A Puzzle, a Solution, and Why It Cannot be Right. Maybe.

In the U.S. in the 20th century, stocks have consistently outperformed bonds. For an economist, this is puzzling. If you consistently get a better return buying stocks than buying bonds, why does anyone buy bonds? One would expect investment to shift out of bonds and into stocks until the return on both investments was equal.

There are several solutions that other people have offered to this puzzle. One is to argue that investors are risk averse and bonds have a more predictable yield; the rebuttal has been that, except over very short time periods, stocks almost always outperform bonds, so nobody investing for more than a few years can reduce his risk by buying bonds. Another is to claim that the U.S. market in the 20th century is a special case; investors in stocks just happened to be lucky, many times over.

I have a different solution, one that is elegant, coherent, and arguably cannot be right. More interesting still, the argument that shows it cannot be right also shows that there is no such thing as insider trading. 

I start with a bit of real world history:

When the Macintosh first came out, I was already familiar with the idea of a graphic interface and convinced that it was a better way of interacting with computers, having seen a video some years earlier on work at Xerox PARC. I observed that the rest of the world, or at least the people I could directly observe, had no idea what was going on; one colleague, told that I was buying a Mac, asked why I wasn't getting a PC Jr. instead, apparently in the belief that they were roughly comparable because of similar size. I concluded that if his response was typical, Apple stock was underpriced, so I bought some.  It turned out to be a correct decision. 

I was an insider for that transaction, not in the legal sense but in the  economic sense; I knew relevant things that most of the market did not know. Imagine a stock market in which every investor is in that sense an insider, each for a different tiny niche, a particular subset of investments with regard to which he has information that other investors do not have and cannot readily obtain. Like any inside trader, the investor can expect a better than market return when he invests on the basis of his inside information.

If expected return was all that mattered, each individual would invest only in the niche where he had specialized information. But individual investors are risk averse, so wish to diversify their investments. Having bought or sold stock in my niche to the point where any further bets would lose me as much in increased risk as they make me in expected return, additional investments will be outside of my niche. My investment income consists in part of a (say) 2% return on my capital, in part of an additional stream of income representing the rent on my specialized knowledge and obtained via a more than 2% return on capital invested in my niche.

It follows that the average return on investment, mine and everyone else's, is higher than the marginal return. My average return, pooling niche and non-niche investment, is something more than two percent. But my marginal return, what I would get if I invested another dollar, is only 2%, since I am already invested in my niche up to the limit imposed by risk aversion. The argument for equalizing returns on stocks and bonds is put in terms of average return—that, after all, is what we can observe. But the logic implies that what is equalized is marginal return. If bonds yield the same 2% return as stocks bought by an outsider—which, outside of my niche, I am—a 2% return on bonds is a sufficient reason not to shift capital out of them. 

We now have an explanation of how, in equilibrium, the average return on stocks can be consistently higher than the average return on bonds.

Unfortunately, the explanation cannot be right. The problem is that the outsider could choose some variant of the strategy sometimes described as throwing darts at the Wall Street Journal, buying stocks at random and so getting the market's average return. If he wishes to eliminate any random element, he could make his investment outside his niche by buying 1/100,000,000 of the stock of every firm on the  exchange,  guaranteeing himself the market's average return. He is  getting the average market return on his outside investments, more than the average market return on his inside investments. So is everyone else. 

Call the average market return R. I have just demonstrated that R equals a weighted average of Rout=R, the return on outside investments, and Rin>R, the turn on inside investments. Hence I have demonstrated that R>R, which is mathematically impossible.

I reached this point in the argument some years ago and eventually gave up, on the assumption that I must be making a mistake.  A day or two ago, it occurred to me that I had not only proved that my explanation of the stock/bond puzzle was wrong, I had also proved that insider trading, as normally imagined, does not exist.

To see why, apply the same argument to a market where only some investors are insiders. Anyone who wants can get the market return by investing in a random collection of stocks—or, to avoid any randomness, an equal fraction of every stock out there. Assuming, as economists routinely do, that investors are rational, all outsiders follow that strategy. Insiders get a return greater than the market return, outsiders get the market return. The market return is a weighted average of the return to insiders and outsiders. Hence R>R.

The only way out of this puzzle that I can see, whether for the general case of insider trading or my explanation of the stock/bond puzzle, is to assume that investors who are not insiders consistently follow a strategy that produces a lower return than another strategy readily available to them. When the insider buys or sells on the basis of his specialized knowledge there is some outsider willing to sell or buy, providing the other side of the transaction—despite knowing that doing so, in a market containing some insiders, is on average a losing game. That appears to contradict the assumption of rational actors, hence to be heretical from the standpoint of conventional economics.

Readers to whom all of this seems like confusing mumbo-jumbo are free to skip over it and wait for my next post, which will be on a different subject. Economist readers are invited to offer some solution to the puzzle that does not depend on investor irrationality.