€¦ · 2 Reading Main Textbook • Bodie, Z., Kane, A., and Marcus, A.J. (2011) Investments, 9th...

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


Lecture 1:The Investment Environment

Portfolio Management


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


11

The UK fund management industry

in the European context


12

The UK fund management industry:

Asset Allocation


13


Active Vs Passive


14


Equity allocation by region

Source: IMA Survey

15


Client Type


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


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.


Lecture 2:

Risk Aversion and Asset Allocation Decisions



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



High 8 -24.24% 46.24% 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 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 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


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


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


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


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


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/


Lecture 3:Portfolio Theory



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


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


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


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,



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



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*



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



70


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


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%


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%


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


• 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%


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


• 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


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


...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.


Lecture 4:Asset Pricing Models



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 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


• £ 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


• 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


• 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


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


Lecture 5:

Market Efficiency and Behavioural Finance



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



……

P9: VW portfolio with the 10% stocks

that have the 2nd highest size




that have the 2nd lowest size




that have the highest size



Amex, Nasdaq, and NYSE stocks sorted by sizeAmex, Nasdaq, and NYSE stocks sorted by 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



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



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


Lecture 6:Style Investing



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


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



• 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


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


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


184



• 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


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


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




(Russell Mid-cap Growth) (Russell Mid-cap) (Russell Mid-cap Value)

Index advantage +138bp Index advantage +219bp Index advantage +119bp




(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


Lecture 7:Portfolio Performance Evaluation



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


• 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


Lecture 8:Active Portfolio Management



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


– 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)


– 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


Lecture 9: Passive Portfolio Management



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]


Lecture 10:

Hedge Funds and Exam Preparation



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


• 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.

http://www.thehfa.org/

http://www.vanhedge.com/

€¦ · 2 Reading Main Textbook • Bodie, Z., Kane, A., and Marcus, A.J. (2011) Investments, 9th...

Documents

Transcript of €¦ · 2 Reading Main Textbook • Bodie, Z., Kane, A., and Marcus, A.J. (2011) Investments, 9th...