So maybe we should tweak the second sentence of Brunnermaier’s definition, to something like: Bubbles arise if the price far exceeds the asset’s fundamental value, to the point that no plausible future income scenario can justify the price. A little clunky, and of course “plausible” is a judgment call. But it does get at the idea that we shouldn’t be calling every last rise in P/E ratios a bubble.
Pointer from Mark Thoma.
I would tweak this definition back in Shiller’s direction. I think you have to know why people are buying the asset in order to know whether it is a bubble. If investors who are buying the asset have estimates of the discounted present value of the income from that asset that imply a negative real return, then it is a bubble.
To simplify, assume no aggregate inflation. That gets out of the way any difference between real income and nominal income or between real returns and nominal returns.
Suppose that I buy an asset that yields an income stream–rents, dividends, or what have you. Suppose that we discount this income stream at the risk-free rate, and the resulting real return is negative. Why, then, am I buying the asset?
1. Perhaps it has a “negative beta,” so it has tremendous diversification value. Let’s rule that one out.
2. I get utility out of owning the asset. This might apply to jewelry or paintings. Or I could get “extra utility” out of owning my house that is over and above what I save by not having to pay rent. Let’s ignore those cases, also.
3. I expect to be able to sell the asset at a higher price to someone else.
When (3) is the only way to get a positive return from holding the asset, then we have a bubble.
The difference between my definition and Fox’s is that his definition requires that we have an objective definition of “plausible.” Mine requires learning from investors what their estimates are for future income from the asset.
So with something like stocks, you have to know whether the people buying are projecting higher future earnings than what you think are plausible (in which case, no bubble) or whether they are projecting earnings that imply negative rates of return (in which case, bubble).