ECN 5141 Financial Economics Lecture 6 EFFICIENT MARKETS AND PREDICTABILITY OF STOCK RETURNS

1. ECN 5141 Financial EconomicsLecture 6 EFFICIENT MARKETS AND PREDICTABILITY OF STOCK RETURNS (Asset Pricing and Portfolio Theory)

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

3. Capital markets • Capital markets trade securities with lives of more than one year • Economic function • Continuous pricing function • Fair price function • Examples of capital markets • The Bursa Malaysia • New York Stock Exchange (NYSE) • Chicago Board Options Exchange (CBOE)

4. Economic Function • The economic function of capital markets facilitates the transfer of money from savers to borrowers • E.g., mortgages, Treasury bonds, corporate stocks and bonds

5. Continuous Pricing function • The continuous pricing function of capital markets means prices are available moment by moment • Continuous prices are an advantage to investors • Investors are less confident in their ability to get a quick quotation for securities that do not trade often

6. Fair price function • The fair price function of capital markets means that an investor can trust the financial system • The function removes the fear of buying or selling at an unreasonable price • The more participants and the more formal the marketplace, the greater the likelihood that the buyer is getting a fair price

7. Efficient Market Hypothesis • The efficient market hypothesis (EMH) is the theory supporting the notion that market prices are in fact fair • Market efficiency research examines the relationship between stock prices and available information • The important research question: Is it possible for investors to “beat the market”

8. Prediction of the EMH theory: If a market is efficient, it is not possible to “beat the market” (except by luck) • Fama (1970): A market in which prices always ‘fully reflect’ available information is called ‘efficient’

9. What Does “Beat the market mean? • The excess return on an investment is the return in excess of that earned by other investments that have the same risk • “Beating the market” means consistently earning a positive excess return.

10. Efficient market hypothesis • 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

11. Formal Definition of the EMH • 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’.

12. Weak forms of the EMH • states that it is impossible to predict future stock prices by analyzing prices from the past • The current price is a fair one that considers any information contained in the past price data • If so, then technical analysis is of little use

13. Tests of Market Efficiency - Weak form Tests • The question is: How well do past returns predict future returns? • The main assumption is that there should be no pattern in the time series of returns • Runs test • Three theories of time series behaviour of prices can be found in the literature: • The fair-game model • The martingale or sub-martingale model • The random walk model

14. 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

15. 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.

16. The fair game model • Is based on the behaviour of average returns’ E (j,t+1) = E [rj,t+1 –E (rj,t+1 |)] = 0 • A fair game means that, on average, across a large number of samples, the expected return on a security equals its actual return

17. The martingale model • It also a fair game, where tomorrow’s price is expected to be the same as today (the expected return is zero) E(Pj,t+1) = Pj,t • The sub-martingale model • Is a fair game with positive returns E(Pj,t+1) > Pj,t

18. The random walk model • The simplest form version is the independently and identically distributed increments case, in which the dynamics of prices are given by the equation: Pt =  + Pt-1 + t t~ IID(0, 2)

19. The random walk model • Hypotheses Ho: Prices follow random walk (efficient) HA: Market is not efficient If the random walk hypothesis holds, the weak form of the EMH must hold, but not vice versa. Thus, evidence supporting the random walk model is the evidence of market efficiency.

20. Semi-Strong Form • The semi-strong form of the EMH states that security prices fully reflect all publicly available information • E.g., past stock prices, economic reports, brokerage firm recommendations, investment advisory letters, etc. • If so, then fundamental analysis is of little use.

21. Semi-Strong Form (cont’d) • Academic research supports the semi-strong form of the EMH by investigating various corporate announcements, such as: • Stock splits • Cash dividends • Stock dividends • This means investor are seldom going to beat the market by analyzing public news

22. Semi-Strong Form (cont’d) • Event studies (dividend announcements, stock splits, earning surprises): market usually reacts as expected • Anomalies small cap stocks, low P/E stocks, low share price stocks : not as expected

23. Strong Form • The strong form of the EMH states that security prices fully reflect all public and private information • This means even corporate insiders cannot make abnormal profits by using inside information • Inside information is information not available to the general public

24. 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’.

25. 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

26. 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.

27. 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

28. Types of Investment Analysis • Technical Analysis • Analyze past prices and their patterns, trading volumes technical market indicators, investor sentiment • Fundamental Analysis • Analyze earnings, dividend, sales prospects, costs, the economy, the industry, competition, capital requirements

29. Some Implications if Markets are Efficient • Security selection becomes less important, because securities will be fairly priced • There will be a small role for professional money managers • It makes little sense to time the market

30. Anomalies • A financial anomaly refers to unexplained results that deviate from those expected under finance theory • Especially those related to the efficient market hypothesis

31. Anomalies: Example • Low PE Effect • Stocks with low PE ratios provide higher returns than stocks with higher PEs • Low Price Stock • Stocks with a “low” stock price earn higher returns than stocks with a “high” stock price

32. Anomalies: Example… • Small Firm Effect • Investing in firms with low market capitalization will provide superior risk-adjusted returns • Implies that portfolio managers should give small firms particular attention • Neglected Firm Effect • Security analysts do not pay as much attention to firms that are unlikely portfolio candidates • Implies that neglected firms may offer superior risk-adjusted returns

33. Anomalies: Example… • January Effect • Stock returns are inexplicably high in January • Possible explanations: • Tax-loss trading late in December (Branch) (in order to write the losses off on their taxes) • The risk of small stocks is higher early in the year (Rogalski and Tinic)

34. Anomalies: Example… • Day-of-the-week Effect • Mondays are historically bad days for the stock market • Wednesday and Fridays are consistently good • Tuesdays and Thursdays are a mixed bag

35. Anomalies: Example… • Day-of-the-week Effect…. • Should not occur in an efficient market • Once a profitable trading opportunity is identified, it should disappear • The day-of-the-week effect continues to persist

36. Predictability of Returns

37. 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 !

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

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

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

41. 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.)

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

43. Return’s Data

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

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

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

47. 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

48. 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)

49. VR of Equity Returns

50. 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