Portfolio Managment 3-228-07 Albert Lee Chun

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Portfolio Managment 3-228-07 Albert Lee Chun. Capital Asset Pricing Model . Lecture 5. 23 Sept 2007. Today’s Lecture. Portfolio Seclection Criteria of Roy, Kataoka and Tessler. Power of Diversification Market Portfolio Revisited 2 Excel Examples

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### Portfolio Managment3-228-07Albert Lee Chun

Capital Asset Pricing Model

Lecture 5

23 Sept 2007

Today’s Lecture
• Portfolio Seclection Criteria of Roy, Kataoka and Tessler.
• Power of Diversification
• Market Portfolio Revisited
• 2 Excel Examples
• Intro to the Capital Asset Pricing Model
Safety First Criterion
• Investors may find it too complex to go through a utility maximization algorithm.
• They may want to avoid bad outcomes, such a scenario where they lose a significant portion of their wealth.
• We look at 3 criteria, that of Roy, Kataoka and Tessler.
Roy’s Criterion

Fix RL

Minimize Prob (Rp< RL)

Maximize k = (E(RP) - RL)/P

Example: RL = 5%

Mean Return 10% 14% 17%

Standard Deviation 5% 4% 8%

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

Roy`s Criteria

Maximize k

kB

kC

kA

k  + RL = E(RP)

RL

Kataoka’s Criterion

Maximize RL

s.t. prob(RP < RL) <= α

Ex: α =.05

RP = RL+1.65

Tessler’s Criterion

Fix RL

Maximize E(Rp)

s.t. prob(RP < RL) <= α

Ex: α =.05

E(RP) >= RL+1.65

Power of Diversification

Risk

Nonsystematic Risk (idiosyncratic, diversifiable)

PortfolioRisk

Market Risk

Systematic Risk

Number of Stocks

8

The Market Portfolio
• The market portfolio represents the entire market of risky securities.
• The weight on each security is therefore its market weight, given by the ratio of the market capitalization of the security divided by the total market capitalization.
• This is an example of a value weighted portfolio.
Market 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%

William 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 Markowitz

http://www.afajof.org/association/historyfinance.asp

Expected Returns Depends on Beta
• The expected return on an asset is determined by the beta of asset, which also measures the covariance between the return on the asset and the return on the market portfolio.
Excess 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 Linear

Betas are linear

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

because

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

Security Market Line

Security market Line

Example

Assume:Rf = 5% (0.05)

RM = 9% (0.09)

Implied market risk premium = 4% (0.04)

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%

All Efficient Securities Lie on the SML

Security Market Line

Negative Beta

When Not in Equilibrium

Return Lies Above the SML

Stock is Undervalued

Droite de marché

Return Lies Below the SML

Stock is Overvalued

For NextWeek

Next week we will:

- Continue our discussion of the CAPM

• Do some more examples
• Talk about preparing for the Midterm
• You should read

Chapter 8, Section 8.1 – 8.3