# FED Model

FED Model (a favorite name for a model which uses aggregate equity market earnings yield and long-term bond yields to predict equity returns - the greater is gap in behalf of stocks, the greater are their subsequent returns and vice-versa) is one of the most controversial models used by practitioners and academics. Countless studies have been written on this subject. Some of them rejected it and others defended it. However summary evidence shows that the gap between the earnings yield and the 10 year treasury yield has some predictive power on short term horizons during the last 40-50 years. We present a simple strategy which uses the difference between earnings yield and bond yield as an independent variable in a regression equation used to predict equity excess return and then uses that prediction as an input to market timing decision. The strategy could be improved by using other variables like the term spread or FED funds premium.

## Fundamental reason

For most investors, bonds and equities are competing assets. Therefore comparing yields on equities with yield on 10 year treasury bonds makes rational sense. Some studies criticize that it is inappropriate to compare nominal yield on bonds to real yields on equities, but defending studies counter with the fact that investors historically have suffered from inflation illusion, i.e. discounting real cash flow streams with nominal interest rates. Studies in this summary show predictive ability of the FED model in the US for short term horizons and especially for historically high gaps between equity and treasury yields, but international tests of FED Model show mixed results.

### Keywords:

## market timing, asset class picking

## Simple trading strategy

Each month, the investor conducts a 1 month predictive regression (using all available data up to that date) predicting excess stock market returns using the yield gap as independent variable. The "Yield gap" is calculated as YG = EY − y, with earnings yield EY ≡ ln (1 ++ E/P) and y = ln (1 ++ Y) is the log 10 year Treasury bond yield. Then, the strategy allocates 100% in the risky asset if the forecasted excess returns are positive and otherwise it invests 100% in the risk-free rate.

## Hedge for stocks during bear markets

Partially - Selected strategy is a class of "Market Timing" strategies which try to rotate out of equities during time of stress. Therefore proposed strategy isn't mainly used as an addon to portfolio to hedge equity risk directly, but it is more an overlay which can be used to manage percentual representation of equities (or "equity like asssets") in a portfolio. "Equity Market Timing" strategy can decrease overall risk of equities in a portfolio and it can improve the risk-adjusted returns. Moreover, as strategy's goal is to hold equity market only in a positive times for equity market factor and be out of equities otherwise, therefore this logic can be maybe used to create amended market timing strategy (using original rules) which is out of equities during positive times and holds bonds (or goes short equities) during bad times. This new amended strategy can be maybe used as a hedge/diversification to equity market risk factor during bear markets. However, performance/risk characteristics and overall correlation and quality of suggested ammended strategy can be find out only by rigorous backtest and source academic research paper doesn't give us any clues on how it will perform...

## Source Paper

Asness: The FED model and expected asset returns

http://www.ebs.edu/fileadmin/redakteur/funkt.dept.finance/DGF/downloads/Paper/No-164.pdf

Abstract:

The earnings yield and long-term bond yields have been widely used to predict asset returns. In this paper, I focus on the predictive role of the stock-bond "yield gap" - the difference between the earnings yield and the 10 year Treasury bond yield - also know as the FED model, and which can be interpreted as a long term yield spread of stocks relative to bonds. Conditional on other forecasting variables, the yield gap forecasts positive excess stock returns, both at short and long forecasting horizons, although the forecasting power is greater at the near horizons. On the other hand, the yield gap forecasts negative excess returns for bonds, at both short and long horizons. A VAR variance decomposition for stock market returns, shows that shocks in the yield gap are highly positively correlated with innovations in both future discount-rate and cash flow news, confirming that the spread conveys information about future earnings and returns. An investment strategy based on the forecasting ability of the Yield gap produces higher Sharpe ratios than passive strategies in both the market index and long-term bond. In the context of an equilibrium multifactor ICAPM, the yield gap has some explanatory power over the cross section of stock returns.

## Hypothetical future performance

## Other Papers

Maio: The 'Fed Model' and the Predictability of Stock Returns

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=531903

Abstract:

The focus of this paper is on the predictive role of the stock-bond yield gap -- the difference between the stock market earnings (dividend) yield and the ten-year Treasury bond yield -- also know as the "Fed model". The results show that the yield gap forecasts positive excess market returns, both at short and long forecasting horizons, and for both value and equal-weighted indexes, and it also outperforms competing predictors commonly used in the literature. These findings go in line with the predictions from a dynamic accounting identity. The absence of predictive power over dividend growth, dividend payout ratios, earnings growth, and future one-period interest rates, actually strengthens the return predictability associated with the log yield gap at very long horizons. By performing an out-of-sample analysis, the results show that the yield gap has reasonable out-of-sample predictability over the equity premium, when the comparison is made against a simple historical average, especially when one imposes a restriction of positive equity premia. Furthermore, the yield gap proxies generally present greater out-of-sample predictability power than alternative forecasting variables. An investment strategy based on the forecasting ability of the \textit{yield gap} produces significant positive certainty equivalent estimates for realistic levels of risk aversion.

Clemens: A Behavioral Defense of the FED Model

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=958800

Abstract:

In any balanced portfolio, investors need to assess the relative attractiveness of equities and bonds, the usual asset classes "competing" for funds. A tool widespread used in asset allocation decisions is the so-called FED. In my view, the critique of the FED model has not always been fair and this paper therefore presents a behavioral defense of the FED model. By combining the FED model and the CAPM model, it becomes evident that the FED model is able to detect time variation in the equity risk premium and behavioral biases in long-term earnings growth expectations. Assuming that share prices are the sum of a fundamental value element and a noise/sentiment element, then the use of statistical tools such as confidence intervals will reduce potential decision biases caused by noise/sentiment and thereby improve the predictive power of the FED model. The results in this paper suggest that the FED model does a better job at predicting relative returns of stocks versus bonds than at predicting absolute stock returns. By basing decisions only on data points outside a predetermined confidence interval, the predictive power is increased manifold, enhancing potential gross returns and reducing transaction costs. The optimal prediction horizon for the FED model appears to be 12-36 months, somewhat shorter than the 5-10 year horizon found for the P/E mean-reversion model a la Campbell-Shiller. Thus, the FED model and the long-term P/E mean reversion model are complementary models of return prediction, not competing model.

Shen: Market-Timing Strategies That Worked

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=445920

Abstract:

In this paper, we present a few simple market-timing strategies that appear to outperform the "buy-and-hold" strategy, with real-time data from 1970 to 2000. Our focus is on spreads between the E/P ratio of the S&P 500 index and interest rates. Extremely low spreads, as compared to their historical ranges, appear to predict higher frequencies of subsequent market downturns in monthly data. We construct "horse races" between switching strategies based on extremely low spreads and the market index. Switching strategies call for investing in the stock market index unless spreads are lower than predefined thresholds. We find that switching strategies outperformed the market index in the sense that they provide higher mean returns and lower variances. In particular, the strategy based on the spread between the E/P ratio and a short-term interest rate comfortably and robustly beat the market index even when transaction costs are incorporated.

Salomons: A Tactical Implication of Predictability: Fighting the FED Model

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=517322

Abstract:

This paper confirms that high earnings yield portend high equity returns. Absolute valuation levels of equity have predictive power over future long run equity returns. The predictability is far less powerful in the short term. On a tactical investment horizon, investors tend to rely on the relative valuation of equity versus bonds to gauge whether equity markets are attractive. The FED model, which compares earnings yield and bond yield, is the preferred yardstick in the finance profession. First, this paper examines the FED model and shows that it is not only theoretically flawed, but it is also not able to predict equity returns over long sample periods. Second, we improve the model by adding corrections for perceived risk enabling a better fit of the data. Third, the main innovation is testing a tactical asset allocation model constructed on the basis of the improved FED model. A model portfolio taking advantage of the short-term deviation in relative value, corrected for risk, leads to superior performance.

Asness: Fight the Fed Model: The Relationship Between Stock Market Yields, Bond Market Yields, and Future Returns

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=381480

Abstract:

The "Fed Model" has become a very popular yardstick for judging whether the U.S. stock market is fairly valued. The Fed Model compares the stock market's earnings yield (E/P) to the yield on long-term government bonds. In contrast, traditional methods evaluate the stock market purely on its own without regard to the level of interest rates. My goal is to examine the theoretical soundness, and empirical power for forecasting stock returns, of both the "Fed Model" and the "Traditional Model". The logic most often cited in support of the Fed Model is that stocks should yield less and cost more when bond yields are low, as stocks and bonds are competing assets. Unfortunately, this reasoning compares a real number to a nominal number, ignoring the fact that over the long-term companies' nominal earnings should, and generally do, move in tandem with inflation. In other words, while it is a very popular metric, there are serious theoretical flaws in the Fed Model. Empirical results support this conclusion. The crucible for testing a valuation indicator is how well it forecasts long-term returns, and the Fed Model fails this test, while the Traditional Model has strong forecasting power. Long-term expected real stock returns are low when starting P/Es are high and vice versa, regardless of starting nominal interest rates. I also examine the usefulness of the Fed Model for explaining how investors set stock market P/Es. That is, does the market contemporaneously set P/Es higher when interest rates are lower? Note the difference between testing whether the Fed Model makes economic sense, and thus forecasts future long-term returns, versus testing whether it explains how investors set current P/Es. If investors consistently confuse the real and nominal, high P/Es will indeed be contemporaneously explained by low nominal interest rates, but these high P/Es lead to low future returns regardless. I confirm that investors have indeed historically required a higher stock market P/E when nominal interest rates have been lower and vice versa. In addition, I show that this relationship is somewhat more complicated than described by the simple Fed Model, varying systematically with perceptions of long-term stock and bond market risk. This addition of perceived risk to the Fed Model also fully explains the previously puzzling fact that stocks "out yielded" bonds for the first half of the 20th century, but have "under yielded" bonds for the last 40 years. Finally, I note that as of the writing of this paper, the stock market's P/E (based on trend earnings) is still very high versus history. A major underpinning of bullish pundits' defense of this high valuation is the Fed Model I discredit. Sadly, the Fed Model perhaps offers a contemporaneous explanation of why P/Es are high, but no true solace for long-term investors.

Durre, Giot: An International Analysis of Earnings, Stock Prices and Bond Yields

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=775426

This paper assesses the possible contemporaneous relationship between stock index prices, earnings and long-term government bond yields for a large number of countries and over a time period that spans several decades. In a cointegration framework, our analysis looks at three hypotheses. First, is there a long-term contemporaneous relationship between earnings, stock prices and government bond yields? Second, does a deviation from this possible long-run equilibrium impact stock prices such that the equilibrium is restored? Third, do government bond yields play a significant role in the long-run relationship or does the latter only involve stock prices and earnings? We also study the short-term impact of changes in long-term government bond yields on stock prices and discuss our short-term and long-term results in light of the recent developments regarding the so-called Fed model.

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