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LECTURE 4 : EFFICIENT MARKETS AND PREDICTABILITY OF STOCK RETURNS

LECTURE 4 : EFFICIENT MARKETS AND PREDICTABILITY OF STOCK RETURNS. (Asset Pricing and Portfolio Theory). Contents. EMH Different definitions Testing for market efficiency Volatility tests and Regression based models Event studies Are stock returns predictable ? Making money ?.

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LECTURE 4 : EFFICIENT MARKETS AND PREDICTABILITY OF STOCK RETURNS

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  1. LECTURE 4 :EFFICIENT MARKETS AND PREDICTABILITY OF STOCK RETURNS (Asset Pricing and Portfolio Theory)

  2. Contents • EMH • Different definitions • Testing for market efficiency • Volatility tests and Regression based models • Event studies • Are stock returns predictable ? • Making money ?

  3. Introduction • Debate between academics and practitioners whether financial markets are efficient • Are stock return predictable ? • Implications for active and passive fund management. • Market timing : switching between stocks and T-bills

  4. Martingale and Fair Game Properties • Stochastic variable : E(Xt+1|Wt) = Xt • Xt is a martingale • The best forecast of Xt+1 is Xt • Stochastic process : E(yt+1|Wt) = 0 • yt is a fair game • If Xt is a martingale than yt+1 = Xt+1-Xt is a fair game • From EMH : for stock markets : yt+1 = Rt+1 – EtRt+1 implies that unexpected stock returns embodies a fair game • Constant equilib. required return : Et(Rt+1 – k)|Wt) = 0 • Test : Rt+1 = a + b’Wt + et+1

  5. Martingale and Random Walk • Stochastic variable : Xt+1 = d + Xt + et+1 where et+1 is iid random variable with Etet+1 = 0 and no serial correlation or heteroscedasticity • Random walk without drift : d = 0 • If Xt+1 is a martingale and DXt+1 is a fair game (for d = 0) • Random walk is more restrictive than martingale • Martingale process does not put any restrictions on higher moments.

  6. Formal Definition of the EMH • fp(Rt+n| Wtp) = f(Rt+n| Wt) hpt+1 = Rt+1 – Ep(Rt+1 | Wpt) • Three types of efficiency • Weak form : • Information set consists only of past prices (returns) • Semi-strong form : • Information set incorporates all publicly available information • Strong form : • Prices reflect all information that are possible be known, including ‘inside information’.

  7. Empirical Tests of the EMH • Tests are mainly based on the semi-strong form of efficiency • Summary of basic ideas constitute the EMH • All agents act as if they have an equilibrium model of returns • Agents possess all relevant information, forecast errors are unpredictable from info available at time t • Agents cannot make abnormal profits over a series of ‘bets’.

  8. Testing the EMH • Different types of tests • Tests of whether excess (abnormal) returns are independent of info set available at time t or earlier • Tests of whether actual ‘trading rules’ can earn abnormal profits • Tests of whether market prices always equals fundamental values

  9. Interpretation of Tests of Market Efficiency • EMH assumes information is available at zero costs  Very strong assumption • Market moves to ‘efficiency’ as the well informed make profits relative to the less well informed • Smart money sells when actual price is above fundamental value • If noise traders (irrational behaviour) are present, the rational traders have to take their behaviour also into account.

  10. Implications of the EMH For Investment Policy • Technical analysis (chartists) • Without merit • Fundamental analysis • Only publicly available info not known to other analysis is useful • Active funds do not beat the market (passive) portfolio)

  11. Predictability of Returns

  12. A Century of Returns • Looking at a long history of data we find (Jan. 1915 – April 2004) : • Price index only (excluding dividends). • S&P500 stock index is I(1) • Return on the S&P500 index is I(0) • Unconditional returns are non-normal with fat tails. • Number of observations (Jan 1915 – April 2004) : 1072 prices and 1071 returns • Mean = 0.2123% • SD = 5.54% • From normal distribution would expect to find 26.76 months to have worse return than 2.5th percentile (-10.64%) • In the actual data however, we find 36 months !

  13. US Real Stock Index : S&P500 (Jan 1915 – April 2004)

  14. US Real Stock Returns : S&P500 (Feb. 1915 – April 2004)

  15. US Real Stock Returns : S&P500 (Feb. 1915 – April 2004)

  16. Volatility of S&P 500 • GARCH Model : Rt+1 = 0.00315 + et+1 [2.09] ht+1 = 0.00071 + 0.8791 ht + 0.0967 et2 [2.21] [33.0] [4.45] Mean (real) return is 0.315% per month (3.85% p.a.) Unconditional volatility : s2 = 0.00071/(1-0.8791-0.0967) = 0.0007276 SD = 2.697% (p.m.)

  17. Conditional Var. : GARCH (1,1) Model (Feb. 1915 – April 2004)

  18. Return’s Data

  19. Stocks : Real Returns (1900 – 2000) Dimson et al (2002)

  20. Bonds : Real Returns (1900 – 2000) Dimson et al (2002)

  21. Bills : Real Return (1900 – 2000) Dimson et al (2002)

  22. US Real Returns (Post 1947) : Mean and SD (annual averages) NYSE decile size sorted portfolios 16 Equally weighted, NYSE 12 S&P500 Average Return (percent) Value weighted, NYSE 8 4 Corporate Bonds T-Bills Government Bonds 0 4 8 12 16 20 24 28 32 Standard deviation of returns (percent)

  23. Simple Models • EtRt+1 rt + rpt • Assuming that k and rp are constant than : Rt+1 = k + g’Wt + et+1 or Rt+1–rt = k + g’Wt + et+1 • Tests : g’ = 0 • Wt can contain : past returns, D-P ratio, E-P ratio, interest rates

  24. Long Horizon Returns Evidence of mean reversion in stock returns Rt,t+k = ak + bk Rt-k,t + et+k Fama and French (1988) estimated models for k = 1 to 10 years • Findings : • Little or no predictability, except for k = 2 and 7 years  b is less than 0. • k = 5 years  b -0.5; -10% return over previous 5 years, on aver., is followed by a +5% over next 5 years

  25. US Long Horizon Returns Dimson et al (2002)

  26. Poterba and Summers (1988) : Mean Reversion • ht,t+k = (pt+k – pt) = km + (et+1 + et+2 + … + et+k) • Under RE, the forecast errors et are iid with zero mean Etht,t+k = km and Var(ht,t+k) = ks2 • If log-returns are iid, then Var(ht,t+k) = Var(ht+1 + ht+2 + … + ht+k) = kVar(ht+1) • Variance ratio statistic VRk = (1/k) [Var(ht,t+k)/Var(ht+1)] ≈ 1 + 2/k S(k-j)rj • Findings : VR > 1 for lags of less than 1 year VR < 1 for lags greater than 1 year (mean reversion)

  27. VR of Equity Returns

  28. Long-Horizon Risk and Return : 1920 – 1996

  29. Predictability and Market Timing • Cochrane (2001) estimates • Rt,t+k = a + b(D/P)t + et+k • US data, 1947-1996 • for one-year horizons : b ≈ 5 (s.e. = 2), R2 = 0.15 • for 5 year horizons : b ≈ 33 (s.e. = 5.8), R2 = 0.6

  30. 1 - Year Excess Returns

  31. 5 – Years Excess Returns

  32. Price-Dividend Ratio : USA (1872-2002)

  33. Predictability and Market Timing (Cont.) • Cochrane (1997) – estimation up to 1996 • Rt+1 = a + b(P/D)t + et+1 (1.) • (P/D)t+1 = m + r(P/D)t + vt+1 (2.) • Predict P/D1997 using equation (2.) and than R1998 using (1.), etc. • Findings : Equation predicts excess return for 1997 to be -8% p.a. and for 2007 -5% p.a.

  34. 1-Year Excess Return and PD Ratio : Annual US Data, 1947-02

  35. Cointegration and ECM • Suppose in the ‘long-run’ the dividend-price ratio is constant (k) d - p = k or p – d = 1/k where p = ln(P) and d = ln(D) • Regression model : Dpt = a0 + b1’(L)Ddt-1 + b2’(L)Dpt-1 – g(z-k)t-1 + et where z = p-d MacDonald and Power (1995) Annual US data 1871-1976(1987) R2 ≈ 0.5

  36. Profitable Trading Strategies ? • Pesaran and Timmermann (1994) ‘Forecasting Stock Returns : …’, Journal of Forecasting, 13(4), 335-67 • Excess returns on S&P500 and Dow Jones indices over one year, one quarter and one month. • SMPL 1960 – 1990 (monthly data) • 3 Portfolios : • Market portfolio (passive) • Switching portfolio (active) • T-bills • If predicted excess return (model based on fundamentals) is positive then hold the market portfolio of stocks, otherwise bills/bond. • Switching strategy dominates the passive portfolio

  37. Predicting Returns and Abnormal Profits : S&P500

  38. Risk Adjusted Rate of Return • Can ‘predictability’ be used to make profits adjusted for risk and transaction costs ? • Transaction costs : bid – ask spread (and other commission) • Risk adjusted rate of return measures • Sharpe ratio : SR = (ERp – rf)/sp • Treynor ratio : TR = (ERp – rf)/bp • Jensen’s alpha : (Rp – rf)t = a + b(Rm-rf)t

  39. Summary • Different forms of market efficiency • Important implications if market are efficient, opportunities if markets are inefficient • Hong horizon returns are less risky than returns over short horizons • Predictability of returns – difficult • Some variable have been identified which help to predict stock returns

  40. References • Cuthbertson, K. and Nitzsche, D. (2004) ‘Quantitative Financial Economics’, Chapters 3 and 4 • Cuthbertson, K. and Nitzsche, D. (2001) ‘Investments : Spot and Derivatives Markets’, Chapter 13

  41. References • Jorion, P. (2003) ‘The Long-Term Risk of Global Stock Markets’, University of California-Irvine Discussion Paper • Dimson, E., Marsh, P. and Staunton, M. (2002) Triumph of the Optimists : 101 Years of Global Investment Returns, Princeton University Press • Cochrane, J.H. (2001) ‘Asset Pricing’, Princeton University Press

  42. References • MacDonald, R. and Power, D. (1995) ‘Stock Prices, Dividends and Retention : Long Run Relationship and Short-run Dynamics’, Journal of Empirical Finance, Vol. 2, No. 2, pp. 135-151 • Pesaran, M.H. and Timmermann, A. (1994) ‘Forecasting Stock Returns : An Examination of Stock Market Trading in the Presence of Transaction Costs, Journal of Forecasting, Vol. 13, No. 4, pp. 335-367. • Cochrane, J.H. (1997) ‘Where is the Market Going?’, Economic Perspectives (Federal Reserve Bank of Chicago), Vol. 21, No. 6.

  43. END OF LECTURE

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