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Market (In)Efficiency Introduction to Quantitative Portfolio Management Professor Matthew Rothman NBA 516 - Introduction to Quantitative Portfolio Management 1 Bill Miller at Legg Mason What is your belief about why Bill Miller has been “the market” in each of the past 15 years? Is this a “violation” of efficient markets? NBA 516 - Introduction to Quantitative Portfolio Management 2 Definition of Market Efficiency Definition: A market is efficient if all available information is used in pricing securities (“informational efficiency”). Types of available information: Weak form efficiency - Historical prices Semi-strong form efficiency – Publicly available information Strong form efficiency - All available information (including private information) NBA 516 - Introduction to Quantitative Portfolio Management 3 The Efficient Market Hypothesis (EMH) and the “joint hypothesis problem” The hypothesis that markets are efficient is called the efficient market hypothesis (EMH). All statements about market efficiency are conditioned on an asset pricing model used to test efficiency. That is, any test of efficiency is a joint test of efficiency and the asset-pricing model. Given a particular pricing model, you might find evidence against market efficiency. Another explanation, however, is that the market is efficient and you are using the wrong pricing model. This is a common dilemma in testing joint hypotheses. NBA 516 - Introduction to Quantitative Portfolio Management 4 The Efficient Market Hypothesis (EMH) and the “joint hypothesis problem” For example, let‟s say you find that a particular trading strategy allows you to make profits above and beyond that predicted by the CAPM. Two possibilities: One: The market is inefficient but the CAPM is the right pricing model for all securities. Two: The market is efficient but the CAPM does not describe the right pricing model for all securities NBA 516 - Introduction to Quantitative Portfolio Management 5 The Joint-Hypothesis Problem “It is a disappointing fact that, because of the joint-hypothesis problem, precise inferences about the degree of market efficiency are likely to remain impossible … Rationality is not established by the existing tests … and the joint- hypothesis problem likely means that it cannot be established.” Market Efficiency & “Making Money” There have been (and still are) many misconceptions about EMH “Market efficiency implies that you cannot make any money.” “Market efficiency implies that stock prices are random walks.” “If stock prices are random walks, then markets are efficient.” “Market efficiency implies that stock prices are not predictable.” All these statements are wrong! NBA 516 - Introduction to Quantitative Portfolio Management 7 “You cannot “make money” if markets are efficient.” Not True! Counter Example: The CAPM is a model of an efficient market In the CAPM, investors expect to make money by holding risky assets The expected return on a risky asset is determined by the risk- free return, the beta of the asset, and the risk premium of the market portfolio. Remember: E(ri) = rf + i [ E(rm) - rf ]. NBA 516 - Introduction to Quantitative Portfolio Management 8 Correct Definition of A Random Walk Definition: A series is a random walk if future changes are i.i.d. (that is, independently and identically distributed) and are unpredictable. Illustration: Pt is the price of a stock at time t. If Pt is a random walk then [Pt+1 - Pt] is unpredictable. If Pt is a random walk then [Pt+1 - Pt] / Pt is unpredictable. Implications: The future value of the price can be arbitrarily large Returns are not serially correlated. NBA 516 - Introduction to Quantitative Portfolio Management 9 Common Misconception of Random Walks Many practitioners use the term „random walk‟ to mean the lack of serial correlation in returns. This is not the correct usage of the term Random walks imply the lack of serial correlation But the lack of serial correlation does not imply random walks, if returns are not normally distributed. NBA 516 - Introduction to Quantitative Portfolio Management 10 Are Stock Prices Random Walks? Empirically: Stock returns have little serial correlation This is an implication of random walks This was found in the early literature on market efficiency (Fama (1965)) This evidence was used to “prove” that markets are efficient Stock returns are not normally distributed Lack of serial correlation does not imply random walk Stock returns have predictable volatility changes The recent finance literature has found ARCH, GARCH models fit the data (Engle‟s Nobel Prize in 2003). This means that stock prices are NOT random walks. NBA 516 - Introduction to Quantitative Portfolio Management 11 Do Random Walks Imply Efficiency? The following statement is true: Even if stock prices follow random walks, that says nothing about market efficiency For example, expected returns could be time-varying. So how do you test for efficiency?!? NBA 516 - Introduction to Quantitative Portfolio Management 12 Tests of Weak form Market Efficiency Technical analysis refers to methods for detecting recurrent patterns in prices. Using only price histories - chartists, moving average, oscillators, Elliot Wave Theory. Sentiment indicators: TRIN, Sentiment Surveys. Academics believe that EMH implies technical analysis has no merit. Some practioners believe technical analysis gives the term “analysis” a bad name. Empirical evidence The weak form of market efficiency is sometimes rejected, but the magnitudes of the inefficiencies are very small relative to transactions costs. A variety of filter rules, price-volume rules, moving average rules and other technical analysis strategies generally fail to find exploitable inefficiencies in the US stock market. (See Fama and Blume (1966), Brock, Lakonishok and LeBaron (1992)). However, there is some evidence of technical strategies working in foreign exchange markets, suggesting foreign exchange markets are weakly inefficient (See Arnott and Pham (1993), Chang (1996).) Short term momentum and long-term reversal results are still debated. For example, Short-term seasonalities like time-of-day, holiday and day-of-week effects, January effect, and momentum. We discuss these later. NBA 516 - Introduction to Quantitative Portfolio Management 13 Tests of Semi-Strong form Market Efficiency Most Common Test is the Event Study • Examine market reaction (abnormal reaction) when new news are announced. • We need to define “Normal” versus “abnormal” returns. • Collect different events where similar news is introduced to eliminate idiosyncratic influences. • Place returns in “event time”. NBA 516 - Introduction to Quantitative Portfolio Management 14 Event Study Methodology 1. Define the event you want to study! Have a research question and a hypothesis. Define Examples include: share splits; dividend initiations and eliminations; expirations of IPO lockups; share repurchases; company name changes; M&A activity; earnings announcements; etc. Clearly define what the announcement date is. Need to understand first public announcement Need a database of historical news reports Select an event window say T days 2. Estimate what is the expected return of the stock during the announcement period. Want to understand ABNORMAL returns. Market Model approach: a. Rt = at + btRmt + et b. Excess Return = (Actual - Expected) et = Actual - (at + btRmt) NBA 516 - Introduction to Quantitative Portfolio Management 15 Event Study Methodology 3. Calculate the abnormal returns and statistical significance AR = Actual Returns – Expected Returns = Abnormal returns (average excess returns for each date) Line up the returns in event time (surrounding announcement dates) across firms. Announcement date is event day 0 Calculate average abnormal return for that date in the announcement window. • This your mean return for that date. • Standard error is the standard error of the announcement return. • Then see if statistically significant. Also people look at CARs: Cumulative Abnormal returns (start at first date of announcement window and add up abnormal returns throughout event study) NBA 516 - Introduction to Quantitative Portfolio Management 16 NBA 516 - Introduction to 17 Quantitative Portfolio Event Study Methodology Example: IPO Lockup expirations The company and the underwriter negotiate the terms of the lockup. Example: Healtheon registered 5,658,184 shares. Insiders (pre-IPO investors such as management and VCs) restricted for 180 days. After this period float gradually increases to 52,254,368 shares. Underwriters can release earlier. Company rules not to sell around earnings announcements. Company may conduct an SEO. NBA 516 - Introduction to Quantitative Portfolio Management 18 Event Study Methodology Example: IPO Lockup expiration Brav and Gompers (2003, Review of Financial Studies) Collect a sample of 2,794 IPO firms conducted over the period 1988 to 1996 What is the event day? What is the period over which we shall determine what “normal” expected return is for every firm in our sample? NBA 516 - Introduction to Quantitative Portfolio Management 19 Histogram of Lock-Up Days 1400 1200 1000 800 600 400 200 0 45 91 150 183 225 360 395 450 548 730 NBA 516 - Introduction to Quantitative Portfolio Management 20 Event Study Methodology Example: IPO Lockup expiration Suppose that we were to estimate the market model with daily data for every IPO firm over the period t-110 through t-10, where t denotes the day in which the lock up expires. End up with 2,794 estimates of at and bt What do these estimates look like? NBA 516 - Introduction to Quantitative Portfolio Management 21 Intercept (at), in % Slopes (bt) Average 0.08 0.74 Median 0.08 0.68 Standard Deviation 0.48 0.98 NBA 516 - Introduction to 22 Quantitative Portfolio Resulting Abnormal Returns (averaged across firms) NBA 516 - Introduction to 23 Quantitative Portfolio Cumulative Abnormal Returns NBA 516 - Introduction to 24 Quantitative Portfolio Buy and Hold Abnormal Returns NBA 516 - Introduction to 25 Quantitative Portfolio Event Studies (Continued) The manner with which abnormal returns are calculated can make a big difference. For example, the choice of the CAPM or the Fama French 3 factor model. But it has been argued that in practice for short-run event studies, how you control for risk does not matter. Why? Because for a short run event study, the amount of systematic risk on a day or two is tiny relative to the size of the event. For example, if the market risk premium is 8% per year and there are 250 trading days then the daily premium is .00032, or a little more than 3/100 of a percent a day (3 basis points) Hence, the joint hypothesis problem is really not an issue and the favorable evidence form short-run event studies has been hailed as supportive of market efficiency. “Evidence tilts … toward the conclusion that prices adjust efficiently firm specific infortmation.” Do you agree? What does Thaler say? For long-run event studies, however, the choice of the asset pricing model is crucial. NBA 516 - Introduction to Quantitative Portfolio Management 26 The Adjustment Of Stock Prices To New Information, Fama, Fisher, Jensen, Roll (1969) NBA 516 - Introduction to Quantitative Portfolio Management 27 Tests of Strong Form Efficiency Strong form strategies assume you have information that the market does not have. Existence of Insider trading tell us that private information is valuable. Jaffee (1974): insiders can profit but so can outsiders from watching insiders Seyhun (1986): insiders can profit but not outsiders Difference is due to use of CAPM. Most of it occurs in small firms where we know the CAPM is not a good model. In general when an insider buy‟s her own stock this is a signal of good future performance. Sales is really complicated though! NBA 516 - Introduction to Quantitative Portfolio Management 28 Tests of Strong Form Efficiency Do Investment Professionals Have Private Information? Can Mutual Fund managers “Beat The Market”? Most evidence supports the view that net of expenses, they cannot. Critical though what your pricing model is: CAPM vs FF 3 factor vs 4 factor. Greatest predictor of future performance is fees. Low fee funds outperform; high fee funds underperform! Performance is not repeatable but can be highly profitable: fund flows. In other words, investors think it is repeatable. Surprisingly, fees are quite sticky. Bad performing funds do not lower fees and high performing funds do not raise them. Indeed, funds close – failure of the “price” system. NBA 516 - Introduction to Quantitative Portfolio Management 29 Caveats Tests of market efficiency has to consider: The Magnitude Issue: Statistical power. It is simply hard to detect small and economically important deviations from market efficiency The Selection Bias Issue: If someone discovered a great money making scheme, they would not publicize it. We are not likely to find out about schemes that work. If I really thought I had discovered a money machine, do you think I‟d publish it or start a hedge fund myself? The Lucky Find Issue: If you flip a fair coin 50 times, you expect to see 50% heads. If 10,000 people each flip a fair coin 50 times we expect to get at least two of them getting 75% heads. Now, suppose any bet can beat the market 50% of the time. Similarly, suppose 10,000 traders each make 50 bets. We expect to get at least two traders beat the market in 75% of their bets! NBA 516 - Introduction to Quantitative Portfolio Management 30 Bill Miller at Legg Mason What is your belief about why Bill Miller has been “the market” in each of the past 15 years? Risk return adjustment: Is it enough for him to have simply “outperformed” the S&P? Could it be luck? NBA 516 - Introduction to Quantitative Portfolio Management 31 Bill Miller at Legg Mason: Risk Risk return adjustment: Is it enough for him to have simply “outperformed” the S&P? What‟s the Beta for his fund? Is loading up on high beta stocks skill? We know CAPM doesn‟t fully explain returns. What is abnormal return relative to the 3 or 4 factor model? NBA 516 - Introduction to Quantitative Portfolio Management 32 Bill Miller at Legg Mason: Risk Characteristics of His Major Holdings Ticker Stock Weighting Beta Price/Book Trailing P/E Market Cap ($ Mil) S Sprint Nextel 6.4% 1.38 2.13 28.9 69,997 UNH United Health Care 5.7% 2.55 4.38 22.7 73,137 AMZN Amazon 5.6% 1.50 62.28 42.9 15,575 TYC Tyco 5.3% 2.13 N/A 15.8 51,953 GOOG Google 4.4% 2.00 11.1 68.3 105,237 AES The AES Corporation 4.2% 2.76 7.88 20.4 11,327 JPM JP Morgan Chase 3.8% 1.68 1.35 17.2 143,443 EBAY eBay 3.4% 1.85 5.36 48.5 54,500 AET Aetna 3.3% 0.31 3.13 18.4 29,173 Q Qwest 3.2% 3.14 N/A N/A 11,795 MCK McKesson 2.9% 0.87 2.79 20.8 8,057 EK Eastman Kodak 2.8% 1.15 4.1 N/A 8,057 HNT Healthnet 2.7% 0.52 3.49 24.4 5,501 CFC Countrywide Financial 2.5% 1.71 1.63 8.4 20,689 IACI IAC 2.5% 1.47 1.07 12.1 9,571 C Citigroup 2.5% 1.28 2.09 10.0 231,447 YHOO Yahoo! 2.5% 2.77 5.01 23.7 45,131 EXPE Expedia 2.3% 0.55 1.12 28.4 6,370 ERTS Electronic Arts (EA) 2.1% 1.32 4.66 62.3 15,747 Miller Portfolio 4.08 28.6 S&P 500 2.82 17.44 Large Cap Growth 4.12 20.89 Number of Funds 19 68.0% Number of Funds 12 51.0% NBA 516 - Introduction to Quantitative Portfolio Management 33 Bill Miller at Legg Mason: Risk Stated Investment Objective Portfolio Mix • The fund, with 41 holdings, is invested primarily in large-capitalization stocks (93.72%) • 5.85% of the fund’s assets are invested in mid-capitalization stocks • 61.77% of the fund’s net assets are invested in the Consumer Discretionary, Healthcare and Financials sectors • The fund’s largest overweight positions relative to the S&P 500 are in the Telecommunication Services and Consumer Discretionary sectors • The fund’s largest underweight positions are in the Financials, Industrials and Consumer Staples sectors with no exposure to the Materials or Energy sectors Investment Philosophy We seek to generate excess returns by owning securities that have been priced by the market at significant discounts to their intrinsic value by our multi-factor valuation analysis. Our analytical approach is not based on traditional, accounting-based valuation measures. We focused on cash earnings – namely, the present value of future cash flows of a company. Shareholder value is the result of cash, not accounting, earnings. In this way, we believe we differ from most value managers. Traditional valuation measures miss many mispriced stocks because those measures do not focus on the value of a business. Primary Risks of this Fund • Market Risk - The risk that prices of securities will go down because of the interplay of market forces, may affect a single issuer, industry or sector of the economy or may affect the market as a whole. • Value-Style Risk - The value approach to investing involves the risk that those stocks deemed to be undervalued by the portfolio NBA 516 - Introduction to Quantitative Portfolio Management 34 Bill Miller at Legg Mason: Luck? • There were approximately 8,044 mutual funds being run at the end of 2004. Of these, 4,600 are U.S. equity mutual funds. • There are approximately 6,500 “dead” U.S. equity mutual funds. So in total, some 11,100 mutual funds have ever existed. • There is a 50% chance of “beating market” as most people define it each year. • Given that, we have had 11,100 mutual funds exist, and have had 40 of funds existing, what number should we expect to have beaten the market for 15 years in row, by pure chance? 5 •There should be more Bill Miller’s out there! Why aren’t there? NBA 516 - Introduction to Quantitative Portfolio Management 35 The impossibility of informationally efficient markets: Grossman and Stiglitz (1980) Go through the following logical steps: If markets are perfectly informationally efficient, Then, informed investors cannot profit by analyzing securities‟ fundamentals If it is costly to analyze then informed investors will stop analyzing because they lose money on average But, if they stop analyzing information there will be no guarantee that publicly available information is incorporated into prices. Thus, the market won‟t be informationally efficient Hence, need some expected profit to attract informed investors. These are normal returns to their investments. An efficient amount of inefficiency in the market! NBA 516 - Introduction to Quantitative Portfolio Management 36 The impossibility of informationally efficient markets (continued) Is the GS argument consistent with passive investment strategies such as indexing? Should we all buy and hold the S&P500? How many investors indexing is too many? Why do people buy stocks anyway? devices? NBA 516 - Introduction to Quantitative Portfolio Management 37 Where Do Anomalies Come From? Why might market inefficiencies exist and persist? Human beings are not rational information processors. They systematically make errors in judgment, use heuristics to help them in decision make processing, and are subject to the follies of greed and fear. Work of Kahneman and Tversky Vernon Smith and others Institutional / Structural Reasons: Short sales constraints Erisa / Prudent Man Laws Limits of Learning / Limits of Arbitrage Data Mining: they don‟t exist, rather you have found quirks in the data NBA 516 - Introduction to Quantitative Portfolio Management 38 Market Anomalies (Selected…) 1. The January effect and the Small Firm Effect. 2. Predictability in Asset Returns. 3. Predictability in Asset Volatility. 4. Very short horizon (1 month) Price Reversal. 5. Post earnings announcement drift (PEAD). 6. Short horizon (3 to 12 month) price momentum. 7. Long horizon (3-5 year) price reversal and B/M effect. 8. Long term performance subsequent to a variety of corporate events (e.g., IPO, SEOs, Repurchases, dividend initiations and omissions). 9. Brokerage Analysts' Earnings Estimates. 10. Accounting Accruals 11. Institutional Ownership 12. Abnormal Trading Volume 13. Measures of Normalized Earnings NBA 516 - Introduction to Quantitative Portfolio Management 39 The Small Firm Effect Banz (1981) found that small firms tend to outperform large firms in total and risk-adjusted basis Divide all NYSE stocks into 5 quintiles according to firm size The average annual return of the firms in the smallest-size quintile was 4.3% higher than the average return of the firms in the largest-size quintile This is called the Small Firm Effect. NBA 516 - Introduction to Quantitative Portfolio Management 40 Average Annual Returns By Period 30% 25% 20% 15% 10% 5% 0% -5% -10% Large Cap Small Cap -15% 1926-30 1931-40 1941-50 1951-60 1961-70 1971-80 1981-90 1991-98 NBA 516 - Introduction to Quantitative Portfolio Management 41 The Small-Firm January Effect Keim (1983), Reinganum (1983), Blume and Stambaugh (1983) found that the small firm effect primarily occurs in January. Potential explanations: Tax loss selling in December Small firms are neglected by large institutional traders Small firms have lower liquidity. NBA 516 - Introduction to Quantitative Portfolio Management 42 Average Stock Return By Month: 1926-82 8% 6% Large Cap Small Cap 4% 2% 0% -2% Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec NBA 516 - Introduction to Quantitative Portfolio Management 43 Average Stock Return By Month: 1983-98 6% 4% Large Cap Small Cap 2% 0% -2% -4% Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec NBA 516 - Introduction to Quantitative Portfolio Management 44 Predictability in Asset Returns Variables that help to predict stock returns: dividend yield spread between long-term and short-term government bonds spread between Moody‟s Baa and Aaa corporate bonds spread between treasury bill rates and inflation rate The R² is low, typically less than 10% Explanations: market inefficiency time varying risk premium, e.g. Ferson and Harvey (1991) data mining NBA 516 - Introduction to Quantitative Portfolio Management 45 Stock Return Regression: 1965-91 Dependent Variable: S&P-Tbill Explanatory Variable Coeff T-stat Constant -0.0165 -1.4131 Dividend Yield (Lag 1) 0.0010 0.3013 Moody's Baa-Aaa (Lag 1) 0.0124 1.7044 Treasury 10y-3m (Lag 1) 0.0088 1.7139 Tbill-CPI (Lag 1) 1.1086 1.2388 R2 0.0430 NBA 516 - Introduction to Quantitative Portfolio Management 46 Predicting Stock Returns: 1970-99 Strategy 1: Tactical Asset Allocation If the S&P-T-bill is predicted to be positive, hold the S&P Otherwise hold T-bill. Strategy 2: Buy and hold S&P. We simulate the returns of these two strategies starting with $100 in December 1969. Here are the average annual return for 1970-99: Period Strategy 1 Strategy 2 1970-79 13.5% 7.0% 1980-89 18.4% 17.6% 1990-99 8.8% 17.7% NBA 516 - Introduction to Quantitative Portfolio Management 47 Predictability in Asset Volatility At daily and weekly intervals, stock return volatility is predictable: there is volatility clustering high volatility days tend to be followed by high volatility days low volatility days tend to be followed by low volatility days volatility reverts back to a normal level Models of volatility: Engle‟s (Econometrica, 1982) ARCH model Bollerslev‟s (J. of Econometrics, 1986) GARCH model Hsieh (J. of Finance, 1991) Bollerslev, Chou, and Kroner (J. of Econometrics, 1992) NBA 516 - Introduction to Quantitative Portfolio Management 48 Ja n -2 8 -15% -10% -5% 0% 5% 10% 15% Ja n -3 1 Ja n -3 4 Ja n -3 7 Ja n -4 0 Ja n -4 3 Ja n -4 6 Ja n -4 9 Ja n -5 2 Ja n -5 5 Ja n -5 8 Ja n -6 1 Ja n -6 4 Ja n -6 7 Ja n -7 0 Ja Portfolio Management n -7 3 Ja n -7 6 NBA 516 - Introduction to Quantitative Ja n -7 9 Ja n -8 2 Ja S&P500 Daily Returns: 1928-99 n -8 5 Ja n -8 8 Ja n -9 1 Ja n -9 4 Ja n -9 7 49 S&P500 Rolling 20-day Historical Volatility 120% 100% 80% 60% 40% 20% 0% 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 n -2 n -3 n -3 n -4 n -4 n -5 n -5 n -6 n -6 n -7 n -7 n -8 n -8 n -9 n -9 Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja NBA 516 - Introduction to Quantitative Portfolio Management 50 S&P Monthly Returns: 1928-99 50% 40% 30% 20% 10% 0% -10% -20% -30% -40% 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 -2 -3 -3 -4 -4 -5 -5 -6 -6 -7 -7 -8 -8 -9 -9 ec ec ec ec ec ec ec ec ec ec ec ec ec ec ec D D D D D D D D D D D D D D D NBA 516 - Introduction to Quantitative Portfolio Management 51 Monthly Standard Deviation of U.S. Stocks NBA 516 - Introduction to Quantitative Portfolio Management 52 Predicting Asset Volatility Very strong evidence of volatility clustering in daily returns Much weaker evidence of volatility clustering in monthly returns Exchange rates, commodity prices, and bond prices also exhibit this type of behavior Uses: Short term risk management (Value-at-risk) NBA 516 - Introduction to Quantitative Portfolio Management 53 Very Short Horizon Reversals Jegadeesh (J. of Finance, 1990) has found that: At the beginning of each month from 1934 to 1987, divide all stocks into 10 deciles based on their previous month‟s return Decile 1 has the worst performing stocks Decile 10 has the highest performing stocks. Now look at the return for the current month Decile 1 has the best performance! Decile 10 has the worst performance! Likely due to microstructure effects (bid-ask bounce) and probably hard to trade on. NBA 516 - Introduction to Quantitative Portfolio Management 54 Monthly Return of Decile Portfolios Ranked On Previous Month’s Performance: 1934-87 1.50% 1.00% 0.50% Monthly Returns 0.00% -0.50% -1.00% -1.50% 1 2 3 4 5 6 7 8 9 10 Deciles NBA 516 - Introduction to Quantitative Portfolio Management 55 Post-Earnings-Announcement Drift (PEAD) Ball and Brown (1968), Foster, Olsen, Shevlin (1984), Bernard and Thomas (1990) stocks with large positive (negative) earnings surprises have a positive (negative) price jump on the announcement day and continue to increase (decrease) in price for 13 weeks. NBA 516 - Introduction to Quantitative Portfolio Management 56 PEAD Standard Methodology Bernard and Thomas (1990) 1974-1986 period Firms are assigned to one of 10 portfolios based on standardized unexpected earnings (SUE) SUE Calculation We need a proxy for expected earnings Regress current earnings on earnings four quarters ago with a drift term. A seasonal random walk model EPSt = a + b EPSt-1 + et We can write down more elaborate time-series models Conduct the regression firm by firm. NBA 516 - Introduction to Quantitative Portfolio Management 57 PEAD Standard Methodology SUE Calculation Expected earnings are therefore: E(EPSt) = a + b EPSt-1 Then, the surprise is the realized EPS (before extraordinary items and discontinued operations) less E(EPSt). The last step is to scale by the estimation standard deviation of the forecast errors to get SUE: SUE = (EPS-EEPS)/(s.d.(error)) Why is it necessary to scale by s.d.(error)? SUE Grouping Take SUE for each firm and group into deciles. Abnormal returns are cumulated beginning the day after the earnings announcement to get the post-earnings announcement drift. NBA 516 - Introduction to Quantitative Portfolio Management 58 PEAD Standard Methodology Source: Bernard and Thomas (1989) NBA 516 - Introduction to Quantitative Portfolio Management 59 PEAD Standard Methodology Source: Bernard and Thomas (1990) NBA 516 - Introduction to Quantitative Portfolio Management 60 PEAD: Results SUE(10) – SUE(1) earns an abnormal return of 8.6 percent. About a half of average abnormal return is concentrated in the first 60 days following the announcement. In the previous graph Bernard and Thomas sort firms by size into large (top 30% NYSE/AMEX), medium (middle 40%) and small (bottom 30%) For small and medium-sized firms, the effect is even greater: 10% The cumulative returns are about 2/3 as large as the cumulative returns during the quarter up to and including the earnings announcement. NBA 516 - Introduction to Quantitative Portfolio Management 61 PEAD: Results About 25% of the effect is concentrated during the next four earnings announcement periods. Stocks held by institutions tend to have less of a drift (controlling for size). Since earnings surprises tend to include both permanent and temporary components, a portion of the initial earnings surprise (about 40%) persists as earnings surprise a quarter later, with progressively smaller amounts later on. The anomaly has been remarkably stable over time and it is not explained, for example, buy either the size or book/market factors (Fama and French (1993)). But now it looks like SUE / PEAD has declined in the 1990s if not dead! NBA 516 - Introduction to Quantitative Portfolio Management 62 Brokerage Analysts' Recommendations Does the market incorporate the information in analysts‟ recommendations? Womack (1996). Extreme recommendation changes For Buy (Sell) recommendations event-day abnormal returns are 3% (-4.7%) Post recommendation drift for Buys is significant but short-lived with size- adjusted return of +2.4% over the first post-event month. For Sells, the post- event drift lasts for 6 months and equals -9.1% Barber, Lehavy, McNichols, and Trueman (1999, 2003). Implement various trading strategies focusing on changes in consensus recommendations. NBA 516 - Introduction to Quantitative Portfolio Management 63 Do Analysts’ Recommendations Have Investment Value? Womack (1996) NBA 516 - Introduction to Quantitative Portfolio Management 64 Womack (continued) NBA 516 - Introduction to Quantitative Portfolio Management 65 Can Investors Profit from the Prophets? Security Analysts Recommendations and Stock Returns, Barber, Lehavy, McNichols, and Trueman (1999, 2003) NBA 516 - Introduction to Quantitative Portfolio Management 66 Barber, Lehavy, McNichols, and Trueman (1999, 2003) NBA 516 - Introduction to Quantitative Portfolio Management 67 Bernstein: Earnings Surprise Alphas NBA 516 - Introduction to Quantitative Portfolio Management 68 Analyst Earnings Revisions NBA 516 - Introduction to Quantitative Portfolio Management 69 Monthly Return of Decile Portfolios Ranked On Previous Month’s Performance: By Cap NBA 516 - Introduction to Quantitative Portfolio Management 70 Short Horizon Price Momentum Jegadeesh and Titman (J. of Finance, 1993) have found that: Over a 3- to 12-month horizon, stock returns have “momentum”: Good recent performance tends to persist Bad recent performance tends to persist Each quarter from 1965 to 1989, rank stocks in deciles based on the previous L (=3,6,9,12) months‟ performance Go long the highest decile and hold for H (=3,6,9,12) months Go short the lowest decile and hold for H months These long/short portfolios generate abnormal returns! (mainly on the short (losers) portfolio). NBA 516 - Introduction to Quantitative Portfolio Management 71 Jegadeesh & Titman (1993) Average Monthly Returns from Buys-Sells NBA 516 - Introduction to Quantitative Portfolio Management 72 Jegadeesh & Titman (continued) NBA 516 - Introduction to Quantitative Portfolio Management 73 Country Momentum Strategies NBA 516 - Introduction to Quantitative Portfolio Management 74 Fama & French, Long Horizon Autocorrelations Table 1. Summary of Multiperiod Autocorrelations (1926-1985): Return Horizons (years 1-6, 8, 10) Portfolio Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 8 Year 10 Food -0.01 -0.24 -0.34 -0.36 -0.34 -0.15 0.01 0.08 Apparel -0.08 -0.18 -0.20 -0.27 -0.30 -0.21 -0.21 -0.27 Drugs -0.02 -0.14 -0.18 -0.12 -0.13 -0.06 -0.09 -0.22 Retail -0.01 -0.17 -0.30 -0.32 -0.33 -0.18 -0.10 -0.02 Durables 0.02 -0.14 -0.26 -0.33 -0.30 -0.09 0.02 0.13 Autos -0.05 -0.22 -0.36 -0.42 -0.35 -0.13 -0.04 -0.02 Construction -0.01 -0.13 -0.27 -0.41 -0.42 -0.21 0.16 0.24 Finance -0.01 -0.17 -0.26 -0.25 -0.15 0.07 0.22 0.35 Misc -0.02 -0.13 -0.25 -0.35 -0.37 -0.18 0.00 0.12 Utilities -0.05 -0.16 -0.27 -0.22 -0.02 0.24 0.14 0.10 Transportation -0.10 -0.20 -0.26 -0.33 -0.32 -0.18 -0.09 0.02 Bus. Equipment 0.01 -0.22 -0.39 -0.41 -0.36 -0.19 0.05 0.13 Chemicals -0.04 -0.33 -0.43 -0.38 -0.37 -0.19 0.01 0.12 Metal Prod. 0.01 -0.20 -0.38 -0.49 -0.52 -0.37 -0.16 -0.05 Metal Ind. -0.08 -0.27 -0.36 -0.36 -0.35 -0.17 0.18 0.28 Mining -0.09 -0.29 -0.37 -0.44 -0.48 -0.28 0.02 0.08 Oil -0.02 -0.23 -0.29 -0.42 -0.40 -0.20 0.17 0.27 Average -0.03 -0.2 -0.3 -0.34 -0.32 -0.14 0.02 0.08 NBA 516 - Introduction to Quantitative Portfolio Management 75 Long Horizon (3-5 year) Price Reversal and the B/M effect. DeBondt and Thaler‟s (1985) evidence. Past long-term losers earn higher future returns than long-term winners with most of the excess return earned in January Lakonishok, Shleifer and Vishny (1994) We have already discussed these findings and the possible interpretations NBA 516 - Introduction to Quantitative Portfolio Management 76 Long-Term Performance of Repurchasing Firms Ikenberry, Lakonishok, and Vermaelen, 1995, “Market underreaction to open market share Repurchases”, Journal of Financial Economics. Why would firms repurchase their stock? Signaling Hypothesis: Asymmetric information firm‟s insiders and investors. Repurchase announcement is a credible signal. With rational expectations investors should respond immediately in an unbiased manner. Underreaction Hypothesis: Less than fully rational reaction which subsequently leads to positive abnormal returns. Data: All repurchases over the period 1980-1990. The benchmark portfolios are i) equal-weighted index, ii) value weighted index, iii) size-based, and iv) size and book-to-market based benchmark. How should we calculate the test statistics? Cumulative abnormal returns or buy and hold returns? Key long-term results: Unconditionally, investing in repurchasing firms leads to positive abnormal returns. Moreover, abnormal return is increasing in the firms‟ book-to-market ratios. NBA 516 - Introduction to Quantitative Portfolio Management 77 Ikenberry, Lakonishok, and Vermaelen, 1995 NBA 516 - Introduction to Quantitative Portfolio Management 78 Abnormal Performance Subsequent to Dividend Initiations and Omissions Price Reactions to Dividend Initiations and Omissions: Overreaction or Drift? By Michaely, Thaler, and Womack (1995) Consistent with the prior literature find that short run price reactions to omissions are greater than for initiations (-7.0% vs. +3.4% three day return) Controlling for the change in the magnitude of dividend yield (which is larger for omissions), the asymmetry shrinks or disappears, depending on the specification In the 12 months after the announcement (excluding the event calendar month), there is: a significant positive market-adjusted return for firms initiating dividends of +7.5% and a significant negative market-adjusted return for firms omitting dividends of -11.0% However, the post dividend omission drift is distinct from and more pronounced than that following earnings surprises A trading rule employing both samples (long in initiation stocks and short in omission stocks) earns positive returns in 22 out of 25 years Do firms that omit (initiate) dividends perform as expected given their characteristics? NBA 516 - Introduction to Quantitative Portfolio Management 79 Summing up... Three definitions of market efficiency: Markets incorporate various levels of information into security prices. Random walks and market efficiency. The impossibility of informationally efficient markets: Grossman and Stiglitz (1980). Anomalies. There are still other anomalies we did not cover… Turn of the Month Effect: Stocks consistently show higher returns on the last day and first four days of the month. The Monday Effect Monday tends to be the worst day to be invested in stocks. Merger related underperformance: Acquiring firms that complete stock mergers underperform while firms that complete cash tender offers do not. One interpretation is that acquirers who use their stock may use it because they believe it to be overvalued. NBA 516 - Introduction to Quantitative Portfolio Management 80 Anomalies or Data Mining? Are these real anomalies? Are these data mining? Data mining: The same data are massaged over and over again. It is not surprising to find something that will “predict” returns. Final point: Most money managers do not beat the market Malkiel article So, if managers do not beat the market, what does that say about market efficiency? NBA 516 - Introduction to Quantitative Portfolio Management 81 But why it is hard to settle these issues? 1) Statistically: No “power” • We cannot just compare current prices to a reliable fundamental value model to determine the existence of a financial anomaly. NBA 516 - Introduction to Quantitative Portfolio Management 82 But why it is hard to settle these issues? 2) Research design: Returns-Based approach The central theme of financial economics has been to assume the existence of capital market equilibrium under some model Then test whether the average returns, covariability, and predictability (or lack of) of returns is consistent with that model. Don‟t actually try to “price” assets. Just look to see if price “changes” are behaving according to posited models. NBA 516 - Introduction to Quantitative Portfolio Management 83 Financial Economists Reject “Fundamental Value”; Embrace Returns Based Research “Financial economists … work only with hard data and are concerned with the interrelationships between the prices of different financial assets. They ignore what seems to many to be the more important question of what determines the overall level of asset prices. … [There is] a deep distrust of research purporting to explore fundamental valuations.” But Such Tests Have Very Low Power “This paper argues that existing evidence does not establish that financial markets are efficient in the sense of rationally reflecting fundamental values. It demonstrates that the types of statistical tests which have been used to date have essentially no power …” NBA 516 - Introduction to Quantitative Portfolio Management 85 Lessons From Market Efficiency Tests Can Time Series/Cross Sectional Tests or Volatility Studies Establish Market Efficiency or Inefficiency? NO Can Long Run Event Studies Establish Market Efficiency or Inefficiency? NO Can Short Run Event Studies Establish Market MAYBE. ALWAYS Efficiency or Inefficiency? ABOUT REACTION NBA 516 - Introduction to Quantitative Portfolio Management 86 Market Efficiency Tests: Bottom Line • We cannot rely on returns-based tests to tell us whether prices are efficient or not. • Such tests may reject market efficiency when prices are efficient because we are using the wrong model of market equilibrium (consider FF three-factor model) • Such tests may fail to reject market efficiency because they assume a model that attributes returns to rational factors (consider same) NBA 516 - Introduction to Quantitative Portfolio Management 87 Concluding Comments BKM, Chapter 12: “We conclude that markets are very efficient, but that rewards to the especially diligent, intelligent, or creative may in fact be waiting.” (page 405) NBA 516 - Introduction to Quantitative Portfolio Management 88