King of the Mountain

By Rob Arnott

SEPTEMBER 2011 Read Time: 10 min

Most of us remember playing “king of the mountain” as children. The goal, often accompanied by a certain measure of roughhousing, was to summit a little hill and stay at the top while others vied to push us off and take our place.

King of the Mountain is not merely a child’s game. The U.S. stock market has been straddling a surprisingly precarious “mountain” in asset valuation for nearly two decades, resisting efforts to push us back below historical norms of valuation levels except for brief periods in 2002 and 2009. We’ve written about the challenges over the past two years. In 2009, we described the coming “3-D Hurricane,” with soaring deficits and debts, in which we expect the post-baby-boom generations to pay down debts that we (1) promised to ourselves, (2) failed to prefund, (3) expect these obligations to be paid, even if our kids and grandkids are less affluent that we are, and (4) failed to consult the generations that will be expected to honor these debts. In 2010, we addressed the consequence of soaring debt burdens in most of the developed world, as compared with the generally well-managed debt burdens of our primary external creditors in the developed world.

In this issue we explore the challenges to our lofty perch in the equity markets. Specifically, we examine the potential consequences of understated inflation and too-low real interest rates, paired with a Fed policy that seems intent on further boosting inflation and eroding real interest rates.

The Valuation Mountain
First, let’s look at how real interest rates and inflation affect valuation multiples. Some years ago, Marty Leibowitz and Anthony Bova1 pointed out a “hill” in valuation multiples. When real interest rates—which we define as 10-year Treasury bond yields less the trailing three-year average CPI Inflation rate—are mid-range, suggesting solid economic growth, the stock market sports a robust P/E ratio, often well above 20 times earnings.2 When real interest rates are either negative (reflecting a desire to aggressively stimulate the economy) or unusually high (reflecting a desire to rein in an overheated economy), the average P/E ratio plummets below 11.

The real-rates valuation hill is illustrated in Figure 1. It’s quite a lofty hill. Over the past 140 years, whenever real short-term interest rates have been in their 3–4% “sweet spot,” the market has exhibited a price 21 times 10-year smoothed real earnings. At real interest rates that are either lofty (above 6% in real terms) or negative, the average P/E ratio tumbles to 11. If we limit ourselves to more recent results, over the past 50 years, we find that the peak is a little bit taller, with more tolerance for slightly lower real rates. But the shape of the curve changes remarkably little. It’s also very interesting to note that this valuation hill accounts for some 40% of the variation in P/E ratios. Real interest rates really matter to equity valuations.

It turns out that there’s another valuation hill, related to the rate of inflation. Of course, inflation generally moves in opposition to real rates: when inflation rises, often real rates fall, until the Fed decides to do something about it. In some ways, this second hill is even more powerful than the real rates hill. As we can see in Figure 2, the peak is taller, with typical P/E ratios of over 23 whenever inflation is 2–3%. However, high inflation is far more damaging to P/E ratios than high real interest rates: When trailing three-year inflation is above 6%, the P/E ratio plunges to an average of 9.4 times average 10-year real earnings.


Because real interest rates and the rate of inflation are negatively correlated, the two hills combine to create an impressive three-dimensional mountain, formed by plotting P/E ratios against both real interest rates and inflation (see Figure 3). Of course, there are some scenarios that either never happened, or happened almost never. Deflation and negative real interest rates would imply negative notional bond yields. For Treasury bond yields, that’s never happened. (PE ratios in scenarios that came close to this “impossible case” were bleak, supporting our basic thesis.)

When real rates are 3–5% (moderately high) and inflation is 1–3% (reasonably benign), the average P/E ratio is 26. But it’s a sharp peak. When real rates are a bit lower (1–3%), the average P/E ratio drops to 19, a drop of more than 25%. When real rates are high (above 5%), the average P/E ratio nearly halves to 14. When inflation is a bit stronger, the average P/E ratio drops to 20; when inflation is a bit weaker, the average P/E ratio drops to 17.

The linkages are strong. The correlation between the indicated P/E ratio drawn from this valuation mountain and the actual Shiller P/E ratio is 68%. To be sure, this is an in-sample comparison, but even after adjusting for overlapping samples, we get a t-statistic of over 7 for this comparison—a strong confirmation of the validity of the data. The bottom line: over half of the variability in P/E ratios over the past 140 years can be explained by real interest rates and the rates of inflation.

Further, the linkages are strong enough to provide an indication of whether valuation multiples ought to be higher or lower. The correlation between the “predicted” real return for stocks, based on the difference between the model P/E ratio and the current actual Shiller P/E ratio, and subsequent five-year real returns is 40%. Again, the t-statistic is significant, topping 4.0.

What does this mean? Modest—or even moderate—inflation seems to have a benign impact on valuation multiples. Modest—or even moderate—positive real interest rates seem to have similarly benign consequences. Indeed, with real rates and inflation ranging from 1–5%, the average Shiller P/E ratio hovers around 22 times 10-year smoothed earnings, give or take a mere 15%. P/E ratios fall off a cliff outside of this range.

Our Current Perch
For most of the past 20 years, we’ve occupied a benign range of low-to-moderate real interest rates and low-to-moderate inflation. Where are we today? It’s hard to know! At the end of August, the S&P 500 stood at 21 times the 10-year average real earnings, the Bureau of Labor Statistics shows trailing three-year inflation at 1% per annum, and the 10-year Treasury bond offered a yield of 2.2%. On that basis, the real yield is 1.2%. History suggests that the normal P/E ratio, when inflation and real yields are both in the 1–3% range, is about 19. So, maybe stocks are about 15% expensive relative to historical norms for benign inflation and low real interest rates.

But, this arithmetic misses something important: radical changes in the way the federal government calculates the Consumer Price Index. Using today’s methods, the 1981 inflation rate of 14% would have been reported as just under 10%. Based on official statistics, today’s method runs 3–4% lower than the 1980s method. To be conservative, let’s assume a far smaller 2% effect. This means that the reported three-year inflation of 1% would, under the old rules, equate to 3%. This, in turn, suggests that real long-bond interest rates are not 1.2%; under the old CPI rules, real yields for 10-year Treasury bonds are negative. What does this do to our outlook? It puts us right on the edge of the valuation sweet spot, with a “normal” P/E ratio of about 18 (compared with 23 before).

The Outlook
What about the future? In the next six months, the deflation from late 2008 will shortly drop out of our three year rates. CPI is up by 7% over the past 30 months, which works out to 2.3% per year. If we add our 2% adjustment to create more of an apples-to-apples comparison with history, “true” inflation is above 4% and the “true” real interest rate is very low, around –2%. At these levels, the normal Shiller P/E ratio would be 13 times our 10-year average earnings, which takes us below 800.

We’re not saying that the P/E ratio will fall to 13 in the year ahead. We’re merely pointing out that the path we’re on—low or negative real interest rates, with a conscious attempt to introduce moderate levels of inflation—is very dangerous. While low interest rates are fueling higher stock market multiples, this policy may haunt investors in the years ahead. The combination of higher inflation and lower real interest rates poses a dangerous threat to stock market valuation levels.

The risk is that current Fed policies may throw the stock market king off the mountain.

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1. Martin L. Leibowitz and Anthony Bova, CFA, 2007, “P/Es and Pension Funding Ratios,” Financial Analysts Journal, vol. 63, no. 1 (January/February):84–96.
2. As many of our readers know, we’re fond of the “Shiller P/E Ratio” as a basis for gauging stock market valuation levels. Thus, we define the P/E ratio as the current real level of S&P 500 prices divided by the 10-year average for real S&P 500 earnings.