0 portfolio managment 3-228-07 albert lee chun capital asset pricing model lecture 5 23 sept 2007

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Portfolio ManagmentPortfolio Managment3-228-073-228-07

Albert Lee ChunAlbert Lee Chun

Capital Asset Pricing Model Capital Asset Pricing Model

Lecture 5Lecture 5

23 Sept 2007

Albert Lee Chun Portfolio Management 2

Today’s LectureToday’s Lecture

Portfolio Seclection Criteria of Roy, Kataoka and Portfolio Seclection Criteria of Roy, Kataoka and Tessler. Tessler.

Power of DiversificationPower of Diversification Market Portfolio RevisitedMarket Portfolio Revisited 2 Excel Examples2 Excel Examples Intro to the Capital Asset Pricing ModelIntro to the Capital Asset Pricing Model


Other Portfolio Selection ModelsOther Portfolio Selection Models


Safety First CriterionSafety First Criterion

Investors may find it too complex to go through a Investors may find it too complex to go through a utility maximization algorithm.utility maximization algorithm.

They may want to avoid bad outcomes, such a They may want to avoid bad outcomes, such a scenario where they lose a significant portion of their scenario where they lose a significant portion of their wealth. wealth.

We look at 3 criteria, that of Roy, Kataoka and We look at 3 criteria, that of Roy, Kataoka and Tessler. Tessler.


Roy’s CriterionRoy’s Criterion

Example: RL = 5%

Mean Return 10% 14% 17%

Standard Deviation 5% 4% 8%

Difference from 5% (k) -1 -2.25 -1.5

Fix RL

Minimize Prob (Rp< RL)

Maximize k = (E(RP) - RL)/P


Roy`s Criteria Roy`s Criteria

0.1

mR

kA

0

RL

kC

kB

k + RL = E(RP)

)E(ri

Maximize k


Kataoka’s CriterionKataoka’s Criterion

Maximize RL

s.t. prob(RP < RL) <= α

Ex: α =.05

RP = RL+1.65

)E(R i

0.1

LR

0


Tessler’s CriterionTessler’s Criterion

Fix RL

Maximize E(Rp)

s.t. prob(RP < RL) <= α

Ex: α =.05

E(RP) >= RL+1.65

)E(R i

0.1

LR

0


Power of DiversificationPower of Diversification

Risk

Number of Stocks

Market Risk

Systematic Risk

PortfolioRisk

Nonsystematic Risk (idiosyncratic, diversifiable)


Market PortfolioMarket Portfolio


The Market PortfolioThe Market Portfolio

The market portfolio represents the entire market of The market portfolio represents the entire market of risky securities.risky securities.

The weight on each security is therefore its market The weight on each security is therefore its market weight, given by the ratio of the market capitalization weight, given by the ratio of the market capitalization of the security divided by the total market of the security divided by the total market capitalization. capitalization.

This is an example of a This is an example of a value weighted portfolio. value weighted portfolio.


Market Portfolio ExampleMarket Portfolio Example

Suppose the total value of the market is $100,000,000 dollars.

Suppose there exists 500,000 shares of a security in circulation with market price of $2 per share.

This security comprises 1% of the total market capitalisation ($1,000,000 / $100,000,000 )

Thus, the weight of this security in the market portfolio is wi=1%


Capital Asset Pricing ModelCapital Asset Pricing Model


William SharpWilliam Sharp

1990 Nobel Prize in Economics

for his contributions to the theory of price formation for financial assets, the so-called, Capital Asset Pricing Model

(CAPM)

Interview with Sharp and Markowitzhttp://www.afajof.org/association/historyfinance.asp


Capital Asset Pricing ModelCapital Asset Pricing Model

2m

m i,

m

mii =

) rVar(

) r ,rCov( =

r - )r( E + r =

r - )r( E )r ,r( Cov

+ r = )r( E

fmif

fm2m

mifi


Expected Returns Depends on BetaExpected Returns Depends on Beta

The expected return on an asset is determined by the The expected return on an asset is determined by the beta of asset, which also measures the covariance beta of asset, which also measures the covariance between the return on the asset and the return on the between the return on the asset and the return on the market portfolio. market portfolio.

r - )r( E )r ,r( Cov

+ r = )r( E fm2m

mifi


Excess Returns and BetaExcess Returns and Beta

The expected excess return of a security is proportional to the expected excess return of the market. The proportionality factor is

beta.

It is the covariance of an asset with the market that determines the excess returns!

Assets with a negative beta reduces the overall risk of the portfolio and investors are willing to accept a rate of return that

is lower than the risk-free rate of return.


Betas are LinearBetas are Linear

Betas are linearBetas are linear

BetaBeta(aA+bB) = a *(aA+bB) = a *BetaBeta(A)+b*((A)+b*(BetaBeta(B)(B)

because because

covcov(aA +bB,M) = a*(aA +bB,M) = a*covcov(A,M)+b*(A,M)+b*covcov(B,M)(B,M)

iip w =


Security Market LineSecurity Market Line

)r-(rr)E(r Mi fif

Security market Line

)(0 =

)(

freerisk

market 1 =

fr

m

0.10 Beta

)E(ri

fr

)E(rm


Example Example

Assume:Assume: Rf = 5% (0.05) Rf = 5% (0.05)

RRMM = 9% (0.09) = 9% (0.09)

Implied market risk premiumImplied market risk premium = 4% (0.04) = 4% (0.04)

Stock Beta

A 0.70B 1.00C 1.15D 1.40E -0.30

E(RA) = 0.05 + 0.70 (0.09-0.05) = 0.078 = 7.8%

E(RB) = 0.05 + 1.00 (0.09-0.05) = 0.090 = 09.0%

E(RC) = 0.05 + 1.15 (0.09-0.05) = 0.096 = 09.6%

E(RD) = 0.05 + 1.40 (0.09-0.05) = 0.106 = 10.6%

E(RE) = 0.05 + -0.30 (0.09-0.05) = 0.038 = 03.8%

r - )r( E r )r( E fmifi


All Efficient Securities Lie on the SMLAll Efficient Securities Lie on the SML

)r -(rr)E(r

fMfi

iNegative Beta

Security Market Line

0.10 Beta

)E(ri

fr

)E(rm


When Not in EquilibriumWhen Not in Equilibrium

Return Lies Above the SML

Stock is Undervalued

Return Lies Below the SML

Stock is Overvalued

Droite de marché

0.10 Beta

)E(ri

fr

)E(rm

Albert Lee Chun Portfolio Management

For Next WeekFor Next Week

Next week we will:Next week we will:

- Continue our discussion of the CAPM- Continue our discussion of the CAPM- Do some more examplesDo some more examples- Talk about preparing for the MidtermTalk about preparing for the Midterm

You should readYou should read

Chapter 8, Section 8.1 – 8.3Chapter 8, Section 8.1 – 8.3

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0 portfolio managment 3-228-07 albert lee chun capital asset pricing model lecture 5 23 sept 2007

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