David Leonhardt presents a somewhat confused warning about stock valuations in his Upshot piece today. Looking at the recent run-up in stock prices the piece tells readers that it's "time to worry about stock bubbles." Actually, it's not. The stock market is high relative to its long-term trend, but there is little basis for fearing a plunge in prices as the piece suggests.

Leonhardt's basic story is that price to earnings ratios are substantially above their long-term average. He uses Robert Shiller's measure the ratio of stock prices to earnings (PE) lagged ten years. He notes that this ratio now stands at 25, which is well above its long term average. Leonhardt then tells readers:

"The average inflation-adjusted return since 1871 (the first year for which Mr. Shiller has data) in the five years after the ratio equals 25 or higher is negative 12 percent."

Leonhardt then warns against any assumptions that things might have changed and that this time is different. In other words, folks should expect some serious negative returns in the years ahead.

Of course folks who look at the data, including Shillers' data (available here), would know better. In the last two decades the stock market has twice hit the 25 PE ratio according to Shiller. The first time was in 1997, when Shiller puts the year-end ratio at 27.5. The average real return over the subsequent five years was -0.7 percent. That's not great, but not exactly a disaster either. Furthermore, the story would look considerably different if we started from the point where the ratio just crossed 25. Shiller puts the 10-year PE at 24.3 at the end of 1996. The average real rate of return for the subsequent five years from that point forward were 8.9 percent. Not much grounds for shedding tears.

The next time the PE crossed the 25 threshold was in 2004 when it hit 27.0. Shiller's data show the real rate of return in the subsequent five years was 1.1 percent. That's not fantastic, but it's probably better than you would have gotten in a money market fund and certainly a hell of a lot better than the negative 12 percent of which Leonhardt warns.

In other words, the last two times the market has crossed this magic 25 PE, investors would have been wrong if they expected a prolonged period of negative real returns. And, since these are the only two times it has crossed this threshold in the last 80 years, we might feel some comfort in using this experience as a basis for expectations of the future.

In fact, projecting stock returns really should not be a great mystery. If we assume that stock prices will on average grow at the same rate as the economy (i.e. we don't see permanently rising or falling PEs or profit shares), then the rate of return will be the rate of growth of the economy plus the portion of profit paid out to shareholders either as dividends or share buybacks. The latter has been in the range of 60- 70 percent in recent decades.

This means that if the ratio of stock prices to current year's earning is around 20 and the rate of growth is between 2.0-2.5 then we should expect real returns averaging between 5-6 percent going forward. (At the low end, we get payouts of 3.0 percent and 2.0 percent real growth. At the high end we get payouts of 3.5 percent and 2.5 percent real growth.) Note, this is a long-term average, not a prediction for next year.

This may take some of the mysticism out of stock returns, but hey, that is the way it is. Unfortunately this is far too simple for economists to understand. You can see a more elegant version of this here.

For those unfamiliar with my writings, I am not a crazy stock market enthusiast. I warned of both the stock bubble and the housing bubble.