I saw a post today on bogleheads.org where the poster was asking whether he should engage in dollar-cost averaging. I've always felt dollar-cost averaging is basically a bunch of baloney (well, under certain reasonable assumptions anyhow), but I didn't feel like attempting to write up a long explanation, in part because I find my argument a little hard to articulate in a convincing fashion. But when I searched on the web, I was unable to find a really good explanation of why dollar-cost averaging is bogus. There were various articles from the popular press that alluded to the fact that many academics find the concept without merit. But no really good write-up from the academics themselves (that I could find). Hence, my own feeble attempt herewith.
For those who aren't familiar with the concept, the scenario where dollar-cost averaging comes into play is when you have some lump sum to invest. To be concrete, let's say you have $100,000 to invest, and you've decided the optimal thing is to put it all in stocks eventually. We can assume you are holding it in your bank account at the moment while you decide what to do. The question you are faced with is whether to simply invest the $100,000 in stocks now, or perhaps invest $10,000 per month over the next ten months. That second approach, where you shift the money gradually into stocks, is dollar-cost averaging.
Intuitively, dollar-cost averaging may seem appealing. Putting the full $100K into stocks overnight may seem dangerous. You may think - what if the stock market crashes tomorrow? I'll be pretty sorry then. Wouldn't it be safer to shift the money over gradually?
Here's a better way to think about it. Let's say that we have some way to quantify the risk of a particular portfolio. For example, it could be the standard deviation of the distribution of annual returns for your portfolio based on certain assumptions about the expected returns and expected volatility of individual asset classes. But it doesn't really matter what method you use. What's important is that that risk value - let's call it R - is just a function of the assets you hold in your portfolio. In particular, your risk today is not a function of what you held yesterday. This should be obvious.
Part of the premise of our story is that the investor has weighted the risks and opportunities of different possible portfolios and has decided that the best allocation, the one he wants to get to eventually (at least) is the one that involves moving the full $100K into stocks. He's decided that the risk R he will face with that portfolio is acceptable, given the expected returns that portfolio offers.
So what's the point? The point is that if the investor has decided he can tolerate a risk of R, then he might as well shift his assets immediately to form that portfolio. The risk he will be taking is precisely R - no more and no less. If one day ago he had 90% of this $100K in stocks, or 0% of this $100K in stocks, it doesn't matter. The risk he is taking is still R.
So am I arguing that dollar-cost averaging is not safer? No, not at all. Since the money is currently in cash, moving the money gradually from cash to stocks over a ten-month period results in a safer (less volatile) portfolio for that ten-month period. But, by supposition, the investor has decided that the money should eventually all be in stocks. So having less in stocks is suboptimal in that it gives up to much return to justify the reduction in risk. If that's true ten months from now, it's true tomorrow.
Now, of course, you can argue that putting all that money in stocks might not be the right thing. Perhaps that's too risky. But that's not an argument for dollar-cost averaging. You're really questioning the premise of our story, and arguing that this investor shouldn't move the full $100K to stocks.
One key assumption I've made is that this investor has no foreknowledge of where the market is going. If you knew that stocks were going to be very volatile in the short term, but their excess-of-normal volatility was going to decrease and go away over the next ten months, then you could probably make a case for dollar-cost averaging. But I don't think investors in general have this sort of knowledge, and anyhow this sort of assumption is not part of the typical arguments for dollar-cost averaging.
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4 comments:
I agree that in the long term it won't matter much, but that doesn't mean it's bogus. Example: would you rather have put your $100K in the stock market on 1 October 2007 or over a 10 month period since then? The risk of both portfolios is the same after those 10 months, but the latter portfolio is guaranteed to outperform the first one. That is not bogus, that is real money. Hindsight is 20/20 and maybe on average you would lose money with dollar-cost averaging, but unless you show me the data, your "risk" argument is clearly not enough to reach that conclusion.
Let's make it a little bit more abstract. Let's approximate the stock market with the following curve: Y = a*t + b + N(0,R), where t = time, a and b are constants and N(0,R) is noise with mean 0 and variance R (representing "risk" / volatility). The volatility at any given time is R, so does that mean dollar-cost averaging is bogus? No, in fact, R is with respect to the _average_ (= noiseless) curve and dollar-cost averaging would allow you to invest your money at something close to the average. Investing all your money on one random day will almost certainly not give you R (in the short term), but something lower/higher, depending on how lucky/unlucky you were. That is, you might face 2*R losses in the short term if you were particularly unlucky. In the long term there is no difference in volatility between the two portfolios, but there will be a difference in performance (absolute $) based on how lucky/unlucky you were when you invested your money.
"would you rather have put your $100K in the stock market on 1 October 2007 or over a 10 month period since then?"
Not sure what this is supposed to prove. Of course, with the benefit of hindsight, we can identify time periods in the past where it would have been better to dollar-cost average (or to hold all cash, or to hold all stock).
My premise is that we have an investor who doesn't know what's going to happen in the future and wants to hold the portfolio that will offer the best expected risk-adjusted return. The portfolio with the best *expected* risk-adjusted return may in fact turn out to do crappy. The future is uncertain.
With respect to modeling the stock market with the function Y = a*t + b + N(0,R). This function differs from the usual random walk model assumed by most finance types (which I am also assuming). In your model, the value of the market at time t gives you information about whether the market will rise or fall between t and t+1. In particular, under your model there is mean reversion. If the random noise component at t is negative, the market is more likely to gain value in the next time increment than if the random noise component were positive at t.
If you believe in reasonably efficient markets, then you should probably prefer a random walk model. If there's information in today's market prices that can help you forecast tomorrow's performance, then smart traders should be taking advantage of that. And in so doing they should drive prices up or down to the point that the market inefficiency no longer exists.
"Not sure what this is supposed to prove."
The example was supposed to make you realize what the point of dollar cost averaging is, which is to buy (or sell) at an average price. I.e., it prevents you from buying at a local maximum or selling at a local minimum. In fact, I think the example is a great one, because it also shows in what kind of climate dollar cost averaging is really going to help you (e.g., current 2008 market). You won't be able to predict when we're going to hit rock bottom and assuming that you believe that there won't be a complete collapse of the financial system and you're in it for the long run, this would be a great time to apply dollar cost averaging. (Of course, no matter how much we believe efficient market theory, it's pretty clear that we haven't hit rock bottom yet.)
"This function differs from the usual random walk model assumed by most finance types (which I am also assuming)."
Random walk might be a reasonable short term model of the market, but if you take a look at the long term (e.g., 50 years) chart of your favorite stock market index, you'll see its looks nothing like a random walk. When people talk about the random walk model, they use it as an argument for not bothering with short term market predictions. And then they go on to tell you that you should buy an index fund and use a buy-and-hold strategy, because in the long term the stock market tends to go up. In fact, the random walk model says that today's price is unlikely to be the lowest (locally) and could in fact be the highest (locally), so why not reduce that risk and get an average price?
"If there's information in today's market prices that can help you forecast tomorrow's performance, then smart traders should be taking advantage of that."
I think you're mistaking efficient markets with rational markets. Anyway, we're not trying to forecast tomorrow's market, we're in it for the long run here.
"In fact, I think the example is a great one, because it also shows in what kind of climate dollar cost averaging is really going to help you..."
Sure, there's no argument that in a down market, dollar-cost averaging will be superior to a lump-sum investment. But, of course, if it had happened that the market was skyrocketing upwards these last few days, I could equally well have turned to you and said: look, this is why you should avoid DCA.
The point is that we don't know the future direction of the stock market. We can't use the experience of the last few months and draw any generalizations (such as that the stock market will always be crashing). I think you understand the point and I don't need to belabor it.
"if you take a look at the long term (e.g., 50 years) chart of your favorite stock market index, you'll see its looks nothing like a random walk"
Care to elaborate? Many finance types will concede that there are some deviations from the random walk model, but insist that they are small or that they may not persist going forward.
Some possible deviations from a random walk are such that they ought to be "arbitraged away" if they were actually to exist. If such deviations exist, it's hard to see how they could fail to be minor.
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