Tuesday, September 2, 2014

A Perennial Argument in Financial Economics

This post addresses the presence of “bubbles” in asset prices. The first task is to define a “bubble,” partially so we know what we’re discussing, and partly so I can stop using scare quotes. The intrinsic value of an asset is the present value of the future cash flows, discounted at the appropriate rate, called the capitalization rate. The capitalization rate is the required return on the asset less the expected growth rate of the cash flows themselves. For equities, the cash flow is the sum of: (1) dividends, (2) capital gains including those arising from buybacks. VNote that a lot of the work in finance is about the correct model for the required return. For example, the Capital Asset Pricing Model (CAPM) and the Fama-French three factor model. I’m not going to go over those specific models in this post, but I will discuss the importance of the required return shortly.

When discussing the stock market as a whole, we can arguably use a simplified valuation equation, known as the Gordon Growth model. The Gordon model assumes a constant growth rate of the cash flows. This simplification allows us to see the three factors that affect asset values: expected future cash flows, required return, and expected growth rate. These factors are the fundamentals of the asset. Now, in financial economics, we think of a “bubble” as a fourth factor, one that causes the market price to deviate from the intrinsic value. The equation would thus be:

So is any deviation from intrinsic value is a bubble? That would be true in a world of perfect information and foresight. But recall we estimate everything, and have imperfect knowledge and information, so the market value can substantially deviate from the intrinsic value without there being a bubble. This fact makes a bubble extremely difficult to detect except (maybe) in hindsight. Essentially the best we can do is to say something like “market values are very difficult to justify based on what we know about stock market fundamentals and what’s likely to happen in the future.” But caution doesn’t put your name in the papers.

My opinion is that most disagreement comes from the growth rate. I remember during the asset price run-up in the late 1990s (the so-called tech bubble) so many talking heads on the financial television shows were spouting “new economy” to justify extraordinary valuations of stocks. That’s basically an argument about growth rates. Another source of disagreement, although less so, is the required return. The problem with required return for the stock market as a whole is that it is often backed out of the valuation equation (2) using current asset values. Thus it amounts to the same bit of information but viewed in a different way.

So now we have the definition of a bubble: market prices that are not justified by the underlying fundamentals. We also now realize how difficult a definition this is to apply. That’s two reasons we see so much fighting about bubbles. And, even if we could positively identify a bubble to everyone’s satisfaction, we have no ability to time the bursting of the bubble.

I recall a paper by Scheinkman, in the early 2000s, in which he showed that a market participant that knew, for a fact, the market was currently in a bubble would still have incentive to trade because of the ‘bigger sucker’ factor. So merely recognizing the bubble exists is not enough to say it should pop. It’s also a question of when others decide there’s a bubble. By the way, there can also be negative asset price bubbles; it’s just that most bubble talk happens when asset prices appear to be abnormally high.

In the interests of responsible journalism, what I’d like to see happen is replacement of the use of “bubble” with “asset prices seem abnormally high/low.” While that might seem mealy-mouthed to some, it’s actually the only truly justifiable statement. And, if you truly believe asset prices are abnormally high, keep your mouth shut and trade: buy puts for example.

To close this post, I'll draw your attention to the trend lines drawn in the graph of Real NYSE prices below. The trend line with the highest slope would be what we'd get if we had the same stock returns during the tech boom. It's off the chart at the top. The trend line with the lowest slope is simply connecting the low point prior to the tech boom and (almost) the low point reached when the real estate crash bottomed out. The third (moderate) trend line is tracing the slope from prior to the tech boom, and assuming that the returns during that period are a reasonable guide. If that moderate trend line is correct, then a large portion of the stock boom since the mid-1990s has been unjustifiably high. But the question is, where's the bubble? It depends on where the trend line "should" be.