1. Inflation and the Stock Market: Understanding the ‘Fed’ Model Geert Bekaert Columbia University and NBER Eric Engstrom Federal Reserve Board This work does not necessarily represent the views of the Federal Reserve System or its staff. 1

2. Bekaert Engstrom, 2008, FedModel 2 Motivation (note: sample ends in 2007) U.S.

3. Bekaert Engstrom, 2008, FedModel 3 Motivation -Equity yields (EY) and safe nominal bond yields (BY) are very highly correlated (correlation = 0.78) -Practitioner’s: Fed Model EY > BY: Equities are attractive BY > EY: Bonds are attractive –Typical practicioner statement “The 10-year Treasury trades at almost 30x earnings, compared to about 14 times for the S&P 500... …The valuation disparity between Treasuries and stocks is as great today in favor of stocks as it was in favor of Treasuries 20 years ago.” –Bill Miller, Legg Mason Value Trust Investment Commentary Q42007

4. Bekaert Engstrom, 2008, FedModel 4 Motivation Fed Model Puzzle: Since inflation compensation is the primary driver of BY, why are EY and BY so highly correlated?

5. Bekaert Engstrom, 2008, FedModel 5 Existing Literature –“Money illusion” is the prevailing explanation: Version 1: when expectations rise nominal rates do too, but investors use these nominal rates incorrectly to discount real equity cash flow growth (Modigliani and Cohn 1979,…) Version 2: investors correctly discount nominal equity cash flows with nominal rates, but fail to rationally boost nominal cash flow growth rate expectations in the face of higher inflation (Sharpe 2002, Campbell and Vuolteenaho 2005, Cohen, Polk and Vuolteenaho, 2007)

6. Bekaert Engstrom, 2008, FedModel 6 What we find –In the U.S. the high EY/BY correlation have arisen as a rational response to instances of stagflation Inflation has tended to move with equity yields only because it is correlated with real slowdowns and economic uncertainty that increase risk aversion –Implication: countries with no stagflationary experiences should not exhibit high EY/BY correlations (and they don’t!)

7. Bekaert Engstrom, 2008, FedModel 7 General Methodology  Create “dynamic” versions of: EY = RRF – EDIV + ERP BY = RRF + EINF + IRP  Decompose EY-BY correlation into correlations among the components  Problem: Identification!

8. Bekaert Engstrom, 2008, FedModel 8 General Methodology  Bond yield decomposition: Ang, Bekaert, Wei (JF, 2008)  We explore alternative identification schemes in robustness exercises residual SPF Forecasts (See Ang, Bekaert, Wei)

9. Bekaert Engstrom, 2008, FedModel 9 General Methodology  Equity yield decomposition: Ang, Bekaert, Wei (JF, 2008) statistical model (VAR) not just residual, take a stand on risk! habit-based a la Campbell and Cochrane survey data residual

10. Bekaert Engstrom, 2008, FedModel 10 Methodology  Armed with an identification strategy, we can decompose

11. Bekaert Engstrom, 2008, FedModel 11 Empirical Results  Non-trivial components of EY-BY comovement: 1.Equity real rate and bond expected inflation 7% 2.Equity expected div’s and bond expected inflation 12% 3.Equity rational risk premium and bond real rates 13% 4.Equity rational risk premium and bond expected inflation 51% 5.Equity risk premium residual and bond expected inflation 8%

12. Bekaert Engstrom, 2008, FedModel 12 Empirical Results  Cross-sectional implications: Fed model should “work” in countries with a high incidence of stagflations  There is indeed lots of cross-sectional variation in the (EY, BY) correlation across countries (see also Estrada, 2006)

13. Bekaert Engstrom, 2008, FedModel 13 Cross Sectional Country Results EY-BY correlation Stagflation Intensity

14. Bekaert Engstrom, 2008, FedModel 14 Conclusions  “Fed model puzzle”: EY and BY are very highly correlated, not because of money illusion but are tied to the incidence of stagflation.  In recessions, economic uncertainty and risk aversion increase, increasing equity yields, which “sometimes” is correlated with high (expected) inflation. –And sometimes not…

15. Bekaert Engstrom, 2008, FedModel 15 Epilogue: data through Dec 2008 U.S.

16. Bekaert Engstrom, 2008, FedModel Epilogue: data through Dec 2008