Your last letter cleared things up. You're wrong, plain wrong--and I see now that we are not at odds over a mere difference of opinion. I can imagine reasons for thinking the Dow should be at 36,000: You might have argued, for instance, that the American economy is going to race away, growing faster than it ever has in the past. This would be bad economics, but at least it would be logically admissible. This is not the kind of argument you're making. Your reasons for believing that the Dow should be at 36,000 are wrong in the same way that it's wrong to say two plus two equals five. That, in fact, is almost literally what you are saying.
According to you, my mistake is that I'm implicitly predicting zero real growth in earnings and dividends. Indeed, you think the market as a whole is making the same error. The fact that earnings have grown faster than inflation for decades is "little understood," you say. If only this record of growth were recognized, the Dow would be already be priced at 36,000.
You're right that earnings have increased in real terms (though you exaggerate the rise by looking at aggregate earnings rather than earnings per share; let that pass). But can you seriously believe that this has been going on decade after decade without the market's noticing? Doesn't that strike you as just a little unlikely? Of course it's been noticed, very much noticed--so adequately noticed, in fact, that the prospect of real growth in both earnings and dividends is already fully priced into the market.
You fail to see this because you haven't understood your "simple finance formula." To get your estimate of 36,000, the formula in effect adds together an infinite stream of stock payouts, discounts them to derive the present value, and expresses this value as a price-to-payout ratio. Fine. But where your formula says "payout," you have taken this to mean earnings. Think about that. If companies pay out every cent of their profits to shareholders, as you implicitly assume, how will they be able to grow, as you also assume, year after year, forever? Growth requires investment, and that must be paid for by stockholders. (There are other ways to pay for investment apart from retaining earnings, but they boil down to the same thing. If the firm borrows to invest, the interest payments are charged against profits. If it sells new stock, that dilutes earnings per share for existing investors.) To achieve growth over the long haul, companies need to invest, one way or another, some of their stockholders' earnings.
In the real world, of course, this is exactly what they do. Companies pay only some of their earnings out as dividends. As a result, they grow. Earnings per share, dividends per share, and the underlying value of companies can and do increase in real terms. Yes, you see, I had noticed this--and so has the market. The Dow's present earnings yield of 4 percent is sufficient to provide, for example, a dividend yield of 1 percent, plus reinvestment of 3 percent of companies' value each year to finance future growth. But given these numbers, it is wrong to do what you do and calculate present value by summing earnings to infinity. In this scenario, three-quarters of earnings are never paid out to shareholders. The right measure of value is the sum of discounted dividends. This fully captures the effect of capital appreciation because dividends are themselves growing along with the worth of the company.
It so happens that the market's average dividend yield right now is not much more than 1 percent, and the corresponding price dividend ratio not much less than 100. These are the sort of figures you have in mind for the Dow--except that you substitute "earnings" for "dividends," thereby inflating your valuation by a factor of four. In other words, the pricing anomaly you claim to have spotted simply isn't there. Using your own method, provided only that you put the right variable into the formula, the market is about fairly valued. This error is nothing to do with the risk premium (though we also disagree about that) and nothing to do with our forecasts for the American economy (though I expect we disagree about those as well). The fact is, you've just got your math wrong.
Now you ask me to justify the claim that America is a bubble economy. I wouldn't want to press the idea too far. It would be ridiculous to argue, for instance, that a broad range of American asset prices are as badly out of line with fundamentals as their Japanese (or even British) equivalents were in the late 1980s. But history suggests that one sign of a bubble in any particular market is the willingness of people to advance--and believe--ever more desperate rationales for the strength of prices. Your reasoning claims to explain why a market that is expensive by any historical measure is actually priced at a quarter of its true value. If you're looking for evidence of an American bubble, that would be a place to start.