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

2. 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

3. Efficient markets: intuition
Price
Realization
Expectation
Price change is unexpected
Time
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4. 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)
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5. S&P500 Daily returns
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6. 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 + ARt ARt0+1
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7. Efficient Market Theory
Announcement Date
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8. Example: How stock splits affect value
-29 30
Source: Fama, Fisher, Jensen & Roll

9. 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)
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10. 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)
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11. What moves the market Who knows? Lot of noise:
: 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
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12. Trading Is Hazardous to Your Wealth (Barber and Odean Journal of Finance April 2000)
Sample: trading activity of 78,000 households
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%)
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13. US Equity Mutual Funds 1982-1991 (Malkiel, Journal of Finance June 1995)
Average Annual Return
Capital appreciation funds %
Growth funds %
Small company growth funds %
Growth and income funds %
Equity income funds %
S&P 500 Index %
Average deviation from benchmark %
(risk adjusted)
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14.  : Excess Return Return  Risk
Excess return = Average return - Risk adjusted expected return
Return
Expected return
Average return 
Risk
Risk
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15. Jensen 1968 - Distribution of “t” values for “” 115 mutual funds 1955-1964
Not significantly different from 0
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16. US Mutual Funds Consistency of Investment Result
Successive Period Performance
Initial Period Performance Top Half Bottom Half
Goetzmann and Ibbotson ( )
Top Half % %
Bottom Half % %
Malkiel, (1970s)
Top Half % %
Bottom Half % %
Malkiel, (1980s)
Top Half % %
Bottom Half % %
Source: Bodie, Kane, Marcus Investments 4th ed. McGraw Hill 1999 (p.118)
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17. Decomposition of Mutual Fund Returns (Wermers Journal of Finance August 2000)
Sample: 1,758 funds
Benchmark 14.8%
+1%
Gross return 15.8%
Expense ratio %
Transaction costs %
Non stock holdings %
Net Return %
Funds outperform benchmark
Stock picking +0.75%
No timing ability
Deviation from benchmark +0.55%
Not enough to cover costs
PhD 01-1

18. Performance evaluation

19. 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
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20. 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
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21. 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
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22. Dollar-Weighted Return
Period Cash Flow
share purchase
1 +2 dividend share purchase
2 +4 dividend shares sold
Internal Rate of Return:
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23. Simple Average Return: (10% + 5.66%) / 2 = 7.83%
Time-Weighted Return
Simple Average Return:
(10% %) / 2 = 7.83%
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24. Arithmetic Mean: Text Example Average: (.10 + .0566) / 2 = 7.81%
Averaging Returns
Arithmetic Mean:
Text Example Average:
( ) / 2 = 7.81%
Geometric Mean:
Text Example Average:
[ (1.1) (1.0566) ]1/2 - 1
= 7.83%
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25. 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
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26. 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
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27. Factors That Lead to Abnormal Performance
Market timing
Superior selection
Sectors or industries
Individual companies
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28. Risk Adjusted Performance: Sharpe
1) Sharpe Index
rp = Average return on the portfolio
rf = Average risk free rate
= Standard deviation of portfolio return P
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29. 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
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30. 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
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31. 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
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32. 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.
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33. 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
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34. 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
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35. 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
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36. Market Timing
Adjusting portfolio for up and down movements in the market
Low Market Return - low ßeta
High Market Return - high ßeta
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37. Example of Market Timing*
rp - rf
rm - rf
Steadily Increasing the Beta
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38. 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
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39. Process of Attributing Performance to Components
Set up a ‘Benchmark’ or ‘Bogey’ portfolio
Use indexes for each component
Use target weight structure
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40. 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
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41. Formula for Attribution
Where B is the bogey portfolio and p is the managed portfolio
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42. Contributions for Performance
Contribution for asset allocation (wpi - wBi) rBi
+ Contribution for security selection wpi (rpi - rBi)
= Total Contribution from asset class wpirpi -wBirBi
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43. 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
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44. Theory of asset pricing under certainty
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45. Passive Portfolio Management
Professor André Farber
Solvay Business School
Université Libre de Bruxelles

46. 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
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47. 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
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48. 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
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49. 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)
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50. 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?
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51. Implications of the EMH for Investment Policy
Technical Analysis
Fundamental Analysis
Active Portfolio Management
market timing
stock selection
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52. Mutual Fund Performances
Malkiel (Journal of Finance June 1995)
239 equity funds
Average excess return
Benchmark Portfolio: Wilshire S&P500
Net returns % %
Gross returns % %
Persistence of Fund Performance:
Winner: rate of return > median
Percent Repeat Winners: 51.7%
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53. Mutual Fund Performances (cont.)
Otten and Barms, WP 2000
506 European equity funds
No Mean Market
Funds Return Return
France
Germany
Italy
Netherland
United Kingdom
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54. 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

55. 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?
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56. Optimal portofolio with borrowing and lending
Optimal portfolio: maximize Sharpe ratio
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57. 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
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58. 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
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59. Capital Asset Pricing Model
Expected return RM Rj
Risk free interest rate βj 1
Beta
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60. Inside CAPM
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61. 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) = Mean 0
cov(εj ,F) = 0 Uncorrelated with common factor
cov(εj ,εk) = 0 Not correlated with other stocks (=key assumption)
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62. 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.
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63. 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:
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64. Equilibrium At equilibrium: No arbitrage condition:
The expected return on a riskless portfolio is equal to the risk-free rate.
At equilibrium:
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65. Risk – expected return relation
Linear relation between expected return and beta
For market portfolio, β = 1
Back to CAPM formula:
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66. Generalization
The approach can easily be generalized to several factors
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67. Empirical challenges Explaining the cross section of returns
Explaining changes in expected returns
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68. Beta
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69. PhD 01-1

70. Size and B/M
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71. File: 25_Portfolios_5x5_monthly.xls
Based on monthly data
File: 25_Portfolios_5x5_monthly.xls
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72. Fama French
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73. Predictability: Interest Rates and Expected Inflation
Sample period (Sample Size) γ
(2,053)
(-3.50)
(1,136)
(-4.58)
(324)
0.114 (0.03)
(228)
(-2.57)
(357)
(-1.08)
Schwert, W., Anomalies and Market Efficiency,WP October
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74. Predictability: D/P
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75. Predictability
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76. PhD 01-1

77. Econometrician wanted…
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