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To learn what stocks are really worth, watch interest rates and inflation

Traders work during the IPO of Parsley Energy Inc on the floor of the NYSETraders work during the IPO of Parsley Energy Inc on the floor of the NYSE

As 10-year Treasury yields reach their highest levels since last October, investors are fretting over what a new regime of rising rates will mean for their portfolios. According to most Wall Street prognosticators, low rates––the lower the better–– justify today’s rich stock market valuations.

Now that the main justification for the bull market may be fading, it’s time to take a deep breath and try to determine what conditions, interest rates or otherwise, will nurture and sustain the type of rich valuations that prevail today. What changes to those conditions can inflict losses on investors? In short, we need a method for forecasting how much money you risk losing when the calm of low interest rates, and the surrounding climate that’s nourished stocks for so long, turns stormy.

Rob Arnott, a leading figure in both academic finance and fund management, has done pioneering work on the issue. Arnott is the co-founder and chairman of Research Affliliates, a firm that oversees $170 billion in investment strategies for mutual funds and ETFs.

Arnott argues that two principal factors determine the market’s price-to-earnings multiples, or PEs, which is an expression of what investors are willing to pay for each dollar in earnings. Those two factors are real interest rates and inflation.

According to traditional stock market theory, the lower the real, or inflation-adjusted, yield, the higher a company’s PE should be. The math is simple: If the number that is used to discount GE or Yahoo’s future earnings declines, the stocks in question merit a higher price. The same math applies to an index such as the S&P 500. As for inflation, most academics would say it doesn’t matter since profits rise and fall in sync with the ebb and flow of consumer prices. The ups and downs in the prices that enterprises charge for pork chops and computers are inflation.

Arnott and his colleagues reach a far different conclusion, one that’s of great consequence to all investors. He uses the metaphor of a valuation “mountain.” PEs climb to the mountain’s peak not when real interest rates go to negative or miniscule numbers, but when they’re in the moderate range of 3% to 5%, around the historical averages. It’s the same with inflation: instead of being irrelevant, the trend in consumer prices is critical to the value of stocks, according to Arnott. Inflation in the 2% to 3% range is a kind of golden mean.

The conclusion: Peak PEs arrive when conditions are calm, seemingly around average and destined to stay there. In other words, markets love moderation.

The numbers are convincing. Arnott examined stock market data from 1871 to the present. For the PE, he uses a 10-year average of inflation-adjusted earnings, a measure developed by Yale economist Robert Shiller that smoothes the typically volatile path of corporate profits. The data demonstrate clearly that different levels of real rates, and varying degrees of inflation, are the primary forces in setting price-earnings multiples.

When real yields are between 2% and 3%, for example, PEs climb to the mountaintop, averaging almost 19. But markets don’t like extremes, in either direction. When real rates drop below 0.5%, PEs plummet to 11.5. When they jump to over 6.5%, price-to-earnings multiples fall into the high-single digits.

A similar pattern governs the relationship between PEs and inflation. At our ideal inflation rate of 2% to 3%, multiples stand at a lofty 20.2. And, as it turns out, a surge in inflation is far more damaging to prices than a sharp rise in rates. As a measure of inflation, Arnott uses the average annual increase in the consumer price index over the past three years. When that number reaches between 5% and 6%, PEs fall below 12, a drop of 9 points, or 45%, on an increase in inflation of just 3%. Flat prices are also bad for stocks, though not as bad.

So, why do markets shudder at extremes for real interest rates and inflation? When both are extremely low, investors worry that it signals a weakening economy, and poor profit growth. Real rates usually fall when inflation rises. When the economy is overheating, the Fed is poised to intervene and raise rates, prompting investors to fear that a slowdown is imminent. As a result, demand for capital falls, driving down the price of that capital, what the real interest rate represents. The two figures rush to opposite extremes, and neither one is a friend to equities.

In fact, examining where real rates and inflation stand, in any given period, helps explain reigning PEs better than any other blend of measures. A given inflation rate, matched with the real yield, shows where valuations should be. And it’s often far from where they actually are. The difference offers a useful measure to determine whether stocks are over or undervalued.

Today, the three-year average inflation rate is at around 1.1%. The 10-year Treasury yield is 2.5%. The inflation-adjusted, or real, yield equals the difference, or 1.4%. On average over the last 144 years, that combination brings a Shiller PE of around 18. That’s almost 10 points below the current Shiller multiple of 27.7.

So, the first conclusion is that stocks appear seriously overvalued, according to the best metrics for explaining valuations. But at a PE of 18, stocks aren’t nearly at the Arnott mountaintop. Surprisingly, the current trends could push them closer to the summit. A rise in real rates has begun, and if they get to the 3% range, valuations would get closer to the ultimate sweet spot of around 22 on the Shiller PE. More inflation would also help to buoy valuations—up to a point. If both of those things happen, the market will still be overvalued, only less so.

Disaster would strike if one or both of the two forces jumps to the far frontiers. It’s unlikely that the real rate will shoot into the danger zone, either high or low, because no one is forecasting either boom times or a severe recession. The big danger is an explosion in prices. “The real threat is inflation,” says Denis Chaves of Research Affiliates. “If the Fed gets behind the curve, prices could rise rapidly. If we get unexpected inflation, it could cause a crash.”

As Chaves acknowledges, that’s a possible, but unlikely, scenario. The Arnott methodology tells us that stocks are currently too expensive and that, at best, future returns will be extremely low. While the real world is messy and doesn’t conform to theory, it’s the data that counts, and the data is a downer.