Bryan Caplan  

Watch the Horizon

Tyler Cowen, Unplugged... Measuring Skill...

Check out Brad DeLong's elegant explanation of the equity premium puzzle. If you look at the 1-year stock vs. bond return spread, it's easy to see why people don't buy more stocks. But if you look at the 20-year stock vs. bond return spread, it's very hard to see:

[T]he reason that the large value of the equity risk premium is called a "puzzle" is that the marginal one-year investor is not the only possible marginal investor. Consider the marginal twenty-year investor: somebody 40 with ten-year-old children who is putting money away to spend on his or her children's college, or somebody 50 saving for expenditures at 70 after they have retired. This marginal investor has to be satisfied with the configuration of asset returns as well. And what does the distribution of twenty-year-returns--either buy and hold a distributed portfolio of stocks (reinvesting the dividends) or buying and rolling over short-term Treasury bonds--look like? The answer is shown in Figure 2, which plots the twenty-year return differential over the twentieth century...

What kind of investor would turn up a 96% chance of gain, associated with an expected more-than-doubling of relative wealth, that carries with it only a 4% chance of any relative loss and a maximum loss of 17% of relative wealth? Where is this twenty-year marginal investor, and what is he or she possibly thinking? All such twenty-year marginal investors should be furiously pulling much more money out of short-term bills and investing it into diversified portfolios of stocks, thus making the equity risk premium lower and stocks less of an overwhelmingly attractive long-run investment. That is the equity premium puzzle.

Overall, I'm convinced that the puzzle is real, and invest accordingly. But sadly, a lot of economists who know better don't.

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The author at Stumbling and Mumbling in a related article titled Wising up to the equity premium writes:
    Bryan Caplan, one of my favourite bloggers, is so convinced of the equity premium that he invests accordingly.I'm not sure this is wise. The problem is that if the equity premium is a genuine anomaly, it should disappear as investors [Tracked on March 6, 2006 8:39 AM]
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KipEsquire writes:

The problem with De Long's analysis is the same as always -- focusing on average annual returns rather than on total returns -- what on Wall Street we call the "fallacy of time diversification."

Think of it this way: if you are a twenty-year investor, then you are not indifferent between losing 50% of your investment at the end of Year 1 and losing 50% of your investment at the end of Year 20.

Tom West writes:

And as so often happens, economists underplays the need for security to make most people happy. There are a *lot* of people who would spend the 20 years anxiously wondering if they were going to fall into the 4% category (including, I suspect, the 4 economists of the previous article).

Do economists really not understand why so many people consider defined-benefits pension the gold standard, and would give their right-arm for a job guaranteed for life?

As I said before, an economist is someone who can tell 20 people that "in 10 years I'm going to kill one of you and give the other 19 a million dollars each" and then wonder why most of the 20 spend a miserable 10 years.

If economists really consider the "equity-premium puzzle" a puzzle, it's no wonder why us non-economists are so reluctant to leave economic policy to them!

Dan Hill writes:

My problem (and I fit perfectly into the 40 seomthing that should have a 20 year investment horizon for retirement) is that I can't rationalise buying into a market that I beleive is seriously overvalued. If you look back, does the 20 year investment still produce above average returns if Year 1 is the peak of the market?

Mark Kritzman has a nice chapter about this in Puzzles of Finance. Chapter 2 is about measuring likelihood of loss. The point is that there are many ways of looking at the probabilities involved and what the risk means.

The stats quoted in the blog post are one of the ways of looking at loss. Other ways Kritzman includes:

  • What is the likelihood of a particular loss cumulatively over several periods?
  • What is the likelihood of a particular loss in at least one of the next several periods?
  • What is the likelihood that at any point during the investment horizon the investment will penetrate a threshold?
  • What is the likelihood of penetrating a threshold on two or more consecutive calendar year-ends?

The numbers range from 0.03% to 77.06%. Different investors could have totally different feelings about how important each question is. That's not necessarily irrational, it's risk preference.

meep writes:

First, there's a big market for bonds (short-term and long-term) -- I work for a large financial institution that has a huge portfolio of bonds... because we're selling insurance products (annuities, in particular). Our credit rating, RBC ratio, etc. is dependent on just how safe our investments are.

That said, a big part of our biz is retirement plans, and way too many people were going with the default allocation of everything to money market (!!) -- because of that fiduciary duty requirement in ERISA, it was deemed safest to have that as the default allocation. However, "lifecycle funds" are now being pushed as the most prudent default allocation for retirement plans -- part of what went into designing those funds (I did some R&D on them) was not just the maximizing of returns (otherwise, we'd go heavier on equities) but the knowledge that the closer one is to retirement, the less people will be able to stomach large fluctuations in their account value. So we looked at one-year losses, as well as achieving a good accumulation by retirement, amongst other metrics.

It is very difficult to get people to think of 20-year investment horizons, and corporations aren't much better. The best one can do in the market, many times, is to balance the need for some short-term stability with the need for good long-term results.

Victor writes:

1) I think KipEsquire's point is critical. (I think it can also be expressed by noting that the standard devation of the average return falls with the square root of the number of years, while the standard deviation of the TOTAL continues to increase by that same root n; clearly it is the total that investors care about rather than a precisely measured average return).

2) On a dollar weighted basis, I find it doubtful that there are a sufficient # of long-term investors.

It's just a fact of the life-cycle that we have large consumption demands while our incomes are lower and we are younger. And capital markets aren't the answer; borrowing when you are young solely to invest for the long-term is clearly risky, both for the possible interim margin calls, as well as point 1. Collateralized assets, like houses, may be an exception to this rule. And note that many people *do* invest in their own house.

ed writes:

"many people consider defined-benefits pension the gold standard"

This is off topic, but I wish people would stop saying this. A defined benefit pension has lower lifetime risk than defined contribution only if you ignore the risk of losing your job or having the firm decide to terminate the pension plan for some reason, as it is fully within it's rights to do. If the pension plan ends, even after many years of service, you will be denied the substantial portion of the benefits that were to accrue during your last few years before retirement. These are real risks and they happen to people all the time.

Radio Clash writes:

DeLong's analysis shows the supposed benefit of investing in stocks for investors with a 20-year horizon. But doesn't the analysis imply that investors have a permanent 20-year horizon? Such an investor does not exist. In reality, an investor with a 20-year horizon will have a 19-year horizon in one year, an 18-year horizon in two years, etc.

In 19 years this investor will have a one-year horizon. At that time safe bonds can look very attractive. In 18 years--with 2 year left in the investment horizon--the investor knows he is going to be a safe investor in one year. He allocates his portfolio appropriately for the one-year it takes to get to year 19. Even though there are two years left his investment horizon, he invests based on an effective one-year horizon. Again, bonds look attractive at the one-year horizon. The same thing happens in years 17 back through year 1. At each time the investor with a long horizon makes a series of decisions for a one-year horizons. So even at the present, the investor makes a one-year bet. So even at the present, bonds look attractive.

Paul Samuelson makes this argument in “The Long Term Case for Equities and How It Can be Oversold.” The Journal of Portfolio Management, vol. 2, no. 1, Fall 1994, p. 15-24. (and other papers going back to the 1960s).

Factoring in labor income, maybe young people can afford to be more aggressive, since stable income substitutes for bond holdings. But just looking at twenty-year average returns is the wrong-way to go.

Anyway, check out Samuelson's Journal of Portfolio Management articles on the subject. Maybe investors are not idiots. Just an idea.

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