportunities.