Fed Model

These blog entries summarize recent critique of and support for the Fed Model and its variants.

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Testing the Fed Model

The guiding belief of the Fed Model of stock market valuation is that investors use a Treasury note (T-note) yield as a benchmark for the expected (forward) earnings yield of the stock market. When the gap between the forward earnings yield and the T-note yield is positive (negative), stocks are relatively attractive (unattractive), and investors bid stocks up (down) to restore yield balance. Does evidence justify this belief? To investigate, we relate the month-end gap between the S&P 500 1-year forward operating earnings yield and the 1-year T-note yield to future returns for the S&P 500 index. We calculate the 1-year forward operating earnings yield from the Earnings Forecast and the level of the S&P 500 Index. Using end-of-month data for the two yields over the period March 1989 (limited by availability of an input variable for the Earnings Forecast) through July 2013 (over 24 years), we find that: Keep Reading

Fed Model or P/E Model for Predicting Stock Market Corrections?

Can investors rely on overvaluation signals from the market price-earnings ratio (P/E) and the Fed Model to predict major stock market corrections? Which model works better? In their July 2013 paper entitled “Does the Bond-Stock Earning Yield Differential Model Predict Equity Market Corrections Better Than High P/E Models?”, Sebastien Lleo and William Ziemba test the power of eight bond-stock earnings yield differential model (BSEYD) variants and eight market P/E model variants to predict stock market corrections. They specify the bond yield for the BSEYD model as that of the 10-year U.S. Treasury note (T-note). They define a stock market correction as a decline of 10% or more within one year. They specify the 16 model variants based on: (1) either BSEYD, the natural logarithm of BSEYD, P/E or the natural logarithm of P/E; (2) either current year or rolling 10-year average stock market earnings; and, (3) either of two ways of calculating the threshold for extreme overvaluation. Both methods of setting the extreme overvaluation threshold for the 16 indicators are out-of-sample based on indicator average and standard deviation over a rolling one-year historical window. They measure success of model variants based on both the proportion of signals followed by corrections within two years and, conversely, the proportion of crashes preceded by signals within the past two years. Using daily S&P 500 Index levels, S&P 500 earnings data and daily T-note yields during 1962 through 2012, they find that: Keep Reading

Fed Model Respecified?

The Fed Model relates the aggregate earnings yield (E/P) of the stock market to Treasury bond or bill yields under the assumption that investors view equities and government bonds as competing ways to achieve yield. Might supply (company management), rather than demand (investors), more precisely drive the relationship between E/P and interest rates? In the April 2011 (incomplete) draft of his paper entitled “Understanding the Fed Model, Capital Structure, and then Some”, J.H. Timmer argues that the stock market earnings yield tends to equilibrium not with the government bond yield but with the average after-tax corporate bond yield as companies adjust capital structure (mix of equity and bonds) to maximize earnings per share. SEC Rule 10b-18 (explicitly allowing share repurchases) enabled fine adjustment toward equilibrium as of 1982. Using annual estimates of one-year forward earnings yields and corporate bond yields for a subset of S&P 500 companies and assuming a constant corporate tax rate of 30% over the period 1968 through 2006, he finds that: Keep Reading

Predictive Power of the Gap Between Stock Earnings Yield and T-note Yield

Does the gap between the aggregate stock market forward-looking earnings yield and the yield on 10-year Treasury notes (T-note) predict future stock market and bond returns? In the November 2008 update to his paper entitled “The FED Model and Expected Asset Returns”, Paulo Maio examines the statistical and economic significance of the Fed model as an indicator of future stock market and bond returns. Said differently, he investigates whether mean reversion in stock and bond yields results in mean reversion of the yield gap. Using monthly data for a broad U.S. stock index and T-notes, and for contemporaneous benchmark indicators, over the period July 1954 through December 2003, he concludes that: Keep Reading

Kicking the Body of the Fed Model

As with many indicators, the Fed Model is presently so far out of multi-generational bounds that reversion seems hopeless. Is the body still warm, or ready for burial? Using the daily S&P 500 earnings yield (E/P) during 1/2/90-12/4/08, as calculated from the historical S&P 500 index and 12-month trailing Standard & Poor’s earnings data, and contemporaneous daily 10-year Treasury note (T-note) yields, we find that… Keep Reading

Long-term Market Timing Model Flyoff

Do long-term stock market timing models work? If so, which type works best? In their October 2005 paper entitled Timing is Everything: A Comparison and Evaluation of Market Timing Strategies, Chris Brooks, Apostolos Katsaris and Gita Persand investigate the profitability of several timing models over a very long sample of S&P 500 index returns. Specifically, they test the timing power of: (1) the ratio of the long-term Treasury bond yield to the stock dividend yield; (2) the spreads between the stock earnings yield and the yields on either the three-month Treasury bills (T-bills) or the 10-year Treasury notes (T-notes); (3) a model for predicting when bear markets will occur based on the spread between T-note and T-bill yields; and, (4) an approach for predicting market turning points based on speculative bubbles. Timing signals trigger binary switching between stocks and T-bills. Using monthly stock return and model parameter data from January 1871-December 1926 for initial model calibration and January 1927-August 2003 for model testing and recalibration (a total of 1,592 months), they find that: Keep Reading

Macroeconomic Shocks and the Stock Market

How strong and persistent are the effects of inflation rate and interest rate shocks on the stock market? In the May 2008 draft of their paper entitled “Inflation, Monetary Policy and Stock Market Conditions”, Michael Bordo, Michael Dueker and David Wheelock quantify the extent to which various macroeconomic and policy shocks (industrial production, inflation, money supply growth, 10-year Treasury note yield and 3-month Treasury bill yield) explain the behavior of U.S. real stock prices and stock market conditions (trend) during the second half of the 20th century. Using monthly data for these variables and the S&P 500 index (as a proxy for stock prices) over the period August 1952 through December 2005, they conclude that: Keep Reading

Inflation as Fed Model Intermediator

Is the Fed Model an artifact of bad investor behavior (money illusion) or rational response? In the April 2008 draft of their paper entitled “Inflation and the Stock Market: Understanding the “Fed Model”, Geert Bekaert and Eric Engstrom carefully re-examine mechanisms that might explain why the Fed Model “works.” Using quarterly inputs for bond yield, S&P 500 index level and dividend yield, the economic forecast and a consumption-based measure of risk aversion spanning the fourth quarter of 1968 through 2007, they conclude that: Keep Reading

Still Irrationally Exuberant?

Are asset prices still in a behavioral bubble, sustained at least in part by wrongly using nominal rather than real interest rates in valuation calculations? In his October 2007 paper entitled “Low Interest Rates and High Asset Prices: An Interpretation in Terms of Changing Popular Economic Models”, Robert Shiller examines the Fed model-like belief that that long-term asset prices are generally high because monetary authorities are keeping long-term interest rates low. Using interest rate and inflation data for 1871-2007 and more recent behavioral evidence, he argues that: Keep Reading

A Fed Model Defense

Is the Fed Model fit only for statistics-challenged practitioners, or does it offer some trading intelligence? In the January 2007 version of his paper entitled “A Behavioral Defense of the Fed Model”, Michael Clemens combines the concepts of mean reversion of key financial variables and confidence intervals to present a behavioral defense of the Fed model. He examines the version of the model based on the spread between the S&P 500 forward earnings yield (E/P) and the yield on the 10-year Treasury note. His defense includes identification of ten potential chinks in the armor of model detractors. Using monthly data for the period January 1979 through August 2006 (322 monthly observations over 26 years) , he finds that: Keep Reading

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