Portfolio Managment 3-228-07 Albert Lee Chun

1
Portfolio Managment3-228-07 Albert Lee Chun
Capital Asset Pricing Model

• Lecture 5

23 Sept 2007
2
Todays 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

3
Other Portfolio Selection Models
4
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.

5
Roys Criterion
Fix RL Minimize Prob (Rplt RL) Maximize k
(E(RP) - RL)/?P
Example RL 5 Mean Return 10 14 17 Stan
dard Deviation 5 4 8 Difference from 5
(k) -1? -2.25? -1.5?
6
Roys Criteria
Maximize k
kB
kC
kA
k ? RL E(RP)
RL
7
Kataokas Criterion
Maximize RL s.t. prob(RP lt RL) lt a Ex a
.05 RP RL1.65?
8
Tesslers Criterion
Fix RL Maximize E(Rp) s.t. prob(RP lt RL) lt a
Ex a .05 E(RP) gt RL1.65?
9
Power of Diversification
Risk
Nonsystematic Risk (idiosyncratic, diversifiable)
PortfolioRisk
Market Risk
Systematic Risk
Number of Stocks
8
10
Market Portfolio
11
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.
  

12
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 wi1

13
Capital Asset Pricing Model
14
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.afaj
of.org/association/historyfinance.asp
15
Capital Asset Pricing Model
16
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.

17
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.
18
Betas are Linear

• Betas are linear
• Beta(aAbB) a Beta(A)b(Beta(B)
• because
• cov(aA bB,M) acov(A,M)bcov(B,M)

19
Security Market Line
Security market Line
20
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
21
All Efficient Securities Lie on the SML
Security Market Line
Negative Beta
22
When Not in Equilibrium
Return Lies Above the SML Stock is Undervalued
Droite de marché
Return Lies Below the SML Stock is Overvalued
23
For Next Week

• 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