Portfolio Management 3-228-07 Albert Lee Chun

1. Portfolio Management3-228-07Albert Lee Chun Market Efficiency Lecture 8 30 Oct 2007

2. Brownian Motion

3. A Little Bit of History • The Roman Lucretius's scientific poem On the Nature of Things (c. 60 BC) : "Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways... their dancing is an actual indication of underlying movements of matter that are hidden from our sight... It originates with the atoms which move of themselves” • Jan Ingenhousz had described the irregular motion of coal dust particles on the surface of alcohol in 1785.

4. A Little Bit of History • Brownian motion is traditionally regarded as discovered by the botanist Robert Brown in 1827. It is believed that Brown was studying pollen particles floating in water under the microscope . • The first person to describe the mathematics behind Brownian motion was Thorvald N. Thiele in 1880 in a paper on the method of least squares. • This was followed independently by Louis Bachelier in 1900 in his PhD thesis "Théorie de la spéculation", in which he presented a stochastic analysis of the stock and option markets.

5. Louis Bachelier Louis Bachelier, in his Ph.D. thesis (Théorie de la spéculation) at the Sorbonne in 1900, wrote: “Past, present, and even discounted future events are reflected in market price.”

6. Louis Was Way Ahead of His Time... • The tragic hero of financial economics was the unfortunate Louis Bachelier. • In his 1900 dissertation written in Paris, Theorie de la Spéculation (and in his subsequent work, esp. 1906, 1913), he anticipated much of what was to become standard fare in financial theory: random walk of financial market prices, Brownian motion and martingales. • Bachelier's work on random walks predated Einstein's celebrated study of Brownian motion by five years.

7. Louis Was Way Ahead of His Time... • His innovativeness, however, was not appreciated by his professors or contemporaries. His dissertation received poor marks from his teachers and, consequently blackballed, he quickly dropped into the shadows of the academic underground. • After a series of minor posts, he ended up obscurely teaching in Besançon for much of the rest of his life. • Virtually nothing else is known of this pioneer - his work being largely ignored until the 1960s.

8. The Life of Louis • 11 March 1870 Louis Jean-Baptiste Alphonse Bachelier is born in Le Havre • 11 January 1889 Father’s death • 7 May 1889 Mother’s death • 1891–1892 Military service • 1892 Student at Sorbonne • October 1895 Bachelor in sciences at Sorbonne • July 1897 Certificate in mathematical physics • 29 March 1900 Bachelier defends his thesis, Th´eorie de la Sp´eculation • 1909–1914 Free lecturer at Sorbonne • 1912 Publication of Calcul des Probabilit´es • 1914 Publication of Le Jeu, la Chance et le Hasard • 9 September 1914 Drafted as a private in the French army • 31 December 1918 Back from the army • 10 December 1919 A member of the French Mathematical Society • 1919–1922 Assistant professor in Besan¸con • 1922–1925 Assistant professor in Dijon • 1925–1927 Associate professor in Rennes • January 1926 Blackballed in Dijon • 1 October 1927 Professor in Besan¸con • 1937 Professor Emeritus • 1 October 1937 Retirement • 1941 His last publication • 28 April 1946 Louis Bachelier dies in Saint-Servan-sur-Mer; and is buried in Sanvic near Le Havre • 1996 The Bachelier Finance Society is founded

9. Efficient Market Hypothesis “Past, present, and even discounted future events are reflected in market price.” Louis Bachelier

10. Portfolio Management Strategies • There are 2 principal classes of portfolio management strategies. 1. Passive 2. Active • Why would an investor choose an active strategy over a passive strategy, or visa versa? • The answer depends on the beliefs of the investors on whether or not the market is efficient.

11. All informationrelevant to a stock Information setof publicly availableinformation Informationset ofpast prices The 3 EMH and Their Information Sets Weak Semi-Strong Strong

12. Fama (1970): 3 Forms of EMH • Weak form efficiency: The past behavior of prices cannot help us predict future movements in prices. Price changes over time are statistically independent. • Semi-strong form efficiency: There is no public information that can help us predict future movements in prices. Prices quickly reflect new value-changing information. • Strong form efficiency: Even the ‘private’ information of experts and insiders cannot help us predict future movements in prices. Professional managers are unable to accurately forecast the future prices of individual stocks.

13. In other words... • Weak form efficiency: Past prices are useless! • Semi-strong form efficiency: Public information is useless! • Strong form efficiency: All available information, including ‘private’ information is useless!

14. Efficient Market Hypothesis Assumptions for Efficient Market Hypothesis: • The number of participants in the market is large and that they are profit maximizing. Think of large banks, hedge funds, institutional investors... • Investors rapidly adjust the prices of securities to reflect any new information. • New information here is defined as a surprise - something random and unpredictable.

15. Implications of Weak Form Efficiency • Implications of Weak Form Efficiency: • Past trading data contains no relevant information about future prices. • Best guess of the future price is the current price plus the expected return on the stock. • Consistent with Random Walk Theory: Movements in stock prices from day to day do not reflect any pattern, they are random.

16. A Note on the Weak Form • Technical analysis is useless if this is true! Technical analysis looks for patterns in past prices, as opposed to fundamental analysis which looks for fundamental value. • Even if there are patterns in the market, the presence of a few smart investors would be cause them to profit from these patterns for a while, but once the market recognizes the pattern it will disappear.

17. Empirical Evidence on EMH • Tests on aggregate stock indices (TSX and NYSE) support weak form efficiency. • However, momentum strategies provide a counterexample to the weak form of the EMH. Momentum strategies are based on the momentum of stock returns, i.e. past performers would outperform past losers.

18. Implications of Semi-Strong Form Efficiency • Implications of Semi-Strong Form Efficiency: • Analysis of financial statements such as income statements and balance sheets will not reveal any relevant information about future prices. • Financial analysts cannot identify mis-priced stocks from financial statements. • Fund managers who try to beat the market by selecting stocks could do no better than earn an average return.

19. Empirical Evidence on EMH • Research has found that fund managers on average do not beat the market. It is really hard to find a fund manager who beats the market consistently. • Passive index-tracking funds perform as well as managed funds.

20. Implications of Strong Form Efficiency • Implications of Strong Form Efficiency • Insider information and insider trading is not useful. • There will be no gradual information leakage.

21. Empirical Evidence on EMH • Insider trading is the trading of a corporation's stock or other securities by corporate insiders such as officers, directors, or holders of more than ten percent of the firm's shares. Illegal insider trading refers to trading a security based on nonpublic information about the security. • Research has shown that insider information is valuable and one can profit from insider trading.

22. Insider Trading Example • In 2002, a Martha Stewart was charged with insider trading regarding the sale of 3,928 shares in pharmaceutical company ImClone, days before its application for a new drug was denied. According to SEC allegations, she avoided a loss of $45,673 by selling all 3,928 shares of her ImClone stock. Stewart was a friend of ImClone cofounder Samuel Waksal. The day following her sale, the stock value fell 16%. Over the next month, the price of the shares dropped 70%.

23. Quick Review of Market Efficiency • Weak Form Efficiency: Prices reflect the information set comprising past market trading data (i.e. prices, volume, dividends, etc.) • Semi-Strong Form Efficiency: Prices reflect the information set comprising past market trading data plus all other currently available public information. • Strong Form Efficiency: Prices reflect all public and private information.

24. Is the Market Efficient? • There is little reason to believe markets are strong form efficient. • There seems to be compelling reason to believe that markets are weak-form efficient. • A compromise: some prices, some of the time, might not reflect all publicly available information, but most assets, most of the time, do reflect this information.

25. Implication of EMH • Competitive forces in the capital markets drive the market prices of securities to their fundamental values. • The more competitive a market, the more efficient it is. • If the markets are efficient, the price of a security today is the best predictor of its fundamental value.

26. Implication of EMH • Efficiency does not imply that the observed prices reflect the fundamental value of the stock at all times. • It implies only that deviations from it's fundamental value are random and unpredictable. • If the markets are not efficient, security prices may deviate from their fundamental value. This implies that there exist strategies for beating the market.

27. Inefficient Markets Reasons for Inefficient Markets 1. Market Segmentation 2. Illiquidity 3. High Costs of Transaction and Information

28. Passive Management Strategies

29. Active vs. Passive Strategy and Efficient Markets • Investor A: Believes the market is efficient and that it is not possible to beat the market and finds it optimal to follow a passive strategy by holding the market index. • Investor B: Believes the market is not efficient and that it is possible to beat the market, and thus seeks to follow an active strategy.

30. Active and Passive Strategies • Passive equity portfolio management • Long-term buy-and-hold strategy • Usually tracks an index over time • Designed to match market performance • Manager is judged on how well they track the target index • Active equity portfolio management • Attempts to outperform a passive benchmark portfolio on a risk-adjusted basis

31. Passive Strategy 1. Buy and Hold: Form a portfolio based on certain criteria and hold for a predetermined period. 2. Portfolio Indexation: Replicate the performance of a market index. The strategy does not try to look for undervalued or overvalued stocks, nor does it try to predict movements in the market.

32. Motivation for Indexing • Theoretical motivation: According to the CAPM, the market portfolio is the portfolio tangent to the efficient portfolio, and it is not possible obtain higher returns for any level of risk using another portfolio. • Costs of Active Management: There are costs of researching information, costs of analyzing information, transaction costs.

33. Motivation for Indexing • Empirical Motivation: 1. Individual investors under-perform the S&P 500. Barber and Odean (1997, 1998, 2000) 2. Institutional investors (who have lowers transactions costs and access to better information) do not outperform the market: Jensen(1968), Malkiel (1995), Cahart (1997). This is also true when you adjust for the price of risk using CAPM or a multifactor model.

34. Percentage of Managers that Beat the S&P 500 Source: Aswath Damodaran (http://pages.stern.nyu.edu/~adamodar/)

35. Active vs. Passive Index Fund Source: Aswath Damodaran (http://pages.stern.nyu.edu/~adamodar/)

39. Empirical Tests of the EMH

40. Event Studies If security prices reflect all available information, then price changes must reflect new information. Suppose that the single index model holds Rt = a + bRmt + et Abnormal returnet = (Actual - Expected) et = Rt - (at + btRmt) Abnormal Returns are those beyond what would be predicted by market movements alone.

41. -t 0 +t AnnouncementDate Event Studies Examine prices and returns over time

42. Stock Price Reaction to CNBC Reports • Response of 172 firms in which a controlling shareholder offered to buy out the minority shareholders. • Acquiring shareholders pay a premium over current market prices. So an announcement should cause prices to jump! • This is evidence of an efficient market in that prices fully reflect the new information within minutes of the announcement. • A positive report gets digested by the market within 5 minutes, whereas a negative report takes on average 12 minutes to digest.

43. Stock Price Reaction to CNBC Reports Minute by minute report of stock prices of firms featured in CNBC’s “Morning” or “Midday Call.”

44. -t 0 +t Cumulative Abnormal Returns Leakage of information occurs when information regarding a relevant event is released to a small group of investors before the official public release. The price might start to increase days or weeks before the announcement and calculating the abnormal return on the announcement date may not best measure the impact of the new information. One should calculate cumulative returns. Cumulative abnormal returns over time 10-43

45. Cumulative Abnormal Returns

46. Are the Markets Efficient? Magnitude Issue How efficient are the markets? Stock prices are very close to efficient values, and only managers of very large portfolios can profit from mis-pricings. Selection Bias Issue Would you publish your successful money making strategy? No. Only those who fail will publish their results to the world. Pre-selection in favor of failed strategies.

47. The Lucky Event Issue • Every take out a coin. • Flip the coin 10 times. • Heads you win, tails you lose! • Count the number of heads. • Who is our big winner? • Now let’s repeat the exercise. • Are successful winners able to repeat! Most likely not! Is it skill or merely luck? It is purely luck.

48. Weak Form Tests • Serial Correlation Positive or negative serial correlation is evidence that stock returns are related to past returns. Evidence: Over very short time horizons evidence of weak price trends. Not enough to suggest the existence of trading opportunities. • Momentum Effect Good or bad performance continues over time for the best and worst recent performers. Evidence: Over 3-12 month holding periods, there is some evidence of positive momentum • Returns over Long Horizons (over multiyear periods) Evidence: pronounced negative correlation, evidence on reversals. Reversal Effect: Winners become losers and losers become winners.

49. Semi-Strong Form Tests Fundamental analysis calls on a much stronger range of information than does technical analysis Tests of fundamental analysis are more difficult to evaluate. We will review a number of anomalies – evidence that seems inconsistent with the efficient market hypothesis. - Small firm in January Effect - Book to Market Ratios - Post Earnings Price Drift

50. Small Firm (January) Effect