LECTURE 4 : EFFICIENT MARKETS AND PREDICTABILITY OF STOCK RETURNS

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