The fed model: The bad, the worse, and the ugly

Abstract

The negative relationship between stock market P/E ratios and government bond yields seems to have become conventional wisdom among practitioners. However, limited empirical evidence and a misleading suggestion that the model originated in the Fed are used to support the model's plausibility. This article argues that the Fed model is flawed from a theoretical standpoint and reports evidence from 20 countries that seriously questions its empirical merits. Despite its widespread use and acceptance, the Fed model is found to be a failure both as a normative and as a positive model of equity pricing.

Introduction

Although many practitioners are fond of simple models, the valuation of stocks and equity markets does not seem to lend itself to such models. And although some investors may be led to believe that simply by comparing two numbers, earnings yields and bond yields, they can easily determine whether the stock market is mispriced, both theory and evidence seem to point against that belief.

A good model has to meet two conditions. First, it must follow from a solid theoretical framework; and second, it must be validated by the data. A third condition, simplicity, is essential if the model is to be adopted and widely used by practitioners. A case in point is the CAPM, the standard model used to estimate required returns on equity, which is simple, follows neatly from a theory of utility maximization, and is to a large extent supported by the data.¹ However, a simple model that has questionable theoretical underpinnings and little empirical support is simplistic rather than simple; the comprehensive evidence from 20 countries reported in this article leads to the conclusion that the Fed model belongs to this category.

The main arguments in this article can be briefly summarized as follows. First, the Fed model is flawed, or at least implausible, from a theoretical standpoint. Second, the evidence based on forward P/Es lends very little support to the model: deviations from the proposed equilibrium are substantial; earnings yields and bond yields are cointegrated in just 2 of the 20 countries considered; and P/Es outperform the Fed model as a tool to forecast real stock returns in 18 of those 20 countries. Third, the longer-term evidence based on trailing P/Es lends even less support to the Fed model.

Asness (2003) argues that although the Fed model fails as a normative model of how stock prices should be set, it does work as a descriptive tool of how stock prices are actually set. Put differently, he argues that the Fed model may be a good behavioral description, but not a rational explanation, of stock market prices. The findings in this article show that the Fed model fails both as a normative and as a positive model of stock prices.

One important caveat: many academics simply dismiss the Fed model; they consider it too simple, too naive, and not worth of much attention. It is important, then, to notice that all the arguments in this article are just as much about the Fed model as they are about the negative relationship between marketwide P/E ratios and interest rates (or inflation). Most investors do seem to be willing to pay higher (lower) P/Es when interest rates and inflation are low (high), though not necessarily the P/Es suggested by the Fed model. Therefore, those that dismiss the Fed model outright should view this article as an inquiry into the validity of the negative relationship between marketwide P/E ratios and interest rates.

This article assembles the largest cross-section of countries and the longest time series available to test both the Fed model and the relationship between marketwide P/E ratios and interest rates. It therefore offers not a partial view for a small subset of countries or short sample periods but a comprehensive view on the validity of this model and this relationship.

Section 2 of this article discusses the pros and cons of the Fed model and evaluates its overall plausibility. Section 3 reports evidence from 20 countries that seriously questions the empirical validity of this model. Finally, Section 4 makes an assessment.