Transcript International Investment

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
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Efficient markets: intuition
Price
Realization
Expectation
Price change is
unexpected
Time
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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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S&P500 Daily returns
0.08
0.06
0.04
Return day t+1
0.02
0
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
-0.02
-0.04
-0.06
-0.08
Return day t
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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
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Efficient Market Theory
Cumulative Abnormal Return (%)
Announcement Date
39
34
29
24
19
14
9
4
-1
-6
-11
-16
Days Relative to annoncement date
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Example: How stock splits affect value
40
35
Cumulative
abnormal
return %
30
25
20
15
10
5
0
-29
0
Month relative to split
Source: Fama, Fisher, Jensen & Roll
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Cumulative abnormal returns
(%)
Event Studies: Dividend Omissions
Cumulative Abnormal Returns for Companies Announcing
Dividend Omissions
1
0.146 0.108
-8
-6
0.032
-4
-0.72
0
-0.244
-2 -0.483 0
-1
2
4
6
8
Efficient market
response to “bad news”
-2
-3
-3.619
-4
-5
-4.563-4.747-4.685-4.49
-4.898
-5.015
-5.183
-5.411
-6
Days relative to announcement of dividend omission
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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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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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!
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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%)
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US Equity Mutual Funds 1982-1991
(Malkiel, Journal of Finance June 1995)
•
•
•
•
•
•
Capital appreciation funds
Growth funds
Small company growth funds
Growth and income funds
Equity income funds
Average Annual Return
16.32%
15.81%
13.46%
15.97%
15.66%
• S&P 500 Index
17.52%
• Average deviation from benchmark
(risk adjusted)
-3.20%
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 : Excess Return
• Excess return = Average return - Risk adjusted expected return
Return
Average
return
Expected return

Risk
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Risk
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Jensen 1968 - Distribution of “t” values for “”
115 mutual funds 1955-1964
35
Not significantly
different from 0
30
25
20
15
10
5
0
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-5
-4
-3
-2
-1
0
1
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US Mutual Funds
Consistency of Investment Result
Successive Period Performance
Initial Period Performance
Top Half
Goetzmann and Ibbotson (1976-1985)
Top Half
62.0%
Bottom Half
36.6%
Malkiel, (1970s)
Top Half
65.1%
Bottom Half
35.5%
Malkiel, (1980s)
Top Half
51.7%
Bottom Half
47.5%
Bottom Half
38.0%
63.4%
34.9%
64.5%
48.3%
52.5%
Source: Bodie, Kane, Marcus Investments 4th ed. McGraw Hill 1999 (p.118)
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Decomposition of Mutual Fund Returns
(Wermers Journal of Finance August 2000)
• Sample: 1,758 funds 1976-1994
Funds outperform
benchmark
• Benchmark
14.8%
+1%
• Gross return
• Expense ratio
• Transaction costs
• Non stock holdings
• Net Return
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15.8%
0.8%
0.8%
0.4%
Stock picking +0.75%
No timing ability
Deviation from benchmark +0.55%
Not enough to cover
costs
13.8%
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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
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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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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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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:
 51
112
 50 

1
(1  r ) (1  r ) 2
r  7.117%
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Time-Weighted Return
53  50  2
r1 
 10%
50
54  53  2
r2 
 5.66%
53
Simple Average Return:
(10% + 5.66%) / 2 = 7.83%
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Averaging Returns
Arithmetic Mean:
Text Example Average:
n
rt
r
t 1 n
(.10 + .0566) / 2 = 7.81%
Geometric Mean:
Text Example Average:
1/ n


r   (1  rt )  1
 t 1

n
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[ (1.1) (1.0566) ]1/2 - 1
= 7.83%
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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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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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Factors That Lead to Abnormal Performance
• Market timing
• Superior selection
– Sectors or industries
– Individual companies
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Risk Adjusted Performance: Sharpe
1) Sharpe Index
rP  rf
P
rp
= Average return on the portfolio
rf
= Average risk free rate
P
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= Standard deviation of portfolio return
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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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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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Risk Adjusted Performance: Treynor
2) Treynor Measure
rp  rf
p
rp = Average return on the portfolio
rf = Average risk free rate
ßp = Weighted average ß for portfolio p
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Risk Adjusted Performance: Jensen
3) Jensen’s Measure
 p  rp  [rf  (rm  rf )  p ]
 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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Appraisal Ratio
Appraisal Ratio = p / (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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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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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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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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Example of Market Timing
rp - rf
* *
* *
*
*
*
*
* **
* *
* * *
** *
*
*
* *
rm - rf
Steadily Increasing the Beta
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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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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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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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Formula for Attribution
n
n
i 1
i 1
rB   wBi rBi & rp   w pi rpi
n
n
i 1
i 1
rp  rB   w pi rpi   wBi rBi 
n
 (w
i 1
r  wBi rBi )
pi pi
Where B is the bogey portfolio and p is the managed portfolio
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Contributions for Performance
Contribution for asset allocation
+
=
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Contribution for security selection
(wpi - wBi) rBi
wpi (rpi - rBi)
Total Contribution from asset class wpirpi -wBirBi
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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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Theory of asset pricing under certainty
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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
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Portfolio Theory
• Portfolio characteristics
•
Expected return
– expected return
– risk (standard deviation)
• Risk determined by covariances
• Efficient frontier
• If riskless asset: one optimal
portfolio
Risk
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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)
1
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Beta
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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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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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Implications of the EMH for Investment Policy
• Technical Analysis
• Fundamental Analysis
• Active Portfolio Management
– market timing
– stock selection
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Mutual Fund Performances
• Malkiel (Journal of Finance June 1995)
• 239 equity funds 1982-1991
• Average excess return
Benchmark Portfolio: Wilshire 5000
Net returns
-0.93%
Gross returns
0.18%
• Persistence of Fund Performance:
– Winner: rate of return > median
– Percent Repeat Winners: 51.7%
S&P500
-3.20%
-2.03%
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Mutual Fund Performances (cont.)
• Otten and Barms, WP 2000
• 506 European equity funds 1991-1998
No
Mean
Funds
Return
France
99
10.9
Germany
57
13.9
Italy
37
15.2
Netherland
9
22.0
United Kingdom 304
12.3
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Market
Return
12.7
15.3
14.9
21.0
14.2
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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
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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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Optimal portofolio with borrowing and lending
M
Optimal portfolio:
maximize Sharpe ratio
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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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Market equilibrium: illustration
Wealth
Risk free
asset
Optimal portfolio
Market
Portfolio
Firm 1
Firm 2
Firm 3
100%
20%
50%
30%
Alan
10
-10
20
4
10
6
Ben
20
-5
25
5
12.5
7.5
Clara
30
15
15
3
7.5
4.5
Market
60
0
60
12
30
18
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Capital Asset Pricing Model
Expected return
R j  RF  ( R M  RF )   j
RM
Rj
Risk free
interest rate
βj
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1
Beta
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Inside CAPM
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Arbitrage Pricing Theory
• Starts from statistical characterization of returns
• Consider one factor model for stock returns:
R j  E( R j )   j F   j
•
•
•
•
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)
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Diversification
• Suppose there exist many stocks with the same βj.
• Build a diversified portfolio of such stocks.
R j  E( R j )   j F
• The only remaining source of risk is the common factor.
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Created riskless portfolio
• Combine two diversified portfolio i and j.
• Weights: xi and xj with xi+xj =1
• Return:
RP  xi Ri  x j R j
 ( xi E ( Ri )  x j E ( R j ))  ( xi  i  x j  j ) F
• Eliminate the impact of common factor  riskless portfolio
xi i  xi  j  0
• Solution:
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xi 
 j
i   j
xj 
i
i   j
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Equilibrium
• No arbitrage condition:
• The expected return on a riskless portfolio is equal to the risk-free rate.
 j
i   j
Ri 
i
i   j
R j  RF
At equilibrium:
E ( Ri )  RF
i
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
E ( R j )  RF
j
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Risk – expected return relation
Linear relation between expected return and beta
E( R j )  RF   j
For market portfolio, β = 1
E( RM )  RF  
Back to CAPM formula:
E( R j )  RF  E(RM )  RF  j
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Generalization
•
The approach can easily be generalized to several factors
R j  E ( R j )    jk Fk   j
N
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Empirical challenges
• Explaining the cross section of returns
• Explaining changes in expected returns
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Beta
18.00
16.00
Durb
14.00
Chem
Mone
Oil
NoDu
12.00
NoDu
Durb
Oil
Chem
Manu
Telc
Util
Shop
Mone
Other
MktPort
RF
Manu
MktPort
Telc
Average return
Shop
Util
Other
10.00
8.00
6.00
4.00
RF
2.00
0.00
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
Beta
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Average return vs market beta for 25 FF stock portfolios 1926-2004
2.00
Size S: S1 smallest - S5 biggest
B/M: BM1 lowest - BM5 highest
1.80
1.60
LowB/M
1.40
HighB/M
Mean return
1.20
Small
0.91
1.29
1.50
1.69
1.83
1.45
Average monthly returns
Big
1.01 1.08 1.01 0.92
1.33 1.26 1.10 0.92
1.46 1.30 1.30 1.03
1.51 1.40 1.35 1.11
1.64 1.53 1.46 1.34
1.39
1.32 1.24 1.07
BM5
0.99
1.18
1.32
1.41
1.56
BM4
S2
S1
BM3S3
S4
BM2
S5
1.00
Mkt
BM1
0.80
0.60
CorpB
0.40
GovB
RF
0.20
-0.20
0.00
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
Beta
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1.80
Size and B/M
2.00
m 1.80
e
a
n 1.60
m 1.40
o
n
t 1.20
h
l 1.00
y
r
e
t
u
r
n
%
Low B/M
Series2
Series3
Series4
High B/M
0.80
0.60
0.40
High B/M
S4
0.20
S3
Value
0.00
S2
1
Small
2
3
Size
Low B/M
4
Big
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SIZE
Av.Ret.
St.Dev.
Beta
Small
1.45
9.47
1.35
1.39
7.59
1.17
1.32
7.03
1.15
1.24
6.70
1.13
Big
1.07
6.45
1.05
1.41
7.10
1.13
High
1.56
8.85
1.32
B/M
Av.Ret.
St.Dev.
Beta
Low
0.99
7.38
1.17
1.18
6.91
1.12
1.32
6.75
1.10
Based on monthly data 192607 200411
File: 25_Portfolios_5x5_monthly.xls
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RM
SMB
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-40
-60
HML
|72
2002
1999
1996
1993
1990
1987
1984
1981
1978
1975
1972
1969
1966
1963
1960
1957
1954
1951
1948
1945
1942
1939
1936
1933
1930
1927
Fama French
Fama French Factors - Annual
80
60
40
20
0
Predictability: Interest Rates and Expected Inflation
Rmt    R ft   t
γ
Sample period (Sample Size)
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
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20 July 2015
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2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
1958
1956
1954
1952
1950
1948
1946
1944
1942
1940
1938
1936
1934
1932
1930
1928
1926
Predictability: D/P
Price/dividend ratio
100.00
90.00
80.00
70.00
60.00
50.00
40.00
30.00
20.00
10.00
0.00
Predictability
Nobs
77
R(t+1)=a+b*R(t)+e(t+1)
Mean
StDev
Slope
Standerror
Stock
0.1190 0.2050
0.03 0.1154
Tbill
0.0421 0.0350
0.92 0.0465
Excess
0.0769 0.2083
0.04 0.1155
Excess(t+x) = a + b (D/P)(t) + e
Horizon
1 year
2 year
3 years
4 years
5 years
20 July 2015
4.17
8.13
11.27
13.69
15.02
PhD 01-1
1.60
2.26
2.62
2.95
3.21
t
R²
0.27
19.79
0.31
0.001
0.838
0.001
2.61
3.60
4.30
4.64
4.67
0.082
0.147
0.200
0.228
0.233
|75
ER(+5)=a+b*(D/P)(t)+e
1.5
Excess Return +5
1
0.5
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
-0.5
-1
D/P
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0.08
19
26
19
28
19
30
19
32
19
34
19
36
19
38
19
40
19
42
19
44
19
46
19
48
19
50
19
52
19
54
19
56
19
58
19
60
19
62
19
64
19
66
19
68
19
70
19
72
19
74
19
76
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
Econometrician wanted…
Excess Return + 5 : Residuals
1.5
1
0.5
0
-0.5
-1
-1.5
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PhD 01-1
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