7Informational Efficiency of Stock Markets7

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The Empirics of Financial Markets 2011

Stan MaesLecture 7: Informational eciency of stock markets

CET - European Commission

April 2011 - KULeuven

Stan Maes (CET - European Commission) Empirics of Financial Markets April 2 01 1 - KULeuven 1 / 29
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Predictability of stock returns (time series evidence)Predictable patterns based on public information

Dividend discount model: start from the identity:

Rk,t+1 =Pk,t+1 + Dk,t+1 Pk,t

Pk,t

Rearranging gives:

Pk,t =Dk,t+1 + Pk,t+1

1 + Rt+1Substituting forward, and taking expectations:

Pk,t =S

j=1

Et [Dk,t+j]

ji=1Et [1 + Rk,t+i]

+Et [Pk,t+S]

Si=1Et [1 + Rk,t+i].

In the absence of speculative bubbles: limit of the last term on the righthand side for S! is zero; limit for S! becomes:

Pk,t =

j=1

Et [Dk,t+j]

ji=1Et [1 + Rk,t+i]

Semi-strong form eciency implies that the dividend discount model holds.

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Variance bound tests of stock market eciency (Shiller 1981)DDM: Pk,t is a forecast of the variable P

k,t, dened as

Pk,t =

j=1

Dk,t+j

(1 + Rk)j

where Pk,t is the ex post rational price and where we assumed aconstant discount rate Rk.The observed price Pk,t is the optimal forecast of P

k,t

Pk,t = Et

Pk,t

(notice that it does not say that Pk,t = Pk,t). This implies that

Pk,t = Pk,t + t

V

Pk,t

= V [Pk,t] + V [t]

Given that V [t] 0, the dividend discount model implies that

V Pk,t V [Pk,t]Stan Maes (CET - European Commission) Empirics of Financial Markets April 2 01 1 - KULeuven 3 / 29
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The variance of the observed price series should be less than or equal tothe variance of the ex post realization Pk,t if the market is ecient!Compare sample estimates of the two variances. Note that Pk,t is not

directly observable. Implementation:

Choose some value for Rk

Use terminal condition, e.g. Pk,T = Pk,T

Construct approximate series for Pk,

tusing P

k,

t=

Pk,t+1+Dk,t+1

(1+Rk)

Sample statistics for price and dividend series (Shiller (1981))S&P 1871-1979 DJI 1928-1979

Average price Pk 145.5 982.6Average dividend Dk 6.989 44.76Average return Rk 0.0480 0.0456(Pkt) 50.1 355.9(Pkt) 9.0 26.8

Note: Prices and dividends are detrended (detrended series assumed to be stationary).

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Overall conclusion: LeRoy and Porter (1981) and Shiller (1981):aggregate stock prices seem to be far more volatile than plausible

measures of expected future dividends. Stock prices (rational forecasts ofex post rational prices) are much too volatile! Evidence against

semistrong form market eciency.Stan Maes (CET - European Commission) Empirics of Financial Markets April 2 01 1 - KULeuven 5 / 29
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Predictability of stock returns (time series evidence)Variance bound tests of stock market eciency (Shiller 1981)

Central assumptions in the early volatility tests have been criticized:

Constant expected returns

If you reverse engineer the time-varying returns that would align theformula: crazy expected return volatility required

Stationarity of stock prices and dividends (otherwise variances do notexist)

Mankiw and Shapiro (1985), Campbell and Shiller (1987) assume unitroots for prices and dividends: results qualitatively unchanged

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Harvey (1991) includes a number of plausible variables, known at time t,

in a cross-country regression:- a constant- the lagged return on a world index RWt- a dummy variable for January JANt+1- the excess return on a 3-month T-Bill RUS3t- the junk bond spread RJUNKt- the dividend yield on the S&P500 index, RDIVt .The full model specication is as follows:

Rk,t+1 = 1 + 2RWt + 3JANt+1 + 4R

US3t + 5R

JUNKt + 6R

DIVt + t+1

where Rk,t+1 is the excess return in country k, while all other returnvariables are dened as excess returns over the one-month T-Bill rate aswell.Main nding: The amount of predictability is too large to be explained by

data-mining alone (Wald tests).Stan Maes (CET - European Commission) Empirics of Financial Markets April 2 01 1 - KULeuven 7 / 29


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Rk,t+1 = 1 + 2RWt + 3JANt+1 + 4R

US3t + 5R

JUNKt + 6R

DIVt + t+1

1 2 3 4 5 6 R2Australia 0.008 0.189 0.022 13.312* -1.131 6.306* 0.073

Austria 0.037* 0.139 -0.034* 2.353 -22.002* 3.074 0.058

Belgium 0.017 -0.017 0.018 6.423* 4.233 8.068* 0.058Denmark 0.002 -0.148 0.016 0.923 19.047 6.831* 0.032

France 0.014 0.071 0.018 2.289 3.403 6.283* 0.013

Germany 0.005 0.098 -0.006 2.490 11.088 5.579* 0.021

Hong Kong 0.026 0.305 0.065* 4.368 -2.551 6.756 0.029

Italy 0.006 0.210 0.027 1.379 -4.783 1.057 0.005

Japan 0.016 0.287* 0.005 -0.416 9.191 5.822* 0.067

Netherlands 0.001 -0.011 0.026 6.205* 15.940 7.154* 0.076

Norway 0.033* 0.083 0.044* 5.398 -27.865 0.932 0.020

Spain 0.019 0.172 0.017 3.757 -18.714 0.329 0.009Switzerland 0.009 -0.049 0.009 5.970* 8.468 7.850* 0.052

U.K. -0.007 -0.039 0.044 9.103* 25.052 9.432* 0.079

U.S.A. -0.014 -0.092 0.020 8.289* 22.980* 6.175* 0.125

World -0.005 0.032 0.018 6.602* 16.848* 6.015* 0.133



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Enormous literature:- earnings-price ratios (Campbell and Shiller (1988))- dividend-price ratios (Campbell and Shiller (1988), Fama and French(1988), Hodrick (1992), Cochrane (1996, 2001)): less accountingdependent and hence more comparable across countries.

- book-market ratios (Lewellen (1999))- yield and credit spreads (Campbell (1987), Fama and French (1989),Keim and Stambaugh (1986))- recent changes in short interest rates (Campbell (1987), Hodrick (1992))- etc.

Importantly, Fama and French (1989) nd that most of these variablesare correlated with each other and with the business cycle. Highexpected returns follow when P/D and interest rates are low(recessions), and vice versa. Quid?



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Predictability of stock returns (time series evidence)

Price-dividend ratio:Link prices to dividends and returns (without taking expectations):

Pt =

j=1

Dt+j

j

i=1(1 + Rt+i)

Price-dividend ratio:

Pt

Dt= 1

(1 + Rt+1)Dt+1

Dt+ 1

(1 + Rt+1) (1 + Rt+2)Dt+2

Dt+1

Dt+1

Dt+ ...

=

j=1

ji=1 Dt+i/Dt+i1

ji=1 (1 + Rt+i)

=

j=1

ji=1 Et [Dt+i/Dt+i1]

ji=1 Et [1 + Rt+i]

=> Low price-dividend ratio implies

=> low future (expected) dividend growth (i.e. a protractedrecession) !!

=> high future (expected) returns (risk aversion)!!

Stan Maes (CET - European Commission) Empirics of Financial Markets April 2011 - KULeuven 10 / 29


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Intuition

Traders will bid up prices if news is revealed to them

that future dividend growth is expected to be higher.that expected returns will be lower.

Hence, if price (dividend) variation

comes from news about dividend growth (naive EMH, constant excessreturns), then price-dividend ratios should forecast dividend growth.comes from news about changing discount rates (expected returns),then price-dividend ratios should forecast returns.

Either returns or dividend growth needs to be predictable by P/D (ora combination of both): which one is it?

Empirical question => on average, market prices(-dividend ratios)are moving almost entirely on expected return news, not ondividend/cash ow growth news.

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Rt:t+K = a + b(Dt/Pt) + t+K Dt+K/Dt = a + b(Dt/Pt) + t+KK b b R

2 b b R2

1 5.3 2.0 0.15 2.0 1.1 0.062 10 3.1 0.23 2.5 2.1 0.06

3 15 4.0 0.37 2.4 2.1 0.06

5 33 5.8 0.60 4.7 2.4 0.12Sample 1947-1996. Standard errors in parentheses use GMM to correct for heteroskedasticity and serial correlation.

Return regression

EMH would predict zero slope, zero R2, constant expected returns, butwe nd positive, signicant coecients and large R2sCaveat: Time-varying expected return is equally possible...

Dividend growth regression: relatively small, statisticallyinsignicant, and even counterintuitive coecients.


D i th C b ll Shill f l b l li i i R it
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Derive the Campbell-Shiller formula by log-linearizing. Rewrite as

Rt+1 =Dt+1 + Pt+1

Pt=

Pt+1

Pt

1 +

Dt+1

Pt+1

or in logsrt+1 = pt+1 pt + ln (1 + exp (dt+1 pt+1))

Apply a rst order Taylor approximation of the last term around a steadystate value of dt+1 pt+1, denoted d p:

ln (1 + exp (dt+1 pt+1))

ln

1 + exp

d p

+exp

d p

1 + exp

d p

dt+1 pt+1

d p

constant + (1) (dt+1 pt

+1)

where

=1

1 + exp

d p

=

1

1 + D/P

and D/P the average dividend price ratio.Stan Maes (CET - European Commission) Empirics of Financial Markets April 2011 - KULeuven 13 / 29

A di id d i ti i 4% > 1/1 04 0 96 S b tit t


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Average dividend price ratio is 4% => = 1/1.04 0.96. Substitute(forget about the constant term):

rt+1 = pt+1 pt + (1) (dt+1 pt+1)

= (pt+1 dt+1) pt + dt+1

where 0 < < 1.Add and subtract dt from the right hand side and rearrange:

rt+1 = (pt+1 dt+1) (pt dt) + (dt+1 dt)

pt dt = (pt+1 dt+1) + (dt+1 dt) rt+1

This is a forward-looking dierence equation, which we solve recursively.Provided that lims!

s (pt+s dt+s) = 0, we get the famousCampbell-Shiller formula

pt dt

s=0

s [(dt+1+s dt+s) rt+1+s]

s=0

s [dt+1+s rt+1+s]

As before, a high price-dividend ratio must imply high future dividend

growth and/or low future returns.Stan Maes (CET - European Commission) Empirics of Financial Markets April 2011 - KULeuven 14 / 29

Cochrane (2006): The dog that did not bark
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Cochrane (2006): The dog that did not barkReasoning: It cannot be that returns and dividend growth are bothunforecastable, because if this were the case, the price dividend ratiowould have to be a constant (which it is not):

Var (pt dt) = Cov

pt dt,

s=0

s (dt+1+s)

!

Covpt dt,

s=0

srt+1+s!=

s=0

sCov(pt dt,dt+1+s)

s=0

sCov(pt dt, rt+1+s)

The fact that the P/D ratio is not constant implies that

the stock market does not behave like a coin ip! (predictability isrequired)

it cannot be that both returns and dividend growth are unpredictable !Stan Maes (CET - European Commission) Empirics of Financial Markets April 2011 - KULeuven 15 / 29
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1930 1940 1950 1960 1970 1980 1990 20000

2

4

6

8

Dividend price ratio

1930 1940 1950 1960 1970 1980 1990 2000-50

0

50Returns

Stock

T Bill


Variance decomposition


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Variance decompositionHistorically we nd that virtually all variation in price-dividend ratios hasreected varying expected returns !!Variance decomposition of value-weighted NYSE price-dividend ratio

Dividends ReturnsReal -34 138

Std. error 10 32

Nominal 30 85Std. error 41 19

Note: table entries are the percent of the variance of the price-dividendratio attributable to dividend and return forecasts,100 Cov

pt dt,

15s=0

s (dt+1+s dt+s)/Var (pt dt) and similarly

for returns.Do high prices reect expectations of high future cash ows or lowexpected risk premia?High prices seem to reect low risk premia, lower expected excessreturns! Time-variation in the reward for risk, not time-variation ininterest rates (or other non-risk explanations such as demand and

supply eects). Stocks act a lot like long term bonds !!Stan Maes (CET - European Commission) Empirics of Financial Markets April 2011 - KULeuven 17 / 29


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Stylised facts on predictability


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Stylised facts on predictabilityRt+1 = a + bRt + t+1 or Ret+1 = a + bR

et + t+1 (ANNUAL data

1926-2008)b t(b) R2 E(R) (Et(Rt+1))

Stock return 0.03 0.27 0.00 11.4 0.77T-Bill return 0.92 19.68 0.84 4.1 3.12Excess return 0.04 0.30 0.00 7.25 0.91

Ecient capital markets: b = 0, R2 = 0, constant expected return.

Stock market returns are characterised by a trivial amount ofmomentum (which is not statistical signicant) and little variation inexpected returns.

But not all returns are unpredictable! T-Bill return predictability is a

much weaker corrective force (as borrowing to invest is not a moneymachine, hence you need to save).

Excess stock returns aim to exclude the predictable component instock returns: measure the willingness to bear risk (rather thanwillingness to save and invest).


Stylised facts on predictability
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Stylised facts on predictabilityCurrent stock prices and other variables may be informative. Results forregressing excess returns on lagged D/P 1926-todayRexcesst+1 = a + b(D/P)t + t+1 and R

excesst,t+5 = a + b(D/P)t + t+1

b t(b) R2 E(R) (Et(Rt+1)1 year 4.17 2.59 0.08 7.3 6.2

5 year, overlap 20.41 4.30 0.21 10.0 6.65 year, no overlap 24.89 2.28 0.29

1 year excess return preditability using D/P: Dramatically dierentresults!

statistical signicanceR2 non-negligibleHuge coecient (unsophisticated investor one-for-one impact of

dividend yield; EMH guy zero; data 4x!!)Huge volatility/swings in expected (market) excess returns !

5 year excess return predictability

R2 signicantly highercoecients about 5 times larger


If


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If

rt+1 = bxt + t+1

xt+1

= xt + t+1

then

rt+1 + rt+2 = (bxt + t+1) + (bxt+1 + t+2)

= b(1 + ) xt + (bt+1 + t+1 + t+2)

rt+1 + rt+2 + rt+3 = b

1 + + 2

xt + (error)

Bottom line (compare with temperature predictions):

Forecasts from persistent variables build up over time and are more

important at long horizons. forecasts from fast-moving variables dieout more quickly.

There is nothing special about long-run forecasts. they are themechanical result of short-run forecasts and a persistent forecasting

variable.Stan Maes (CET - European Commission) Empirics of Financial Markets April 2011 - KULeuven 21 / 29
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Dividends are fairly stable, hence the top line reects stock price swings. A7-year return of 1 means 100%.total return, not annualised.



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Results for regressing dividend growth on lagged D/P 1926-todayDt+1

Dt= a + bDPt + t+1

DDt,t+5 = a + b(D/P)t + t+1b t(b) R2

1 year 0.17 0.14 0.00

5 year, overlap 2.28 0.79 0.01

5 year, no overlap

0.

37

0.

05 0.

001 year/ 5 year dividend growth preditability: Dramatic dierence withprevious table results

statistically insignicant resultslow R2

low coecient values, counterintuitive sign



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1940 1950 1960 1970 1980 1990 2000

-0.5

0

0.5

1

1.5

Actual and forec ast 5 year exces s returns

forecast

actual

1940 1950 1960 1970 1980 1990 2000

0

1

2

3

4

Actual and forec ast 10 year exces s returns

forecast

actual



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1940 1950 1960 1970 1980 1990 2000

0.5

1

1.5

2

Actual and forecast 5 year dividend growth

forecast

actual

1940 1950 1960 1970 1980 1990 2000

1

1.5

2

2.5

Actual and forecas t 10 year dividend growth

forecast

actual




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Predictability of stock returns (time series evidence)Conclusions

Predictability does not mean "being able to predict with certainty",

but the question is whether there is a way to know that "the odds arein favour" on some days/weeks/months and against you in others(above or below average returns).

Momentum or mean reversion? Current returns imply something aboutfuture returns.Other signals?

If there is (some) predictability Rt+1 = a + bxt + t+1we might be able to make money, or alternativelyexpected returns vary over time in a rational way: E [Rt+1] = a + bxt

Key question: Are stock returns like coin ips or are there "seasons"in stock returns?

Expected return of a fair coin ip is constant over time.Expected temperature changes slowly and gradually between Winterand Summer seasons.




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- Mixed evidence about weakform market eciency (depending on datafrequency)- Strong evidence against semi-strong form market eciency: stock returnsare predictable by dividend-price ratios and other public information.

- Basic lesson of the fact of return predictability: recession-related, slowtime varying risk premium.- December 2008: You "Dividend yields are high, so returns going forwardlook better than they have in years." Investor: "thanks, I know that, but Iam about to loose my job, my company may not be able to roll over itsdebt, and my house is about to foreclose. I cannot take more risk rightnow."


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Two generations of return predictability studies which come to 100%opposite conclusions!First generation of return predictability studies- Returns are unpredictable (driven by free entry and competition).

- Expected returns are constant (or vary only marginally).- Prices are close to random walks- Technical analysis is nearly useless.- There is no good or bad time to invest.- Markets are informationally ecient.

- Low P/D implies that the market expects declines in dividend growth.Variations in P/D are driven by cash ow news.- The only way to earn larger returns is by taking on additional risk.




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New generation of return predictability studies: views exactly theopposite !!- Returns are predictable.- Over business cycle and longer horizons, variables including thedividend-price ratio can in fact predict substantial amounts of stock return

variation.- Technical analysis is still close to useless after transaction costs.- The new view does not overturn the view that markets are reasonablycompetitive and therefore reasonably ecient. It does enlarge our view ofwhat activities provide rewards for holding risks, and it challenges our

economic understanding of those risk premia.- Our focus should be on huge swings in expected market return, ratherthan cash ows and beta: CAPM-based corporate nance calculus: value= Expected cash owExpected return =

Expected cash owRf+E(RmRf)

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7Informational Efficiency of Stock Markets7

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