Post on 01-Aug-2020
www.icmacentre.ac.uk
Dr Ioannis Oikonomou
Portfolio Management Background information
2
Reading
Main Textbook
• Bodie, Z., Kane, A., and Marcus, A.J. (2011) Investments, 9th International
edition, McGraw-Hill, New York
Other useful textbooks
• Elton, E., Gruber, M.J., Brown S.J. and Goetzmann W.N. (2010) Modern
Portfolio Theory and Investment Analysis 8th edition, Wiley.
• Reilly, F.K. and Brown, K.C. (2000) Investment Analysis and Portfolio
Management 6th edition, South Western Publishing.
• Lofthouse, S. (2001) Investment Management 2nd edition, Wiley
3
Brief Outline of Topics Covered
• Topic 1. The Investment Environment
• Topic 2: Risk Aversion and Asset Allocation Decisions
• Topic 3: Portfolio Theory
• Topic 4: Asset Pricing Models
• Topic 5: Market Efficiency and Behavioural Finance
• Topic 6: Style Investing
• Topic 7: Performance Evaluation
• Topic 8: Active Portfolio Management
• Topic 9: Passive Portfolio Management
• Topic 10: Hedge Funds and Exam Preparation
www.icmacentre.ac.uk
Lecture 1:The Investment Environment
Portfolio Management
Dr Ioannis Oikonomou
5
What is Portfolio Management?
• Portfolio management involves
– Constructing a portfolio of assets that best matches the client’s
preferences and needs
– Portfolio construction will involve looking at the returns, risks, relationships between the asset payoffs (correlations)
– Evaluating the performance of the portfolio
– Adjusting the composition of the portfolio over time as necessary
• Portfolio management has a broader base than security analysis
– This involves looking at individual assets in isolation and
determining whether they are correctly priced or not
6
Investment companies
• Collect funds from individual investors and invest those funds in a potentially wide range of securities
• Perform several important roles to investors – Diversification: Investment into assets that do not move
perfectly in tandem (low correlation)
– Reducing paperwork, administration, and time spent on asset selection
– Ability to satisfy client’s desires
– Ability to forecast which sector / stocks will perform well
– Low transaction costs
– Funds are typically very liquid: Asset managers agree to repurchase the shares of investors upon request
– Often able to switch to another fund in the family at zero cost
7
Investment companies:
Open versus closed end funds
Open end fund (Mutual fund)
• Floating number of shares
• Stands prepared to issue or redeem shares at net asset value (NAV)
• 90% of AUM (Asset under management)
• Fidelity, Vanguard, Putnam, Dreyfus, Morley, L&G…
Closed end fund
• Like any corporation, shares are listed in a stock exchange
• Fixed number of shares (unless issues new shares)
• Trades at market prices and thus could trade at a premium or discount from NAV
• Premium or discount = (current market price – NAV) / NAV
sharesNumber of
sLiabilitie-AssetsNAV
8
Mutual funds categories
• Money market funds: Short term securities
• Fixed income funds:
– Income funds: Regular coupons, Income stability
– High yield funds: Junk bonds
• Equity funds:
– Income funds: High dividend stocks
– Growth funds: High capital gains and low dividends – riskier
– “Value” funds (low P/E or MV/BV)
– Blend: Income and growth
– Small capitalisation fund (Small capitalisation or small size stocks)
– Large capitalisation fund (Large companies)
• Asset allocation funds: Mix of money market instruments, bonds, and equities
9
The UK fund management industry: top 10 firms in terms
of funds under management
Source: IMA Survey, 2014
• High competition: top ten firms represent 46% of the industry
• Around £1.5 trillion of AUM were managed in the UK in 2014
• Total industry headcount at 31,800 with an increasing trend
10
Staff activity in the industry
Asset Allocation
Source: IMA Survey, 2014
11
The UK fund management industry
in the European context
Source: IMA Survey, 2014
12
The UK fund management industry:
Asset Allocation
Source: IMA Survey, 2014
13
The UK fund management industry:
Active Vs Passive
Source: IMA Survey, 2014
14
The UK fund management industry:
Equity allocation by region
Source: IMA Survey
15
The UK fund management industry:
Client Type
Source: IMA Survey, 2014
16
Asset Allocation
• The key problem in portfolio management is asset allocation
• How much of the investor’s wealth should be invested in
– Equities
– Bonds
– Property
– Cash
– Derivatives?
17
Asset classes and subcategories
Equities Fixed Income Money Market Alternative Assets
UK Equities UK Fixed Income Cash and Money Market Commodities
- Large capitalisation - UK Treasury bonds - Cash, Physical holdings
- Mid capitalisation - Municipal - Bank balance Hedge Funds
- Small capitalisation - Corporate - UK Treasury bills
- Micro capitalisation - Asset-backed - Municipal notes Private Equity
- Growth - Commercial papers
- Value (Income) High Yield - Certificates of deposit Real Estate
- Blend (Value and Growth) - Repurchase agreement
- Preference shares Convertible Securities - Banker acceptances Art
- Non UK instruments
Other Developed Markets Other Developed Markets
- North America - North America
- Europe - Europe
- Japan - Japan
Emerging Markets Emerging Markets
- Africa - Africa
- Asia ex Japan - Asia ex Japan
- Emerging Europe - Emerging Europe
- Latin America - Latin America
- Middle East - Middle East
18
Equity (Ordinary shares)
• Claim that entitles the holder to a share of firm’s profits
• Rationale for investment – Ownership claim
– High returns
– Rational pricing (Efficient market place)
– Sector / style potential
• Risks and concerns – High risk: Dividends and capital gains are neither scheduled nor
specified
– Residual claim in case of bankruptcy
– Long term cycles
Source: Darst, 2003
19
Fixed income
• Long term (>1 year) borrowing by firms and governments
• Rationale for investment – Low risk: Payments of coupons and par-value are both scheduled and
specified
– Senior claim in case of bankruptcy
– Higher return than cash
– Portfolio diversifier (Low correlation)
• Risks and concerns – Low returns
– Interest rate risk
– Inflation risk
– Credit risk
– Reinvestment risk
20
Convertible preference shares
and convertible bonds
• Bonds and preference shares (shares with fixed dividend and higher seniority than ordinary shares in case of bankruptcy) that can be converted into ordinary shares
• Rationale for Investment
– Equity-debt hybrid
– Claim senior to equity
– Portfolio diversifier (Low correlation)
• Risks and Concerns
– Prepayment risk (Callable)
– Claim junior to bond
– Yields below ordinary shares or bonds
21
Cash and money market instruments
(Treasury-bills, commercial papers,
certificates of deposit…)
Rationale for Investment
• Safe haven in periods of
negative financial returns
• Low standard deviation
• Portfolio diversifier (Low
correlation)
• High liquidity
Risks and Concerns
• Low average return
• Reinvestment risk
• Inflation risk
• Credit exposure
• Costs and attention
22
UK financial market real returns
and risks: 1955 – 2000
Source: Dimson and Marsh, 2001
Micro-cap
equities
Low-cap
equities
All equities
High-cap
equities
Long-maturity
bondsMid-maturity
bonds
T-bill
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
0% 5% 10% 15% 20% 25% 30%
Standard Deviation
Avera
ge R
eal R
etu
rn
High-cap: 90% largest capitalisation stocks
Low-cap: Next 9% largest stocks
Micro-cap: 1% smallest stocks
Market capitalisation = Number of stocks * Share price
23
Number of years each UK asset class
performed the best: 1955 – 2000
5
2
4
1
10
4
20
0
5
10
15
20
25
Nu
mb
er
of
Ye
ars
Treasury Bill Mid Maturity
Bonds
Long Maturity
Bonds
All Equities High-Cap
Equities
Micro-cap
Equities
Low-Cap
Equities
Asset Class
UK equities beat UK bonds:
76% of the time
UK bonds beat UK equities:
24% of the time
Source: Dimson and Marsh, 2001
24
The Historical Returns to Different Assets
Ibbotson SBBI Chart: Stocks, Bonds, Bills and Inflation 1926-2008
Source: Ibbotson
25
Source: Datastream The higher the risk, the higher the average return
Argentina
Austria Belgium
Canada Denmark
France
Germany
Hong Kong
Italy
Japan
South Korea
Mexico
Portugal
Spain
Switzerland Taiwan Thailand
Turkey
UK
USA
-10%
0%
10%
20%
30%
40%
50%
60%
0% 10% 20% 30% 40% 50% 60%
An
nu
ali
sed
Ret
urn
s
Annualised Standard Deviation
Risk and return in developed and
emerging economies: 1990 – 2010
26
Designing an investment process
Utility
functions Risk tolerance / aversion Investment horizon
Views on Risk and return
Views on
markets
Asset
classesStocks
Money
Market
Alternative
Investments
- inflation
- rates
Countries - growth
Valuation
based on Market efficiency
- Cash flows Private - Can you beat
- Ratios Which stocks? Which bonds? Which real assets? information the market?
- Charts
Trading costs Trading systems
- Commissions - How often do you trade? Trading - How does
- Bid ask - How large are your trades? speed trading affect
- Price impact - Do you use derivatives to manage or enhance risk? prices?
Market - How much risk did the portfolio manager take? Stock
timing - What return did the portfolio manager make? selection
- Did the asset manager underperform or outperform?
Domestic
Security Selection
Performance Evaluation and Risk Management
The Risk Manager's Job
The client
Risk models:
CAPM and APT
The Portfolio Manager's Job
- CAPM, APT
- Diversification
- Measuring risk
Execution
Bonds
Asset Allocation
Non domestic
27
References
• BKM, 9th edition, Chapter 2, Chapter 4
• Elton, E., Gruber, M.J., Brown S.J. and Goetzmann W.N.
(2010), Chapter 2 and Chapter 3.
www.icmacentre.ac.uk
Lecture 2:
Risk Aversion and Asset Allocation Decisions
Portfolio Management
Dr Ioannis Oikonomou
29
Risk and risk premium: An example
• Consider the following 1-year risky investment
000,22£000,100£000,122£ profitExpected
000,122£000,804.000,1506.
1 21
WppWWE
000,000,176,1
000,122000,804.000,122000,1506.
1
22
22
21
2
WEWpWEWp
000,22£86.292,34£
000,000,176,1
W1 = £150,000
W = £100,000
W2 = £80,000
p=0.6
p=0.4
30
Risk and risk premium: Example Continued
• One-year risk-free investment into T-bill at 5%
• Risk premium earned as compensation for risk: £22K - £5K = £17K
• Is the premium commensurate with the risk borne? See later lectures
• Is the investor willing to take a risk of £34,293 in the hope of a profit of £22,000?
Profit: £50,000
A: Invest into
risky asset
Loss: £20,000
W = £100,000
B: Invest into
risk free T-bill Profit: £5,000
p = .6
p = .4
31
Risk aversion
• A risk averse investor considers
– either risk-free investments
– or risky investments with positive risk premia
• Risk aversion does not mean that the investor will systematically rule out risky projects
• Utility: Score that each investor assigns to risky investments based on their expected return and risk
– A: Coefficient of risk aversion of the client
– Utility rises with expected return, falls with risk and risk aversion
– The more risk averse the investor, the higher his A
25. AREU
32
Risk aversion: Going back
to the previous example
• Rf = 5%, E(R) = 22%, = 34%
• Utility of investing into the risk-
free asset: 5% (f = 0)
• Investors are utility maximisers;
i.e., choose investment with the
highest utility; e.g., for an investor
with A = 5
• A risk tolerance quiz can be used
to define an investor’s A 25. AREU
25. A
069.05. RiskyfreeRisk UU
Level of risk
aversion
Coefficient
of risk
aversion A Utility
Downward
adjustment of
E(R) due to risk
Investment
decision
Low 1 16.22% 5.78% Risky asset
2 10.44% 11.56% Risky asset
3 4.66% 17.34% Risk-free asset
Moderate 4 -1.12% 23.12% Risk-free asset
5 -6.90% 28.90% Risk-free asset
6 -12.68% 34.68% Risk-free asset
7 -18.46% 40.46% Risk-free asset
High 8 -24.24% 46.24% Risk-free asset
9 -30.02% 52.02% Risk-free asset
Very high 10 -35.80% 57.80% Risk-free asset
33
Indifference curves of risk averse investors
Locus of portfolios in a risk – expected return space that offer an investor the
same utility: The investor with an A of 4 is indifferent between P and Q
Risk (P)
E(RP)
P
Q
Indifference curve
of an investor
with a moderate
aversion
to risk (A = 4)
Indifference
curve of a very
risk averse
investor
(A = 10)
Indifference curve
of an investor
with a low
aversion to
risk (A = 2)
X% X% X%
Larg
e
Mediu
m
Sm
all
34
Risk aversion, neutrality, and loving
• Q is more risky than P but the additional risk is compensated by an increase in expected return, so P and Q are equally desirable and lie on the same indifference curve
• The more risk averse an investor, the higher his coefficient of risk aversion (A), the steeper his indifference curve and the higher the return he requires for taking on an extra unit of risk
• A risk neutral investor judges risky investments solely in terms of expected return (A = 0)
• A risk lover is willing to invest in gambles, for the “fun” of risking it all (A<0)
• In modern finance theory, all investors are assumed to be risk averse: they only invest in risky portfolios if the additional risk is compensated by a commensurate increase in expected return
35
Normal distribution
• We saw that risky projects have more than one possible outcome.
• This does not mean that we are clueless as we can look at past returns and get an idea of the range of possible future returns
• Frequency distribution
• If we increase the number of returns and the number of ranges, the distribution will look increasingly like a bell shaped curve (Normal distribution)
Probability distribution: S&P 500 returns
3%
8%
13%
20%
23%
15% 15%
3% 3%
0%
5%
10%
15%
20%
25%
-30
to -2
0
-20
to -1
0
-10
to 0
0 to 1
0
10 to
20
20 to
30
30 to
40
40 to
50
50 to
60
S&P500 annual returns
Pro
ba
bilit
y (
%)
36
Normal distribution
• The entire return distribution of stock A is fully described by its mean E(RA) and standard deviation A (or variance A
2)
• When the outcomes are not equally likely (pi: Prob. that state i occurs)
• When the outcomes are equally likely
N
i
AiiA RpRE1
N
i
AiA RN
RE1
1
N
i
AAiA RERN
1
22
1
1
N
i
AAiiA RERp1
222AA
37
Properties of the normal distribution
• 68% of returns lie within ± 1 standard deviation of the mean
• 95% of returns lie within ±2 standard deviations of the mean
• 99.7% of returns lie within ± 3 standard deviations of the mean
• Symmetric around its mean (zero skewness)
• Skinny tails (zero excess kurtosis)
38
Examples for single assets
15.15.1.
1.4.25.5.
ARE
State of the
economyExpansion Recession
Deep
recession
Probability 0.5 0.4 0.1
Risk free asset 5% 5% 5%
Stock A 25% 10% -15%
Stock B 8% 1% 20%
N
i
AiiA RpRE1
064.BRE
05.fRE
N
i
AAiiA RERp1
22
015.15.15.1.
15.1.4.15.25.5.
2
222
A
1225.015. A
0561.B 02 ff
39
Examples for single assets:
Covariance
When the price of A rises,
– the price of B falls,
– the price of the risk-free asset does not change
N
i
BiBAAiiAB RERRERp1
0022.064.2.15.15.1.
064.01.15.1.4.
064.08.15.25.5.
AB0fA
: ?QfB
40
Examples for single assets:
Correlation coefficient
• Scales the covariance to a value between -1 and +1
• When the price of A goes up
– the price of B goes down
– the price of the risk-free asset does not change
32.
0561.1225.
0022.
BA
ABAB
0fA
41
Examples for portfolios of assets
• Portfolio P1 with 20% in A and 80% in B
• Portfolio P2 with 50% in the risk-free asset and 50% in A
• Expected return of P1 and P2
BAAAP RERERE 1
0812.064.8.15.2.1 PRE
1.15.5.05.5.2 PRE
42
Examples for portfolios of assets
• Variance and standard deviation of P1 and P2
ABAABAAAP 121 22222
001908.0022.8.2.200314.8.015.2.222
1 P
0437.1 P
00375.015.5.2222
2 AAP
0612.2 AAP
43
Asset allocation between
a risk-free asset and a risky portfolio
• Asset allocation decision
– How much should an investor invest in stocks, bonds, bills…?
– 94% of the difference in total returns achieved by fund managers
• Example: You are managing a portfolio P made of 60% stocks (S) and
40% bonds (B)
1 BSf
1 Pf
Asset E(R) Weight
Risk-free 0.07 0 F
Portfolio P 0.15 0.25 PBS
44
Asset allocation between
a risk-free asset and a risky portfolio
• Asset allocation for an investor who requires an E(R) of 13%
• Per £1 invested, the investor invests £.25 in Treasury bills (lends £.25
to the government) and £.75 in portfolio P (i.e., £.45 in S and £.3 in B)
PfPPffPPPC RRERRRERE 08.07.1
3.75.4.
45.75.6.
25.75.1
75.
13.08.07.
B
S
f
P
P
PBS
1875.25.75. PPC
45
Asset allocation between
a risk-free asset and a risky portfolio
• Asset allocation for an investor who requires a SD of 10%
• Per £1 invested, the investor invests £.6 in Treasury bills (lends £.6 to the government) and £.4 in portfolio P (i.e., £.24 in S and £.16 in B)
16.4.4.
24.4.6.
6.4.1
4.
1.25.
B
S
f
P
P
PPC
102.15.4.07.6. CRE
46
0%
5%
10%
15%
20%
25%
0% 5% 10% 15% 20% 25% 30% 35% 40% 45%
Standard deviation
Exp
ecte
d r
etu
rn
Rf
PC1
C2
C3
C4
18.75%
13%
21%
10.2%
16.6%
43.75%
Lending
portfolio
Borrowing
portfolio
Capital allocation
line (CAL)
The Capital Allocation Line (CAL)
0f
0f
The CAL is the set of portfolios that are feasible;
i.e, that can be formed by combining the risk-free asset and P
47
The Capital Allocation Line
• Equation of the CAL
• Slope of the CAL = Reward to variability ratio
• All the portfolios on the same CAL have the same RVar
CC
P
fPfC
RRERRE
32.07.
P
fPP
RRERVar
2
2
1
1
C
fC
C
fC RRERRE
48
Risk tolerance and asset allocation:
Analytical solution
• Summarising thus far,
• The utility maximisation problem can be expressed as
fPPfC RRERRE
PPC
25. PPfPPf ARRERMaxUMax
PP
25. AREU
49
Risk tolerance and asset allocation:
Analytical solution
• Setting the derivative of Max(U) equal to 0 and solving for P yields the
optimal asset allocation in P (Assume A = 4)
• Characteristics of the optimal portfolio C
32.
25.4
07.15.22
*
P
fPP
A
RRE
68.1 ** Pf
0956.07.15.32.07. CRE
08.25.32. C
P
C
fCC RVar
RRERVar
32.
08.
07.0956.
50
Risk tolerance and asset allocation:
Graphical solution
• The optimal asset allocation problem can also be solved graphically using
the investor’s indifference curves
• E(R) required for a given risk by an investor with a risk aversion of 4 (A = 4)
• The indifference curve is the plot of E(R) versus SD for a given utility
U = 0.05 U = 0.07 U = 0.09
0 0.05 0.07 0.09
0.05 0.055 0.075 0.095
0.1 0.07 0.09 0.11
0.15 0.095 0.115 0.135
0.2 0.13 0.15 0.17
0.25 0.175 0.195 0.215
0.3 0.23 0.25 0.27
0.35 0.295 0.315 0.335
07.1.45.05.5.22 AURE
51
Risk tolerance and asset allocation:
Graphical solution
0%
10%
20%
30%
40%
50%
60%
70%
0% 5% 10% 15% 20% 25% 30% 35%
Standard deviation
Exp
ecte
d r
etu
rn
A = 2, U = 0.07 A = 4, U = 0.05 A = 4, U = 0.07 A = 4, U = 0.09 A = 9, U = 0.07
A = 9
Very risk averse
investor A = 4
Investor with an
average level of RA
A = 2
Investor with a below
average level of RA
52
Risk tolerance and asset allocation: Graphical solution -
Reconciling preferences (indifference curves) and
opportunities (CAL)
0%
5%
10%
15%
20%
25%
30%
35%
40%
0% 5% 10% 15% 20% 25% 30% 35%
Standard deviation
Exp
ecte
d r
etu
rn
P
8%
9.56%
Rf
Indifference curves
for an investor with A = 4
U = .09, U = .082, U = .07,
U = .05 respectively
CAL
U = .09
U = .05
P2
P3
P1
53
• P1 is not optimal: A given increase in risk is compensated by an increase in E(R) that is too small for the investor
• P2 is not feasible
– Given the choice, the investor would prefer P2 to P3 since P2 maximises his utility and offers a higher E(R) for the same risk
– But P2 is not on the CAL, so there is no combination of the risk-free asset and the risky portfolio that will generate a risk – E(R) trade-off similar to P2
• P3 is the investor’s optimal portfolio. It is
– on the capital allocation line (so, it is feasible)
– tangent to his indifference curve (A given increase in risk is compensated by an increase in E(R) that is proportional to what the investor requests)
– At P3, the investor’s preferences for risk and E(R) (indifference curve) are reconciled with the opportunities offered on the CAL
Risk tolerance and asset allocation: Graphical solution -
Reconciling preferences (indifference curves) and
opportunities (CAL)
54
Key points
• Utility function: Function that describes an investor’s preferences for risk and
E(R)
• The higher A, the more risk averse the investor and the higher the premium
he requires for taking on an additional unit of risk
• Indifference curve: Graphical representation of utility function
• Optimal capital allocation between a risk-free asset and a risky portfolio
– Capital allocation line: Locus of feasible portfolios
– Optimal asset allocations can be defined graphically or analytically as
25. AREU
CfCP
fPfC RVarR
RRERRE
2*PfPP ARRE
55
Further Examples of Portfolio Maths in Use
You manage a passive fund that mimics the FTSE100 stock index. This fund yields an expected rate of return of 15% with a standard deviation of 20%. The return on the risk-free asset is 8%.
1. Client X wants to form a portfolio with a 15% standard deviation.
– What is his optimal asset allocation?
– What is the expected return of the combined portfolio?
– Define the equation of the Capital Allocation Line
Optimal asset allocation:
Expected return:
CAL equation:
MMX 25. ,75. f
M
XM
1325.08.25.15.75. XRE
PPPRE 35.08.2.
08.15.08.
56
Further Examples of Portfolio Maths in Use
2. Client Y wants to form a portfolio with a 22% expected return.
– How would you construct such a portfolio?
– What is the standard deviation of the combined portfolio?
– What is the reward to variability ratio of Y? Comment.
Optimal weights:
Standard deviation:
Reward to variability ratio of Y:
22.1 MMfMY RERRE
1 ,2 fM
4. MMY
35.
4.
08.22.
Y
fYY
RRERVar
57
Further Examples of Portfolio Maths in Use
3. Client Z has a degree of risk aversion of 4
– What is his optimal asset allocation?
– What is the standard deviation and expected return of the combined
portfolio?
– What is the utility that Client Z will derive from the combined portfolio?
– What is the reward to variability ratio of Client Z? Comment.
Optimal weights:
Standard deviation:
Expected return:
Utility:
5625. ,4375.
2
f
M
fM
MA
RRE
0875. MMZ
1106.ZRE
0953.5. 2 ZZ AREU 35. MYZ RVarRVarRVar
58
References
• BKM, 9th edition, Chapter 5, Chapter 6
• Elton, E., Gruber, M.J., Brown S.J. and Goetzmann W.N. (2010),
Chapter 4
• Investment Risk Tolerance quiz: http://njaes.rutgers.edu/money/riskquiz/
www.icmacentre.ac.uk
Lecture 3:Portfolio Theory
Portfolio Management
Dr Ioannis Oikonomou
60
The benefits of diversification
• Risk of a portfolio made of Compaq stocks
– Systematic risk of Compaq (depends on general market conditions)
– Firm specific risk of Compaq (depends on R&D, personnel, marketing...)
• Risk of a portfolio made of 50% Exxon and 50% Compaq
– Systematic risk of Compaq and Exxon
– Firm specific risk of Compaq and Exxon
• Firm specific risks of Compaq and Exxon tend to offset one another
• Including more assets significantly decreases firm specific risk without sacrificing expected returns - This is what Markowitz (1952) is all about!
61
10
The benefits of diversification
Unsystematic risk
Systematic risk
No. of assets in portfolio
Total risk
20
ij
2P
Do not put all your eggs (money) in the same basket (stocks)
: Average covariance between any 2 pairs of assets in the portfolio ij
62
As N gets bigger, the variance of an equally weighted portfolio equals the average covariance . The average variance of the individual stocks no longer contributes to the variance of the portfolio
The benefits of diversification
ijijN
PN NN
11limlim
22
Individual risk
Unique risk
Unsystematic risk
Diversifiable risk
Firm specific risk
Market risk
Systematic risk
Non diversifiable risk
Covariance risk
Total risk
See appendix for a derivation
2ij
63
The benefits of diversification
Assume that the average variance of return for an individual security is
.5 and that the average covariance is .1. What is the standard deviation
of an equally weighted portfolio of 5, 10 and 15 securities?
• For a portfolio of 5 assets,
• For a portfolio of 10 assets,
• For a portfolio of 15 assets,
The decrease in SD from adding 5 assets to a 10 stock portfolio is less
than the decrease in SD from adding 5 assets to a 5 asset portfolio
Q: How many stocks do we need for a well diversified portfolio?
A: Between 30 and 40 for randomly selected stocks (Statman, 1987)
424.1.5
11
5
5.11
1 2
ijP
NN
374.1.10
11
10
5.
P
356.1.15
11
15
5.
P
64
Appendix: The power of diversification shown
mathematically
• Actual return:
• Expected return: Weighted average of the expected returns on the
individual assets included in the portfolio
• Variance covariance matrix of returns: Consists of N diagonal variances
and N2-N = N(N-1) off-diagonal covariances
N
i
itiPt RR1
N
i
iiP RERE1
N
i
N
j
ijji
N
i
N
ijj
ijji
N
i
iiP
1 11 11
222
ij
2i
65
The power of diversification Continued
• Now assume that the portfolio is equally weighted
• Factoring out 1/N from the 1st summation and (N-1)/N from the 2nd
where : Average variance of returns
: Average covariance of returns
N
i
N
ijj
ij
N
i
iPNNN
1 11
22
2 111
N
i
N
ijj
ij
N
i
iP
NNN
N
NN1 11
22 1
1
111
ijPN
N
N
11 22
2
ij
Nji
1
66
Measuring portfolio risk and expected return:
The case with two risky assets
• Expected return on P (made of A and B)
• Standard deviation of returns on P
– A and B=1-A : Portfolio weights (% of wealth invested in A and B)
– AB: Correlation coefficient between A and B =
BAAAP RERERE 1
212222 121 ABBAAABAAAP
BA
AB
212222 2 ABBABBAAP
67
1 0.14 0.0196 0.1400 P1
0.5 0.14 0.0148 0.1217 P2
0 0.14 0.0100 0.1000 P3
-0.5 0.14 0.0052 0.0721 P4
-0.85 0.14 0.0018 0.0429 P5
212222 2 ABBABABBAAP
AB PRE 2P P
Stock A B
Investment weights 0.2 0.8
Expected return 0.22 0.12
Standard deviation 0.3 0.1
Measuring portfolio risk and expected return:
The case with two risky assets
Portfolio
68
10%
12%
14%
16%
18%
20%
22%
24%
0% 5% 10% 15% 20% 25% 30% 35%
Annualised standard deviation
An
nu
ali
sed
mean
retu
rn
P5 P4 P3 P2 P1
B
A
P*
Measuring portfolio risk and expected return:
The case with two risky assets
Thus far, the portfolio weights were A = 20%, B = 80% (Portfolios P1 to P5)
To obtain the locus of all feasible portfolios, change A from 0 to 1
P*: Minimum variance portfolio
AB = -.85
AB = 0
AB = -.5
AB = .5
AB = 1
69
• How much do we need to invest in A to obtain P*, the minimum variance portfolio?
• If AB = 0,
ABBABA
ABBAB
ABBA
ABBA
22 22
2
22
2*
*
*
10%
90%
A
B
ABBABBAAPAA
MinMin
222222
0
121 2222
A
ABAABAAA
13%PE R 9.49%P
Measuring portfolio risk and expected return:
The case with two risky assets
70
Measuring portfolio risk and expected return:
The case with N risky assets
N
E(RP)
Z
’
A
P*
Z Z’’
B
p
Feasible set
Minimum variance
opportunity set
Markowitz’s mean
variance efficient
frontier
P*: Minimum variance portfolio
71
Measuring portfolio risk and expected return:
The case with N risky assets
• All the portfolios on and within AZ’Z’’P*B are feasible
• N is not feasible
• Portfolios on P*Z’’Z’A dominate the others; i.e., they offer:
– a higher E(R) for a given risk (Z’ dominates Z)
– a lower risk for a given E(R) (Z’’ dominates Z)
• Step 1: Define Markowitz’s mean variance efficient frontier; i.e, set of portfolios that offer the highest E(R) for any risk
72
1. With N risky assets, calculate
- N means,
- N variances,
- N(N-1)/2 covariances Q: why N(N-1)/2 ?
2. Define the minimum variance opportunity set: Find the portfolio weights i that minimise portfolio std deviation
subject to
3. Define the Markowitz’s mean variance efficient frontier; i.e., choose the portfolios that offer the highest E(R)
0
1
R
N
1
P
i
i i
KE
Pi
Min
For a given E(R)
The mandate is fully invested
No short-selling
Methodology
73
AAffP RERRE
AAP
P
E(RP)
Rf
A
A
Capital
Allocation
Line (CAL)
A
fA RRERVarESR
Choice between one risky asset A
and one risk-free asset Rf
ESR = Expected Sharpe ratio
E(RA)
74
Rf
P
E(RP)
B
A
M CAL1
CAL2
M
Sharpe’s Capital Market Line (CML)
= New mean variance efficient
frontier for risky portfolios
P
M
fMfP
RRERRE
Capital Market Line
E(RM)
75
Methodology
• Search for the CAL with the highest reward-to-variability ratio (the
steepest slope); i.e., find the portfolio weights that maximise the
expected Sharpe ratio
subject to
• Given i (i = 1,…, N), calculate the mean and SD of M
P
fP RREMax
i
0
i
PfP RRE
0
1 N
1
i
i i
76
• Every investor will invest in M, the tangency portfolio
• Two fund separation theorem: In the presence of capital markets,
rational risk-averse investors always select efficient portfolios that lie on
the CAL with the highest expected Sharpe ratio; i.e., the CML. To do
so, they combine Rf and M
Two fund separation theorem
77
Tobin’s separation theorem
• You can separate the portfolio construction problem into two steps
– First, find the tangency portfolio; i.e., the unique mean variance efficient combination of risky assets that is tangent to the line emanating from the risk-free asset
– Then, decide whether your client should borrow or lend depending of his/her attitude towards risk
• Every investor chooses a portfolio on the CML that matches his/her preference toward risk and E(R)
78
M
I2
I2’
I1 I1’
E(RP)
P
Rf
More risk
averse investor
Less risk
averse investor
P
Q
P’
Q’
Capital
market line
Investor’s optimal portfolio
79
E(Ri)
i
RB
RL
K
Mean variance
efficient frontier
RLLBC
C
Less risk
averse investor Investor with an
average degree
of risk aversion
Very risk
averse
investor
The points on the dashed lines are non attainable
Different lending and borrowing rates
L
B
80
Different lending and borrowing rates
• Usually investors face borrowing restrictions
• If they can’t borrow, optimal portfolio is Q instead of Q’
• If RB > RL, the mean variance efficient frontier will be kinked (RLLBC)
– Risky portfolio selected by all defensive investors L: Tangency point
between Markowitz and line originating at RL
– Risky portfolio selected by all aggressive investors B: Tangency
point between Markowitz and line originating at RB
– The market portfolio is somewhere between L and B
81
Portfolio construction problem solved in 3 steps
1. Identify the risk – E(R) combinations available from N risky assets and
Markowitz’s mean variance efficient frontier
– Benefits from diversification when correlation < 1
– Markowitz’s efficient frontier: Locus of portfolios that offer the
highest possible E(R) for any given risk
2. Introduce the risk-free asset and identify the tangency portfolio by
finding the weights that result in the steepest CAL
– Capital market line
– Two fund separation theorem
3. Introduce investor’s degree of risk tolerance and maximise expected
utility
82
Some definitions / reminders
• Minimum variance opportunity set: Locus of risky portfolios with the
lowest possible risk for a given E(R)
• Mean-variance efficient portfolio: Portfolio that offers the highest
possible E(R) for a given risk
– In the absence of capital markets, efficient frontier = upper half of
the minimum variance opportunity set
– In the presence of capital markets, efficient frontier = CML = CAL
with the highest expected Sharpe ratio
• Investor’s optimal portfolio: Mean-variance efficient portfolio that
maximises investor’s expected utility; i.e., tangent to his indifference
curve
83
An example – how to form a portfolio
• You manage a portfolio made of the UK T-Bill and 15 UK stocks
• Define the optimal asset allocation of clients with different degrees of
risk aversion
i
fii
RREESR
IndustryAnnualised
mean
Annualised
std deviation
Expected
Sharpe ratio
UK T-bill rate Government 4.48% 0.23%
Aviva Insurance -1.71% 39.23% -0.1579
Balfour Beatty Engineering 39.79% 42.16% 0.8374
Barclays Banking 9.45% 26.76% 0.1856
BBA Group Transport -4.07% 36.88% -0.2320
BHP Billiton Ressources 18.11% 32.36% 0.4211
Boots Group Retail 4.70% 24.14% 0.0089
BP Oil & Gas -1.81% 21.31% -0.2952
De Vere Group Leisure 14.41% 25.94% 0.3827
Gartmore UK Tracker Investment company -1.89% 16.43% -0.3881
GlaxoSmithKline Pharmaceutical -5.06% 20.14% -0.4737
ICI Chemicals -3.15% 50.77% -0.1504
ITV Media -4.97% 47.73% -0.1980
M&S Retail 7.13% 29.17% 0.0908
Slough Estates Real estate 12.15% 23.35% 0.3284
Unilever Consumer goods 5.62% 25.50% 0.0444
84
End of month data for a 5-year period
ICIITV
Aviva
BBA GroupGlaxoSmithKline
BP
Gartmore
UK Tracker
UnileverBoots Group
M&S
Barclays
Slough Estates
De Vere GroupBHP Billiton
Balfour Beatty
T-Bill
-10%
0%
10%
20%
30%
40%
50%
0% 30% 60%
Annualised standard deviation
An
nu
ali
se
d a
ve
rag
e r
etu
rn
85
Correlation matrix
Minimum -0.08
Maximum 0.72
Average 0.32
Aviva
Balfour
Beatty Barclays
BBA
Group
BHP
Billiton
Boots
Group BP
De Vere
Group
Gartmore
UK Tracker
GlaxoSmith
Kline ICI ITV M&S
Slough
Estates Unilever
Aviva 1
Balfour Beatty 0.41 1
Barclays 0.63 0.40 1
BBA Group 0.52 0.29 0.39 1
BHP Billiton 0.36 0.16 0.28 0.41 1
Boots Group 0.51 0.40 0.44 0.38 0.26 1
BP 0.35 0.25 0.31 0.37 0.52 0.30 1
De Vere Group 0.07 0.18 0.17 0.35 0.10 0.08 0.24 1
Gartmore UK Tracker 0.62 0.34 0.67 0.72 0.52 0.44 0.54 0.34 1
GlaxoSmithKline 0.26 0.27 0.26 0.02 -0.03 0.27 0.19 -0.08 0.11 1
ICI 0.62 0.22 0.43 0.54 0.37 0.37 0.14 0.18 0.54 0.06 1
ITV 0.46 0.04 0.44 0.64 0.32 0.25 0.20 0.21 0.69 -0.07 0.60 1
M&S 0.32 0.32 0.32 0.16 0.32 0.44 0.22 0.12 0.24 0.05 0.19 0.06 1
Slough Estates 0.48 0.38 0.35 0.49 0.46 0.57 0.55 0.11 0.63 0.32 0.36 0.41 0.14 1
Unilever 0.44 0.28 0.36 0.31 0.10 0.50 0.03 0.17 0.21 0.16 0.32 0.04 0.22 0.25 1
86
The case with no short sale of risky assets:
Markowitz’s and Sharpe’s MVE frontiers
P5
P4
Min SD
portfolio
P2Min E(R)
portfolio
P7
P6
Optimal
portfolio
P9
Max E(R)
portfolio
Balfour Beatty
BHP Billiton
De Vere Group
Slough Estates Barclays
M&SUnilever
Boots GroupGartmore
UK Tracker
AvivaBP
ICI
BBA GroupITVGlaxoSmithKline
-10%
0%
10%
20%
30%
40%
50%
60%
0% 30% 60%
Annualised standard deviation
An
nu
alised
avera
ge r
etu
rn
Capital Market Line
Markowitz's mean
vairance efficient frontier
Q
R
Rf
87
Minimum risk
portfolio
Tangency
portfolio
Portfolio with
maximum return
Aviva 0% 0% 0%
Balfour Beatty 0% 47.41% 100%
Barclays 0% 0% 0%
BBA Group 0% 0% 0%
BHP Billiton 0% 26.14% 0%
Boots Group 0% 0% 0%
BP 7.09% 0% 0%
De Vere Group 12.81% 26.45% 0%
Gartmore UK Tracker 31.93% 0% 0%
GlaxoSmithKline 30.70% 0% 0%
ICI 0% 0% 0%
ITV 0% 0% 0%
M&S 7.49% 0% 0%
Slough Estates 0% 0% 0%
Unilever 9.97% 0% 0%
Sum weights 100% 100% 100%
Annualised average return 0.47% 26.91% 39.79%
Annualised standard deviation 12.09% 25.16% 42.16%
The case with no short sale of risky assets:
Optimal asset allocation for some Markowitz’s or
Sharpe’s MVE portfolios
88
The case with no short sale of risky assets
• Benefits of diversification: Compared to any individual assets (aside from Balfour Beatty), diversification
– reduces risk for a given level of expected return
– increases expected return for a given level of risk
– increases expected utility
• Equation of the Capital Market Line (CML)
PPPOpt
fOptfP
RRERRE
891.0045.0
25.0
045.027.0045.0
89
The case with no short sale of risky assets
• Each investor chooses the portfolio on the CML that is tangent to his/her indifference curve
• This optimal portfolio is either
– to the left of the risky assets only optimal portfolio: Investor with a high level of risk aversion (e.g., A of 8) who wants to lend at the risk-free rate
– the same as the risky assets only optimal portfolio: Investor with an average level of risk aversion (e.g., A of 4 or 5)
– to the right of the risky assets only optimal portfolio: Investor with a low level of risk aversion (e.g., A of 2) who wants to borrow at the risk-free rate
90
The case with up to 20% short sale
of risky assets
Optimal
portfolio
Max E(R)
portfolio
Min E(R)
portfolio
CML with short sale
Rf
-50%
0%
50%
100%
150%
200%
250%
300%
0% 40% 80% 120% 160% 200%
Annualised standard deviation
An
nu
alised
avera
ge r
etu
rn
Markowitz's
with short sale
Markowitz's and Sharpe's
without short sale
91
The case with up to 20% short sale of risky assets
• Short selling risky assets shifts the MVE frontier to the North-West of
the mean-standard deviation graph
• Compared to the case without short sale,
– Increase in expected return for a given level of risk
– Decrease in risk for a given expected return
– Increase in the expected Sharpe ratio
– Increase in investor’s utility
• Equation of the Capital Market Line (CML)
PPPOpt
fOptfP
RRERRE
62.1045.0
439.0
045.0757.0045.0
92
The case with no short sale of risky assets
• Each investor chooses the portfolio on the CML that is tangent to his/her indifference curve
• This optimal portfolio is either
– to the left of the risky assets only optimal portfolio: Investor with a high level of risk aversion (e.g., A of 8) who wants to lend at the risk-free rate
– the same as the risky assets only optimal portfolio: Investor with an average level of risk aversion (e.g., A of 4 or 5)
– to the right of the risky assets only optimal portfolio: Investor with a low level of risk aversion (e.g., A of 2) who wants to borrow at the risk-free rate
93
Benefits of MV optimisers
• Satisfaction of clients’ objectives and constraints
– Short position allowed?
– Limits on the amount of cash in the portfolio?
– Restrictions on assets with low liquidity?
– Socially responsible investment (SRI) screens
• Control of portfolio risk exposure
– Portfolio with a beta of less than 1,
– Portfolio with no exposure to inflation…
• Implementation of style objectives and market outlook
– Optimisation reflects investment style, philosophy, or outlook (e.g. value vs. growth, small vs. large cap...) by choosing the appropriate exposure to various risk factors, to various stocks and appropriate benchmarks
• Quick processing of a large amount of information
94
Theoretical limitations of MV optimisers
Mean-variance optimisers assume
– Returns are normally distributed
– Utility functions are quadratic
These assumptions are often not valid
First, asset returns are not always normally distributed, especially for portfolios that include options; e.g., hedge funds, commodities
Second, utility may not be quadratic: If investors also value skewness (3rd moment of return distribution) and kurtosis (4th moment)…, these should be part of the investor’s utility function
Utility functions are also difficult to define. Value of the risk aversion index A?
PPPP KurtbSkewbbREU 212
0
25.0 AREU
95
Practical limitations of MV optimisers
1. Inexperience with modern financial technology: Optimisers make conceptual demands on portfolio managers who are used to more informal analysis
2. Political reasons: Investment policy committees (i.e., senior members of the organisation) make investment decisions. The use of optimisers would transfer decision power to quantitative analysts
3. Historical means, standard deviations and correlations do change. The optimiser assumes that the past will repeat itself.
96
Practical limitations of MV optimisers
Standard deviations are not constant…
0%
10%
20%
30%
40%
50%
60%
70%
80%
Average Annual Volatility During US Business Cycles
Expansion StDev Recession StDev
Data from Dec 1987 - Nov 2009
Source: MSCI & NBER websites
97
Practical limitations of MV optimisers
...Correlations are not constant either
Source: Credit Suisse Global Investment Yearbook 2010
98
References
• BKM, 9th edition, Chapter 7
• Elton, E., Gruber, M.J., Brown S.J. and Goetzmann
W.N. (2010), Chapter 5 and Chapter 6.
• Meir Statman, How many stocks make a diversified
portfolio?, Journal of Financial and Quantitative Analysis,
1987.
www.icmacentre.ac.uk
Lecture 4:Asset Pricing Models
Portfolio Management
Dr Ioannis Oikonomou
100
The CAPM: Assumptions
• Investors assumptions
– Investors are risk-averse
– Investors are price takers
– Investors have a one-period horizon
– Homogeneous expectations of asset returns: Same input list
– Investors are mean-variance (MV) optimisers; i.e., they use Markowitz’s portfolio selection model
• Asset and market assumptions
– All assets are marketable
– Assets are perfectly divisible
– Returns are normally distributed
– There exists an unique risk free asset
– No taxes, no transaction costs, free information (no frictions)
101
The market portfolio
• If all investors
– use Markowitz’s analysis
– apply it to the same set of assets (same input list)
– for the same time horizon
– and face the same lending and borrowing rate,
• they will all define
– the same Markowitz’s MV efficient set
– the same tangency portfolio
102
The market portfolio
• In equilibrium the tangency portfolio is the market portfolio M. The
weight allocated to each risky asset in the market portfolio
corresponds to the market value (MV) of the asset expressed as a
proportion of the total market value of all risky assets
• Implication for asset management: A passive investor, who does
not attempt to beat the market but merely opts for a buy and hold
strategy, may view the market index as a reasonable first
approximation to an efficient portfolio
N
i i
ii
MV
MV
1
103
For Relevant measure of risk
Individual asset held in isolation Total risk = i
Non diversified portfolio Total risk = P
Well diversified portfolio Systematic risk =
Individual asset held as part of a
well diversified portfolioSystematic risk = P
• Quantifiable relationship between risk and expected return for single assets in equilibrium (Sharpe, 1964; Lintner, 1965; Mossin, 1966)
• Beta measures
– an asset’s systematic risk (non diversifiable risk)
– the sensitivity of its returns to the market excess returns; i.e., the covariation between the asset returns and the excess return on the market as a whole
Beta
ij
2M
iMi
104
Defensive securities: < 1, e.g., utilities
Aggressive securities: > 1, e.g.,
high tech industry, airlines stocks
Market: = 1
Rit
time
Beta
High-beta (Low-beta) stocks have greater (lower) volatility in their returns
than the market portfolio. The market portfolio has a beta of 1 (Q: why?)
= 1.4: Stock returns on average rise (fall) 40% faster than the market in up (down) markets
105
2M
fMiMffMifi
RRERRRERRE
Market price
per unit of risk
Market risk
premium Quantity
of risk
M
i
E(Ri)
E(RM)
Rf
Market risk premium
Risk-free rate
SML
M = 1
The Security Market Line (SML)
as a visual representation of the CAPM
106
Portfolio performance – Treynor index
• Measure of performance that relates the fund’s average excess return
to its
• (Q: what is the Treynor
ratio of the market portfolio?)
Ri
i
A
B
SlopeRR
TreynorP
fPP
SML
M
fP RR
AR
BR
Rf
A B M = 1
A outperformed
the market
B underperformed
relative to the market
107
Portfolio performance - Jensen’s alpha
• Deviation from the SML / CAPM: Difference between the actual return
on a fund and the return the fund should have earned given its risk (i.e.,
the fund expected return as defined by CAPM)
i
A
B
fMPfPP RRRR
M
BR
AR
BRE
0A
0B
ARE
A over
performed
B underperformed
M = 1 A B
108
Security valuation
• Using the zero growth dividend discount model
• Using the constant growth dividend discount model
• The CAPM can also be used in project appraisal, where beta is used to
risk-adjust the cashflows.
fMifitt
i
iRRER
Div
RE
Div
RE
DivP
00
1
0
1
gRRER
Div
gRE
gDiv
RE
gDivP
fMifitt
i
t
i
10
1
0 1
1
1
109
Relaxation of the assumptions
• No risk-free rate
• Different lending and borrowing rates
• Price making investors (large institutions)
• Heterogeneous expectations about asset returns
• Assets returns are not normally distributed: leptokurtic distribution
• Presence of personal taxes
• Non marketable assets e.g., human capital
110
The Consumption-based CAPM
• Under certain assumptions, return on assets should be linearly
related to the growth rate in aggregate consumption if the
parameters of the linear relationship can be assumed to be
constant over time.
– where Rit = the rate of return on asset i in period t.
Ct = the growth rate in aggregate consumption per
capita at time t.
• The growth rate of per capita consumption has replaced the rate
of return on the market portfolio.
ittiiit eCR
111
General predictions of the model
• Higher systematic risk is compensated by higher expected return:
E(RM) – Rf > 0
• Linear relationship between risk and expected return
• No factor other than beta explain average return; e.g., Unsystematic
risk, Size, Price-to-book value… are not priced
• The slope of the empirical SML equals the average excess return on
the market portfolio
• The intercept of the empirical SML equals the average return on the
risk-free asset
• The market portfolio is mean-variance efficient
112
Empirical testing of the CAPM:Two step
methodology
• Collect 60 month rates of return on
– 100 shares Rit (i = 1,…,100; t = 1,…,60)
– proxy of the market portfolio; e.g., FTSE; RMt
– Risk-free rate; Rft
• Step 1: Time series regression of the excess return on each stock on
a constant and the excess return on the market portfolio
60,...,1t
itftMtiiftit eRRbRR
113
Empirical testing of the CAPM:Two step
methodology
• Step 2: Use the 100 estimated bi in a cross sectional regression; i.e.,
regress the 100 mean returns on a constant and the 100 estimated bi
Average return on stock i (over the 60 obs)
• CAPM valid if and
fR0
iii bR 10
:iR
fM RR 1
100,...,1i
114
Two step methodology: Variations from 2nd step
(1)
– Included to test for non linearity in beta
– Residual variance from the 1st step regressions, included to
test for pricing of unsystematic risk
(2)
– MVi: Size (Market value) of portfolio i
– BMi: Book-to-Market Value of portfolio i
CAPM is valid if 2 = 0 and 3 = 0 in (1) and (2); i.e., differences in
average returns are only due to differences in
ieiii ibbR 2
32
210
:2ib
:2
ie
100,...,1i
iiiii BMMVbR 3210
115
Early tests: Black, Jensen and Scholes (1972);
Fama and MacBeth (1973)
• Qualitative support of the CAPM
– Positive relationship between risk and average return (1>0)
– The relationship is linear (2=0)
– Diversifiable risk does not command a risk premium (3=0)
• No quantitative support: Estimated relationship is flatter than expected
– the estimated intercept .002 exceeds the average return on the risk
free asset over the period (.0013)
– the estimated market risk premium .0114 is less than the average
risk premium observed in the market (.013)
(1.11) (-.86) (1.85) (.55)
0516.00026.0114.002. 22PePPP P
bbR
(t-ratios in parenthesis)
116
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
0 0.5 1 1.5
Estimated MRelationship
identified by
Fama and McBeth
Average observed
relationship
over the period
Observed M
002.0 0013.fR
013. fM RR 0114.1
Early tests: Black, Jensen, and Scholes (1972);
Fama and MacBeth (1973)
117
Roll’s critique (1977)
• The only testable hypothesis is the mean-variance (MV) efficiency of
the true market portfolio. The linear relationship between beta and
average return is a direct consequence of it.
– If we use in the tests a proxy of the market portfolio that is MV
efficient, sample betas will always be linearly related to sample
returns. This however does not prove the validity of the CAPM, just
the MV efficiency of the selected proxy
– Conversely, if the proxy is not MV efficient w.r.t. the set of risky
assets considered, there will be no perfect fit between actual and
expected returns. This simply proves that the selected proxy was
MV inefficient and cannot be used to rule out the CAPM
• Since the true market portfolio is not observable, the CAPM will never
be tested
118
Pricing anomalies that cannot be explained by
market risk (CAPM)
• Firm size anomaly
• Value anomaly
• Seasonality in returns
– January returns are higher
– Monday returns are the lowest and negative
– Monday returns are only positive in January
– Positive returns around holidays
– High returns around the turn of the month
• These effects (size, P/B, seasonality…) are not accounted for in terms of beta
risk and have consequently been termed “anomalies”
119
Key points on the CAPM
• The market only rewards beta (systematic) risk
• The CAPM linearly relates beta to expected return
• The early tests support the CAPM qualitatively in that matters, while
2 and e2 do not. They however fail to validate its quantitative
predictions
• Roll’s critique: The CAPM will never be tested
• Anomaly literature: It is an open debate as to know whether or not the
CAPM is dead
• Still the CAPM is widely used for capital budgeting, pricing risky assets,
and evaluating portfolio performance. So do not dismiss it straight
away!
120 8.01.08.05.13
1
3
13
1
CBAi
iiP
Arbitrage Pricing Theory: An example
• The APT relies on the law of one price: If 2 identical assets trade at
different prices in 2 markets and the price differential exceeds the costs
of trading, a simultaneous trade in the 2 markets ensures risk-free
profits
• Consider the following 4 well diversified portfolios. An equally weighted
portfolio P made of A, B and C outperforms portfolio D in all scenarios
Summary statistics
1 2 3 4 E (R ) β
Probability 25% 25% 25% 25%
Portfolio A £100 -6% 5% 10% 20% 7.25% 1.50
Portfolio B £100 -2% 3% 3% 4% 2.00% 0.80
Portfolio C £100 10% 5% -1% -8% 1.50% 0.10
Portfolio D £100 -2% 2% 3% 5% 2.00% 0.80
P = A +B +C £300 0.67% 4.33% 4.00% 5.33% 3.58% 0.80
State of natureCurrent
price
Buy P
Short sell 3 times D
0725.02.01.005.006.04
14
1
i
AiiA RERE
121
Arbitrage Pricing Theory: An example
• Arbitrage strategy
– Short sell 3 times portfolio D
– Use the proceeds to form portfolio P (i.e., to buy 1 portfolio A, 1
portfolio B and 1 portfolio C)
• The arbitrage portfolio (long P, short D)
– Has no unsystematic risk: Eliminated through diversification
– Has no systematic risk
– Requires no initial wealth (the proceeds of the short sale of D are
used to purchase A, B and C)
– Offers a profit in all scenarios
08.2
18.
2
1
2
1
2
12
1
DPi
iiArbitrage
122
Arbitrage Pricing Theory: An example
• £ profits in each of the four scenarios
• As long as a few investors take very large positions, the price of D will fall, the prices of A, B and C will rise until the arbitrage opportunity ceases to exist
State of nature
1 2 3 4
Portfolio A £100 -£6 £5 £10 £20
Portfolio B £100 -£2 £3 £3 £4
Portfolio C £100 £10 £5 -£1 -£8
Portfolio D -£300 £6 -£6 -£9 -£15
Long P , Short D £0 £8 £7 £3 £1
Investment
123
The APT Model Motivations and Assumptions
• Developed by Ross (1976) as an alternative to overcome some of the short-comings of the CAPM e.g.
– Assets’ returns are not in general normally distributed.
– Reliance on a single risk factor, .
– Problems with market portfolio.
• The APT assumes that the rate of return on any stock is a linear function of k factors.
• The CAPM can be shown to be a special case of the APT.
• The APT is based on the law of one price: Two assets that are the same (in term of risk) cannot sell at different prices in different markets. A violation of this law will lead to strong pressures to restore equilibrium.
Assumptions
• More assets than factors
• All investors believe that returns are linearly related to a set of systematic risk factors (Homogenous expectations)
• Perfect and frictionless markets
124
The APT model, Ross (1977)
• We previously split total risk into systematic risk and unsystematic risk. If
we do the same for total return
• Assume the excess return on any asset is described by K factors
• Taking expectations and as E(eit) = 0
Systematic component
of return (affect all
stocks to a higher
or lower extent)
Error term:
Unexpected
unsystematic
return
itKtiKtiiftit eFactorFactorRR ...11
Average
unsystematic
return
KiKiifi FactorEFactorERRE ...11
(1)
(2)
125
The APT model, Ross (1977)
• Subtract equation (2) from equation (1)
– E(Ri) = Expected return on stock i
– Fjt = Unexpected risk factor j (i.e., deviation of the factor from its
expected value) that impacts the returns on all stocks to a lower or
a greater extent
– ij = Sensitivity of the return on stock i to factor j
– eit = Error term
itKtiKtiiit eFFRER ...11
Systematic
component
of return
Unsystematic
component
of return
0 jjtj FactorEFactorEFE
126
The APT model, Ross (1977)
• Consider a 2 factor model for an asset i and a portfolio P
• Construct an arbitrage portfolio; i.e., a portfolio P that
– requires no wealth: Use profits of short sales to buy new assets:
– has no systematic risk: Choose i such as:
– has no unsystematic risk (well-diversified portfolio):
• In equilibrium, this portfolio should earn a zero E(R):
ittitiiit eFFRER 2211
01
N
i i
0,01i 21i 1
Nii
Nii
01
N
i itie
01
N
i iiP RERE
N
iiti
N
itii
N
itii
N
iiiPt eFFRER
1122
111
1
127
• As a mathematical consequence of the above, expected returns can be expressed as a linear combination of the sensitivities
• Generalising for K factors
– 0 = Risk-free rate
– j = Price of systematic risk (Risk premium) associated with factor j
– Rj = Return on a portfolio with a sensitivity of 1 to factor j and no sensitivity to all other factors
• If there is only one factor and this factor is the true market portfolio, the APT collapses to the CAPM
22110 iiiRE
iKKiiRE ...110
iKfKiffi RRERRERRE ...11
The APT model, Ross (1977)
128
Macroeconomic and financial variables
Chen, Roll and Ross (1986)
• Dividend discount model:
• Any factor that affects Div or r is potentially a source of systematic risk
• These factors could include
– Unexpected inflation: Actual inflationt – Expected inflationt
– Change in expected inflation
– Shocks to the term structure of interest rates (Term structure = Yield on long-term maturity T-bond – 3-month T-bill rate)
– Shocks to default spread (Default spread = Difference in yields between BAA and AAA rated bonds)
– Unexpected industrial production
• It is the unexpected component (surprise) in the announcement and not the announcement itself that is source of priced risk
1
01t
tr
DivP
129 1.65 -1.65
Macroeconomic and financial variables
Chen, Roll and Ross (1986)
1.88- 2.97 2.38- 1.60- 3.05 0.63- 2.76
59.083.008.0012.0176.124.007.1 ,,,,,, PTSPDSPUIPEIPIPPMPP bbbbbbR
(t-ratios in
parenthesis)
Priced factors; i.e., Factors commanding a significant risk
premium
– Risk-free asset (Intercept)
– Industrial production (IP)
– Unexpected inflation (UI)
– Default spread (DS)
– Term structure (TS)
Non priced factors; i.e., Factors not commanding a
significant risk premium
– Market (M), suggesting that CAPM is dead (the sign is opposite to what we would expect)
– Change in expected inflation (EI)
t-ratio
(t-statistic)
Accept H0: = 0
The risk factor does not
enter the APT Reject H0: > 0
The risk factor
enters the APT
Reject H0: < 0
The risk factor
enters the APT
-1.96 1.96
We are testing
H0: = 0
130
APT versus CAPM
APT is more robust than CAPM because:
1. APT requires no assumptions about the distribution of asset returns
2. APT requires of investors only that they want to maximise their
wealth and are risk averse
3. APT allows asset returns to be dependent on many factors
4. No assumptions about mean variance efficiency (MVE) of the
market portfolio - the APT holds for any well diversified portfolio of
assets
5. APT can easily be extended to a multi-period framework (Ross,
1976)
6. APT is more closely tied to the fundamental concept of arbitrage
131
Problems with the APT
1. APT still requires homogeneous beliefs about future
asset returns
2. How can the APT help us to decide which assets to buy?
APT is inherently more complex than CAPM
3. What are the factors?
– Ross and the original formulation do not suggest what (or even how
many) factors there should be.
– We can use factor analysis to determine the factors.
132
• Use of mimicking portfolios (portfolios of stocks that mimic size and BM
factors and are expected to explain average returns)
– rPt = Returns on portfolio P in excess of the risk-free rate at time t
– rMt = Returns on an equity portfolio in excess of the risk-free rate
– SMBt = Small [cap] Minus Big = Difference in returns on a portfolio of
small stocks and a portfolio of large stocks
– HMLt = High [book/market] Minus Low = Difference in returns on a
portfolio of high book-to-market stocks (Value) and a portfolio of low
book-to-market stocks (Growth)
– ePt = Error term
– P, bP, sP, hP = Estimated coefficients
Special cases of APT: Fama and French (1993)
three factor model
PttPtPMtPPPt eHMLhSMBsrbr
133
• Addition of a fourth factor to the Fama and French three factor model that is related to momentum
– Momt = Difference in returns on a portfolio of stocks with high return over the past year and a portfolio of stocks with low return over the past year
• Why a 4th factor? Positive serial correlation in short horizon returns
– Stocks that have been doing well in the recent past continue to do so (what goes up tends to keep rising)
– Stocks that have been doing poorly in the recent past continue to do so (what goes down tends to keep falling)
• mP defines whether the manager is a momentum trader
– If mP > 0, the manager follows a momentum strategy
– If mP < 0, the manager follows a contrarian strategy (see next week)
– If mP = 0, the manager does not follow a momentum or contrarian strategy
PttPtPtPMtPPPt eMommHMLhSMBsrbr
Special cases of APT: Carhart (1997) four
factor model
134
Similarities
• Both models assume perfect and frictionless markets, homogenous
expectations
• Both models postulate that the same risk factors explain the pricing of
all assets
• Linear relationship between risk and expected return
• Both models are useful tools for asset valuation, capital budgeting,
performance evaluation and risk management
135
Theoretical differences
• The CAPM assumptions (investors are mean-variance optimisers,
returns are normally distributed…) are much more restrictive than those
of the APT. The no-arbitrage assumption from the APT is consistent
with actual behaviour
• The CAPM is a special case of the APT: If there is one risk factor and
this factor is the true market portfolio, the APT collapses to the CAPM
• The APT is multidimensional in risk
• The APT does not require the market portfolio to be mean-variance
efficient (testable alternative to the CAPM)
The APT is potentially superior to the CAPM
136
• Chen, Roll and Ross (1986) show that the market portfolio has no role to play when macroeconomic and financial variables are included as risk factors
• Fama and French (1992) show that MV (size) and BM explain average returns better than market beta
• Relative performance of the two models
– If the CAPM is valid, 1 = 1 and 2 = 0
– If the APT is valid, 1 = 0 and 2 = 1
1 = 0 and 2 = 1: The data support the APT
PAPTPCAPMPP eRERER ,2,10
Empirical differences: The data support
the APT more than the CAPM
137
Key points on the APT
• Relationship between risk and expected return that does not rely on the
mean-variance efficiency of the true market portfolio (Testable
alternative to the CAPM)
• The APT, derived from the no-arbitrage condition, linearly relates factor
sensitivities to expected return
• Both macroeconomic, financial and firm specific variables have been
specified as potential candidates for the risk factors. Multifactor models
are useful both for risk management and performance evaluation
• The APT seems to be superior to the CAPM
iKKiiRE ...110
138
References
• BKM , 9th edition, Chapters 9 and 10
• Elton, E., Gruber, M.J., Brown S.J. and Goetzmann W.N. (2010), Chapters
13,14,15,16
www.icmacentre.ac.uk
Lecture 5:
Market Efficiency and Behavioural Finance
Portfolio Management
Dr Ioannis Oikonomou
140
How should prices behave
in an efficient market?
The efficient market hypothesis (EMH) is a statement about how an asset's price
should react to new information – An efficient market neither over or under-reacts
Days, weeks, months,
or years relative to
announcement of a
good news
Price
-2 -1 0 1 2 3
Efficient response
Overreaction / Correction:
Bubble – Inefficient response
Contrarian strategy
Under-reaction:
Inefficient response
Momentum strategy
141
How should prices behave
in an efficient market?
• Fama (1970): A market is efficient if prices fully and instantaneously
reflect available information
• In an efficient market competition between informed traders will ensure
that the price reaction is instantaneous and unbiased; i.e., prices
always reflect true value
• If so, an investor using the same information as the rest of the market
will only be able to achieve an average return proportionate to the risk
he took. He cannot earn an abnormal return by using information that is
already available
142
Three forms of market efficiency
Strong form (SF): Today price
includes today’s private information
Semi-strong form (SSF): Today price
includes today’s public information
Weak form (WF): Today price
includes price information
A market that is strong form efficient is also
semi-strong and weak form efficient
143
Weak form of market efficiency
• Weak form (WF): Prices reflect past information contained in share prices only
• Implication for asset management: Technical analysis is useless
• Technical analysis: Search for recurrent patterns in stock prices on which to base investment strategy
• Chartists: Technical analysts that study records of past prices in the hope of disclosing shifts in these trends and profitable investment strategies
144
Serial correlation
• Positive serial correlation (b > 0): Trends in price movements (price rises are followed by price rises)
• Negative serial correlation (b < 0): Price reversals (price falls are followed by price rises)
• Zero: Random walk (b = 0)
– t = Error term that reflects new information (unpredictable)
– The best estimate of today’s price is yesterday’s price
ttttt PbaPPP 11
ttt PP 1
145
Momentum and contrarian strategies
Momentum strategy
over short horizon returns
• Continuation in price direction
• What went up over the recent past (less than 1 year) tends to keep rising – the winners keep on winning, so buy them today
• What went down over the recent past tends to keep falling – the losers keep on losing, so sell them short today
Contrarian strategy
over long horizon returns
• Mean reversion
• What went up over the distant past (3 to 5 years) tends to come down – the winners become losers, so sell them short today
• What went down over the distant past tends to come up – the losers become winners, so buy them today
146
Price momentum: Average return
over different holding periods
P10 - P1 =
• 8.8%, 6 months after portfolio formation period (PFP)
• 16.4%, 12 months after PFP
• -0.6%, 24 months after PFP
• 1.2%, 36 months after PFP
-5%
0%
5%
10%
15%
20%
25%
30%
Av
era
ge
Re
turn
in
Ho
ldin
g
Pe
rio
d
P1:
Low
Return
P2 P3 P4 P5 P6 P7 P8 P9 P10:
High
Return
P10 -
P1
6 Months after PFP12 Months after PFP
24 Months after PFP36 Months after PFP
Portfolios Sorted on Past Return
Source: Chan, Jegadeesh and Lakonishok (1999)
147
Contrarian strategies
Source: De Bondt and Thaler (1985)
Cu
mu
lative
re
turn
in
exce
ss o
f th
e m
ark
et re
turn
Months after the portfolio formation period
Portfolio formation period: Last 3 years
Portfolio holding period: Next 3 to 5 years
Loser
portfolio
Winner
portfolio
148
Semi-strong form of market efficiency
• Semi-strong form (SSF):
– Past and publicly available information is included into today’s price
– Public information: Price to book ratio, Dividend yield, Size, Balance sheet composition, Quality of management, Earning forecasts…
• Implication for asset management
– Fundamental analysis is useless
– Fundamental analysis: Use of fundamental information (earnings, dividends forecasts, ratio analysis, detailed economic analysis, industry prospect…) to identify and trade on mispricing
• To increase E(R) in an efficient market, you have to take on more risk. Yet some stocks offer a higher return than expected given their risk
– Size anomaly: Small cap stocks offer a higher average return than large cap stocks even after accounting for their higher risk
– Value anomaly: Value stocks offer a higher return than growth stocks even though they are exposed to less market risk
149
Size anomaly
The portfolios are formed at the end of June and rebalanced every year over
the period Jan 1934 – Dec 2003 (French website)
Amex, Nasdaq, and NYSE stocks sorted by sizeAmex, Nasdaq, and NYSE stocks sorted by size
P1: Value weighted (VW) portfolio
with the 10% stocks that have the lowest size
P1: Value weighted (VW) portfolio
with the 10% stocks that have the lowest size
……
P9: VW portfolio with the 10% stocks
that have the 2nd highest size
P9: VW portfolio with the 10% stocks
that have the 2nd highest size
P2: VW portfolio with the 10% stocks
that have the 2nd lowest size
P2: VW portfolio with the 10% stocks
that have the 2nd lowest size
P10: VW portfolio with the 10% stocks
that have the highest size
P10: VW portfolio with the 10% stocks
that have the highest size
Amex, Nasdaq, and NYSE stocks sorted by sizeAmex, Nasdaq, and NYSE stocks sorted by size
P1: Value weighted (VW) portfolio
with the 10% stocks that have the lowest size
P1: Value weighted (VW) portfolio
with the 10% stocks that have the lowest size
……
P9: VW portfolio with the 10% stocks
that have the 2nd highest size
P9: VW portfolio with the 10% stocks
that have the 2nd highest size
P2: VW portfolio with the 10% stocks
that have the 2nd lowest size
P2: VW portfolio with the 10% stocks
that have the 2nd lowest size
P10: VW portfolio with the 10% stocks
that have the highest size
P10: VW portfolio with the 10% stocks
that have the highest size
150
Average excess return vs. abnormal excess
return (Alpha) of size-sorted portfolios
• The size premium (excess return of small versus large cap) is not solely a compensation for beta risk: The difference in average returns persists after accounting for difference in betas
• Huge impact on the investment community: Many asset managers follow a small cap strategy to capture the small cap premium
16%
4.4%
14.1%
2.4%
13.2%
2.2%
12.8%
2.1%
12.4%
1.9%
11.5%
1.5%
11.3%
1.4%
10.4%
0.9%
9.7%
0.8%
8.1%
0%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
Av
era
ge
Re
turn
in
Ex
ce
ss
of
Ris
k F
ree
Ra
te
P1 -
Small MV
P2 P3 P4 P5 P6 P7 P8 P9 P10 -
Large MV
Size Sorted Portfolio
Average Excess Return Alpha: Average Excess Return Not Explained by Risk
151
Value anomaly
Value stocks (Tortoise)
• Cheap stocks with lots of earnings and book value: Low P/E, low P/B: i.e., Stocks with good fundamentals (earnings, book value) that trade at a bargain
• Mature companies with few prospects, so high dividend yield
• Typically utilities, energy, raw materials…
Growth stocks (Hare)
• Expensive stocks with low earnings today but with lots of potential: High P/E, high P/B, low or zero dividend yield
• Young companies with lots of prospects
• Typically, high tech, aeronautical, pharmaceutical…
152
Average excess return vs. abnormal excess
return (Alpha) on P/B sorted portfolios
• The value premium (excess return of low P/B versus high P/B portfolios) is not a compensation for beta risk: The difference in average returns persists after accounting for difference in betas
• Huge impact on the investment community: Many asset managers follow a value strategy to capture the value premium
12.6%
5.1%
11%
4.2%
11.3%
4.7%
9.5%
3%
9.4%
2.7%
9.3%
2.7%
7.6%
0.4%
8%
0.5%
7.7%
0%
6.4%
-1.9%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
Av
era
ge
Ex
ce
ss
Re
turn
vs
. A
lph
a
P1 - Low
P/B: Value
P2 P3 P4 P5 P6 P7 P8 P9 P10 - High
P/B:
Growth
Portfolios Sorted on Price to Book Value
Average Excess Return Alpha: Average Excess Return Not Explained by CAPM
153
Evidence of Bubble Formation?
Source: Datastream
Nasdaq Composite Index: Jan 1991 - Oct 2005
Feb 2000
4,696.69
Sept 2002
1,172.06
0
1,000
2,000
3,000
4,000
5,000
6,000
Jan-
91Ju
l-91
Jan-
92Ju
l-92
Jan-
93Ju
l-93
Jan-
94Ju
l-94
Jan-
95Ju
l-95
Jan-
96Ju
l-96
Jan-
97Ju
l-97
Jan-
98Ju
l-98
Jan-
99Ju
l-99
Jan-
00Ju
l-00
Jan-
01Ju
l-01
Jan-
02Ju
l-02
Jan-
03Ju
l-03
Jan-
04Ju
l-04
Jan-
05Ju
l-05
Date
Ind
ex p
oin
ts
Fair value?
154
What is a bubble?
• No agreement in the literature on how to define bubbles or
even on whether they exist.
• One simple definition “a bubble is that part of asset price
movement that is unexplainable based on fundamentals”
• Kindleberger’s definition “an upward price movement over an
extended range that then implodes”
– No mention of fundamentals.
– Garber calls this “the chartist’s view of bubbles”.
– But prices could be rising because economic growth is very high
(e.g. China, India today).
155
The Anatomy of a Bubble
• Do all bubbles look the same?
• DJIA 1929 and 1987
250
750
1250
1750
2250
2750
3250
04
/82
06
/82
09
/82
12
/82
03
/83
05
/83
08
/83
11
/83
02
/84
04
/84
07
/84
10
/84
01
/85
04
/85
06
/85
09
/85
12
/85
03
/86
05
/86
08
/86
11
/86
02
/87
04
/87
07
/87
10
/87
01
/88
03
/88
Date 1987
DJ
IA 1
98
7
0
50
100
150
200
250
300
350
400
450
04
/24
06
/24
09
/24
12
/24
03
/25
06
/25
08
/25
11
/25
02
/26
05
/26
07
/26
10
/26
01
/27
04
/27
06
/27
09
/27
12
/27
03
/28
05
/28
08
/28
11
/28
02
/29
04
/29
07
/29
10
/29
01
/30
03
/30
Date 1929
DJ
IA 1
92
9
Dow Jones Industrial Average 1987
Dow Jones Industrial Average 1929
156
Actual prices versus “fundamentals” Equity REITs
0
100
200
300
400
500
600
700
De
c-7
1
De
c-7
2
De
c-7
3
De
c-7
4
De
c-7
5
De
c-7
6
De
c-7
7
De
c-7
8
De
c-7
9
De
c-8
0
De
c-8
1
De
c-8
2
De
c-8
3
De
c-8
4
De
c-8
5
De
c-8
6
De
c-8
7
De
c-8
8
De
c-8
9
De
c-9
0
De
c-9
1
De
c-9
2
De
c-9
3
De
c-9
4
De
c-9
5
De
c-9
6
De
c-9
7
De
c-9
8
De
c-9
9
De
c-0
0
De
c-0
1
De
c-0
2
De
c-0
3
De
c-0
4
De
c-0
5
De
c-0
6
De
c-0
7
De
c-0
8
Actual Fundamental
157
Examples of bubbles through history
All could be viewed as large and persistent mis-valuations that were eventually corrected.
• Tulipmania (c1637).
• The Mississippi bubble (1719-1720).
• The South-Sea bubble (1720).
• The undervaluation of world stock markets from 1974-1982.
• The Japanese stock and land price bubble of the 1980’s.
• USD (1980’s).
• The technology, media and telecommunications (TMT) bubble of 1999-2000
• Bond markets c.2005? US and UK real estate 2002-2007?
158
How are bubbles formed?
• In many models, bubbles start with good news for some investors that they profit from.
• Quite often, bubbles arise when there is a new technology at the time of good earnings growth.
• Smart investors will buy in early.
• Once the bubble comes close to the peak, according to Shleifer (2000), it needs an “authoritative blessing”.
• For example, politicians will say “this is a new paradigm”, “it really is different this time.”
• “In the 1920’s, even the US president said that “stock prices have reached a new, higher plateau.”
159
How are bubbles formed? 2
• Investors get used to the stock market rising quickly and begin to think that this is normal.
• Even modest inflation in all prices will make investors feel that the market is rising when in real terms it is not.
• When prices have recently risen, people feel less risk averse because they feel that they are now betting with someone else’s money.
• Even if people believe that prices are rising very quickly, they may attribute this to prices having been too low previously.
• The news media helps bubble growth by encouraging people to all think in the same way.
• Information cascades and herding behaviour
• Bubbles as Ponzi schemes?
160
Are bubbles irrational?
• Schiller and Greenspan think so – “irrational exuberance”.
• Some evidence in favour of irrational bubble formation rather than fundamentals:
– Fundamentals only change slowly during bubble growth.
– Fundamentals improve only for some firms.
• A popular early view of bubbles was that “only some bizarre, self-delusion or blindness could have prevented a participant from seeing the obvious, so these episodes are called forth almost as a form of ridicule for such losers.” (Garber, 2000).
161
Newer rational bubble theories
• New bubble theories and models do not require irrationality to form.
• These theories suggest that investors are compensated for the increasing probability of bubble collapse by ever higher returns.
• Bubbles are self-fulfilling
– They exist because investors believe that they will continue to exist.
• Based on “greater fool theory”
– I know the asset overvalued but I think I can still sell it on later for even more.
• As the bubble grows bigger, the probability of the bubble collapsing will increase.
• But returns increase more and more as the bubble gets bigger until it eventually collapses. So if investors sell too early, they will miss out on further potentially huge gains before the collapse.
162
Can you profit from a bubble?
• The skill is obviously knowing when a “bandwagon” is forming and to jump on it, and knowing when to jump off.
• But calling the top of the market is very difficult.
• In the early stages of the bubble, the probability of it collapsing is low, but so are the returns.
• In the latter stages, returns will probably be higher, but the probability of a collapse will be high.
• In early 1999, Amazon.com was worth $30bn, a rise of 20x since 1998, yet it had never made a profit.
163
Strong form of market efficiency
• The strong form (SF) of the efficient market hypothesis states that past, public and private information is included into today’s price
• Implication for asset management: Even inside traders and active portfolio managers, those privy to this information, cannot beat the market
• But there is persistent evidence that insider trading is both rife and lucrative
• Markets are strong form inefficient (insiders have private information and use it!) and semi-strong form efficient (Once the frauds became public, share prices fell or even plummeted, with some companies filing for bankruptcy)
164
Do active portfolio managers beat
passive portfolio managers?
Efficient market type
Passive portfolio management
• Long buy and hold strategy that
aims at tracking the market
• No attempt to outsmart the
market, just follow the ups and
downs of the market
• Index funds
• e.g., if Glaxo represents 2% of the
FTSE100 index, invest 2% of your
client mandate in Glaxo
Inefficient market type
Active portfolio management
• Attempt to beat the market on a
risk and transaction cost
adjusted basis
• Trade mispriced securities,
follow momentum, contrarian
strategies, implement style
rotation strategies (Lecture 7)…
• e.g., if you think Glaxo is cheap,
invest 3% of your client
mandate in Glaxo
165
Do active portfolio managers beat
passive portfolio managers?
Source: B. Malkiel (2003)
52%
63%
71%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 Year 5 Years 10 Years
Time period ending 31 December 2001
Percentage of active general equity funds that were beaten
by Vanguard (S&P) Index Fund after expenses
Over the period 1992-2001, 71% of actively managed equity funds have produced, after
expenses, total returns that were less than the returns on the Vanguard (S&P) index fund
166
Do active portfolio managers beat
passive portfolio managers?
1311
28
34
29
21
17
31 1
0
5
10
15
20
25
30
35
40
Nu
mb
er
of
Fu
nd
s
-4% or
less
-4% to -
3%
-3% to -
2%
-2% to -
1%
-1% to
0%
0% to
+1%
1% to
2%
2% to
3%
3% to
4%
4% or
more
Under or Over Performance of Surviving Active Funds
Relative to Index Fund (1970 - 31 Dec 2001)
22 Winners86 Losers 55 Market Equivalent
Number of Funds:
- 1970: 355
- 2001: 158
Non Survivors: 197
167
What is behavioural finance?
• Behavioural finance is the study of investor behaviour that derives from
the psychological principles of decision making.
• It is the fusion of finance and psychology.
• The theory upon which modern finance is built relies upon
“representative agent” models.
• But investors appear to exhibit behaviour that is not consistent with
rationality.
168
An awesome array of anomalies
1. Calendar effects.
2. Small firm effects.
3. Short-term under-pricing and long-term underperformance of IPO’s.
4. Short-term momentum and long-term over-reaction in stock returns.
5. The value premium.
6. Investors trade too much.
7. The zero equity holding puzzle.
8. The equity risk premium puzzle.
9. Firms pay dividends even though in the US they are taxed at higher rates.
10.Price changes are excessively volatile.
11.Existence of speculative bubbles.
12.Investors sell winners too early and ride losers.
13.The existence of resistance or support levels in asset prices.
169
How can we explain the anomalies?
Rational model-based explanations
• The anomalies are not there.
• The pricing models are incorrect.
• The risk factors in the models are not correct.
• The anomalies cannot be exploited – limits to arbitrage (– is this behavioural?)
– Michaud (2001) argues that most market anomaly studies have little practical investment value.
Behavioural explanations
• The models are useless because they do not capture the characteristics of human behaviour.
• People are irrational.
170
The pricing models are not correct
or the risk factors are not correct
• Remember that tests of the EMH are joint tests.
• The CAPM has been found to work poorly.
• Extensions to the CAPM (e.g., consumption CAPM, multi-period CAPM, conditional CAPM) still don’t do the job.
• Led to the development of other asset pricing and risk attribution models, e.g.
– APT.
– Fama-French 3-factor model.
– Fama-French + momentum.
• But these models are empirically rather than theoretically motivated – the anomalies that the model is trying to explain become the risk factors!
171
The two building blocks of behavioural finance
1. Limits to arbitrage.
- When the arbitrage pricing theory was developed, “arbitrage was taken to imply a riskless, zero cost profit opportunity”.
- Such an opportunity never exists.
- In fact, arbitrage strategies can involve significant (although sometimes not obvious) risks.
2. Cognitive biases and heuristics
- Essentially, cognitive biases are errors in human decision-making.
- Heuristics are simple “rules of thumb” that people employ when trying to make hard decisions or analyse complex situations.
• Both can lead to irrationality and sub-optimal decision-making.
• Both elements are necessary for anomalies to arise
– Without irrational sentiment, no arbitrage opportunities arise.
– Without limits to arbitrage, any opportunities that appeared would disappear very quickly.
172
Limits to arbitrage
• Pricing models assume that arbitrage forces will ensure that pricing anomalies disappear fairly quickly.
• Efficient markets require “the right price” and that there is “no free lunch”.
• But while prices are right no free lunch, the converse is not necessarily true.
• No free lunch but with prices still not being right occurs when arbitrage is not possible for some reason or is too costly.
• Arbitrage requires the existence of close substitute securities (that can be long or short sold to complete the arbitrage trade).
• Without close substitutes, arbitrage can be very risky.
• If there is “no free lunch”, the markets could still be viewed as informationally efficient.
• If “the price is not right”, the markets could still be informationally efficient depending on the definition.
173
Cognitive biases and heuristics
• Mental accounting – separating or combining decisions in order to make one feel better. E.g. Two bets at the horse races – one wins £10, the other loses £5. Conclusion “Net, I am £5 up”. Now suppose one bet wins £5 and the other loses £10. Conclusion: “I won one bet and I lost one, so I am even”.
• Related to the idea of mental compartmentalisation.
– People think of part of their investment being safe and the other part as the chance to get rich.
– They would be very upset if their safe part lost money, even if the risk-taking part had simultaneously made a lot of money.
• Excessive optimism - “It won’t happen to me”.
• The disjunction effect – people want to wait to make decisions until after information has been received, even if the information is irrelevant.
174
Other Cognitive biases
• Anchoring bias and recency
• The search for confirmatory evidence
• The pain of regret – reluctance to sell at a loss
• The representativeness bias
• Herding and the desire to fit in
175
General conclusion: So are markets efficient?
• Quoting Richard Roll, an outstanding financial economist and an active
money manager,
"I have personally tried to invest money, my client's and my own, in
every single anomaly and predictive result that academics have
dreamed up. And I have yet to make a nickel on any of these supposed
market inefficiencies. An inefficiency ought to be an exploitable
opportunity. If there's nothing investors can exploit in a systematic way,
time in and time out, then it's very hard to say that information is not
being properly incorporated into stock prices." (Wall Street Journal, 28
December 2000)
• The evidence presented here makes you rethink Jensen’s (1978) quote
“There is no other proposition in economics which has more solid
empirical evidence supporting it than the Efficient Market Hypothesis”…
At best doubtful but very mixed evidence.
176
Key points
• Some evidence that markets may be inefficient
– Momentum / contrarian strategies
– Market bubbles
– Size and value anomalies
– Insider trading
• Underperformance of active mutual funds and pension funds relative to passive funds
• Existence of bubbles with a lot of money made and lost – are they irrational?
• Even though some evidence point towards market inefficiency, asset managers have no easy time beating the market
• The so-called anomalies may just be an efficient compensation for taking on more risk
• The behavioural explanation for pricing anomalies has grown in acceptability over the past 15 years.
177
References
• BKM, 9th edition, Chapters 11 and 12
• Elton, E., Gruber, M.J., Brown S.J. and Goetzmann W.N.
(2010), Chapter 17 and Chapter 18
www.icmacentre.ac.uk
Lecture 6:Style Investing
Portfolio Management
Dr Ioannis Oikonomou
179
Total excess return vs. abnormal excess return
(Alpha) on size sorted portfolios: 1934 – 2003
16%
4.4%
14.1%
2.4%
13.2%
2.2%
12.8%
2.1%
12.4%
1.9%
11.5%
1.5%
11.3%
1.4%
10.4%
0.9%
9.7%
0.8%
8.1%
0%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
Ave
rag
e R
etu
rn in
Ex
ce
ss
of
Ris
k F
ree
Rate
P1 -
Small MV
P2 P3 P4 P5 P6 P7 P8 P9 P10 -
Large MV
Size Sorted Portfolio
Average Excess Return Alpha: Average Excess Return Not Explained by Risk
Source: French website
180
Size premium around the world
Source: Dimson and Marsh, 2001
14%
10.3%
8.5%
9.3%
8.0%
10.7%
6.4%
11%
8.7%
11.0%
6.6%
0%
5%
10%
15%
Me
an
Re
turn
UK (1955 - 1999) US (1926 - 1999) Canada (1950 - 1987) Germany (1954 -
1988)
Japan (1971 - 1992)
Micro-Cap Equities Low-Cap Equities All Equities
UK and non UK high-cap: 90% largest capitalisation stocks
UK low-cap: Next 9% largest stocks
UK micro-cap: 1% smallest stocks
Non UK low-cap: 10% of smallest capitalisation stocks
Market capitalisation = Number of stocks * Share price
181
Risk-based explanations:
Small firms are firms in distress
• 66% of small capitalisation firms have fallen from higher quintiles (small cap
are doing poorly) while 41% of large capitalisation firms have risen from
lower quintiles (large cap are doing well)
• Selected accounting ratios
– Return on asset ratio =
– Interest expense ratio =
assets Total
ondepreciati before income OperatingROA
ondepreciati before income Operating
Interests
Source: Chan and Chen, 1991
Average ratio
across industriesSmall firms Large firms
Return on asset ratio 12.10% 17.80%
Interest expense ratio 25% 14.40%
182
Risk-based explanations:
Small firms are firms in distress
• Small caps have a propensity to cut dividends
– 67% of firms that cut dividends by 100% were in the smallest quintile
– 1% of firms that cut dividends by 100% were in the largest quintile
Source: Chan and Chen, 1991
1% 4%
12%16%
25%
10%
67%
54%
31%24%
13%
26%
0%
20%
40%
60%
80%
Pe
rce
nta
ge
-100% (-100%, -50%) (-50%, 0%) 0% (0%, 50%) > 50%
Smallest quintile
Largest quintile
Change in dividends
183
36%
24%
18%
14%
8%
10%14%
19%24%
33%
0%
10%
20%
30%
40%
Pe
rce
nta
ge
of
firm
s
Low leverage 2 3 4 High leverage
Smallest quintile
Largest quintile
Leverage
Risk-based explanations:
Small firms are firms in distress • Small caps are more levered
– 10% (36%) of firms with low leverage were in the smallest (largest) quintile
– 33% (8%) of firms with high leverage were in the smallest (largest) quintile
tyue of equiMarket val
shareseference debt Long termabilities Current liLeverage
Pr
Source: Chan and Chen, 1991
184
Risk-based explanations:
Small firms are firms in distress
• High mortality rate
• Inefficient producers
• Low liquidity and high transaction costs
• Tax loss selling hypothesis: Partly explains why the size effect is stronger in January
– Realise capital losses at tax-year-end and re-balance portfolios in early new year (applies only to countries where tax-year and calendar year are the same, e.g. Germany, China, Portugal, Ireland)
– Because of their high volatility, small firms are likely candidates for tax-loss selling, explaining why the size effect mainly appears in January
• These rational explanations indicate that the size effect is not the result of semi-strong form market inefficiency. The evidence support the idea that the premium compensates for risks not captured by beta
185
Style rotation strategy based on size
Small caps perform better than large caps in periods of expansion
Size premium (small minus large) over the business cycle
1st Gulf
War
Jan 91
Oct 87
crash
Oct 89
crash
Asian
crisis
Q3 87Russian
crisis
Q3 98
Sept 11
012nd Gulf
War
Q1 03
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Q4
1987
Q4
1988
Q4
1989
Q4
1990
Q4
1991
Q4
1992
Q4
1993
Q4
1994
Q4
1995
Q4
1996
Q4
1997
Q4
1998
Q4
1999
Q4
2000
Q4
2001
Q4
2002
Q4
2003
Time
Siz
e p
rem
ium
(Q
ua
rte
rly
re
turn
sp
rea
d
be
twe
en
FT
SE
Sm
all
Ca
p a
nd
FT
SE
10
0 I
nd
ice
s)
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
Ye
ar-
on
-ye
ar
ch
an
ge
in
in
du
str
ial
pro
du
cti
on
(B
us
ine
ss
cy
cle
)
Size premium Business cycleCorrelation between size premium
and business cycle = 0.32
Internet
bubble
98-00
Burst of
internet
bubble
00-02
Sm
all
outp
erf
orm
sLarg
e o
utp
erf
orm
s
186
Value investing versus growth investing
• Value investing
– Warren Buffett’s strategy
– The market is overly pessimistic with regards to the value of value stocks. The stock valuation will improve once the consensus realises its mistake. Value managers thus look for stocks that sell at cheap multiples: low P/Book, low P/Earning, low P/Cash flow
– Companies with lots of earnings; thus, high dividend yields
– Value (low price relative to fundamentals) does not mean junk (fall in price)
• Growth investing
– Look for stocks that have a proven superior track record of earnings growth and hold them for as long as they grow faster than the market; i.e., pick up today the Microsoft of tomorrow
– Stocks that trade at high multiples: high P/B, high P/E, high P/CF
– Companies with lots of positive NPV projects, so low dividend yields
187
Total excess return vs. alpha on portfolios sorted
according to price-to-book: 1951-2003
12.6%
5.1%
11%
4.2%
11.3%
4.7%
9.5%
3%
9.4%
2.7%
9.3%
2.7%
7.6%
0.4%
8%
0.5%
7.7%
0%
6.4%
-1.9%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
Ave
rag
e E
xc
es
s R
etu
rn v
s.
Alp
ha
P1 - Low
P/B: Value
P2 P3 P4 P5 P6 P7 P8 P9 P10 - High
P/B:
Growth
Portfolios Sorted on Price to Book Value
Average Excess Return Alpha: Average Excess Return Not Explained by CAPM
Source: The data are from French website
188
The value anomaly persists irrespective of the proxy
used for value – Here price-to-earnings ratio
15.3%
7.6%
13.1%
6.1%
12.8%
6.1%
11.4%
4.8%
10.1%
3.3%
7.8%
0.7%
8.1%
1.1%
7.8%
0.7%
5.8%
-1.7%
5.7%
-3.1%
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
16%
Ave
rag
e E
xc
es
s R
etu
rn v
s.
Alp
ha
P1: Low
P/E
Value
P2 P3 P4 P5 P6 P7 P8 P9 P10:
High P/E
Growth
Portfolios Sorted on P/E Ratio
Average Excess Return Alpha: Average Excess Return Not Explained by CAPM
189
Value premium in developed markets
Source: Fama and French, 1998
18%
5%
15%
11%
17%
9%
13%
10%
27%
19%
5%
11%
17%
7%
16%
13%
22%
12%
21%
13%
14%
10%
18%
13%
15%
8%
15%
7%
0%
5%
10%
15%
20%
25%
30%A
ve
rag
e R
etu
rn in
Exc
es
s o
f th
e U
S T
Bill R
ate
Austra
lia
Belgium
Franc
e
Ger
man
y
Hon
g Kon
gIta
ly
Japa
n
Net
herla
nds
Singa
pore
Swed
en
Switz
erland U
KUS
Dev
elop
ed M
arke
ts
Value (Low P/B) Growth (High P/B)
190
The market efficiency view
• Do value stocks beat growth because value is more risky? Fama and French
(1998) say YES
• Value companies (stocks selling at cheap prices relative to fundamentals) are
companies in distress
– Mature companies with few prospects
– High leverage
– High interest payments relative to operating income
– Substantial earnings risk
191
The behavioural view:
The risk explanation might not add up
Value and growth stocks have similar standard deviations
18.4 17.6
0.8
13.9
19.2
-5.3
18.019.3
-1.3
17.218.8
-1.6
29.3
15.214.1
-10
-5
0
5
10
15
20
25
30
35
An
nu
ali
se
d s
tan
da
rd d
ev
iati
on
P/B (1951 - 2003) DY (1951 - 2003) P/E (1951 - 2003) P/CF (1951 - 2003) Size (1934 - 2003)
Ratio on which style is defined
Standard deviation of value, growth, small and large portfolios
Value Growth Value - Growth
Small
Large
Value vs Growth
Small -
Large
192
The behavioural explanation:
The value premium might well be a free lunch
• Extrapolative biases
– Relative to growth, value stocks have a history of lower growth in earnings, lower growth in sales, lower growth in cash flows
– As analysts look at the past to forecast the future, they have a favourable (unfavourable) view of growth (value)
– As a result, value become underpriced and growth become overpriced relative to fundamentals
• As earnings announcements are made public (i.e., actual growth materialises),
– Over-enthusiastic growth investors end up being disappointed as actual earnings fall short of expectations
– Unduly pessimistic value investors end up pleasantly surprised as actual earnings exceed expectations
– As a result, value stocks beat growth
• Conclusion: Markets seem semi-strong form inefficient (prices of value and growth stocks do not reflect fundamentals)
193
Style rotation strategy based on value and growth
Only over the period 1987-1996 did value outperform growth in expansion
Value premium (value minus growth) over the business cycle
Asian
crisis
Q3 97
1st Gulf
War
Jan 91
Oct 89
crash
Oct 87
crash
Russian
crisis
Q3 98
11 Sept
01
2nd Gulf
War
Q1 03
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Q4
1987
Q4
1988
Q4
1989
Q4
1990
Q4
1991
Q4
1992
Q4
1993
Q4
1994
Q4
1995
Q4
1996
Q4
1997
Q4
1998
Q4
1999
Q4
2000
Q4
2001
Q4
2002
Q4
2003
Time
Va
lue
pre
miu
m (
Qu
art
erl
y r
etu
rn
sp
rea
d b
etw
ee
n F
TS
E3
50
Va
lue
an
d
FT
SE
35
0 G
row
th)
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
Ye
ar-
on
-ye
ar
ch
an
ge
in
in
du
str
ial
pro
du
cti
on
(B
us
ine
ss
cy
cle
)
Value premium Business cycle
Correlation of 0.21 (Q4 1987 - Q3 2004)
Correlation of 0.47 (Q4 1987 - Q4 1996)
Correlation of -0.07 (Q1 1997 - Q3 2004)
Internet
bubble
98-00
Burst of
internet
bubble
00-02
Valu
e o
utp
erf
orm
sG
row
th o
utp
erf
orm
s
194
Peer group comparison: Fund performance
across investment styles
Growth Blend Value
102 funds 126 funds 129 funds
Category average 17.89% Category average 15.60% Category average 13.37%
Index benchmark 19.92% Index benchmark 17.55% Index benchmark 14.70%
(S&P 500 Growth) (S&P 500) (S&P 500 Value)
Index advantage +203bp Index advantage +195bp Index advantage +133bp
63 funds 36 funds 48 funds
Category average 18.14% Category average 14.10% Category average 12.77%
Index benchmark 19.52% Index benchmark 16.29% Index benchmark 13.96%
(Russell Mid-cap Growth) (Russell Mid-cap) (Russell Mid-cap Value)
Index advantage +138bp Index advantage +219bp Index advantage +119bp
33 funds 22 funds 23 funds
Category average 17.12% Category average 12.99% Category average 11.74%
Index benchmark 13.01% Index benchmark 13.73% Index benchmark 12.91%
(Russell 2000 Growth) (S&P 600 Growth) (Russell 2000 Value)
Index advantage -411bp Index advantage +74bp Index advantage +117bp
Larg
e c
apitalis
ation
(>$1 b
illio
n)
Mediu
m
capitalis
ation
Sm
all
capitalis
ation
Source: Malkiel (2003)
195
References
• BKM, 9th edition, Chapter 24 (sections 24.4 and 24.5)
• K. C. Chan and N. F. Chen, Structural and return characteristics of small and
large firms, Journal of Finance, 1991, Only read pages 1467-1474 and the
conclusion
• L. Chan and J. Lakonishok, Value and growth investing: Review and update,
Financial Analysts Journal, January-February 2004
• L. Kander, Warren Buffett
http://www.salon.com/people/bc/1999/08/31/buffett/
• Go to http://www.stockselector.com/valuationscreen.asp to screen value and
growth stocks
www.icmacentre.ac.uk
Lecture 7:Portfolio Performance Evaluation
Portfolio Management
Dr Ioannis Oikonomou
197
The Problem
• How do we measure the performance of a fund manager?
– Against a benchmark?
– By comparing with other managers?
• How do we compute the average return achieved by a fund manager over a number of investment periods?
– There are several approaches
– The issue is complicated by interim inflows and outflows that are outside the manager’s control
• We need to measure risk-adjusted performance
– The manager should not be rewarded simply for taking very risky positions that happened to perform well by chance
– How do we adjust the portfolio return for risk?
198
Ex post versus ex ante returns
• Ex post returns are realised returns
– Calculated using historical data
• Ex ante returns are expected returns
– Theoretical predictions
– Different models are likely to give different predictions
• Performance measurement compares ex post returns on a portfolio with
– Ex post returns on other portfolios
– Ex ante returns predicted by some model, e.g., the CAPM, but using ex post returns on the market portfolio.
199
Abnormal returns
• Abnormal returns are the difference between ex post return and
the ex ante return:
AR(t) = r(t) – E[r(t)]
• Example: CAPM benchmark
AR(t) = r(t) – [rf(t)+{rM(t)-rf(t)}]
Not: AR(t) = r(t) – [rf(t)+{E(rM(t))-rf(t)}]
200
Arithmetic, geometric (time-weighted),
and money ($) weighted means
• In the case of a one-period investment
• In the case of a multi-period investment
– Arithmetic mean
– Geometric mean (time-weighted mean): Industry standard
– Money ($) weighted mean ( : Additional fund; : Redemption)
Beg
BegEndP
V
VIncomeVR
T
RRR PTP
P
...1
11...111
21 T
PTPPP RRRR
TP
EndT
tt
P
T
tt
P
BegR
V
R
F
R
FV
111 00
FF
201
Arithmetic and geometric mean: An example
• The end-of year returns for a mutual fund over a 4-year period are
10%, 25%, -20% and 25%.
• Arithmetic mean
• Geometric mean
%104
%25%20%25%10
PR
%29.8125.18.25.11.141
PR
202
Money weighted returns – an example
• Suppose that the following happens
Period Action
0 Purchase 1 share at $50
1 Purchase 1 share at $53
Stock pays a $2 dividend
2 Stock pays a $2 dividend
Stock is sold at $54
Period Cashflow
0 -50 share purchase
1 +2 dividend -53 share purchase
2 +4 dividend +108 shares sold
203
Money weighted returns – an example
• Internal rate of return
• = 7.12%
• Calculating the returns for each period:
r1 = (53-50+2)/50 = 10%, r2 = (54-53+2)/53 = 5.66%
• Simple average return = (10+5.66)/2 = 7.83%
• Geometric return = [(1.1)(1.0566)]1/2 -1 = 7.81%
22111
108
1
4
1
2
1
5350
PPPP RRRR
TP
EndT
tt
P
T
tt
P
BegR
V
R
F
R
FV
111 00
PR
204
Money weighted versus time-weighted returns
• Money weighted or “dollar weighted” returns are really internal
rates of return, and have all the problems associated with IRR
calculations.
• They take into account any cashflows coming to or from an
investment
• But this makes little sense to do, as the flows arise from investor
decisions not fund manager decisions
• If the investor makes a large investment just before a run of poor
performance, then the money-weighted return will look very bad.
• So we use time-weighted returns, which are not weighted by the
investment amount.
205
Which is best – arithmetic or geometric means?
• When evaluating past performance, geometric means are better
– As a rule of thumb, rG = rA – ½ 2
• Geometric returns give the fixed return on the portfolio that would
have been required to match the actual performance
• But geometric returns are always less than or equal to the
arithmetic returns, and so are a downward-biased predictor of
future performance
• Thus for predicting future returns, use the arithmetic average of
past returns
206
Systematic risk versus specific risk
• We can split the total risk that a fund manager took into the systematic part (for example, measured by the CAPM) and the unsystematic part
• Regress the excess return, r(t)-rf(t) = + [rM(t)-rf(t)] + (t)
– The systematic part is [rM(t)-rf(t)] and the unsystematic part is (t)
• We can decompose the variance of the excess returns into the systematic parts and unsystematic parts, to obtain a formula for the total risk as the sum of the systematic and unsystematic risks
– i2 = i
2M2 + 2
(Q: why?)
207
Treynor ratio
M
SML: Security market line
Slopeβ
RRT
P
fPP
Q
P
Risk - expected return trade-off for Q
Average
return
QR
MR
PR
Rf
P M = 1 Q
208
Treynor ratio
• Portfolio average excess return measured relative to its level of systematic risk
• Pictured via the SML or trade-off between risk - expected return for managed portfolios
• The higher the Treynor index, the better the fund’s performance
• Treynor index for benchmark: MLSlope of SRRT fMM
209
Sharpe ratio
M
CML: Capital market line
SlopeRR
SESRP
fPP
Q
P
Risk - expected return trade-off for Q (also called
Capital Allocation Line)
Average
return
QR
PR
MR
P MQ
Rf
210
• Portfolio average excess return measured relative to its level of total
risk
• Sharpe index for benchmark:
• The higher the Sharpe index, the better the fund’s performance
• For well diversified portfolios, Sharpe and Treynor give the same
ranking (Q:why?) : Correlation between the 2 rankings = 0.97
MLSlope of CRR
SM
fMM
Sharpe ratio
211
Information ratio or Appraisal ratio:
Two measures
• Either relates annualised
average active return to
annualised active risk (tracking
error)
• Or relates annualised residual
return (Return independent of
the benchmark: Jensen’s alpha)
to annualised residual risk
(Standard deviation of the
residuals from the market
model) BtPt
BPP
RR
RRIR
P
PP
eIR
212
M2 (Modigliani and Modigliani) measure
Average
return CML
Capital allocation
line for P
P
P*
M
M2
MP RRM *2
*PR
MR
PR
Rf
213
M2 (Modigliani and Modigliani) measure
• Relates average returns to total risk (similar to Sharpe index)
• Methodology
– Move along the capital allocation line (CAL) for P until you reduce (increase) the standard deviation of your portfolio to the standard deviation of the benchmark. Call the resulting portfolio P*
– M2 is the vertical distance (difference in average return) between P* and M
• M2 < 0 means
– the CAL for P is below the CML
– the slope of the CAL is less than the slope of the CML
– the Sharpe ratio of the portfolio is less than the one of the benchmark
– the managed portfolio underperformed its benchmark
214
Jensen’s alpha
Deviation from the SML / CAPM: Difference between the actual return
on a fund and the return the fund should have earned given its risk (i.e.,
the fund expected return)
i
A
B
fMPfPP RRRR
M
BR
AR
BRE
0A
0B
ARE
A over
performed
B underperformed
M = 1 A B
SML: Security market line
215
Sensitivity of Jensen’s alpha
to benchmark definition
• Instead of assuming that the funds attempt to beat an unique
benchmark, measure Jensen’s alpha relative to a set of benchmarks
that reflect the style / asset allocation of the funds
– Market excess return
– Small size premium
– Value premium
– Bond excess return
– Factors extracted from the covariance matrix of returns…
• Performance superior to routine passive strategies is far from common.
Studies show either that managers cannot outperform passive
strategies or that if there is a margin of superiority after accounting for
transaction costs, it is very small
216
Problems with standard risk measures • Essentially, the Sharpe ratio, the Treynor ratio, Jensen’s alpha and the
information ratio are all based on the mean-variance framework of analysis. This requires that the distribution of returns can be fully explained by its first two moments (mean and variance) so higher moments (such as skewness and kurtosis) are irrelevant.
• This is very restrictive, usually does not hold in practise and can lead to paradoxical choices. For example:
A 1/9 +40% B 1/9 +76%
7/9 +10% 7/9 +10%
1/9 -20% 1/9 -20%
SharpeA =0.707 SharpeB =0.587
So an investor who trusts the Sharpe ratio as a RAPM would choose asset A
instead of B despite the fact that B offers exactly the same or better return with
the same probability attached to them!
This is in contradiction with what is called stochastic dominance (and, more
importantly, it is in contradiction with common sense).
217
The Adjusted Sharpe Ratio
• The adjusted Sharpe ratio incorporates skewness and kurtosis in its
calculation and thus is much less likely to lead to a paradoxical
investing choice (but is still not guaranteed to be always consistent with
stochastic dominance):
where μ3 and μ4 are the skewness and kurtosis of the return distribution.
• The ASR can be obtained by using a Taylor series expansion of an
exponential utility function and is an approximate version of the
Generalised Sharpe Ratio (GSR).
2
3 4[1 ( / 6) (( 3) / 24) ]ASR SR SR SR
218
Downside risk measures
• Psychologically, as well as practically, investors are concerned with
downside risk, the risk of underperformance, captured by the deviation
of returns below a certain target. However, standard risk measures
capture deviation both above and below mean/target return.
• Downside risk metrics strictly capture the risk of underperformance:
i i
n2
i i
<μ
im 2
1s = (R -μ ) Markowitz (1959)
n
[( ) min( ,0)]β = Bawa and Lindenberg (1977)
[min( ,0)]
[( ) min( ,0)]β =
[min( ,0)
i
R
i f m fBL
m f
HR i i m mim
m m
E R R R R
E R R
E R R
E R
2 Harlow and Rao (1989)
]
219
Downside RAPMs
• Downside RAPMs are based on the same philosophy as downside risk metrics.
• Sortino ratio (Sortino and Van der Meer, 1991) is essentially the downside
modification of the Sharpe ratio:
where T is the target return and the denominator is the target semideviation
(or more correctly, the square root of the second order lower partial moment).
• Other widely used RAPMs include the risk-adjusted return on capital (RAROC),
the return over value at risk (RoVar) and many others...
i
n2
i
<T
( )
1(R -T)
n R
E R TS
220
Separating asset allocation from security selection
• If fund managers are generating (positive or negative) abnormal returns, we want to be able to determine where this is coming from: stock selection or market timing.
• We do this by separating the total performance into the two parts.
• This is achieved by setting up a benchmark or “bogey” portfolio
• We first compare the overall performance of the benchmark and of the actual portfolio
• Then we compute the return on the benchmark with portfolio weights and with actual benchmark weights and the difference is the excess return due to asset allocation
• Finally we compute the performances of the benchmark and of the actual portfolio, this time using actual portfolio weights and the difference is the excess return due to security selection
221
Separating asset allocation from security
selection: an example
Portfolio
Component
Portfolio
Weight
Portfolio
Return
Benchmark
Component
Benchmark
Weight
Benchmark
Return
Equity 0.70 7.28% FTSE100 0.50 5.81%
Fixed-
income 0.07 6.89%
UK
Corporate
bond index
0.40 5.45%
Cash 0.23 2.48% Money
market 0.10 2.48%
Questions:
1. How did the portfolio do compared to the
bogey/benchmark?
2. To what can the performance of the portfolio be attributed?
222
Asset allocation versus security selection –
example continued
• First find the excess return of the portfolio:
Return on portfolio = (0.7 x 7.28) + (0.07 x 6.89) + (0.23 x 2.48)
= 6.15%
Return on benchmark = (0.5 x 5.81) + (0.4 x 5.45) + (0.1 x 2.48)
= 5.33%
Excess return of portfolio over benchmark = 6.15% - 5.33%
= 0.82%
223
Asset allocation versus security selection –
example continued
• How much of the excess return is due to asset allocation?
• Methodology What is the return difference of investing in the
benchmark using portfolio weights versus benchmark weights?
Return on benchmark with actual portfolio weights
= (0.7 x 5.81) + (0.07 x 5.45) + (0.23 x 2.48)
= 5.02%
Return on benchmark with benchmark weights
= (0.5 x 5.81) + (0.4 x 5.45) + (0.1 x 2.48)
= 5.33%
Contribution of asset allocation = 5.02% - 5.33% = -0.31%
224
Asset allocation timing versus security selection
– example continued
• How much of the excess return is due to security selection?
• Methodology: What is the return difference of investing in the
portfolio vs. the benchmark using the portfolio weights for both?
Return on portfolio with actual portfolio weights
= (0.7 x 7.28) + (0.07 x 6.89) + (0.23 x 2.48)
= 6.15%
Return on benchmark with actual portfolio weights
= (0.7 x 5.81) + (0.07 x 5.45) + (0.23 x 2.48)
= 5.01%
Contribution of security selection = 6.15% - 5.01% = 1.13%
225
References
• BKM, 9th edition, Chapter 24
• Elton, E., Gruber, M.J., Brown S.J. and Goetzmann W.N. (2010),
Chapter 25
• B. Malkiel, Passive investment strategies and efficient markets,
European Financial Management, 2003, 9, 1, 1-10
• E. O’Neal, Industry momentum and sector mutual funds, Financial
Analysts Journal, July/August 2000, 37-49
• M. Mullarley and A. Perold, Measuring mutual fund performance,
Harvard Case Study, May 25, 1998
www.icmacentre.ac.uk
Lecture 8:Active Portfolio Management
Portfolio Management
Dr Ioannis Oikonomou
227
What is Active Portfolio Management?
• Active portfolio management seeks to exploit perceived market inefficiencies
• Active portfolio management is based on both macroeconomic and firm-specific information
• Actively managed portfolios may or may not be well diversified
• The existence of active managers is important to the effective functioning of the stock market pricing mechanism – If all managers were passive, only individuals would be trading stocks outside the
index
228
The case for International Portfolio Diversification
(IPD): UK and world market capitalisation
US
49%
Canada
2%
UK
9%
France
4%Germany
3%
Sw itzerland
2%
Netherlands
2%
Italy
2%
Spain
1%
Japan
11%
Hong-Kong
2%
Australia
1%
Taiw an
1%Emerging markets
5%
North America: 51.2%
Developed Europe: 28.4%
Developed Pacific Basin: 15.8%
Emerging Markets: 4.6%
229
The case for IPD: UK investors can benefit from
higher returns abroad
Percentage change in yearly GDP
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
China India Hong-Kong Singapore USA UK Germany France
1990 - 2003 1996 - 2003 2000 - 2003
Reason: More profitable investments available abroad
230
# of assets in portfolio
US stocks
Global stocks
100
50
27
11.7
Total
risk (%)
10 20 30 40 1
Half of the US systematic risk is unsystematic at the global level
The case for IPD: US investors substantially
reduce their risk by investing abroad
231
An example of Global Asset Allocation (GAA)
• Objective: Show that IPD increases the expected Sharpe ratio of an UK investor and shifts the MV efficient frontier to the North West
• Monthly UK Tbill and monthly returns in UK £ on 23 MSCI indices over the period: 31 Dec 98 - 31 Dec 03
America Europe Asia
Argentina Austria Australia
Canada Belgium China
Mexico Denmark Hong Kong
USA France India
Germany Japan
Italy South Korea
Portugal Taiwan
Spain Thailand
Switzerland
Turkey
UK
232
An example of GAA using Excel:
Correlation matrix of UK £ returns U
K T
-bill
Arg
en
tin
a
Au
str
alia
Au
str
ia
Be
lgiu
m
Ca
na
da
De
nm
ark
Ch
ina
Fra
nce
Ge
rma
ny
Ho
ng
Ko
ng
Ind
ia
Ita
ly
Ja
pa
n
So
uth
Ko
rea
Me
xic
o
Po
rtu
ga
l
Sp
ain
Sw
itze
rla
nd
Ta
iwa
n
Th
aila
nd
Tu
rke
y
UK
US
A
UK T-bill 1
Argentina -0.05 1
Australia -0.04 0.21 1
Austria -0.14 0.10 0.40 1
Belgium -0.09 0.06 0.45 0.65 1
Canada 0.05 0.28 0.72 0.33 0.41 1
Denmark 0.01 0.22 0.57 0.43 0.60 0.71 1
China 0.12 0.09 0.09 -0.03 -0.01 0.17 0.10 1
France 0.02 0.25 0.65 0.43 0.72 0.75 0.72 0.18 1
Germany -0.05 0.27 0.65 0.48 0.72 0.69 0.71 0.19 0.93 1
Hong Kong -0.02 0.31 0.61 0.42 0.36 0.68 0.49 0.11 0.56 0.59 1
India -0.10 0.23 0.41 0.04 0.13 0.46 0.32 0.24 0.40 0.39 0.38 1
Italy 0.00 0.26 0.54 0.47 0.63 0.60 0.57 0.17 0.83 0.78 0.48 0.46 1
Japan -0.04 0.03 0.58 0.25 0.20 0.62 0.47 0.12 0.44 0.36 0.56 0.47 0.35 1
South Korea -0.12 0.23 0.71 0.28 0.30 0.60 0.51 0.23 0.51 0.53 0.65 0.41 0.34 0.58 1
Mexico 0.09 0.38 0.66 0.35 0.38 0.67 0.51 0.16 0.64 0.65 0.71 0.41 0.62 0.49 0.61 1
Portugal -0.05 0.12 0.41 0.31 0.57 0.51 0.60 0.04 0.71 0.68 0.31 0.47 0.70 0.17 0.23 0.35 1
Spain -0.06 0.30 0.62 0.47 0.65 0.64 0.66 0.13 0.84 0.84 0.55 0.41 0.76 0.37 0.52 0.63 0.73 1
Switzerland -0.03 -0.02 0.55 0.51 0.78 0.55 0.67 0.06 0.75 0.67 0.43 0.18 0.64 0.41 0.40 0.41 0.52 0.62 1
Taiwan -0.11 0.41 0.46 0.30 0.24 0.49 0.41 0.30 0.45 0.51 0.58 0.38 0.37 0.35 0.67 0.55 0.28 0.46 0.24 1
Thailand -0.20 0.24 0.61 0.33 0.23 0.49 0.36 0.08 0.30 0.37 0.51 0.27 0.18 0.45 0.67 0.46 0.14 0.35 0.27 0.55 1
Turkey -0.05 0.33 0.45 0.17 0.23 0.49 0.27 -0.08 0.52 0.53 0.44 0.22 0.52 0.31 0.33 0.53 0.27 0.46 0.27 0.37 0.28 1
UK -0.01 0.18 0.63 0.54 0.71 0.68 0.68 0.01 0.83 0.80 0.62 0.19 0.68 0.49 0.51 0.69 0.48 0.75 0.77 0.39 0.39 0.57 1
USA 0.04 0.18 0.71 0.35 0.53 0.84 0.71 0.20 0.79 0.77 0.63 0.34 0.59 0.57 0.67 0.75 0.46 0.71 0.63 0.55 0.52 0.52 0.85 1
Average -0.04 0.20 0.51 0.32 0.41 0.54 0.49 0.12 0.57 0.57 0.48 0.31 0.50 0.37 0.45 0.51 0.39 0.54 0.45 0.40 0.34 0.52 0.56
233
An example of GAA using Excel:
Markowitz’s and Sharpe’s MVE frontiers
Germany
Spain
France
ItalyUSA
JapSW
UKPortugal
Belgium
Argentina
Sth Korea
Thailand
Turkey
Taiwan
India
Mexico
China
T-billAustria
Australia
Canada
Denmark HK
-0.1
0
0.1
0.2
0.3
0.4
0.5
Annualised SD
An
nu
ali
se
d m
ea
n r
etu
rn
Optimal
portfolio
PP
P
Opt
fOpt
fP
RRERRE
644.047.32.
047.252.047.
CML
Markowitz’s
MVE frontier
234
An example of GAA using Excel
• Markowitz’s MVE frontier dominates all individual stock indices (apart from Turkey)
• Equation of the CML
• Expected Sharpe ratio
– of an UK investor:
– of an international investor:
PP
Opt
foptfP
RRERRE
644.047.
553.
UK
fUKUK
RREESR
644.
Opt
fOpt RRE
235
GAA in practice: The impact of home bias on
the MVE frontier of a UK investor
-20%
-10%
0%
10%
20%
30%
40%
50%
0% 10% 20% 30% 40% 50% 60% 70% 80%
Annualised SD
Annualis
ed m
ean r
etu
rn
MV efficient frontier
with home bias:
60% investment
in the UK
MV efficient frontier
without home bias
UK
236
GAA in practice: Home bias
Country allocation
Source: IMA 2004 survey
UK
56%
North America
9%
Europe
14%
Japan
12%
Emerging
markets
4%
Other
equities
5%
237
GAA in practice: Home bias
Country allocation
• Shares mostly held by domestic investors
• Why do investors shun foreign shares? Constraints and perceived misconceptions
– Lack of familiarity with foreign markets and cultures
– Regulations and political risk
– Lack of liquidity on foreign assets
– Currency risk
– Transaction costs
– Rising and time-varying correlations
• Home bias at home: Local US mutual funds tend to invest more in firms geographically located near the home of the fund!
Source: The Economist
238
Is IPD so Useful in Practice?
However correlations are unstable and tend to rise
• Growing political, economic and financial integration
• Increase in correlations in turbulent periods (e.g., oil shocks of 1974, international crash of October 1987, Gulf crisis of 1990)
• This is unfortunate since it’s when the volatilities are high that the benefits of IPD would be the most appreciated
239
Volatilities and correlations are not what
they seem to be
Data through June 2002
Source: Harvey website
-0.2
0
0.2
0.4
0.6
0.8
1
Aus
tralia
Aus
tria
Bel
gium
Can
ada
Den
mar
k
Finla
nd
France
Ger
man
y
Hon
g K
ong
Irel
and It
aly
Japa
n
Net
herla
nds
New
Zea
land
Nor
way
Portuga
l
Spain
Sw
eden
Switz
erla
nd U
K US
World
World
ex-
US
EA
FE
Expansion correlation with US Recession correlation with US
Correlations During U.S. Business Cycle Phases
0
10
20
30
40
50
60
Aus
tralia
Aus
tria
Bel
gium
Can
ada
Den
mar
k
Finla
nd
France
Ger
man
y
Hon
g K
ong
Irel
and It
aly
Japa
n
Net
herla
nds
New
Zea
land
Nor
way
Portuga
l
Spain
Sw
eden
Switz
erla
nd U
K US
World
World
ex-
US
EA
FE
Expansion std.dev. Recession std.dev.
Average Annual Volatility During U.S. Business Cycle Phases
Standard deviations and correlations
are not constant: They rise in periods
of recession
240
Where do the benefits of IPD come from?
Industrial composition of the indices
• Low correlation between country indices because countries are specialised in specific industries and these industries are imperfectly correlated
• Example: An investment in the stock indices of Switzerland, Sweden and Indonesia represents a disproportionate bet on banking, energy and oil and rubber stocks respectively. The Swiss, Swedish and Indonesian stock indices are imperfectly correlated because the banking, energy and rubber industries do not move exactly in tandem
• Implication for GAA
– Allocate portfolio weights to different industries
– Use industry analysts to select the most attractive stocks in each sector
241
Where do the benefits of IPD come from?
Country effect
• Low correlation between indices because economic shocks have different effects across countries
– Local shocks
– Different responses of national markets to global shocks
• Example: The Swiss, Swedish and Indonesian stock indices are imperfectly correlated because each country is subject to independent, country-specific shocks and not because Swiss has more banks, Sweden more oil and Indonesia more rubber companies
• Implication for GAA
– Allocate portfolio weights to different countries
– Select the most attractive stocks in each country
242
Which factor explains best the benefits of IPD?
Country effect no longer dominates industry effect
• Relative importance of countries and sectors over time: Country effect no longer dominates industry effect
Source: Baca, Garbe and Weiss (2000)
243
Why did the benefits of IPD disappear?
• Supports the notion of increasing market integration
– Decline in trade barriers resulting from the GATT agreements
– On-going expansion of large multinational companies
– Emergence of large economic blocks (European Community and the EMU, North American Free Trade Agreement, Association of Southeast Asian Nations)
• Implication for GAA
– Until the mid to end 90s, allocate portfolio weights to different countries and select the most attractive stocks in each country
– Country-orientated approach to global equity management is now less effective. Global industry factors constitute an increasingly important dimension of investment strategy
244
Technical Analysis/Chartism
• Some complex patterns may be difficult to define statistically, they are too
dependent on the context, but might be perceived by trained observers
• Chartists can be separated into two schools:
– Those who read from charts (pure chartists)
– Those who seek trading rules based on indicators and test these rules
(statistical technical analysts)
• Chartism, they say, reveals the complex dynamics of a particular security
and the psychology of a market (like graphology may reveal personality
traits or psychology may explain everything)
• It is also possible that belief in chartism is self-fulfilling (as belief in
homeopathy may create beneficial results). Mimicking the behaviour of
peers may confer an evolutionary advantage!
245
The Charts
• Chartists have learnt to discover patterns by using a wide variety of charts:
– Line
– Bar
– Candlesticks
– Point & figure
• Of importance are:
– The scaling of prices (e.g. log scale)
– The choice of time-scale (or no time scale for P&F)
– Seeing very short-term price fluctuations
• Any information not on the chart should be disregarded
(ideally, the name of the security should not be on the chart)
246
Bar Chart
247
Candlestick
248
Detecting Patterns
Chartists recognise repetitive patterns that indicate
bull, bear, or neutral (range bound) markets, primary
trends, breaks and corrections:
– Rising trend – linking the lows (support)
– Descending trend – linking the highs (resistance)
– Ranges – horizontal lines of resistance and support
(ascending or descending)
– Triangles, pennants, diamonds
– Double tops (bottom)
– Triple tops (bottom)
– Rounded top (bottom)
– Head & shoulder (reverse H&S)
– Gaps
249
Technical Indicators
• Technical indicators are price series derived from market prices to
emphasize some features. They can be used to
– generate trading signals. Trading strategies so defined can be
tested on historical data, or
– Confirm signals from the price chart
• Main indicators:
– Moving averages (MA)
– Centered Oscillators:
Moving Average Convergence Divergence (MACD):difference
(MA12 – MA26)
Rate-of-Change (ROC) – percentage price change over period
– Banded oscillators
Relative strength Indicator (RSI)(Welles Wilder) – 100Up/(Up+Dn)
Stochactic Oscillator (STO) – 100(Cl – Lo)/(Hi – Lo)
250
Moving Averages
251
Relative Strength Indicator (RSI)
252
Elliot Wave Theory
• Markets move in 5 steps on the upside and 3 on the downside
• There are waves within waves to many levels
- 62% retracements (golden ratio) are frequent
R.N. Elliot (1938) “The wave principle”
Upside: 1 to 5
Downside: A to C
253
Security Analysis
• This area describes the approaches that analysts use to discover mis-priced securities
• It is more of an art form than a science – a collection of different ideas and philosophies rather than a defined methodology
• Important limitations of security analysis - Most of the techniques are extrapolative
- For the ideas to work systematically would require exploitable market inefficiencies
- “The market can stay inefficient longer than you can stay solvent!”
• Two general approaches
- Top-down analysis: Portfolio manager starts his analysis by looking at international and national macroeconomic indicators. He then narrows his focus to regional/ industry analysis and lastly he goes on to choose the best assets in the market and industry that have the best prospects.
- Bottom-up analysis: Portfolio manager starts with security selection, regardless of the region and industry that the respective firm operates.
• We’ll focus on top-down analysis.
254
Top-down analysis: The global economy
• What is the global rate of growth?
• What is the current stage of the global economic cycle?
• What are the overall prospects and greatest innovations in the
global business environment?
• Geopolitical evolutions and risks
• Volatility
• Exchange rates
• International legislation and commercial treaties
255
Top-down analysis: The domestic macroeconomy
Key statistics:
- Gross domestic product (GDP), gross national product (GNP) and
respective rates (on a quarter on quarter or year on year basis)
- Industrial production (focuses on manufacturing)
- Unemployment rate
- Capacity utilisation rate (ratio of actual over potential factory output)
- Inflation (usually measured by the percentage change of the
consumers price index, the producers price index or the GDP deflator)
- Interest rates
- Budget surplus/deficit
- Balance of payments surplus/deficit
- Consumer/producer sentiment
256
Top-down analysis: The domestic macroeconomy
• Additional important factors:
- Fiscal policy (government spending and tax actions)
- Monetary policy (money circulation and changes on the base interest
rate)
- Business cycle (slump, recession, trough, recovery, boom, peak)
• Predicting the evolution and exact timing of the business cycle is
crucial. A series of economic indicators are used for this purpose.
These can be:
- Leading indicators, which move in advance of the economy
(e.g. average weekly hours of production workers, initial claims of
unemployment insurance, new orders of nondefense capital goods etc.)
- Coincident indicators, which move in tandem with the economy
(e.g. employees on non-agricultural products, industrial production etc.)
- Lagging indicators, which move somewhat after the economy
(e.g. average duration of unemployment, ratio of trade inventories to
sales etc.)
257
Top-down analysis: Focusing on specific industries
Key factors:
- Sensitivity of sales to the business cycle
- Operating leverage
- Financial leverage
- Industry life cycle (firms can
be slow growers, stalwarts, fast
growers, cyclicals, turnarounds
or asset plays)
- Threat of entry
- Level of competition
- Pressure from substitute products
- Bargaining power of buyers and suppliers
Sensitivity to the
business cycle
258
Porter’s model of competitive forces
Forces internal and external to the industry determine the
overall level of competition and thus the profitability of that
industry. The higher the competition, the less attractive the
industry is.
259
Top-down analysis: Equity valuation
• After deciding on the markets and industries where there are
attractive investment opportunities, the portfolio manager has to
make an estimate of the “fair price” of the securities and take
advantage of any deviations between this and the market price.
• Valuation models:
- Valuation by comparables
- Dividend discount models
- Free cash flow models
260
Valuation by comparables
• Rationale: Compare a variety of accounting/financial ratios for each firm
with the respective industrial averages to spot mispriced securities
Financial ratios used (sign shows relationship with buy opportunity)
- Price/EPS (- ,market ratio)
- Price/Book (- ,market ratio)
- Price/Cash flows (- ,market ratio)
- Return on equity (+, profitability)
- Return on assets (+, profitability)
- Net profit margin (+, profitability)
- Debt/Equity (+/-, leverage)
- EBIT/Interest expense (+, leverage)
- Sales/Fixed assets (+,asset utilisation)
- Cost of goods sold/average inventory (+,asset utilisation)
- Current assets/Current liabilities (+, liquidity)
- (Cash + marketable securities)/Current liabilities (+, liquidity)
261
Valuation by comparables
Advantages
• Simplicity
• Industry and time relevant
• Insignificant information cost
• Considers a variety of different
business aspects
Disadvantages
• Opposes the EMH since each
purpose is to spot mispricing
through the use of publicly
available information but uses
industrial averages as accurate
benchmarks. So the market is
correct at the industry level but
can be wrong at the firm level!
• Perhaps so simple and cost
efficient that inefficiencies do not
hold for long
• Series of accounting-related
issues: inventory valuation me-
thodology, depreciation, inflation
effects, quality of earnings...
262
Dividend discount models
• Rationale: The only real cash flows that accrue from the firm to the
stockholders are the dividends paid. Consequently, stock price should
reflect the present value of the entire future stream of dividend estimates.
• Constant-growth DDM:
• Multistage growth model: Useful for relaxing the constant growth
assumption and reflect the industry and firm life cycles.
• Dividend growth rates will be generally expected to fall until they reach a
level after which they will remain constant. One way to calculate growth
rates: where p is the dividend payout ratio. So g reflects
the percentage of profits that is reinvested in the firm every year.
• DDMs can be combined with the valuation of comparables approach
(especially with market ratios such as P/E).
00 1 0
1
(1 )(1 )
(1 )
ii ii
i
D D gV with D D g or V
k k g
(1 )g ROE p
263
Free cash flow models
• Rationale: Alternative to DDMs. Uses cash flows net of capital
expenditures as the additional value that is effectively available to
stockholders every year. Particularly useful when firms do not pay
dividends but promise significant capital gains (e.g. Google).
• Three calculation steps:
1) Estimate free cash flow to the firm (FCFF):
where t=tax rate, NWC= net working capital.
2) Estimate free cash flow to equityholders(FCFE):
3) Discount future FCFEs at the cost of equity:
Where g is the constant growth rate when firm has reached maturity.
(1 ) . .FCFF EBIT t Depreciation Cap Exp Increasein NWC
(1 )FCFE FCFF Interest Expense t Increaseinnet debt
10
1
,(1 ) (1 )
Tt T T
Tt Tt E E E
FCFE V FCFEV whereV
k k k g
264
Valuation by DDMs and FCF models
Advantages
• Forward looking approaches
• Can provide exact estimate of
“fair price” instead of qualita-
tive assessment of whether a
security is underpriced or
overpriced
• More methodologically specific
than valuation by comparables
• Combine objective informa-
tion with subjective estimates
(art and science of security
selection)
Disadvantages
• Extreme sensitivity of valuation
to certain factors (especially the
growth rate)
• Subjective forecasting of future
growth rates and constant cost
of equity may prove to be very
inaccurate
• Some accounting-related issues
remain: depreciation, quality of
earnings, capital expenditures
265
The Wells Fargo stock evaluation system
• Combines the DDM approach with capital market theory to create a
successful security selection technique
- Step 1: Equate a stock’s market price with the present value of its expected
dividends using a multi-period growth model. Back out the discount rate
(expected return)
11
1 1 20 1
1
11
(1 ) (1 )1
(1 )
N
N
N
g
D g gkP D
k g k
assumed/forecasted
unknown observed
Note: The WF system actually makes use of a
three-period DDM
266
The Wells Fargo stock evaluation system
- Step 2: Estimate the security’s beta using historical data and
modifying according to analysis of fundamental characteristics of the
firm
- Step 3: Plot a security market line using the expected returns and
beta estimates from Steps 1 and 2. This represents the relationship
between expected return and expected betas
- Step 4: Buy (sell) the securities that are above (below) the SML
267
References
• BKM, 9th edition, Chapter 25 (Chapters 17, 22, 23 and 27 are also relevant)
• Elton, E., Gruber, M.J., Brown S.J. and Goetzmann W.N. (2010), Chapter 19, Chapter 20 and Chapter 27
www.icmacentre.ac.uk
Lecture 9: Passive Portfolio Management
Portfolio Management
Dr Ioannis Oikonomou
269
What is indexing?
• Also called tracking or passive portfolio management
• Long term buy and hold strategy: Designed to match the performance of an index – Slightly under-performs the target due to fees and commissions
• Manager is judged on how low his/her tracking error is
• Increased in popularity
– Introduced by Wells Fargo Bank in the early 70s
– Industry leader: Vanguard (John Bogle)
– Nowadays 25% of equity fund assets are managed passively
• Index funds exist across asset classes but are predominant in equities
– Large-cap benchmarks: S&P500, FTSE100, Nasdaq 100…
– Small-cap benchmarks: Russell 2000, FTSE Small cap…
– Value and growth benchmarks: FTSE 250 Growth, FTSE 250 Value…
– Bond benchmarks: Lehman-Brothers Aggregate Bond Index
270
Indexing is grounded in theory:
Portfolio theory and CAPM
• Offers the benefits of diversification
• According to the CAPM, the true market portfolio is mean-variance efficient, so we should all hold a share of it
• The market portfolio is made of all assets present in the economy where the weight allocated to each asset depends on the contribution of that asset to total wealth
• Indexing attempts to realistically form that mean-variance efficient portfolio by investing wealth in a similar way as the index
i
ii
MV
MV
271
Indexing is grounded in theory:
Strong-form market efficiency
• “There are 3 classes of people who don’t think markets work: the Cubans, the North Koreans and active managers” Rex Sinquefield
• Active managers under-perform after accounting for fees
– Also, no persistence in fund performance and so hard to pick winning funds
– Counter to this is the “smart money effect”
– With an index fund, the risk of underperformance is reduced at the cost of not benefiting from serious over-performance
• Expense ratio: Percentage of fund assets that fund managers may withdraw each year to pay for operating expenses
– Typically 0.5% for an index fund (can be as low as 0.18%): The costs are low due to no asset selection or market timing research, low turnover, low marketing research and low taxes on capital gains
– 2% for an active fund: These fees are hard to overcome on a risk-adjusted basis (in addition to typical front loaded fees of 5%)
272
Measuring tracking error
• Risk that the portfolio will perform differently from the benchmark
• Measured as the standard deviation of the difference between the portfolio
returns and the benchmark (FTSE) returns: Pt = RPt – RFTSEt
• Or measured as the portfolio’s residual (unsystematic) risk: Standard deviation
of the residuals from a regression of the fund excess returns on a constant and
the benchmark’s excess return
N
t Pt
N
t PPtPN
EN
TE1
2
1
2
1
1
1
1
PtftFTSEtftPt RRRR
273
Full replication
• All securities are purchased according to their index weight
• Ensures very close tracking
• Disadvantages
– High transaction costs since all the constituents are bought and the dividends need to be re-invested
– Might not be optimal if the index includes many assets and if the securities are illiquid
274
Stratified sampling
• Buy a representative sample of stocks in the index according to their weights in the index
• The universe of stocks is stratified according to certain criteria (industrial sector, market capitalisation, P/E, country…). The passive portfolio is constructed by selecting a certain number of securities in each stratum
• Examples of stock selection within a stratum
– If IT represents 10% of the index, make sure that your portfolio contains 10% of IT stocks
– Select the top 200 highest capitalisation stocks and weight them according to their MV in the index
275
S&P500 stock index - Tracking error versus size
0
0.4
0.8
1.2
1.6
2
2.4
50 100 150 200 250 300 350 400 450 500
Number of issues
Tra
ckin
g e
rro
r (%
)
Stratified sampling
• Fewer stocks mean lower transaction costs, reinvestment of dividends is less
difficult but also higher tracking error
Even with full replication,
tracking error exists
The returns of a basket of 250 stocks will
mismatch the S&P500 by 0.6%: There is a
68% probability that the returns of the portfolio
will fall within 0.6% of the S&P500 returns
276
Optimised sampling
• Construct a portfolio whose performance will be similar to that of a given
benchmark index; i.e., find portfolio weights i that minimise the portfolio
tracking error TEP
subject to
FTSEt
N
i
itiFTSEtPtP RRSDMinRRSDMinTEMinii 1
0
1
1
i
N
i
i
277
Optimised sampling
• Advantages
– Fewer stocks need to be held
– Initial transaction costs are low
– Reinvestment of dividends is less of a problem
– Illiquid stocks can easily be avoided
• Disadvantages
– Tracking error is substantial
– Historical means, standard deviations and correlations (input list) may
change
– Mean-variance optimisers tend to overweight stocks with historical low
tracking errors and underweight stocks with historical high tracking errors
– Small changes in input list may lead to large changes in optimal asset
allocations
278
Limitations of asset-based indexation:
Full replication, stratified sampling
and optimised sampling
• Need to change portfolio weights to reflect change in index weights. Over time the portfolio weights are adjusted for additions (spin-offs, new issues, stock split, IPO) or deletions (M&A, bankruptcy, delisting) from the index
• Need to track and reinvest dividends
• Transaction costs
• Liquidity
• Difficulty to remain constantly 100% invested: Funding may not be available at a level sufficient to buy all the names in the index
High tracking error = 0.2% or more
279
Synthetic indexing
• Replicates the payoff on a passive portfolio by buying stock index futures and investing cash in a risk-free asset
• Advantages
– Overcomes problems of portfolio weights. No need to adjust the portfolio weights for deletions or additions to the index
– Dramatic cost savings over asset-based indexing: One trade only
– Ample liquidity
– Access to 90% of the world capitalisation through futures
– Extra profits from investing the cash in an enhanced cash strategy (0.5% more than T-bill rate); i.e., Modest alpha creation
• Evidence that futures based indexing is better (Lower tracking error)
280
Problems with synthetic indexing:
Tracking error still exists as…
• Basis risk (Basis = Futures price - Spot price)
– If the futures is overpriced relative to the spot (Positive basis), buying a synthetic index will be expensive
– If the spot is overpriced relative to the futures (Negative basis), buying a synthetic index will be cheap
• Rollover risk: All futures have a finite life, they usually expire every 3 months
– You will make a loss on the roll-over trade if the price of the near maturity contract (that you’re closing) is below the price of the distant maturity contract (that you’re buying); i.e., if the market is in contango
– You will make a profit on the roll-over trade if the market is in backwardation: The price of the nearby contract (that you’re closing) is higher than the price of the distant contract (that you’re buying)
281
Problems with synthetic indexing:
Tracking error still exists as…
• Margins need to be maintained
• Margin calls need to be paid
• Commissions (but much lower than for conventional index funds)
• Trading hours: Closing times differ between futures (4.15pm) and spot (4pm) markets
• Relatively limited range of futures contracts; e.g., impossible to duplicate the Wilshire 5,000 index
282
Exchange traded funds
• Listed shares that mimic the performance of an index
• Most popular ETFs
– SPDRs (Standard and Poor’s Depository Receipt, nicknamed “Spider”) tracking the S&P500 index, launched in 1993
– QQQs (“Cubes”) tracking the Nasdaq 100
– DIAMONDS tracking the DJIA
• ETFs now mimic equity, bond, country specific, industry specific, style indices. Commodity ETFs introduced in Nov 2004
• Industry leaders
– BGI: ETFs marketed as iShares
– Vanguard: ETFs marketed as Vipers (Vanguard Index Participation Equity Receipts)
283
The evolution of US ETFs
Source: Investment Company Institute and Strategic
Insight Mutual Fund Research and Consulting
1 1 2 2
17
2
1712
17
13
1755
25
68
34
66
39
8
72
41
6
0
20
40
60
80
100
120
Nu
mb
er
of
ET
Fs
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Number of exchange-traded funds in the US, 1993-2003
Domestic (US) Global Bond
Total annual assets of ETFs in the US, 1993-2003
-
20
40
60
80
100
120
140
160
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
An
nu
al
as
se
ts (
in b
illi
on
s o
f d
oll
ars
)
Domestic (US) Global Bonds All Funds
284
Advantages and disadvantages of ETFs
• Advantages
– Diversified portfolio in one trade
– Unlike mutual funds (open-end funds which trade at the previous day NAV, net asset value), ETFs trade continuous throughout the day
– Exempt from the uptick rule: Can be sold short at any time
– Very liquid
– Low tracking error
– Expense ratios as low as 0.09% a year for Spiders, while the typical index (active) fund charges 0.5% (2%)
• Disadvantages
– Small investors may find the commissions and bid-ask spreads expensive and may rather invest into open-end funds
– ETFs trade at market price not at NAV (as open-end funds would) and thus could be expensive relative to open-end funds
285
Key points • Increased in popularity due to low cost, under performance of active funds and
grounded in theory (Portfolio theory, CAPM, Market efficiency)
• The objective is to minimise the portfolio tracking error via full replication, stratified sampling, optimised sampling or synthetic indexing – The latter generates the lowest tracking error
• The index effect shows that there are market impacts around the time of new entrants to stock indices
• ETFs are a recent development in the indexing industry
286
References
• BKM, 9th edition351-352, 351-352, 925-927.
• Elton, E., Gruber, M.J., Brown S.J. and Goetzmann W.N. (2010), Chapter 27
[This topic is poorly covered in most of the textbooks]
www.icmacentre.ac.uk
Lecture 10:
Hedge Funds and Exam Preparation
Portfolio Management
Dr Ioannis Oikonomou
288
What is a hedge fund?
• Hedge funds are pooled investment vehicles that are privately organised, administered by professional investment managers and not widely available to the general investing public
• “The hedge fund” term does not mean that the managers hedge in the conventional sense
• Due to their private nature, hedge funds have less restrictions on the use of leverage, short-selling and derivatives than more regulated vehicles such as mutual funds
• This allows them to follow investment strategies that are significantly different from the non-leveraged, long-only strategies traditionally followed by investors
289
How are hedge funds organised?
• They are usually organised as limited liability partnerships (LLPs).
• This allows for a “pass through” tax treatment.
– The fund then does not pay any taxes on its investment returns
– Investors pay taxes at their personal rates when they receive returns
290
What fees do hedge funds charge?
• They are usually different from mutual fund structures and are dependent on performance.
• There is usually
– A management fee (1%-2% of AUM)
– An incentive fee of 10% to 30% of positive returns over the high water mark
• No incentive fee is payable if the value of the assets is less than at the end of the last period (this is the high water mark)
291
How hedge fund manager fees vary with returns
• Slide by Nick Motson
292
How the high water mark operates
• Slide by Nick Motson
293
The Size of the Hedge Fund Industry • The industry now has over $1.1 trillion AUM, with 8000+ funds
• Size doubled in the 5 years to 2007 but then fell by around $350bn in 2008
• Source of figure: Eurekahedge
294
Hedge Fund Location and Clients
295
Why invest in hedge funds?
• Flexibility that hedge fund managers have to invest in a wide range of securities
should enhance returns (push efficient frontier outwards)
• Recent historical performance has been impressive, except for 2008
• Supposedly low correlation with traditional asset classes, although in fact many
classes of hedge funds’ returns are highly correlated with stock or bond index returns
• Hedge fund managers are remunerated by “incentive fees” that reward good
performance; mutual fund fees are fixed even if performance is poor
296
Measuring Hedge Fund Performance
Not an easy task since
– Hedge funds often invest in illiquid assets which cannot be marked to market regularly
• This results in systematic downward biases in the volatility of their return distributions
• The true underlying volatility is much higher
– Hedge fund return distributions are different from those of traditional assets
• They are more non-normal, with more negative skew and more kurtosis
• A lottery ticket has an expected return of -45% but a lot of positive skew
– Hedge fund databases suffer from important biases, e.g.
• Back-filling bias
• Survivorship bias (30% of hedge funds do not last even 3 years)
• Survivorship bias accounts for around 3% in annual performance and backfilling bias 1%-5%.
297
Relative Performance of Hedge Funds, 1998-
2004
298
Performance of Hedge Funds in “Down Markets”
299
More Recent Hedge Fund Performance
• Source: Hedge Fund Performance in 2008 by V. Le Sourd, EDHEC
300
Funds of Hedge Funds
• These are simply portfolios of hedge funds
• They allow investors to “spread their eggs between several baskets”
• Their other advantages over direct hedge fund investment include
– Built-in due diligence
– Access to closed funds
– Professional optimisation.
• Their average returns are lower than the average of those of the hedge funds that they
invest in because of the additional layer of fees
301
Disadvantages of Investing in Hedge Funds
• Lock in periods
• Difficulties in assessing performance
• Lack of transparency
– Until recently, hedge funds did not even have to be registered with the SEC, let alone fulfil reporting requirements.
• Leverage
– Some funds make extensive use of borrowing, but 20% use no leverage at all
– The leverage allows hedge funds to sell beta as alpha.
• High management fees (e.g. 3% annual charge plus 30% of performance)
302
Should Hedge Funds be Regulated?
• Predictably, the industry says “no”. Experts and commentators have mixed views.
• What should you regulate? – Information provision?
– Excessive use of leverage?
– Strategies?
– Liquidity?
• Regulation that is too tight in some countries could force hedge funds off-shore, where hedge fund investor protection is even weaker than it is currently in the US and Europe
• Regulation will add to running expenses and will push down net returns
• Regulation may help to prevent fraud, but disasters like LTCM could still occur
303
The Future of the Hedge Fund Industry
• Recent growth has been vast – can it continue?
• Possibility of “capacity constraints”
– Some types of funds are invested in very similar strategies
– There may (eventually) be too much money chasing the strategies
– Returns will diminish
– This could encourage hedge fund managers to take on ever more risk or to form ever more complex and obscure strategies
• Capacity constraints are less of a problem with broader strategies such as global macro or emerging market, and more serious for event-driven funds.
• There are also new classes of funds emerging (e.g., based on energy or real estate) and funds investing in countries that they did not before, where there is significant growth potential (Brazil, Russia, India, China)
• Lack of liquidity, high fees, lack of transparency can be off-putting and limit the greater use of hedge funds by pension funds, for example.
304
References
• BKM, 9th edition, Chapter 26
• None of the textbooks provide really a useful coverage of this topic except for
the 9th edition of BKM, which is much better than the rest.
• The web is also a good resource for this topic. Useful sites include
–www.thehfa.org
–www.vanhedge.com
Some of the material used here is adapted from these sources. Thanks also to
Nick Motson, from whom I have borrowed a couple of slides.