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

Bekaert Engstrom, 2008, FedModel 2

Motivation (note: sample ends in 2007)U.S.

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

Bekaert Engstrom, 2008, FedModel 4

Motivation

:

:

:

:

:

:

EY equity cash yield

BY long bond yield

RRF real risk free rate

ERP equity risk premium

EDIV real cash flow growth

IRP inflation risk premium

EY RRF EDIV ERP

BY RRF EINF IRP

Fed Model Puzzle:Since inflation

compensation is the primary driver of BY, why are EY and BY

so highly correlated?

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)

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!)

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!

Bekaert Engstrom, 2008, FedModel 8

General Methodology

Bond yield decomposition:

Ang, Bekaert, Wei

(JF, 2008)

t t t tBY RRF EINF IRP

We explore alternative identification schemes in robustness exercises

residual SPF Forecasts

(See Ang, Bekaert, Wei)

Bekaert Engstrom, 2008, FedModel 9

General Methodology

Equity yield decomposition:

Ang, Bekaert, Wei

(JF, 2008)

t t t tEY RRF EDIV ERP

statistical model (VAR)

not just residual,

take a stand on risk!

1 2 tt t tERP a b RiskAversion b Uncertainty u

habit-based a la Campbell and Cochrane

survey data residual

Bekaert Engstrom, 2008, FedModel 10

Methodology

( , )

( , ) ( , ) ( , )

( , ) ( , ) ( , )

( , ) ( , ) ( , )

COV EY BY

COV EDIV EINF COV EDIV RRF COV EDIV IRP

COV RRF EINF COV RRF RRF COV RRF IRP

COV ERP EINF COV ERP RRF COV ERP IRP

Armed with an identification strategy, we can decompose

Bekaert Engstrom, 2008, FedModel 11

Empirical Results Non-trivial components of EY-BY comovement:

1. Equity real rate and bond expected inflation7%

2. Equity expected div’s and bond expected inflation12%

3. Equity rational risk premium and bond real rates13%

4. Equity rational risk premium and bond expected inflation51%

5. Equity risk premium residual and bond expected inflation8%

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)

Bekaert Engstrom, 2008, FedModel 13

Cross Sectional Country ResultsE

Y-B

Y c

orre

lati

on

Stagflation Intensity

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…

Bekaert Engstrom, 2008, FedModel 15

Epilogue: data through Dec 2008U.S.

Bekaert Engstrom, 2008, FedModel

1.00

2.00

3.00

2004 2006 2008

12345678

equity (left scale)

bond (right scale)

1.3

1.8

2.3

2.8

2004 2006 2008

expected inflation

2.4

2.6

2.8

3.0

2004 2006 2008

risk aversion

0.0

0.2

0.4

0.6

0.8

1.0

2004 2006 2008

uncertainty

Epilogue: data through Dec 2008