March 04, 2003

The Equity Premium Puzzle

Rajnish Mehra has a nice new working paper out explaining why all the attempts to resolve the "equity premium puzzle" (the puzzle of the large gap between expected returns on stocks and government bonds that he and Ed Prescott singlehandedly brought to the forefront of economists' concerns nearly two decades ago) are unconvincing:

The Equity Premium: Why is it a Puzzle?: Rajnish Mehra | NBER Working Paper No. w9512 | Issued in February 2003 | This article takes a critical look at the equity premium puzzle the inability of standard intertemporal economic models to rationalize the statistics that have characterized U.S. financial markets over the past century. A summary of historical returns for the United States and other industrialized countries and an overview of the economic construct itself are provided. The intuition behind the discrepancy between model prediction and empirical data is explained. After detailing the research efforts to enhance the model's ability to replicate the empirical data, I argue that the proposed resolutions fail along crucial dimensions.

Normally I'd just quote the abstract, and I'd be done. But Rajnish's abstract stops just where things get interesting. "I argue that the proposed resolutions fail along crucial dimensions"--sheesh!

So let me summarize:

  • It's not risk aversion: a degree of risk aversion necessary to generate the observed rate of return on stocks also generates an unacceptably-high value for the risk-free interest rate.
  • Alternative assumptions about preferences (Abel 1990; Benartzi and Thaler 1995; Campbell and Cochrane 1999; Constantinides 1990; Epstein and Zin 1991) don't work: preferences in which agents are risk averse but do not desire to smooth consumption over time are hard to wrap one's mind around, and solve only the risk-free rate puzzle, not the entire equity-premium puzzle; habit-formation models require much more evidence that people are averse to reductions in their consumption levels and a mechanism for this aversion to be convincing.
  • Modified probability distributions to admit rare but disastrous events (Rietz 1988) don't work: real interest rates should vary systematically with the likelihood of catastrophe, and they do not seem to.
  • Survivorship bias (Brown, Goetzmann, and Ross 1995) doesn't work: it cannot explain the stock-bond differential because things like the German hyperinflation that the U.S. has fortunately avoided are equally catastrophic for stocks and bonds.
  • Incomplete markets (Constantinides and Duffie 1996; Heaton and Lucas 1997; Mankiw 1986; Storesletten, Telmer, and Yaron 1999) don't work unless they create short horizons in the marginal investor.
  • Market imperfections (Aiyagari and Gertler 1991; Alvarez and Jermann 2000; Bansal and Coleman 1996; Constantinides, Donaldson and Mehra(2002); Heaton and Lucas 1996; McGrattan and Prescott 2001; Storesletten et al.) don't work for a number of different reasons...

Short horizons of marginal investors and large uninsurable risks are, I think, the only live options to be explored, at least if one restricts oneself to standard economists' models and their cousins...

Posted by DeLong at March 4, 2003 01:32 PM | TrackBack


Paging Daniel Davies.....

Posted by: Jason McCullough on March 4, 2003 02:11 PM

Indeed, heheheh.

I know John Quiggin and Simon Grant have worked up something on the EP puzzle, and I think it's AER forthcoming. Don't quote me on that and don't ask me what they said, but if we can drag John and DD from their respective blogs, this could get interesting! :)

Posted by: Michael Harris on March 4, 2003 03:35 PM

Silly me. It's out, September edition, and I think it's about implications rather than causes. Still, where's JQ & DD when you need them?

Posted by: Michael Harris on March 4, 2003 05:45 PM

A Paranoid Theory of Premium Priced Bonds

How be, instead of looking to explain the yield premium on equities, we try explaining the premium prices paid for bonds, the opposite side of the same coin?

If we go looking there, I can think of a couple of hypotheses, and I'm sure other people can think of more.

Both of mine start from the premise that "securities are sold, not bought," i.e. that there is a large sales force out there of people who make their livings by pushing securities onto people who might otherwise prefer to buy retirement homes in Costa Rica, or whatever.

Why would the paper-pushing class have an incentive to push bonds preferentially, to such an extent that bonds ended up selling at premium prices and diminished yields?

Two thoughts. First, there's a large difference between male and female investing styles, and women own more of everything than men do. Men, to an extent large enough to make a noticeable dent in their overall returns, like to trade stocks, perhaps genuinely for the ridiculous reason usually suggested, to have something to talk about at the 19th hole. Women, by contrast, are substantially more buy-and-hold investors, and paying less brokerage get higher returns overall. Might it be that a.) Women see bonds as natural purchases for their buy-and-hold style, and that women's greater purchasing power pushes up the prices of bonds? b.) That salesmen, knowing that they are not going to make as much from women's turn-over, try harder to make higher margins on bond prices? or c.) not likely, women be less price discriminating in their purchases of things they see themselves holding for the long haul?

That bunch of thoughts apart, I have a paranoid notion that led to my heading above. I am struck by the inteligence, wealth, and prestige of many bond traders and bond trading houses, and I wonder why this is. Might it be that there is a reasonably large group of people who make good money not out of brokerage and sales margins but on buying low, selling high, on the basis of genuine skill and knowledge? If such a group existed, surely they would be more interested in the market for bonds, which make huge swings on the basis of broad interest rates, rather than in stocks, the swings of which are complicated by all sorts of day to day news, noise, fads? If these two were plausible, mightn't these intelligent and skillful people put enough of their time into promoting the mythology and allure of bonds that they ended up having, on average, price premiums, and hence eroded returns?


Posted by: David Lloyd-Jones on March 4, 2003 08:41 PM

Hi Michael,

The links will be up on my blog any moment now. Comments much appreciated.

Posted by: John Quiggin on March 4, 2003 10:11 PM

Oddly enough, I'm currently writing something for my blog about uninsurable risks in general. One other matter that's always concerned me, though, has been the use of the dividend reinvestment assumption. Surely it's not possible for the market as a whole to reinvest its dividends ... but most (not all) studies of the ERP that I've seen have assumed dividend reinvestment. I don't have much of a handle on how much of a bias this introduces into the data, but I suspect it might be large.

Posted by: dsquared on March 4, 2003 11:52 PM

And providing the usual ferreting service for those of us who don't subscribe to the NBER distribution:

Posted by: dsquared on March 4, 2003 11:57 PM

And finally, as a post-Keynesian patriot, I'd point out that Mehra's treatment of Bansal & Coleman's liquidity preference modelling is a bit weak. Liquidity isn't just a "transactions service", and his statements about government bonds aren't really very convincing.

Posted by: dsquared on March 5, 2003 12:15 AM

What about Mordecai Kurz's Rational Beliefs Equilibrium model? That one seems the most promising to me

Posted by: arnold kling on March 5, 2003 06:58 AM

That's just a special case of uninsurable risks and/or short horizons, innit?

Posted by: dsquared on March 5, 2003 07:25 AM

To expand on the above, I seem to remember that the heavy lifting of the Rational Beliefs modelling in the Kurtz & Beltratti paper is in doing the work to show that a rational beliefs equilibrium is one in which agents have to bear undiversifiable risk. Once that conclusion is established, it just gets plugged into a representative agent model in which the RB characteristics aren't really driving the conclusion. I don't see it as an advance (in this particular question) on Mankiw's simply assuming by fiat that there is uninsurable residual risk in the economy.

None of which is to disparage RB in general, btw, which I don't understand enough to criticise, but which actually looks to me as if it might be a promising approach if we still think that neoclassical economics is worth saving ...

Posted by: dsquared on March 5, 2003 07:36 AM

Probably a dumb question here, but why is hyperinflation equally disasterous for stocks and bonds? Owning a stock is owning the right to future cash flows - dividends - which are not fixed and indeed which should hyper-increase should there be hyper-inflation. Owning a bond gives you fixed future cash flows.

Posted by: Andrew Boucher on March 5, 2003 08:22 AM

In principle you're right, but in practice the only way to stop a hyperinflation is to create a teeth-grinding recession which knackers your real cash flows on equity. Some exceptions to this, I'm sure (a currency reform must have worked *somewhere*, *once*), but for the big economies, it's been the historical experience.

Also, if there's hyperinflation, it's very difficult to persuade people to extend working capital loans, which throws a huge handful of sand into the wheels of commerce.

Posted by: dsquared on March 5, 2003 08:54 AM

I recall a recent popular book which contains time series over the last century for various major economies. Just eyeballing them, it looked like although equity returns may have been miserable in countries which got WWI or WWII fought in their vicinity, bond returns were pretty much wiped out completely.

That's not very quantitative, (and surely we'll do better at not killing each other in this century, right?), but it did seem like an obvious difference.

Ah! just remembered the title: "Triumph of the Optimists"

Posted by: Dave Long on March 5, 2003 10:24 AM

There is a Yale paper about that relates the equity premium to generational changes in population. The boomers are 25 million more than their parents and 15 million more than their children, so as the boomers hit peak earnings years and thought more of retirement they invested more and the market gained in multiple from 1983 to 2000. Look out for the coming contraction of investing population.

Also, starting poing is everything. Warren Buffett, folks. With an S&P p/e ratio of 8 in 1980, what a wonderful time to invest. With a p/e of 15 by 1990, there were still all sorts of fine investments. A p/e of 34 by 2000 - oops.

Posted by: anne on March 5, 2003 12:26 PM

For those wanting links to John Quiggin's blogging re his own EPP with Simon Grant:

or just should do it.

Posted by: Michael Harris on March 5, 2003 03:59 PM

What about management charges? Equity investment has been historically huge in comparison with cash management. All those investment banking salaries come from somewhere.

I'm sure the "units of consumption" issue is as big a measurement problem as beta too. Back to Mr Squared's problems with risk free rates I guess.

Posted by: Jack on March 5, 2003 04:31 PM
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