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 a 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 that 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 the yield on 10-year treasury bonds makes rational sense. Some studies criticize that it is inappropriate to compare the 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 the predictive ability of the FED model in the US for short term horizons and especially for historically high gaps between equity and treasury yields. Still, international tests of the FED Model show mixed results.

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Markets Traded
bonds, equities

Backtest period from source paper

Confidence in anomaly's validity
Moderately Strong

Indicative Performance

Notes to Confidence in Anomaly's Validity

OOS back-test shows slightly negative performance. It looks, that strategy’s alpha is deteriorating in the out-of-sample period.

Notes to Indicative Performance

per annum, annualized (geometrically) monthly return 0,874%, data from table XI panel A, benchmark buy and hold equity index ~ 11.1%

Period of Rebalancing

Estimated Volatility

Notes to Period of Rebalancing

Notes to Estimated Volatility

annualized monthly volatility 2,902%, data from table XI panel A, benchmark buy and hold equity index ~15.14%

Number of Traded Instruments

Maximum Drawdown

Notes to Number of Traded Instruments

Notes to Maximum drawdown

not stated

Complexity Evaluation
Moderately complex strategy

Sharpe Ratio

Notes to Complexity Evaluation


Financial instruments
ETFs, funds, futures

Simple trading strategy

Each month, the investor conducts a one-month predictive regression (using all available data up to that date) predicting excess stock market returns using the yield gap as an 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 - The selected strategy is a class of “Market Timing” strategies that try to rotate out of equities during the time of stress. Therefore the proposed strategy isn’t mainly used as an add-on to the portfolio to hedge equity risk directly. Still, it is more an overlay that can be used to manage the percentual representation of equities (or “equity-like assets”) in a portfolio. “Equity Market Timing” strategy can decrease the 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 amended strategy can be found out only by rigorous backtest and source academic research paper doesn’t give us any clues on how it will perform…

Source paper
Out-of-sample strategy's implementation/validation in QuantConnect's framework (chart+statistics+code)
Other papers

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