## Thursday, July 3, 2008

### Dollar-Cost Averaging Truth and Myth

Patrick at A Loonie Saved did an experiment with historical stock data to determine the value of dollar-cost averaging. His results were that spreading investments out over short periods of time seems to make no difference. This is because the usual way of explaining dollar-cost averaging is based on a myth.

Here is the usual way of explaining dollar-cost averaging. Suppose that you spread the investment of \$1800 in a stock over three months (\$600 per month):

Month 1: Share price \$30, 20 shares bought.
Month 2: Share price \$60, 10 shares bought.
Month 3: Share price \$30, 20 shares bought.

In the end you have 50 shares at an average price of \$1800/50=\$36. But the average share price over the three months has been (30+60+30)/3=\$40. Through the miracle of dollar-cost averaging you have saved \$4 per share.

The problem with this reasoning is that the average share price calculation is simply not relevant to anything. If you had spent the \$1800 all at once, you would have got either 60 shares in months 1 or 3, or 30 shares in month 2. The average result is (60+30+60)/3=50 shares, the same result as spreading out your investment.

The advantage you do get from dollar-cost averaging is reduced volatility. However, the effect is smaller than the examples often given make it seem. Looking at my example, it’s not very common for a stock to double one month, then get chopped in half the next month.

The main advantage of dollar-cost averaging is that if you’re doing it, then you are saving regularly instead of spending all your money. This is more important than any other supposed benefit.

Some investors have been led to believe that they must invest money every month or even more frequently to avoid missing out on dollar-cost averaging. This is simply not true. There is nothing wrong with letting cash build up for a few months until you have say \$1000 or more to invest, as long as you aren’t tempted to waste it before you get a chance to invest.

The advantage of waiting for the money to build up before say buying more of a low-cost index ETF is that you’ll save money on commissions. This saving has to be balanced against the cost of being out of the stock market while the cash builds up.

1. Looks like the proper expected average price from the lump sum investment is not the arithmetic mean, but the harmonic mean.

2. Patrick: That's right. The relevant mean for both lump sum investing and spreading out investments is harmonic.

3. As long as we're busting myths here... What do you think of technical analysis?

4. Patrick: I don't think the information that will determine a stock's future is in its history of trades. No amount of analysis can find information that isn't there. I haven't spent enough time thinking about technical analysis to say much more than this.

5. Personally I think technical if technical analysis had any actual predictive value, then that would be factored into the stock price, making technical analysis self-defeating.

6. Patrick: Interesting. This would mean that all the mumbo-jumbo in technical analysis books may have had some value at one time, but no longer. I guess it's just an academic exercise to figure out whether it has always been bunk or whether it quickly became bunk as overuse made it self-defeating.