Stock Market Predictability

                                 Professor Lu Zhang

                        Stephen M. Ross ...
Motivation
Time-varying expected return and volatility




So far all the models we have studied are unconditional in natu...
Motivation
Dow rewind: the first quarter performance of 2004


                                                            ...
Outline




1    Predicting Stock Market Excess Return


2    Predicting Stock Market Volatility


3    Time-Varying Marke...
Predicting Stock Market Excess Return


Predicting Stock Market Excess Return
Empirical method




Many empirical methods ...
Predicting Stock Market Excess Return


Predicting Stock Market Excess Return
Shiller (2000): the price-earnings ratio pre...
Predicting Stock Market Excess Return


Predicting Stock Market Excess Return
Fama and French (1989): the market risk prem...
Predicting Stock Market Excess Return


Predicting Stock Market Excess Return
Economic interpretation




Rational time-va...
Predicting Stock Market Volatility


Predicting Stock Market Volatility
Estimation method




To implement asset allocatio...
Predicting Stock Market Volatility


Predicting Stock Market Volatility
Schwert’s chart on the annualized volatility from ...
Predicting Stock Market Volatility


Predicting Stock Market Volatility
Schwert’s chart on the annualized volatility from ...
Predicting Stock Market Volatility


Predicting Stock Market Volatility
Schwert (1990): sources of time-varying volatility...
Time-Varying Market Sharpe ratio


Time-Varying Market Sharpe Ratio
The market Sharpe ratio is countercyclical

Stronger c...
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Stock Market Predictability

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Stock Market Predictability

  1. 1. 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
  2. 2. Motivation Time-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, constant slope 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, we need to understand how expected return and conditional volatility of stock market return behave over time, and why Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 2 / 16
  3. 3. Motivation Dow rewind: the first quarter performance of 2004 Dow Rewind: The Index’s Jan. 14 Trade deficit shrinks; J.P. Morgan and Bank One merger announced. First-Quarter Performance The average rises 1.07% to The Dow Jones Industrial Average in the first quarter of 2004. Jan. 5 After Fed Feb. 11 11000 Governor Ben Comcast-Disney merger March 8–11 Bernanke plays Jan. 23 proposed; Fed Chairman Alan Reports that an al Qaeda-linked group claimed down risk of A streak of of eight Greenspan says the economy responsibility for the terror attack in Madrid, falling dollar and consecutive weekly gains March 5 is managing a “vigorous” coming on the heels on March 5’s disappointing suggests Fed will ends; the DJIA finishes the Martha week down 0.3%. expansion. The DJIA climbs to Stewart jobs report, push the DJIA down a total of 467.17 10800 keep rates low, a 2µ-year high: 10737.10. points, or 4.4%, the biggest four-day percentage DJIA surges convicted. decline since January 2003. 134.22 points to 10544.07. March 25 10600 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. 28 10400 Jan. 2 The Fed says it “can be patient ” but omits the March 31 After a 25% gain in phrase “considerable period," leading some The DJIA 2003, DJIA begins investors to believe the Fed is now closer to finishes the new year with raising interest rates. The 10-year Treasury quarter at 10357.70, 10200 44.07-point loss. bond yield leaps to 4.17% from 4.08%. The DJIA falls 1.3% to 10468.37. down 96.22 points, or 0.9%. March 16 The Fed March 23 10000 holds rates The DJIA falls almost to 10000 steady. before recovering amid worries about terrorism, oil prices and Asian stability. 9800 January February March Sources: WSJ Market Data Group; WSJ reporting Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 3 / 16
  4. 4. 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
  5. 5. Predicting Stock Market Excess Return Predicting Stock Market Excess Return Empirical method Many empirical methods used to measure predictability of future stock market returns; few, if any, are associated with strong evidence A direct approach is the predictive regression: rmt+1 = a + b Xt + t+1 where rmt+1 is the market excess return and Xt is a vector of conditioning variables known at time t Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 6 / 16
  6. 6. Predicting Stock Market Excess Return Predicting Stock Market Excess Return Shiller (2000): the price-earnings ratio predicts future stock market returns negatively Annualized ten-yearreal return (%) 20 19 20 49 21 50 15 48 47 89 1882 ~ 52 B8 e.o. 53 55 45 8fi3 s.-3 86 746 10 2485 "42 58 2¥ 96* 44 97*56 22 RiJJ 111 26 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 02 846 74 38 07J9 31 0~8 1~8 05 64 30 0 13 29 09 70 73 66 1210 72 6968 11 65 -5 5 10 15 20 25 30 Price-eamings ratio for January of year indicated Figure 1.3 Price-Earnings Ratio as Predictor of Ten-Year Returns Scatterdiagram of annualized ten-year returns against price-earnings ratios. Horizontal axis shows the price-earnings ratio (asplotted in Figure 1.2)for January of the year indicated, dropping the 19from twentieth-century years and dropping the 18 from nineteenth-century years and adding an asterisk (*). Vertical axis shows the geometric averagereal annual return per year on investingin the S&PCompositeIndex in Januaryof the year shown,reinvesting dividends, and selling ten yearslater. Source: Author's calculationsusing data from sourcesgiven in Fi~re 1.1.Seealso note 2. RDbert J. Shiller, Irrational Exubemnce,Princeton University Press, 2000 Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 7 / 16
  7. 7. Predicting Stock Market Excess Return Predicting Stock Market Excess Return Fama 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
  8. 8. Predicting Stock Market Excess Return Predicting Stock Market Excess Return Economic 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 assets Bad times, more risk averse investors require higher returns Irrational investor sentiment: Good times, over optimistic investors buy stocks despite their high prices; observationally equivalent to requiring low expected returns Bad times, over pessimistic investors sell stocks despite their low prices; observationally equivalent to requiring high expected returns Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 9 / 16
  9. 9. Predicting Stock Market Volatility Predicting Stock Market Volatility Estimation method To implement asset allocation, we need to estimate volatility with precision sufficient to identify its fluctuations It helps to have high-frequency such as daily data; each month’s volatility is based on the volatility of the daily returns within the month Let σt denote the volatility estimate of month t, then ˆ √ σt = 20 σd,t ˆ ˆ where σd,t is the within-month daily standard deviation for month t ˆ Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 11 / 16
  10. 10. Predicting Stock Market Volatility Predicting Stock Market Volatility Schwert’s chart on the annualized volatility from daily returns to the DJIA, 1885–2004 Volatility of the Dow Jones Industrial Average, 1885-2004 120% 100% Annualized Standard Deviation of Returns 80% 60% 40% 20% 0% 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 © G. William Schwert, 2000-2004 Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 12 / 16
  11. 11. Predicting Stock Market Volatility Predicting Stock Market Volatility Schwert’s chart on the annualized volatility from daily returns to the Nasdaq, 1/1973-3/2004 Rolling Annualized Standard Deviation of Nasdaq Daily Returns, 1973-2004 100% 90% Annual Standard Deviation of Returns 80% 70% 60% 50% 40% 30% 20% 10% 0% 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 © G. William Schwert, 2002-2004 Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 13 / 16
  12. 12. Predicting Stock Market Volatility Predicting Stock Market Volatility Schwert (1990): sources of time-varying volatility Given volatility of the asset return, high financial leverage means high risk for the equity holders, inducing high volatility of its stock returns Large amounts of operating leverage make the value of the firm more sensitive to economic conditions, resulting in high stock return volatility But the leverage effects do not explain much of the variation in market volatility; 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
  13. 13. Time-Varying Market Sharpe ratio Time-Varying Market Sharpe Ratio The market Sharpe ratio is countercyclical Stronger cyclical variation in market risk premium than in market volatility Figure 3: Conditional Sharpe Ratio Quarterly Sharpe Ratio 2.00 2.00 1.75 1.75 1.50 1.50 Estimate 1.25 Based on 1.25 CRSP Data 1.00 1.00 0.75 0.75 0.50 0.50 0.25 0.25 0.00 0.00 Campbell- -0.25 Cochrane -0.25 Model -0.50 -0.50 1953 1957 1961 1965 1969 1973 1977 1981 1985 1989 1993 1997 2001 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Note: Shading denotes quarters designated recession by the NBER Sources: Authors’ Calculations, Campbell and Cochrane (1999) Professor Lu Zhang (2007) Stock Market Predictability 2007 Winter-A 16 / 16

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