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In a previous post I argued that stock indices are not expected to grow faster than NGDP. After all, the only index I know of that goes back 100 years (the Dow) has risen slower than NGDP over that period. But that’s not why I made the claim, rather it seemed illogical that a sub-sample of stocks would out-perform NGDP, when the total value of all stocks would be expected to rise with NGDP in the very long run. Now there are some possible weaknesses in my argument. NASDAQ has a lower dividend yield, and hence a higher expected gain, but I doubt it dramatically affects my overall claim.

Then the argument got sidetracked on to a discussion of total returns, a different question. That seemed to be where the real objection lay. Here’s Kevin Erdmann:

I, for one, am tickled by the irony that in the comment section of this excellent post about the pessimistic bias, Scott has been pulled into an argument where he is saying that a 4% equity risk premium that persisted for a century is the result of a lucky break – that a cumulative excess return of some 5000% over that time doesn’t reflect an expected return premium for equities. On average, less than every 20 years, equity portfolios have doubled government bond portfolios.

Sorry, but this is a misuse of statistical significance. The 100 year time frame does not in any way prove that the returns were expected. Here’s a counterexample. Take the 3 most successful stocks in the Dow over the past 100 years. I have no idea what there are, let’s say IBM (NYSE:IBM), GE (NYSE:GE) and Exxon (NYSE:XOM). Now compute their total returns. Since the overall market has done well, obviously the three best would have done amazingly well. But no one would claim that their actual returns tell us anything about their expected returns. And that’s because you had cherry picked some very impressive investments, ex post. And that’s despite the fact that you would be working with 100 years of data.

In the case of the US stock market you are not just cherry picking, but double cherry picking. You are selecting one of the most impressive economies in the world over the past 100 years. A country that never adopted socialism, was never destroyed by war, revolution or hyperinflation. Even many major economies like Germany, Japan, Russia and China suffered enormous problems at various stages of the past 100 years. The commenter “dlr” shows that the US stock market has outperformed all of the other big economies. And he compares the US to other countries that have done relatively well, leaving out places like Russia, China, Argentina, Venezuela, etc. So by looking at the US you have cherry picked the most successful big economy in world history, during its golden age. But that’s not enough to explain the entire equity premium, as dlr notes. Other countries also have rather large returns.

This leads to the second form of cherry picking, you are studying what has turned out (ex post) to be the Cadillac of investments — stocks. Today we think of stocks as a perfectly normal investment. I’ve had all my 401k in stocks for almost my entire working life, and that’s not considered particularly weird. But 100 years ago stocks did not have the prestige they have today. Bonds and bank accounts would have been more typical investments. I would have had railroad bonds in my 401k. The stock market turned out to be the premier investment of the past century (for many complex and unexpected reasons), but no one knew that in 1914.

I know that people will want to latch on to the 100 years of data — surely that is statistically significant? I will admit that if stocks consistently earned large returns then you could say that investors should have caught on. Suppose that the excess returns were always positive, but ranged from 1% to 9%, averaging 5%. Then yes, 100 years would be enough. But look at this data for the Dow:

March 11, 1914 Dow = 81.57, CPI = 9.9 real Dow = 8.24

August 12, 1982, Dow = 776.92 CPI = 97.7 real Dow = 7.95

In real terms the Dow went nowhere in 68 years. Yes, the total real returns were positive because of dividends, and indeed probably larger than bonds (which were crushed by unexpected inflation after we left gold.) But a real yield equal to slightly less than the dividend yield is not all that impressive for 68 1/2 years. Now look at the next 18 years:

April 11, 2000 Dow = 11287 CPI = 171.3 real Dow = 65.9

The real Dow exploded more than 8-fold. That’s an awesome return, which doesn’t even include dividends. And then another 14 years of so-so, even given the extraordinary bull market of recent years:

March 11, 2014 Dow = 16351 CPI = 233.9 real Dow = 69.9

Yes, other indices like S&P 500 would probably have been different. The early period would probably look better, weakening my argument. But the 1982-2000 explosion would look even bigger, and the 2000-2014 slowdown even worse, both strengthening my argument. The basic picture is that in 1982-2000 the market experienced something analogous to the “inflation” of the early universe, when values just exploded.

My pathetic attempt to explain that growth would involve many factors such as slowing inflation and lower taxes on capital gains. But one factor might have been a growing awareness among investors that with modern investing techniques and longer lives and lots of people putting money away for 40 or 50 years in 401ks those massive excess returns that did occur were not “justified.” On this point theory is on my side. The equity premium puzzle. They were not expected to occur, and when they did stocks rose to a level where they are not expected to repeat, from this point forward. I think this may be why Robert Shiller seems to have never said “BUY,” at least since 1996. Perhaps his model doesn’t factor in the new normal of higher equity values due to a realization the equity premium (ex post) was too big in the past.

Don’t be lulled into thinking that 100 years of data is statistically significant. Didn’t people in 2006 say “real housing prices in America never go down on a nationwide basis.” How’d that work out?

PS. I’m not saying you should not own stocks. I’m still fully invested, and still feel they are a bit better than bonds. Just don’t count on those massive gains of the previous century, which were heavily concentrated in 18 years. My claim is that going forward, returns will be (expected to be) similar to the other 82 years — basically the dividend yield in real terms, perhaps a bit more if the dividend yield has trended downward over time. Somewhere between the US and Japanese performance since 1991.

PPS. For non-American readers the phrase “Cadillac of investments” means roughly the “Mercedes of investments.”

PPPS. Fat tails

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