Econ 219BPsychology and Economics:

Applications(Lecture 10)

Stefano DellaVigna

March 31, 2004

Outline

1. CAPM for Dummies (Taught by a Dummy)

2. Event Studies

3. Event Study: Iraq War

4. Attention: Introduction

5. Attention: Oil Prices

1 CAPM for Dummies (Taught by

a Dummy)

1.1 Summary

• Capital Asset Pricing Model: Sharpe (1964) andLintner (1965)

• Tenet of Asset Pricing II

Assumptions:

• All investors are price-takers.

• All investors care about returns measured over oneperiod.

• There are no nontraded assets.

• Investors can borrow or lend at a given riskfree in-terest rate (Sharpe-Lintner version of the CAPM).

• Investors pay no taxes or transaction costs.

• All investors are mean-variance optimizers.

• All investors perceive the same means, variances, andcovariances for returns.

Implications:

• All investors face the same mean-variance tradeofffor portfolio returns

• All investors hold a mean-variance efficient portfolio.

• Since all mean-variance efficient portfolios combinethe riskless asset with a fixed portfolio of risky assets,all investors hold risky assets in the same proportionsto one another.

• These proportions must be those of the market port-folio or value-weighted index that contains all riskyassets in proportion to their market value.

• Thus the market portfolio is mean-variance efficient.

1.2 Mean-Variance Optimization

• Assume investors care only about mean (positively)and variance (negatively)

• (Can motivate with normally distributed assets)

• Mean-variance analysis with one riskless asset andN risky assets.

• The solution finds portfolios that have minimum vari-ance for a given mean return, Rp.

• These are called “mean-variance efficient” portfoliosand they lie on the “minimum-variance frontier”.

• Define:

— R as the vector of mean returns for the N riskyassets and Rf as the return of the riskless asset

— Σ as the variance-covariance matrix of returns

— w as the vector of portfolio weights for the riskyassets

— ι as a vector of ones and 1 − w0ι is the weightin the portfolio for the riskless asset

• Rewrite maximization as min Variance s.t. given re-turn Rp:

minw

1

2w0Σw s.t. (R−Rfι)

0w = Rp −Rf

Lagrangian:

L(w, λ) = 1

2w0Σw + λ(Rp −Rf − (R−Rfι)

0w)

First Order Conditions:

∂L(w, λ)∂w

= Σw − λ∗(R−Rfι) = 0

∂L(w, λ)∂λ

= Rp −Rf − (R−Rfι)0w∗ = 0

Rearranging,

w∗ = λ∗Σ−1(R−Rfι)

Rp −Rf = (R−Rfι)0w∗

Solve for λ?

Substitute for w∗ in the second equation using the firstequation

Rp −Rf = (R−Rfι)0λ∗Σ−1(R−Rfι)

λ∗ =Rp −Rf

(R−Rfι)0Σ−1(R−Rfι)

Consequently,

w∗ =⎛⎝

³Rp −Rf

´(R−Rfι)

0Σ−1(R−Rfι)

⎞⎠ ³Σ−1(R−Rfι)´

Implications:

• w∗i increasing in return of asset i Ri

• w∗i decreasing in variance of asset i σ2i (see Σ)

• Different portfolio choices with different risk aver-sion?

— Only Rp varies

— more risk-averse —> lowerRp —> hold fewer riskyassets, more riskless assets (w∗ lower)

— Everyone holds same share of risky assets: if writedown wi/wj, the parenthesis disappears

1.3 Asset Pricing Implications

• Assume that w is a vector of weights for a mean-variance efficient portfolio with return Rp.

• Consider the effects on the variance of the porfolioreturn for very small change in the weights of twoassets wi and wj such that dRp = 0.

dV ar(Rp) = 2Cov(Ri,Rp)dwi + 2Cov(Rj,Rp)dwj

• Must be dV ar(Rp) = 0, or initial portfolio was notoptimal.

• Substituting,

2Cov(Ri,Rp)dwi = 2Cov(Rj,Rp)

Ã(Ri −Rf)

(Rj −Rf)

!dwi

Ri −Rf

Cov(Ri,Rp)=

Rj −Rf

Cov(Rj,Rp)

• Use relationship for mean-variance return (j = p):

Ri −Rf

Cov(Ri,Rp)=

Rp −Rf

V ar(Rp)

Ri −Rf =Cov(Ri,Rp)

V ar(Rp)(Rp −Rf)

• Write for market return Rm (which is mean-varianceefficient under null of CAPM):

Ri −Rf =Cov(Ri,Rm)

V ar(Rm)(Rm −Rf)

• Cov(Ri,Rm)/V ar(Rm) is the famous Beta!

• Test of CAPM in a regression:

Rit −Rf = αi + βim(Rmt −Rf) + εit

• Jensen’s αi should be zero for all assets. (rejected indata)

• Point of all this: stock return of asset i depends oncorrelation with market.

• High correlation with market —> higher return tocompensate for risk

1.4 Implications for Event Studies

• Assume an event (merger announcement, earningannouncement) happened to company i

• Want to measure effect on stock return i

• Can just look at Rit before and after event?

• Better not. Have to control for correlation with mar-ket

• Should look at³Rit −Rf

´− βim(Rmt −Rf)

• Otherwise bias.

• In reality two deviations from CAPM:

1. Control for both α and β

2. Neglect Rf

• Typical estimation of abnormal return:

— Run (daily or monthly) regression:

Rit = αi + βiRmt + εit

for days (-150,-10) prior to event

— Obtain α̂i and β̂i

— Abnormal return is

ARit = Rit − α̂i + β̂iRmt

— Use this as dependent variable

2 Event Studies

• Examine the impact of an event into stock prices:

— merger announcement —> Mergers good or bad?

— earning announcement —> How is company do-ing?

— campaign-finance reform —> Effect on compa-nies financing Reps/Dems

— election of Bush/Gore —> Test quid-pro-quo parties-firms

— Iraq war (later in class) —> Effect of war

• How does one do this?

• Three main methodologies:

1. Regressions

2. Deciles

3. Portfolios

• Illustrate with earning announcement literature

• Event is earning surprise st,k

• Methodology 1. Run regression:r(h,H)t,k = α+ φst,k + εt,k

• Details:

— Use abnormal returns as dependent variable r

— (For short-term event studies, can also use netreturns rt,k − rt,m)

— Look at returns at multiple horizons: (0,0), (1,1),(3,75), etc.

— Worry about cross-sectional correlation: clusterby day

— Can add control variables to allow for time-varyingeffects, size-related effects

• Identification:

— time-series (same company over time, differentannouncements)

— cross-sectional (same time, different companies)

• Issues:

— Do you know event time?

∗ earning surprise?

∗ legal changes

— Need unexpected changes in information

• Methodology 2. Create deciles (Fama-French)

• Sort event into deciles (quantiles):

— Decile 1 d1t,k: Bottom 10% earnings surprises

— Decile 2 d2t,k: 10% to 20% earnings surprises

— etc.

• Estimate average return decile-by-decile

• Equivalent to running regression:

r(h,H)t,k =

10Xj=1

φjdjt,k + εt,k

• Details:

— Use buy-and-hold returns

— Worry about correlation of standard errors

• Issues:

— Plus: Non-linear specification

— Minus: Cannot control for variables

• Finance uses (abuses?) this ‘decile’ methodology

• Examples:

— Small firms and large firms — deciles by size

— Growth vs. value stocks — deciles by book-marketratios

• Methodology 3. Form portfolios

• Aggregate stock of a given category into one port-folio

• Observe its daily or monthly returns

• Idea: can you make money with this strategy??!

• Examples:

— Size.

∗ Form portfolio of companies by decile of size

∗ Hold for one/2/10 years

∗ Does a portfolio of small companies outper-form a portfolio of large companies?

— Momentum

∗ Form portfolio of companies by measure ofpast performance

∗ Hold for one/2/10 years

∗ Do stocks with high past returns outperformother stocks?

• Big difference from methodology 2:

— Now there is only one observation for time period(day/month)

— Have aggregated all the small firms into one port-folio

• Details:

— Run regression of raw portfolio returns on marketreturns as well as other factors:

rsmallt = α+ βrt,m + β2rt,2 + β3rt,3 + εt,k

— Standard Fama-French factors:

∗ control for market returns rt,m

∗ control for size ‘factor’ rt,2

∗ control for book-to-market ‘factor’ rt,3

— Idea: Do you obtain outperformance of an eventbeyond things happening with the market, withfirms size, and with book-to-market?

• Issues:

— Pluses: Get rid of cross-sectional correlation –now only have one ebservation per time period

— Minus: Cannot control for variables

3 Event Study: Iraq War

• See Additional slides

4 Attention: Introduction

• Attention as limited resource:

— Satisficing choice (Simon, 1955)

— Heuristics for solving complex problems (Gabaixand Laibson, 2002; Gabaix et al., 2003)

• In a world with a plethora of stimuli, which ones doagents attend to?

• Psychology: Salient stimuli (Fiske and Taylor, 1991)

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4.1 Attention to Non-Events

• Remember Huberman and Regev (2001)?

• Timeline:

— October-November 1997: Company EntreMedhas very positive early results on a cure for cancer

— November 28, 1997: Nature “prominently fea-tures;” New York Times reports on page A28

— May 3, 1998: New York Times features essen-tially same article as on November 28, 1997 onfront page

— November 12, 1998: Wall Street Journal frontpage about failed replication

• In a world with unlimited arbitrage...

• In reality...

Figure 5: ENMD Closing Prices and Trading Volume 10/1/97-12/30/98

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10/1/97 10/31/97 12/3/97 1/6/98 2/6/98 3/11/98 4/13/98 5/13/98 6/15/98 7/16/98 8/17/98 9/17/98 10/19/98 11/18/98 12/21/98

Pri

ce [

$]

November 28,1997

May 4,1998

November 12,1998

• Which theory of attention explains this?

• We do not have a theory of attention!

• However:

— Attention allocation has large role in volatile mar-kets

— Media is great, underexplored source of data

• Suggests successful stategy on attention papers:

— Do not attempt geneal model

— Focus on specific deviation

5 Attention: Oil Prices

• Idea here: People do not think of indirect effects thatmuch

• Josh’s slides.