Yes, Virginia, The S&P 500 Is Overvalued

06/08/2012 10:43 am EST

Focus: MARKETS

Bulls who dream of bubbles and high P/Es should want interest rates to be somewhere in the middle, writes Norman Rothery of The Globe and Mail.

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. But 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, Shiller's method divides the stock's price by its average inflation-adjusted earnings over the last ten years. He calls the result a cyclically adjusted P/E ratio, or CAPE.

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 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%, 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. 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.

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. If you just consider times when interest rates have dipped below 3%, 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% 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.

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