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Yes Virginia, the S&P 500 really is overvalued

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There is something deeply satisfying about seeing an investment theory splatter on the windshield of the market. The road is littered with the carcasses of past investment theories.

But today let's look at the notion that Shiller's P/E should be high when long-term interest rates are low.

Before driving into the details it's good to review what Professor Robert Shiller's P/E ratio is all about. At first glance the ratio looks a lot like the familiar price-to-earnings ratio. But while the standard P/E formula divides a stock's price by its earnings per share over the last year, Prof. Shiller's method divides the stock's price by its average inflation-adjusted earnings over the last 10 years. He calls the result a cyclically adjusted P/E ratio, or CAPE.

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In contrast to a standard P/E ratio, CAPE gives you a much better picture of how prices stack up against a stock's typical earnings power. It smoothes out temporary gains or losses.

CAPE is particularly interesting when you apply it to the entire market, which Prof. Shiller does for the S&P 500 . As things stand the market's ratio is fairly high at 20.5 when compared to its historical average of 16.4. Bears use the ratio as evidence that the S&P 500 is overvalued by roughly 20 per cent, all else being equal.

However, an esteemed colleague recently pointed out that Shiller's P/E is impacted by interest rates and made the case that the ratio should be high when long-term interest rates are low. Problem is, practice tells a different tale.

It turns out the relationship between Shiller's P/E and interest rates isn't straightforwardly linear. It has a bit of a hump, which you can see in the accompanying graph that displays how average CAPEs vary by interest rate.

You'll immediately notice that low interest rate environments haven't automatically resulted in high P/Es even though high rates have historically led to P/Es. Instead, bulls who dream of bubbles and high P/Es should want interest rates to be somewhere in the middle.

Let's focus on times when interest rates are low. The second graph shows just such a period. It covers the two decades from 1935 to 1955, which saw a wide range of economic and geopolitical conditions.

As you can see, it is entirely possible for the market to trade at low ratios when rates are low. If anything the recent ratios have been high compared to past levels.

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If you just consider times when interest rates have dipped below 3 per cent, you'll find that Shiller's P/E has averaged 13.6.

As a result, history provides even more meat for the bears because it bolsters their arguments that stocks are pricey. A decline of about 34 per cent would be needed to bring Shiller's P/E back to its historic norms after adjusting for interest rates, all else being equal.

But there is a fair amount of variability in the data, which holds out a slender reed of hope for the bulls that this time may be different.

Infographic: Getting a handle on valuations

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About the Author

Norman Rothery, Ph.D., CFA, is the founder of StingyInvestor.com and has been catering to value investors since 1995. He publishes the Rothery Report, a value stock newsletter. Norm obtained a Ph.D. in atomic physics from York University before following his passion for investing. More

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