International Investment 2005-2006 Professor André Farber Solvay Business School Université Libre de Bruxelles

Notions of Market Efficiency An Efficient market is one in which: Arbitrage is disallowed: rules out free lunches Purchase or sale of a security at the prevailing market price is never a positive NPV transaction. Prices reveal information Three forms of Market Efficiency (a) Weak Form Efficiency Prices reflect all information in the past record of stock prices (b) Semi-strong Form Efficiency Prices reflect all publicly available information (c) Strong-form Efficiency Price reflect all information PhD 01-1

Efficient markets: intuition Price Realization Expectation Price change is unexpected Time PhD 01-1

Weak Form Efficiency Random-walk model: Pt -Pt-1 = Pt-1 * (Expected return) + Random error Expected value (Random error) = 0 Random error of period t unrelated to random component of any past period Implication: Expected value (Pt) = Pt-1 * (1 + Expected return) Technical analysis: useless Empirical evidence: serial correlation Correlation coefficient between current return and some past return Serial correlation = Cor (Rt, Rt-s) PhD 01-1

S&P500 Daily returns PhD 01-1

Semi-strong Form Efficiency Prices reflect all publicly available information Empirical evidence: Event studies Test whether the release of information influences returns and when this influence takes place. Abnormal return AR : ARt = Rt - Rmt Cumulative abnormal return: CARt = ARt0 + ARt0+1 + ARt0+2 +... + ARt0+1 PhD 01-1

Efficient Market Theory Announcement Date PhD 01-1

Example: How stock splits affect value -29 30 Source: Fama, Fisher, Jensen & Roll

Event Studies: Dividend Omissions Efficient market response to “bad news” S.H. Szewczyk, G.P. Tsetsekos, and Z. Santout “Do Dividend Omissions Signal Future Earnings or Past Earnings?” Journal of Investing (Spring 1997) PhD 01-1

Strong-form Efficiency How do professional portfolio managers perform? Jensen 1969: Mutual funds do not generate abnormal returns Rfund - Rf =  +  (RM - Rf) Insider trading Insiders do seem to generate abnormal returns (should cover their information acquisition activities) PhD 01-1

What moves the market Who knows? Lot of noise: 1985-1990: 120 days with | DJ| > 5% 28 cases (1/4) identified with specific event (Siegel Stocks for the Long Run Irwin 1994 p 184) Orange juice futures (Roll 1984) 90% of the day-to-day variability cannot explained by fundamentals Pity financial journalists! Voir Siegel (1992) chap 12 PhD 01-1

Trading Is Hazardous to Your Wealth (Barber and Odean Journal of Finance April 2000) Sample: trading activity of 78,000 households 1991-1997 Main conclusions: 1. Average household underperforms benchmark by 1.1% annually 2. Trading reduces net annualized mean returns Infrequent traders: 18.5% Frequent traders: 11.4% 3. Households trade frequently (75% annual turnover) 4. Trading costs are high: for average round-trip trade 4% (Commissions 3%, bid-ask spread 1%) PhD 01-1

US Equity Mutual Funds 1982-1991 (Malkiel, Journal of Finance June 1995) Average Annual Return Capital appreciation funds 16.32% Growth funds 15.81% Small company growth funds 13.46% Growth and income funds 15.97% Equity income funds 15.66% S&P 500 Index 17.52% Average deviation from benchmark -3.20% (risk adjusted) PhD 01-1

 : Excess Return Return  Risk Excess return = Average return - Risk adjusted expected return Return Expected return Average return  Risk Risk PhD 01-1

Jensen 1968 - Distribution of “t” values for “” 115 mutual funds 1955-1964 Not significantly different from 0 PhD 01-1

US Mutual Funds Consistency of Investment Result Successive Period Performance Initial Period Performance Top Half Bottom Half Goetzmann and Ibbotson (1976-1985) Top Half 62.0% 38.0% Bottom Half 36.6% 63.4% Malkiel, (1970s) Top Half 65.1% 34.9% Bottom Half 35.5% 64.5% Malkiel, (1980s) Top Half 51.7% 48.3% Bottom Half 47.5% 52.5% Source: Bodie, Kane, Marcus Investments 4th ed. McGraw Hill 1999 (p.118) PhD 01-1

Decomposition of Mutual Fund Returns (Wermers Journal of Finance August 2000) Sample: 1,758 funds 1976-1994 Benchmark 14.8% +1% Gross return 15.8% Expense ratio 0.8% Transaction costs 0.8% Non stock holdings 0.4% Net Return 13.8% Funds outperform benchmark Stock picking +0.75% No timing ability Deviation from benchmark +0.55% Not enough to cover costs PhD 01-1

Performance evaluation

Introduction Complicated subject Theoretically correct measures are difficult to construct Different statistics or measures are appropriate for different types of investment decisions or portfolios Many industry and academic measures are different The nature of active management leads to measurement problems PhD 01-1

Dollar- and Time-Weighted Returns Dollar-weighted returns Internal rate of return considering the cash flow from or to investment Returns are weighted by the amount invested in each stock Time-weighted returns Not weighted by investment amount Equal weighting PhD 01-1

Text Example of Multiperiod Returns Period Action 0 Purchase 1 share at $50 1 Purchase 1 share at $53 Stock pays a dividend of $2 per share 2 Stock pays a dividend of $2 per share Stock is sold at $108 per share PhD 01-1

Dollar-Weighted Return Period Cash Flow 0 -50 share purchase 1 +2 dividend -53 share purchase 2 +4 dividend + 108 shares sold Internal Rate of Return: PhD 01-1

Simple Average Return: (10% + 5.66%) / 2 = 7.83% Time-Weighted Return Simple Average Return: (10% + 5.66%) / 2 = 7.83% PhD 01-1

Arithmetic Mean: Text Example Average: (.10 + .0566) / 2 = 7.81% Averaging Returns Arithmetic Mean: Text Example Average: (.10 + .0566) / 2 = 7.81% Geometric Mean: Text Example Average: [ (1.1) (1.0566) ]1/2 - 1 = 7.83% PhD 01-1

Comparison of Geometric and Arithmetic Means Past Performance - generally the geometric mean is preferable to arithmetic Predicting Future Returns- generally the arithmetic average is preferable to geometric Geometric has downward bias PhD 01-1

Abnormal Performance What is abnormal? Abnormal performance is measured: Benchmark portfolio Market adjusted Market model / index model adjusted Reward to risk measures such as the Sharpe Measure: E (rp-rf) / p PhD 01-1

Factors That Lead to Abnormal Performance Market timing Superior selection Sectors or industries Individual companies PhD 01-1

Risk Adjusted Performance: Sharpe 1) Sharpe Index rp = Average return on the portfolio rf = Average risk free rate = Standard deviation of portfolio return P PhD 01-1

M2 Measure Developed by Modigliani and Modigliani Equates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-bills and the managed portfolio If the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the market PhD 01-1

Managed Portfolio: return = 35% standard deviation = 42% M2 Measure: Example Managed Portfolio: return = 35% standard deviation = 42% Market Portfolio: return = 28% standard deviation = 30% T-bill return = 6% Hypothetical Portfolio: 30/42 = .714 in P (1-.714) or .286 in T-bills (.714) (.35) + (.286) (.06) = 26.7% Since this return is less than the market, the managed portfolio underperformed PhD 01-1

Risk Adjusted Performance: Treynor 2) Treynor Measure rp = Average return on the portfolio rf = Average risk free rate ßp = Weighted average ß for portfolio p PhD 01-1

Risk Adjusted Performance: Jensen 3) Jensen’s Measure  p= Alpha for the portfolio rp = Average return on the portfolio ßp = Weighted average Beta rf = Average risk free rate rm = Avg. return on market index port. PhD 01-1

Appraisal Ratio = ap / s(ep) Appraisal Ratio divides the alpha of the portfolio by the nonsystematic risk Nonsystematic risk could, in theory, be eliminated by diversification PhD 01-1

Which Measure is Appropriate? It depends on investment assumptions 1) If the portfolio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market. 2) If many alternatives are possible, use the Jensen or the Treynor measure The Treynor measure is more complete because it adjusts for risk PhD 01-1

Limitations Assumptions underlying measures limit their usefulness When the portfolio is being actively managed, basic stability requirements are not met Practitioners often use benchmark portfolio comparisons to measure performance PhD 01-1

Market Timing Adjusting portfolio for up and down movements in the market Low Market Return - low ßeta High Market Return - high ßeta PhD 01-1

Example of Market Timing * rp - rf rm - rf Steadily Increasing the Beta PhD 01-1

Performance Attribution Decomposing overall performance into components Components are related to specific elements of performance Example components Broad Allocation Industry Security Choice Up and Down Markets PhD 01-1

Process of Attributing Performance to Components Set up a ‘Benchmark’ or ‘Bogey’ portfolio Use indexes for each component Use target weight structure PhD 01-1

Process of Attributing Performance to Components Calculate the return on the ‘Bogey’ and on the managed portfolio Explain the difference in return based on component weights or selection Summarize the performance differences into appropriate categories PhD 01-1

Formula for Attribution Where B is the bogey portfolio and p is the managed portfolio PhD 01-1

Contributions for Performance Contribution for asset allocation (wpi - wBi) rBi + Contribution for security selection wpi (rpi - rBi) = Total Contribution from asset class wpirpi -wBirBi PhD 01-1

Complications to Measuring Performance Two major problems Need many observations even when portfolio mean and variance are constant Active management leads to shifts in parameters making measurement more difficult To measure well You need a lot of short intervals For each period you need to specify the makeup of the portfolio PhD 01-1

Theory of asset pricing under certainty PhD 01-1

Passive Portfolio Management Professor André Farber Solvay Business School Université Libre de Bruxelles

Academic Foundations of Passive Investment Portfolio Theory (Markowitz 1952) Benefits of diversification Capital Asset Pricing Model (Sharpe, Lintner) Relationship between expected return and risk Market Efficiency (Fama 1970) Stock prices reflect all available information. Mutual Fund Performance (Jensen 1968) Professionally managed portfolio seem unable to make consistent abnormal returns PhD 01-1

Portfolio Theory Risk Portfolio characteristics expected return risk (standard deviation) Risk determined by covariances Efficient frontier If riskless asset: one optimal portfolio Expected return Risk PhD 01-1

Capital Asset Pricing Model Equilibrium model, optimal portfolio = market portfolio Risk of individual security = beta (systematic risk) Risk - expected return relationship E(r) = Risk-free rate + Market risk premium x Beta Expected return E(rmarket) Beta 1 PhD 01-1

Efficient Market Hypothesis (EMH) Strong version: “Security prices fully reflect all available information” Weaker version: “Prices reflect information to the point where the marginal benefit of acting on information (the profit to be made) do not exceed the marginal costs” (Fama 1991) PhD 01-1

EMH (continued) A theoretical result: Bachelier (1900) Théorie de la spéculation Samuelson (1965) Proof that properly anticipated prices fluctuate randomly. A vast empirical litterature “weak-form tests”: do past returns provide information? “semistrong-form”: is public information reflected in stock prices? “strong-form tests”: do stock prices reflect private information? PhD 01-1

Implications of the EMH for Investment Policy Technical Analysis Fundamental Analysis Active Portfolio Management market timing stock selection PhD 01-1

Mutual Fund Performances Malkiel (Journal of Finance June 1995) 239 equity funds 1982-1991 Average excess return Benchmark Portfolio: Wilshire 5000 S&P500 Net returns -0.93% -3.20% Gross returns 0.18% -2.03% Persistence of Fund Performance: Winner: rate of return > median Percent Repeat Winners: 51.7% PhD 01-1

Mutual Fund Performances (cont.) Otten and Barms, WP 2000 506 European equity funds 1991-1998 No Mean Market Funds Return Return France 99 10.9 12.7 Germany 57 13.9 15.3 Italy 37 15.2 14.9 Netherland 9 22.0 21.0 United Kingdom 304 12.3 14.2 PhD 01-1

Excess return = Realized return - Expected return EMH: faith or fact? All empirical tests based on asset pricing model: Excess return = Realized return - Expected return Any test of the EMH is a joined test Still looking for the Capital Asset pricing model anomalies (calendar, size) missing factors (book-to-market, value vs growth) time variation of market risk premium international diversification PhD 01-1

From Theory to Practice First index fund: 1971 launched by Wells Fargo (Samsonite pension fund) and American National Bank Fidelity vs Vanguard Benchmarking Asset classes Expense ratio Outliers: talent or luck? PhD 01-1

Optimal portofolio with borrowing and lending Optimal portfolio: maximize Sharpe ratio PhD 01-1

Capital asset pricing model (CAPM) Sharpe (1964) Lintner (1965) Assumptions Perfect capital markets Homogeneous expectations Main conclusions: Everyone picks the same optimal portfolio Main implications: 1. M is the market portfolio : a market value weighted portfolio of all stocks 2. The risk of a security is the beta of the security: Beta measures the sensitivity of the return of an individual security to the return of the market portfolio The average beta across all securities, weighted by the proportion of each security's market value to that of the market is 1 PhD 01-1

Market equilibrium: illustration Wealth Risk free asset Market Portfolio Firm 1 Firm 2 Firm 3 Optimal portfolio 100% 20% 50% 30% Alan 10 -10 20 4 6 Ben -5 25 5 12.5 7.5 Clara 30 15 3 4.5 60 12 18 PhD 01-1

Capital Asset Pricing Model Expected return RM Rj Risk free interest rate βj 1 Beta PhD 01-1

Inside CAPM PhD 01-1

Arbitrage Pricing Theory Starts from statistical characterization of returns Consider one factor model for stock returns: Rj = realized return on stock j E(Rj) = expected return on stock j F = factor – a random variable E(F) = 0 εj = unexpected return on stock j – a random variable E(εj) = 0 Mean 0 cov(εj ,F) = 0 Uncorrelated with common factor cov(εj ,εk) = 0 Not correlated with other stocks (=key assumption) PhD 01-1

Diversification Suppose there exist many stocks with the same βj. Build a diversified portfolio of such stocks. The only remaining source of risk is the common factor. PhD 01-1

Created riskless portfolio Combine two diversified portfolio i and j. Weights: xi and xj with xi+xj =1 Return: Eliminate the impact of common factor  riskless portfolio Solution: PhD 01-1

Equilibrium At equilibrium: No arbitrage condition: The expected return on a riskless portfolio is equal to the risk-free rate. At equilibrium: PhD 01-1

Risk – expected return relation Linear relation between expected return and beta For market portfolio, β = 1 Back to CAPM formula: PhD 01-1

Generalization The approach can easily be generalized to several factors PhD 01-1

Empirical challenges Explaining the cross section of returns Explaining changes in expected returns PhD 01-1

Beta PhD 01-1

PhD 01-1

Size and B/M PhD 01-1

File: 25_Portfolios_5x5_monthly.xls Based on monthly data 192607 200411 File: 25_Portfolios_5x5_monthly.xls PhD 01-1

Fama French PhD 01-1

Predictability: Interest Rates and Expected Inflation Sample period (Sample Size) γ 1831-2002 (2,053) -2.073 (-3.50) 1831-1925 (1,136) -3.958 (-4.58) 1926-1952 (324) 0.114 (0.03) 1953-1971 (228) -5.559 (-2.57) 1972-2002 (357) -1.140 (-1.08) Schwert, W., Anomalies and Market Efficiency,WP October 2002 http://ssrn.com/abstract_id=338080 PhD 01-1

Predictability: D/P PhD 01-1

Predictability PhD 01-1

PhD 01-1

Econometrician wanted… PhD 01-1