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

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

3. Introduction Debate between academics and practitioners whether financial markets are efficient Debate between academics and practitioners whether financial markets are efficient Are stock return predictable ? 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(X t+1 |  t ) = X t Stochastic variable : E(X t+1 |  t ) = X t –X t is a martingale –The best forecast of X t+1 is X t Stochastic process : E(y t+1 |  t ) = 0 Stochastic process : E(y t+1 |  t ) = 0 –y t is a fair game If X t is a martingale than y t+1 = X t+1 -X t is a fair game If X t is a martingale than y t+1 = X t+1 -X t is a fair game From EMH : for stock markets : y t+1 = R t+1 – E t R t+1 implies that unexpected stock returns embodies a fair game From EMH : for stock markets : y t+1 = R t+1 – E t R t+1 implies that unexpected stock returns embodies a fair game Constant equilib. required return : E t (R t+1 – k)|  t ) = 0 Constant equilib. required return : E t (R t+1 – k)|  t ) = 0 Test : R t+1 =  +  ’  t +  t+1 Test : R t+1 =  +  ’  t +  t+1

5. Martingale and Random Walk Stochastic variable : X t+1 =  + X t +  t+1 Stochastic variable : X t+1 =  + X t +  t+1 where  t+1 is iid random variable with E t  t+1 = 0 and no serial correlation or heteroscedasticity Random walk without drift :  = 0 Random walk without drift :  = 0 If X t+1 is a martingale and  X t+1 is a fair game (for  = 0) If X t+1 is a martingale and  X t+1 is a fair game (for  = 0) Random walk is more restrictive than martingale Random walk is more restrictive than martingale –Martingale process does not put any restrictions on higher moments.

6. Formal Definition of the EMH f p (R t+n |  t p ) = f(R t+n |  t ) f p (R t+n |  t p ) = f(R t+n |  t )  p t+1 = R t+1 – E p (R t+1 |  p t ) Three types of efficiency Three types of efficiency –Weak form : Information set consists only of past prices (returns) Information set consists only of past prices (returns) –Semi-strong form : Information set incorporates all publicly available information Information set incorporates all publicly available information –Strong form : Prices reflect all information that are possible be known, including ‘inside information’. 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 Tests are mainly based on the semi-strong form of efficiency Summary of basic ideas constitute the EMH 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 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 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 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) Technical analysis (chartists) –Without merit Fundamental analysis 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) : Looking at a long history of data we find (Jan. 1915 – April 2004) : Price index only (excluding dividends). 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 Number of observations (Jan 1915 – April 2004) : 1072 prices and 1071 returns Mean = 0.2123% Mean = 0.2123% SD = 5.54% SD = 5.54% From normal distribution would expect to find 26.76 months to have worse return than 2.5 th percentile (-10.64%) From normal distribution would expect to find 26.76 months to have worse return than 2.5 th percentile (-10.64%) In the actual data however, we find 36 months ! 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)

16. Volatility of S&P 500 GARCH Model : GARCH Model : R t+1 = 0.00315 +  t+1 [2.09] [2.09] h t+1 = 0.00071 + 0.8791 h t + 0.0967  t 2 [2.21] [33.0] [4.45] [2.21] [33.0] [4.45] Mean (real) return is 0.315% per month (3.85% p.a.) Unconditional volatility :  2 = 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) Inflation Real Returns Arith.GeomArith.MeanSD s. e. Geom Mean Min.Max. UK4.34.17.620.02.05.8 -57 (1974) +97 (1975) USA3.33.28.720.22.06.7 -38 (1931) +57 (1933) WorldN.A.N.A.7.217.01.76.8N.A.N.A. Dimson et al (2002)

20. Bonds : Real Returns (1900 – 2000) Inflation Real Return Arith.Geom. Arith. Mean SDs.e. Geom. Mean UK4.34.12.314.51.4N.A. USA3.33.22.110.01.01.6 WorldN.A.N.A.1.710.31.01.2 Dimson et al (2002)

21. Bills : Real Return (1900 – 2000) Inflation Real Return Arith.Geom. Arith. Mean SDs.e. UK4.34.11.26.60.7 USA3.33.21.04.70.5 Dimson et al (2002)

22. US Real Returns (Post 1947) : Mean and SD (annual averages) Standard deviation of returns (percent) Average Return (percent) 0 48121620242832 4 8 12 16 Government Bonds Corporate Bonds T-Bills S&P500 Value weighted, NYSE Equally weighted, NYSE NYSE decile size sorted portfolios

23. Simple Models E t R t+1  r t + rp t E t R t+1  r t + rp t Assuming that k and rp are constant than : Assuming that k and rp are constant than : R t+1 = k +  ’  t +  t+1 or R t+1 –r t = k +  ’  t +  t+1 Tests :  ’ = 0 Tests :  ’ = 0  t can contain : past returns, D-P ratio, E-P ratio, interest rates  t can contain : past returns, D-P ratio, E-P ratio, interest rates

24. Long Horizon Returns Evidence of mean reversion in stock returns R t,t+k =  k +  k R t-k,t +  t+k Fama and French (1988) estimated models for k = 1 to 10 years Findings : Findings : –Little or no predictability, except for k = 2 and 7 years   is less than 0. –k = 5 years   -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 h t,t+k = (p t+k – p t ) = k  + (  t+1 +  t+2 + … +  t+k ) h t,t+k = (p t+k – p t ) = k  + (  t+1 +  t+2 + … +  t+k ) Under RE, the forecast errors  t are iid with zero mean Under RE, the forecast errors  t are iid with zero mean E t h t,t+k = k  and Var(h t,t+k ) = k  2 If log-returns are iid, then If log-returns are iid, then Var(h t,t+k ) = Var(h t+1 + h t+2 + … + h t+k ) = kVar(h t+1 ) Variance ratio statistic Variance ratio statistic VR k = (1/k) [Var(h t,t+k )/Var(h t+1 )] ≈ 1 + 2/k  (k-j)  j Findings : 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 Country 1 Year 3 Year 5 Year 10 Year Monthly Data, Jan 1921 – Dec 1996 US1.00.9940.9900.828 UK1.01.0080.9640.817 Global1.01.2111.3091.238 Test stats, 5%, 1-sided -0.7120.5710.314 MCS (Normality) Median VR -0.9600.9160.810 5 th percent -0.7310.5980.398

28. Long-Horizon Risk and Return : 1920 – 1996 Probability of Loss 1 year 5 years 10 years US (Price change) 36.634.333.7 US (total Return) 30.820.715.5 UK (Price change) 40.332.545.2 UK (total Return) 30.122.130.8 Median (P. change) – 30 countries 48.246.848.2 Median (total Ret.) – 15 countries 36.126.919.9 Global index (P. c.) 37.835.435.2 Global index (t. R.) 30.218.212.0

29. Predictability and Market Timing Cochrane (2001) estimates Cochrane (2001) estimates R t,t+k = a + b(D/P) t +  t+k R t,t+k = a + b(D/P) t +  t+k US data, 1947-1996 US data, 1947-1996 –for one-year horizons : b ≈ 5 (s.e. = 2), R 2 = 0.15 –for 5 year horizons : b ≈ 33 (s.e. = 5.8), R 2 = 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 Cochrane (1997) – estimation up to 1996 R t+1 = a + b(P/D) t +  t+1 (1.) R t+1 = a + b(P/D) t +  t+1 (1.) (P/D) t+1 =  +  (P/D) t + v t+1 (2.) (P/D) t+1 =  +  (P/D) t + v t+1 (2.) Predict P/D 1997 using equation (2.) and than R 1998 using (1.), etc. Predict P/D 1997 using equation (2.) and than R 1998 using (1.), etc. Findings : 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) 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 : Regression model :  p t =  0 +  1 ’(L)  d t-1 +  2 ’(L)  p t-1 –  (z-k) t-1 +  t where z = p-d MacDonald and Power (1995) Annual US data 1871-1976(1987) R 2 ≈ 0.5

36. Profitable Trading Strategies ? Pesaran and Timmermann (1994) ‘Forecasting Stock Returns : …’, Journal of Forecasting, 13(4), 335-67 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) Market portfolio (passive) Switching portfolio (active) Switching portfolio (active) T-bills 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 Market Port. Switching Port. T-Bills Transaction Costs Stocks0.00.51.00.00.51.0-- Bills---0.00.10.10.00.1 Sharpe Ratio 0.310.300.300.820.790.76 Wealth at end of period ($ 100 invested in Jan. 1960) 1,9131,8841,8553,8333,5593,346749726

38. Risk Adjusted Rate of Return Can ‘predictability’ be used to make profits adjusted for risk and transaction costs ? 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 = (ER p – r f )/  p Sharpe ratio : SR = (ER p – r f )/  p Treynor ratio : TR = (ER p – r f )/  p Treynor ratio : TR = (ER p – r f )/  p Jensen’s alpha : (R p – r f ) t =  +  (R m -r f ) t Jensen’s alpha : (R p – r f ) t =  +  (R m -r f ) t

39. Summary Different forms of market efficiency Different forms of market efficiency Important implications if market are efficient, opportunities if markets are inefficient Important implications if market are efficient, opportunities if markets are inefficient Hong horizon returns are less risky than returns over short horizons Hong horizon returns are less risky than returns over short horizons Predictability of returns – difficult Predictability of returns – difficult Some variable have been identified which help to predict stock returns 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. (2004) ‘Quantitative Financial Economics’, Chapters 3 and 4 Cuthbertson, K. and Nitzsche, D. (2001) ‘Investments : Spot and Derivatives Markets’, Chapter 13 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 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 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 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 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. 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. Cochrane, J.H. (1997) ‘Where is the Market Going?’, Economic Perspectives (Federal Reserve Bank of Chicago), Vol. 21, No. 6.

43. END OF LECTURE