money illusion in the stock market: the modigliani...

money illusion in the stock market: the modigliani-cohn

hypothesis

Christopher PolkNorthwestern University

(with Randy Cohen andTuomo Vuolteenaho)

Frontiers of Finance 2005Bonaire

money illusion in the stock market

OVERVIEW


Research questionsCan studying the cross-section of average returns shed light on whether investors confuse nominal and real rates of cash-flow growth?

How does one generate a consistent spread in market beta among stocks?

Is there a positive cross-sectional premium for market risk?

Does keeping inflation “under control” have implications for market efficiency?


ContributionsPresent evidence for a persistent behavioral bias on the part ofinvestors: Modigliani and Cohn’s (1979) money illusion

Introduce a new methodology for estimating the excess slope and intercept of the security market line

Explain the empirical puzzle that high-beta stocks have not historically outperformed low-beta stocks by the market premium

Take a disciplined approach to behavioral finance: use a simple, plausible theory and test implications the theory was not designed to explain


THE IDEA


Effect of money illusionAssume inflation is high (e.g. 1982)Bond yields are high

AGGREGATE MARKET EFFECT (prior papers)Investors sell stocks, buy bonds until stock yields (minus a risk premium) are reasonably close to bond yieldsHowever stock and bond yields are not directly comparable

Stocks are claims on real assets while bonds are notIn that sense, the nominal component of the bond yield is only an illusionary return

So stocks have higher expected returns than they would in the absence of this illusion


Effect of money illusionAssume inflation is high (e.g. 1982)Bond yields are high

INDIVIDUAL STOCK EFFECT (this paper)Illusion makes the aggregate stock market cheapInvestors, thinking the forward-looking premium is modest, price high-beta stocks only a little cheaper than low-beta stocksThe realized market premium will exceed the (erroneous) expectation by inflation (plus noise). CAPM tests will fail

high beta stocks were priced to only outperform low beta stocks by the difference in betas times the modest expected premiumnot by the difference in betas times the actual equity premium (plus noise)


Effect of money illusion - exampleStock A has a β=1.5, stock B has a β=0.5Investors demand a constant equity premium of four percentInflation is three percent

CAPMStock A earns a premium of six percent over the T-billStock B earns a premium of two percent over the T-billSML slope (four percent) = equity premium (four percent)

CAPM and money illusionInvestors fail to realize that stocks are claims on real assets

Stocks are undervaluedThe rational expectation of the equity premium becomes seven percent

Stock A earns a premium of nine percent over the T-billStock B earns premium of five percent over the T-billSML slope (four percent) ≠ equity premium (seven percent)


THE FED MODEL


The Fed modelThe Fed model states that the aggregate stock yield (earnings yield or dividend yield) should equal the bond yield plus a risk premium

From the Federal Reserve Board’s Monetary Policy Report to the Congress of July 1997:

Still, the ratio of prices in the S&P 500 to consensus estimates of earnings over the coming twelve months has risen further from levels that were already unusually high. Changes in this ratio have often been inversely related to changes in long-term Treasury yields, but this year’s stock price gains were not matched by a significant net decline in interest rates.

The intuition is that stocks and bonds compete for space in investors' portfolios. For both to be held in equilibrium, they must have equal risk-adjusted yields

Asness (2000): If the market uses the Fed model, the dividend yield on stocks should be well explained by the bond yield and a proxy for the relative riskiness of stocks.


The Fed model explains prices. . .

Source: Campbell and Vuolteenaho (2004)


. . .but does not forecast returns

Cross-sectional price of risk is black. Smooth earnings/price is blue.Smooth earnings/price minus T-bond yield is green.

Source: Polk, Thompson, and Vuolteenaho (2004)


Money illusion in the Fed modelModigliani and Cohn (1977), Ritter and Warr (2000), Asness (2003), and Campbell and Vuolteenaho (2004) point out a serious logical flaw within the Fed model:

Stock yields are "real" – future nominal earnings and dividends grow with inflationBond yields are "nominal" – future coupons and principal do not grow with inflationComparing real stock yields to nominal bond yields assumes that the nominal growth rate of stocks' cash flows is constant

Consequence: Model undervalues stocks at times of positive (high) inflation and overvalues stocks at times of negative (low) inflation


Money illusion in the Fed modelPut differently, Fed-model investors apparently use the following inputs in their present value calculation

Constant nominal cash-flow growth rates (perhaps a historical average)Discount rates equal to the nominal bond yield plus a risk premium

But while the nominal bond yield adjusts for current inflation, the historical nominal growth rate does not

Consequence: Model undervalues stocks at times of positive (high) inflation and overvalues stocks at times of negative (low) inflation


Time-series decomposition


Standard VAR analysis provides three facts•Inflation is positively correlated with expected dividend growth•Inflation is negatively correlated with the subjective risk premium•Inflation is positively correlated with future risk-adjusted returns


Money illusion in the Fed model

Mispricing

Inflation

0.88 correlation !!!


Time-series evidence


MODELING


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D is dividend, P is price, R is the subjective discount rate, and G is expected dividend growth. All variables are either in real terms or in nominal terms. The subscript e denotes variables in excess of the risk-free rate

This equation holds for all firmsRational pricing: R corresponds to the long-horizon expected excess return (if returns are constant over time)

Irrational pricing: G corresponds to biased expected long-horizon dividend growth,

Firm-level valuation

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Model of market equilibriumAssume the following

1) The only valuation mistake made by investors is to fail to adjust expected nominal growth rates with inflationSpecifically, pricing errors are εi,t = εM,t = γ1+ γ2 πt-1,where γ2 > 0 (since inflation is the same for all stocks)

2) Subjective expected returns are determined by the Sharpe-Lintner CAPMSpecifically, investors price the cross section of stocks to yield a risk premium equal to beta times the subjective equity premium

Implication: Low inflation implies an expected-return beta relation that’s too steep, high inflation implies an expected-return beta relation that’s too shallow


Money Illusion kills the CAPM!

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Define mispricing

Assumption 2:CAPM benchmark

Assumption 1:Money Illusion mispricing


Excess intercept and slope of SML

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10 beta-sorted portfolios


METHODOLOGY


Formal testsThree-stage process

Stage 1: Create portfolios

Sort stocks into N portfolios on past estimated betasEstimate the post-ranking betas for these N portfolios with a K-month trailing window

We focus on N=20, K=36 but results are robust to these choices



Stage 2: Fama-MacBeth cross-sectional regressions

Each month, regress the future excess returns of these N portfolios on an intercept and past estimated post-ranking betasThe time series of coefficients represents the returns on a managed portfolio with past beta of 0 (for the coefficients on the constant) or 1 (for the coefficients on beta)Call these the “intercept portfolio” and the “slope portfolio”respectivelyIntercept portfolio is unit-investment; slope is zero-investment



Stage 3: Black-Jensen-Scholes time-series regressions

Run two time series regressions: Regress the intercept portfolio's returns and the slope portfolio's returns on a constant, the market's contemporaneous excess return, and lagged inflationSolve for the excess slope and excess intercept of the SML as a function of inflation (i.e. adjust for fact that actual betas of slope and intercept portfolio are not exactly 0 and 1)


RESULTS


Table 1: Time-Series Regressions of Intercept and Slope Portfolios

K N a1 a2 b1 b2 c1 c2 R2intercept R2

slope 36 20 0.0008

(0.36) -0.0009(-0.40)

0.0041(0.14)

1.0205(34.38)

1.5048 (2.41)

-1.4784(-2.35)

0.44% 58.03%

36 10 0.0008 (0.33)

-0.0009(-0.40)

-0.0344(-1.12)

1.0558(34.15)

1.4588 (2.23)

-1.4151(-2.16)

0.49% 57.69%

36 40 0.0007 (0.33)

-0.0004(-0.21)

0.0575(2.07)

0.9732(34.75)

1.5099 (2.57)

-1.5722(-2.65)

1.02% 58.58%

24 20 -0.0001 (-0.06)

-0.0001(-0.03)

0.0589(2.10)

0.9641(34.02)

1.6340 (2.73)

-1.5561(-2.57)

1.12% 57.19%

48 20 0.0016 (0.70)

-0.0017(-0.72)

-0.0163(-0.53)

1.0394(33.55)

1.2269 (1.86)

-1.2224(-1.85)

0.22% 57.23%


Excess slope and interceptExcess slope:

Define πt-1 as demeaned inflationg0 + g1 πt-1

g0 ≡ a2/b2

g1 ≡ c2/b2

Excess intercept (or excess zero-beta rate)Define πt-1 as demeaned inflationh0 + h1 πt-1

h0 ≡ a1-a2*(b1/b2)h1 ≡ c1-c2*(b1/b2)


Hypothesis testsWe test predictions of the CAPM and of the joint hypothesis of the CAPM and money illusion:

Hypothesis 1 (CAPM): g1 = h1 = 0

Hypothesis 2 (Joint): g1 = -h1

Hypothesis 1 is generally rejected; Hypothesis 2 is not rejected


Table 2: Excess Intercept and Slope of the Security Market K N g0 g1 h0 h1 [g1, h1]’=0 g1 + h1 = 0

36 20 -0.0009 (-0.40)

-1.4487(-2.35)

0.0008(0.36)

1.5108(2.40)

5.82[0.05]

0.00[0.96]

36 10 -0.0009 (-0.40)

-1.3403(-2.16)

0.0007(0.33)

1.4126(2.23)

5.20[0.07]

0.00[0.95]

36 40 -0.0004 (-0.21)

-1.6155(-2.64)

0.0007(0.32)

1.6029(2.57)

7.12[0.03]

0.00[0.99]

24 20 -0.0001 (-0.06)

-1.6140(-2.56)

-0.0001(-0.05)

1.7290(2.71)

8.37[0.02]

0.01[0.93]

48 20 -0.0016 (-0.72)

-1.1761(-1.85)

0.0016(0.71)

1.2077(1.86)

3.46[0.18]

0.00[0.98]


Table 3: Results from Expanded Asset Sets

20 beta-sorted and 10 ME-sorted portfolios K g0 g1 h0 h1 [g1, h1]’=0 g1 + h1 = 0

36 0.0005 (0.22)

-1.6660(-2.55)

0.0002(0.07)

1.5911(2.41)

6.94[0.03]

0.00[0.95]

20 beta-sorted and 10 BE/ME-sorted portfolios K g0 g1 h0 h1 [g1, h1]’=0 g1 + h1 = 0

36 0.0001 (0.03)

-1.9251(-3.12)

-0.0000(-0.02)

2.0335(3.23)

10.90[0.00]

0.01[0.93]

20 beta-sorted, 10 ME-sorted, and 10 BE/ME-sorted portfolios

K g0 g1 h0 h1 [g1, h1]’=0 g1 + h1 = 0

36 0.0012 (0.52)

-2.0503(-3.13)

-0.0007(-0.30)

2.0644(3.13)

9.86[0.01]

0.00[0.99]


Table 4: Inflation and the Spread between Borrowing and Treasury Rates

48-month car loans from commercial banks, spread over the 48-month T-note yield

constant (t-stat) slope on π (t-stat) Adj. R2 N 3.4327 (13.9) -0.0489 (-0.9) 0.01 124

24-month personal loans from commercial banks spread over the 24-month T-note yield


Credit card accounts (interest rates), spread over the 90-day T-bill yield


Credit card accounts (assessed interest), spread over the 90-day T-bill yield



Table 5: Results for the Fama-French Three-Factor Model

20 beta-sorted portfolios K g0 g1 h0 h1 [g1, h1]’=0 g1 + h1 = 0

36 0.0003 (0.11)

-1.2788(-1.75)

-0.0003(-0.13)

1.2787(1.71)

3.13[0.21]

0.00[1.00]

20 beta-sorted and 10 ME-sorted portfolios K g0 g1 h0 h1 [g1, h1]’=0 g1 + h1 = 0

36 -0.0018 (-0.76)

-0.9980(-1.51)

0.0018(0.75)

1.0099(1.52)

2.30[0.32]

0.00[0.99]

20 beta-sorted and 10 BE/ME-sorted portfolios K g0 g1 h0 h1 [g1, h1]’=0 g1 + h1 = 0

36 -0.0014 (-0.40)

-0.9099(-3.12)

-0.0009(-0.35)

0.9615(1.36)

2.28[0.32]

0.00[0.99]

20 beta-sorted, 10 ME-sorted, and 10 BE/ME-sorted portfolios K g0 g1 h0 h1 [g1, h1]’=0 g1 + h1 = 0

36 -0.0014 (-0.62)

-1.1630(-1.80)

0.0012(0.60)

1.1950(1.84)

3.54[0.17]

0.00[0.98]


CONCLUSIONS


ConclusionsPuzzle: high-beta stocks fail to sufficiently outperform low beta stocks in several sub-periods (e.g. 1950s, 1980s)Money illusion is one of the oldest and most plausible theories in behavioral finance

The theory’s time-series predictions fit the data, but this finding suffers from the problems of all such tests (few data points)Our cross-sectional test does not have this problem and is truly out-of-sample

Data are entirely consistent with the joint hypothesis of money illusion and the CAPMOur paper both supports the money illusion theory and explains the beta-return puzzleMultifactor models and Black’s CAPM do not explain our findingsMonetary policy aimed at keeping inflation low and predictable may make markets more efficient, improving capital allocation

money illusion in the stock market: the modigliani...

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