stock market predictability
TRANSCRIPT
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
Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 2 / 16
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
Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 3 / 16
Outline
1 Predicting Stock Market Excess Return
2 Predicting Stock Market Volatility
3 Time-Varying Market Sharpe ratio
Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 4 / 16
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
Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 6 / 16
Predicting Stock Market Excess Return
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
Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 7 / 16
Predicting Stock Market Excess Return
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
Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 8 / 16
Predicting Stock Market Excess Return
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
Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 9 / 16
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
Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 11 / 16
Predicting Stock Market Volatility
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%
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Annu
alize
d St
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of R
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© G. William Schwert, 2000-2004
Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 12 / 16
Predicting Stock Market Volatility
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
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Annu
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of R
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Rolling Annualized Standard Deviation of Nasdaq Daily Returns, 1973-2004
© G. William Schwert, 2002-2004
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Predicting Stock Market Volatility
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
Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 14 / 16
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
Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 16 / 16