The "Fed Model" of stock valuations is that the yield on treasury bonds controls the discount rate that's applied to corporate earnings, and so moves in treasury yields ought to be reflected in moves in stock valuations (i.e., treasury rate changes ought to result in changes in P/E ratios). This paper argues that this is an error because treasury yields are based on nominal dollars and P/E ratios are based on real dollars.
Asness's argument is as follows: Expected nominal return on a stock should be equal to nominal payouts (dividends) plus nominal earnings growth rate Expected real return on a stock can be calculated as expected nominal return minus inflation. Under gentle assumptions this results in a formula to calculate expected real return as half of the earnings yield (E/P instead of P/E) plus the real earnings growth rate. Rearranging this formula says that you should be able to determine the P/E ratio from the expected real return and the real earnings growth rate. Nominal treasury yield decomposes into inflation plus real yield Let's say you observe that nominal treasury yields went up. If the real yield stays constant (today, we could observe this if TIPS bond yields don't change), then the market is saying that inflation is expected to go up. But inflation doesn't show up directly in the formula for P/E ratio derived above (which, recall, is a function of the expected real return on the stock and the real earnings growth rate). So the P/E ratio would only change if inflation affects the expected real return and the real earnings growth rate. Almost by definition, inflation ought not to have a strong effect on expected real return and real earnings growth rate. And this is backed up by historical regressions (as of 2003) for predicting nominal earnings growth based on realized inflation. Therefore, a change in nominal treasury yield not accompanied by a change in TIPS yield should not justify a significant change in the P/E ratio. The P/E ratio is effectively a real quantity. The paper also goes through refutations of some common justifications for linking P/E ratio to nominal treasury yield.
The article was published in 2003. TIPS were just starting to be sold at that time, with a 10-year TIPS yield (real yield) of about 2.25% in 2003. In 2021 we have a 10-year TIPS yield of about -0.75%. So companies ought to have a higher P/E ratio today than in 2003 based on the TIPS yield. It just so happens that inflation has been quiescent during this period, so nominal treasury rates have gone the same direction as TIPS yields.