stock market predictability

Stock Market Predictability

Professor Lu Zhang

Stephen M. Ross School of Business

University of Michigan

FIN 608: Capital Markets and Investment Strategies

Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 1 / 16

MotivationTime-varying expected return and volatility

So far all the models we have studied are unconditional in nature:Constant mean and market volatility in portfolio choice, constantslope of CML, and constant slope of SML

In the realistic, dynamic world, these moments are time-varying

To implement dynamic portfolio choice and the conditional CAPM, weneed to understand how expected return and conditional volatility of stockmarket return behave over time, and why


MotivationDow rewind: the first quarter performance of 2004

9800

Sources: WSJ Market Data Group; WSJ reporting

10000

10200

10400

10600

10800

11000

Jan. 2 After a 25% gain in

2003, DJIA begins

new year with

44.07-point loss.

March 8–11Reports that an al Qaeda-linked group claimed

responsibility for the terror attack in Madrid,

coming on the heels on March 5’s disappointing

jobs report, push the DJIA down a total of 467.17

points, or 4.4%, the biggest four-day percentage

decline since January 2003.

Jan. 14 Trade deficit shrinks; J.P. Morgan

and Bank One merger announced.

The average rises 1.07% to

March 23 The DJIA falls almost to 10000

before recovering amid worries

about terrorism, oil prices and

Asian stability.

March 25 The quarter’s biggest one-day

percentage gain, 1.7%, on news of

4.1% fourth-quarter economic growth

and a surge in corporate profits.

Jan. 23 A streak of of eight

consecutive weekly gains

ends; the DJIA finishes the

week down 0.3%.

Jan. 28The Fed says it “can be patient ” but omits the

phrase “considerable period," leading some

investors to believe the Fed is now closer to

raising interest rates. The 10-year Treasury

bond yield leaps to 4.17% from 4.08%.

The DJIA falls 1.3% to 10468.37.

Feb. 11 Comcast-Disney merger

proposed; Fed Chairman Alan

Greenspan says the economy

is managing a “vigorous”

expansion. The DJIA climbs to

a 2µ-year high: 10737.10.

March 5 Martha

Stewart

convicted.

March 16

The Fed

holds rates

steady.

March 31

The DJIA

finishes the

quarter at

10357.70,

down 96.22

points, or 0.9%.

Jan. 5After Fed

Governor Ben

Bernanke plays

down risk of

falling dollar and

suggests Fed will

keep rates low,

DJIA surges

134.22 points to

10544.07.

Dow Rewind: The Index’s First-Quarter PerformanceThe Dow Jones Industrial Average in the first quarter of 2004.

January February March


Outline

1 Predicting Stock Market Excess Return

2 Predicting Stock Market Volatility

3 Time-Varying Market Sharpe ratio


Predicting Stock Market Excess Return

Predicting Stock Market Excess ReturnEmpirical method

Many empirical methods used to measure predictability of future stockmarket returns; few, if any, are associated with strong evidence

A direct approach is the predictive regression:

rmt+1 = a + b Xt + εt+1

where rmt+1 is the market excess return and Xt is a vector of conditioningvariables known at time t



Predicting Stock Market Excess ReturnShiller (2000): the price-earnings ratio predicts future stock market returns negatively

Annualized ten-year real return (%)20

1920 49

21 5015 48 47 89

e.o. 521882 ~ B8

53 5545

8fi3 s.-3 86 74610 2485 "42 58 2¥ 96*44 97*56

22 RiJJ 26111 91* 95*77 ~.s7 %11* ~

7~ 25 35 85* 4183~*5 32 176 84~8* 04 00* 36~* 01 99*

15 16 34 86* Ai1 0362 02846

74 38 07J9 31 0~81~8 05 64 30

0 13 29

09 70 73 66

1210 726968

11 65

-55 10 15 20 25 30

Price-eamings ratio for January of year indicated

Figure 1.3Price-Earnings Ratio as Predictor of Ten- Year Returns

Scatter diagram of annualized ten-year returns against price-earnings ratios.Horizontal axis shows the price-earnings ratio (as plotted in Figure 1.2) forJanuary of the year indicated, dropping the 19 from twentieth-century yearsand dropping the 18 from nineteenth-century years and adding an asterisk(*). Vertical axis shows the geometric average real annual return per year oninvesting in the S&P Composite Index in January of the year shown, reinvestingdividends, and selling ten years later. Source: Author's calculations using datafrom sources given in Fi~re 1.1. See also note 2.

RDbert J. Shiller, Irrational Exubemnce, Princeton University Press, 2000



Predicting Stock Market Excess ReturnFama and French (1989): the market risk premium is countercyclical

Fama and French (1989) use the dividend-price ratio, default premium,short-term interest rate, and term premium

The market risk premium correlate positively with countercyclical variables,but negatively with procyclical interest rate



Predicting Stock Market Excess ReturnEconomic interpretation

Rational time-varying risk aversion or risk:Bad times, higher amount of uncertainty on the business conditions,investors require higher expected returns to hold risky assetsBad times, more risk averse investors require higher returns

Irrational investor sentiment:Good times, over optimistic investors buy stocks despite their highprices; observationally equivalent to requiring low expected returnsBad times, over pessimistic investors sell stocks despite their lowprices; observationally equivalent to requiring high expected returns


Predicting Stock Market Volatility

Predicting Stock Market VolatilityEstimation method

To implement asset allocation, we need to estimate volatility with precisionsufficient to identify its fluctuations

It helps to have high-frequency such as daily data; each month’s volatilityis based on the volatility of the daily returns within the month

Let σ̂t denote the volatility estimate of month t, then

σ̂t =√

20 σ̂d ,t

where σ̂d ,t is the within-month daily standard deviation for month t



Predicting Stock Market VolatilitySchwert’s chart on the annualized volatility from daily returns to the DJIA, 1885–2004

Volatility of the Dow Jones Industrial Average, 1885-2004

0%

20%

40%

60%

80%

100%

120%

1897

1899

1902

1904

1907

1909

1912

1915

1917

1920

1923

1925

1928

1930

1933

1935

1938

1941

1943

1946

1948

1951

1954

1957

1960

1963

1966

1969

1972

1975

1978

1982

1985

1988

1991

1994

1997

2000

2003

Annu

alize

d St

anda

rd D

eviat

ion

of R

etur

ns

© G. William Schwert, 2000-2004



Predicting Stock Market VolatilitySchwert’s chart on the annualized volatility from daily returns to the Nasdaq,1/1973-3/2004

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

Annu

al St

anda

rd D

eviat

ion

of R

etur

ns

Rolling Annualized Standard Deviation of Nasdaq Daily Returns, 1973-2004

© G. William Schwert, 2002-2004



Predicting Stock Market VolatilitySchwert (1990): sources of time-varying volatility

Given volatility of the asset return, high financial leverage means high riskfor the equity holders, inducing high volatility of its stock returns

Large amounts of operating leverage make the value of the firm moresensitive to economic conditions, resulting in high stock return volatility

But the leverage effects do not explain much of the variation in marketvolatility; aggregate leverage does not change much over time

Business conditions: Market is more volatile during economic recessions

High trading volume (the arrival of new information) raises market volatility


Time-Varying Market Sharpe ratio

Time-Varying Market Sharpe RatioThe market Sharpe ratio is countercyclical

Stronger cyclical variation in market risk premium than in market volatility

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

1953Q1

1957Q1

1961Q1

1965Q1

1969Q1

1973Q1

1977Q1

1981Q1

1985Q1

1989Q1

1993Q1

1997Q1

2001Q1

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

Figure 3: Conditional Sharpe Ratio

Quarterly Sharpe Ratio

Note: Shading denotes quarters designated recession by the NBERSources: Authors’ Calculations, Campbell and Cochrane (1999)

EstimateBased on

CRSP Data

Campbell-Cochrane

Model


stock market predictability

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priceeamings ratio

year indicatedfigure

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