Bryan Caplan  

The Fallacy of Time Diversification: Mea Culpa?

Stimulus?... I Have Conditions...

How many times have I made this argument:

"At your young age, you have enough time to recover from any dips in the market, so you can safely ignore bonds and go with an all stock retirement portfolio." This kind of statement makes the implicit assumption that given enough time good returns will cancel out any possible bad returns. This is nothing more than a popular version of the supposed "principle" of time diversification. It is usually accepted without question as an obvious fact, made true simply because it is repeated so often, a kind of mean reversion with a vengeance.

In the investing literature, the argument for this principle is often made by observing that as the time horizon increases, the standard deviation of the annualized return decreases. I most frequently see this illustrated as a bar chart displaying a decreasing range of historical minimum to maximum annualized returns over increasing time periods. Some of these charts are so convincing that one is left with the impression that over a very long time horizon investing is a sure thing.

John Norstad says it's all wrong, and enough smart people agree that I'm close to conceding. What's the problem?
While the basic argument that the standard deviations of the annualized returns decrease as the time horizon increases is true, it is also misleading, and it fatally misses the point, because for an investor concerned with the value of his portfolio at the end of a period of time, it is the total return that matters, not the annualized return. Because of the effects of compounding, the standard deviation of the total return actually increases with time horizon. Thus, if we use the traditional measure of uncertainty as the standard deviation of return over the time period in question, uncertainty increases with time.


For an example of a bar chart which shows a better picture of uncertainty and risk over time, see the Appendix below.

Smart people also assure me that this doesn't make the equity premium puzzle go away. This further confuses me, but I'll follow the advice I've often given to others: Once you strongly suspect that you've been wrong about something, stop talking about it and cede the floor to clearer heads.

Perhaps you're one of them? If so, please enlighten us.

HT: John Nye

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COMMENTS (14 to date)
Arnold Kling writes:

Zvi Bodie has an even more compelling argument against the view that the variance in portfolio returns somehow is smaller in the long run. If that were true, then none of the equilibrium models of option prices would be correct.

Maniakes writes:

1. I'm skeptical of the random walk model used to generate the results. While short-run stock market fluctuations do appear to be random, I'd expect them to even out in the long run -- there shouldn't be a strong preponderance of bad years unless the entire economy is tanking, in which case you're screwed no matter what you invest in.

2. The question is not the spread in actual returns of one investment strategy. The question is which spread of returns is better -- an all-cash portfolio would have a spread of returns of zero, but there's a 99+% chance that an all-stock portfolio would outperform it. Where do mixed stock/bond portfolios stand relative to an all-stock portfolio?

David Robinson writes:

"Once you strongly suspect that you've been wrong about something, stop talking about it and cede the floor to clearer heads."

While generally this policy sounds very reasonable, won't it lead to making the debate environment worse, not better? People who are considering the possibility that they're wrong will view the evidence more objectively since they're not tied to a particular viewpoint.

This is similar to what Eliezer Yudkowsky was describing with "evaporative cooling"- if everyone who considers the possibility they're wrong leaves the debate, then they're not leaving the cooler heads, they're leaving the most cognitively biased.

KipEsquire writes:

There isn't a shoeshine boy on Wall Street who doesn't understand the fallacy of time diversification. It's also covered in detail in the CFA curriculum.

The way I try to explain it to laypersons is as follows: If you have a 20-year investment horizon, then losing 50% of your money at the end of Year 1 is NOT the same as losing 50% of your money at the end of Year 20.

That usually registers.

Blakeney writes:

I'd say the conventional wisdom is still correct, but not for the commonly-supposed reason: For younger workers, investing in equities is a better strategy overall, but NOT because "time-diversification" reduces the need for a low-risk portfolio component. It's because young workers already have a low-risk asset: their own future earnings.

Lord writes:

I would argue most real investors are not interested in the value of their portfolio at the end of a period of time, but the real income it can sustain over time. With current real bond rates of 1-2%, that isn't much, in fact, about the same as dividends. Historically, the longer the time frame, the more that must be invested in stock to see that it will last.

Dog of Justice writes:

I was going to chime in, but Blakeney beat me to the point I was going to make.

John writes:

I'm gonna agree with Arnold, the option pricing argument is definitely the most convincing. The other arguments seem to be just playing with numbers. I don't think KipEsquire is clear enough in what he means. For example, if you lose 50% in year 1 (or year 20) and then get 6% return in the remaining 19 periods. Then, if you have a 20 year time horizon, your average return and standard deviation would be the same in both cases at the end of the period. Questions like this really depend on the utility preferences of the investor. For example, in experimental economics, they typically find that people might prefer certain losses today compared to uncertain losses in the future. In general, people would not expect the 50% drop to occur in the future and would therefore prefer that to the loss today. It really doesn't explain the fallacy though. The answer to the fallacy is that stocks are empirically riskier without reference to preferences, but based on the argument Kling referred to regarding the cost of portfolio insurance. (put simply, you could invest in 6% money market fund or the S&P, but you could buy puts so that you make at least 6%. How much is the put and what happens as the time horizon increases?)

I admit that as intuitive as this argument is to me, it has some problems. For example, Black-Scholes is a guideline and is not perfect for valuing options. Option values are actually set by supply and demand and the preferences of investors. It would be proper to say that investors who buy and sell options estimate that the risk to the S&P increases as time horizon increases. Fundamentally, though, uncertainty is unquantifiable (See F. Knight), but the market price of risk increases over time. If anyone thinks the market is wrong, write puts like SoGen did.

Gary Rogers writes:

As far as strategies go, I recommend revisiting the EconTalk from last April where Nassim Taleb discusses his theory of Black Swans. Putting yourself in a position to maximize the probability of unforseen but highly profitable events happening whild minimizing the probability unforseen but highly costly events makes a lot of sense. He makes the case much better than I could.

bull writes:

I'm not so sure what's confusing here. Annualized return is the mean return. The variance of the sampling distribution of the mean decreases with the sample size. This doesn't say anything about the variation in the total return. I really doubt there are any investors out there who are unaware that total market returns can vary widely. Those graphs may be misleading, but they are advertising. If we want our money to grow faster than inflation, stocks have been the way to go historically. Higher variance also means we can have higher returns. I think DeLong's explanations 2 and 4 of the equity premium puzzle are right on the money (pun intended).

Chuck writes:

It seems to me that a good way to approach a market that is imperfect, is this:

1) identify the average return
2) when prices deviate above the average return by some preset amount, move money into bonds (sell high)
3) when prices deviate blow the average return by some amount, move money into stocks (buy low)

Would that basically guarentee that, over the long run, you get a better than average return?

Matt writes:

Risk is miscalculated.

The true risk of an investment is the root mean square of my personal and investment uncertainty.

When I am young, I gain a greater return with a refrigerator rather than an investment in a refrigerator company.

One can ask the inverse question. Why would a corporation sell stock rather than borrow?

fundamentalist writes:

Kyosagi, author of the Rich Dad, Poor Dad series, figured out the "time diversification" fallacy a long time ago. He warns against investing in the stock market, but writes that if you must invest in stocks, please by insurance against price declines with put options. It's pretty cheap insurance against major losses.

Steve writes:

Am I dense? I don't understand why I should care more if I lose 50% of my investment in year one or year 20.

Either way, my total return would be the same, right?

Please help. What am I missing?

It's like people who claim that a Roth IRA is better than a traditional IRA because that 25% tax bite is a lot bigger number in year 30 than in year 1. I do recognize that there are other factors (changing tax rates over time, ability to withdraw funds without penalty, etc.).

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