## Warranted Stock Market Valuations and the Price-Earnings Equation Once Again

It can be shown http://delong.typepad.com/sdj/2007/05/a_teaching_note.html that the "right" way to value the stock market is with the price-earnings equation:

P = E/[r - (1/θ - 1)ρ]

Where E are the earnings--the sustainable permanent cyclically-adjusted, and correctly accounted for Haig-Simons earnings--paid on the index, r is the appropriate real rate at which to discount cash flows of the riskiness of the stock market, θ is the payout ratio of dividends to earnings, andρ is the wedge (which may be posititive or negative) between the appropriate external real interest rate r and the internall rate of return the firm can earn on its reinvested earnings.

If we are willing to assume that ρ is close to zero, than this equation is approximately:

P/E = 1/r

The price-to-permanent earnings ratio is one divided by the market's expected discount rate.

Mark Gongloff presents the ratio of prices to a ten-year lagging average of earnings for the S&P 500--the idea being that the ten-year moving average irons out transitory fluctuations in profits and gives you permanent earnings.

This is not quite right. This gives you permanent earnings five years ago. To get permanent earnings today you have to grow the average by five years of the trend growth rate of real earnings--which has been 6% per year over the past twenty years. The current value of 28 for the price-to-moving-average-of-lagged-earnings ratio corresponds to a price-to-permanent-earnings ratio today of roughly 21, and to a current r of4.8% per year.

That looks pretty good when compared to current Treasury TIPS real interest rates of 0.6% per year for five years, 1.31% per year for ten years, and 1.81% per year for twenty years. It's not the six percent per year average equity premium of days of yore. It is, however, at least half that. If you are a buy-rebalance-and-hold investor--and you should be--equities are still looking good.

But that's not the way the mind of Wall Street works. Exhibit: Mark Gongloff:

Ahead of the Tape - WSJ.com: [A] look at a stalwart measure of cheapness -- the price-to-earnings ratio -- from various vantage points suggests stocks might be dear.... The Standard & Poor's 500-stock index trades at 15 times forecast operating earnings this calendar year. But that's not much of a deal when compared with the 60-year average of about 12.... Other takes on P/E lead to a still-more-bearish conclusion. When measured against the past 12 months' reported earnings, the S&P 500's P/E ratio jumps to about 21, above its 60-year average of roughly 16.

Benjamin Graham and David Dodd... suggest weighing prices against earnings averaged over a period of as long as 10 years. On that basis, the S&P 500 today trades at roughly 28 times reported earnings. That's lower than the peak of about 48 at the height of the dot-com bubble, but hardly a bargain; for the past 60 years, that P/E ratio has averaged about 21....

James Montier, global equity strategist at Société Générale, said his screening had uncovered a rich vein of short-selling opportunities. "If one finds lots of shorts, and not many longs, it suggests that the market is generally overvalued," Mr. Montier says....

"Are there securities where valuations are high? Absolutely," says Tim Ghriskey, chief investment officer at Solaris Asset Management. "But we do not have the risk we had in 2000, where valuations were at historic extremes."

Surely not. But we're not at a low extreme, either.

It's just worth pointing out that whenever the stock market is at valuation ratios that Gongloff and company consider "normal" then equities are an absolutely amazing deal relative to all kinds of bonds