# Breaking Down The Fed Model

The beginning of the 21st century was witness to the advancement of the Fed Model as a stock valuation methodology by Wall Street gurus and the financial press. The Fed Model compares stock yield versus bond yield. Proponents almost always point to the following three attributes to explain its popularity:
• It is simple,

• It is backed by empirical evidence and

• It is backed by financial theory.
This article will take a look at the basic ideas behind the Fed Model - how it works and how it was developed. We will also discuss challenges to its success and theoretical soundness.

What Is the Fed Model?
The Fed Model is a valuation methodology that states there is a relationship between the forward earnings yield of the stock market (typically the S&P 500 index,) and the 10-year Treasury bond yield to maturity (YTM). The yield on a stock is the expected earnings over the next 12 months divided by the current stock price and is symbolized in this article as (E1/PS). This equation is the inverse of the familiar forward P/E ratio, but when shown in this yield form it highlights the same concept as the bond yield (YB) - that is, the concept of a return on investment.

Some advocates of the Fed Model think the yield relationship varies over time, so an average of each period's yield comparison is used. The more popular method appears to be one where the relationship is fixed at the particular value of zero. This technique is referred to as the strict form of the Fed Model because it says the relationship is strict equality.

In the strict form, the relationship is such that the forward stock yield equals the bond yield:
 (E1/PS) = YB

Two conclusions can be drawn from this:
1. The difference in (E1/PS)-YB = 0,
2. Alternatively, the ratio of (E1/PS)/YB = 1.

The premise behind the model is that bonds and stocks are competing investment products. An investor is constantly making choices between investment products as the relative prices between these products change in the market place.

Origins
The name "Fed Model" was manufactured by Wall Street professionals in the late 1990s and it's important to note that this system is not officially endorsed by the Federal Reserve Board. On July 22, 1997, The Fed's "Humphrey-Hawkins Report" introduced a graph of the close relationship between long-term Treasury yields and the forward earnings yield of the S&P 500 from 1982 to 1997 (Figure 1).

 Equity Valuation and Long-Term Interest Rate Figure 1 Note: Earnings-price ratio is based on the I/B/E/S International, Inc. consensus estimate of earnings over the coming 12 months. All observations reflect prices at mid-month. Source: Board of Governors of the Federal Reserve System Monetary Policy Report to the Congress Pursuant to the Full Employment and Balanced Growth Act of 1978; July 22, 1997 http://www.federalreserve.gov/boarddocs/hh/1997/july/FullReport.pdf

Shortly thereafter, in 1997 and 1999, Ed Yardini at Deutsche Morgan Grenfell published several research reports further analyzing this bond yield/stock yield relationship. He named the relationship the "Fed's Stock Valuation Model", and the name stuck.

The original use of this type of analysis is not known, but a bond yield versus equity yield comparison has been used in practice long before the Fed graphed it out and Yardini began marketing the idea. For example, I/B/E/S has been publishing the forward-earnings yield on the S&P 500 versus the 10-year Treasury since the mid-1980s. One would suspect that due to its simplicity this type of analysis was probably in use some time before that as well. In their March 2005 paper entitled "The Market P/E Ratio: Stock Returns, Earnings, and Mean Reversion," Robert Weigand and Robert Irons comment that empirical evidence suggests that investors began using the Fed model in the 1960s soon after Myron Gordon described the Dividend Discount Model in the seminal paper "Dividends, Earnings and Stock Prices" in 1959.

Using the Model
The Model evaluates whether the price paid for the riskier cash flows earned from stocks is appropriate by comparing expected return measures for each asset - YTM for bonds and E1/PS for stocks.

This analysis is typically done by looking at the difference between the two expected returns. The value of the spread between (E1/PS)-YB indicates the magnitude of mispricing between the two assets. In general, the bigger the spread, the cheaper stocks are supposed to be relative to bonds and vice versa. This valuation suggests a falling bond yield dictates a falling earnings yield which will ultimately result in higher stock prices. That is PS should rise for any given E1 when bond yields are below the stock yield.

Sometimes financial market pundits carelessly or possibly ignorantly say, "Stocks are undervalued according to the Fed Model (or interest rates)." Although this is a true statement, it is careless because it implies that stock prices will go higher. The correct interpretation of a comparison between the stock yield and the bond yield is not that stocks are cheap/expensive, but that stocks are cheap/expensive relative to bonds. It may be that stocks are expensive and priced to deliver returns below their average long-run returns, but bonds are even more expensive and priced to deliver returns far below their average long-run returns.

It could be possible that stocks could continuously be undervalued according to the Fed Model while stock prices fall from their current levels.

Observational Challenges
Opposition to the Fed Model has been based on both empirical, observational evidence and theoretical shortcomings. To begin, although stock and long-term bond yields appear to be correlated from the 1960s forward, they appear to be far from correlated prior to the 1960s.

Also, there may be statistical issues in the way the fed model has been calculated. Originally, statistical analysis was conducted using ordinary least-squares regression, but it may appear that both bond and stock yields are co-integrated, which would require a different method of statistical analysis. Professor Javier Estrada wrote a paper in 2006 called "The Fed Model: The Bad, The Worse, And The Ugly" where he looked into the empirical evidence using the more appropriate co-integration methodology. His conclusions suggest that the Fed model may not be as good of a tool as originally thought.

Theoretical Challenges
Opponents of the Fed Model also pose interesting and valid challenges to its theoretical soundness. Concerns arise over comparing stock yields and bond yields because YB is the internal rate of return (IRR) of a bond and accurately represents the expected return on bonds. Remember that IRR assumes that all coupons paid over the life of the bond are reinvested at YB; whereas, E1/PS is not necessarily the IRR of a stock and does not always represent the expected return on stocks.

Furthermore, E1/PS is a real (inflation-adjusted) expected return, while YB is a nominal (unadjusted) rate of return. This difference causes a breakdown in the expected return comparison.

Opponents argue that inflation does not affect stocks like it does bonds. It is typically assumed that inflation will be passed through to stock holders via earnings, but coupons to bond holders are fixed. So, when the bond yield rises due to inflation, PS is not affected because earnings rise by an amount that offsets this increase in the discount rate. In short, E1/PS is a real expected return and YB is a nominal expected return. Thus in periods of high inflation the Fed Model will incorrectly argue for a high stock yield and depress stock prices, and in low inflation it will incorrectly argue for low stock yields and increase stock prices.

The above circumstance is called the illusion of inflation which Modigliani and Cohn put forth in their 1979 paper "Inflation, Rational Valuation and the Market". Unfortunately, the inflation illusion isn't as easy to demonstrate as it seems it should be when dealing with corporate earnings. Some studies have shown that a great deal of inflation does pass through to earnings while others have shown that very little does.

The Bottom Line
The Fed Model may or may not be a very good investment tool, but one thing is certain: If you think stocks are real assets and pass inflation through to earnings, then you cannot logically invest your capital based on the Fed Model.