Download - Investment - JOnes - chp 9
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MODELS FOR THE PRICING OF
ASSETS
CHAPTER 9
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CAPM Assumptions
All investors:
Use the same information to
generate an efficient frontier
Have the same one-periodtime horizon
Can borrow or lend money at
the risk-free rate of return
No transaction costs, no
personal income taxes, no
inflation
No single investor canaffect the price of a stock
Capital markets are in
equilibrium
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Risk-Free Lending
Riskless assets can be
combined with any
portfolio in the efficient set
AB
Set of portfolios on line RF
to T dominates all
portfolios below it
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Risk
B
A
TE(R)
RF
L
Z X
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Borrowing Possibilities
Investor no longer restricted to own wealth
Interest paid on borrowed money
Higher returns sought to cover expense
Assume borrowing at RF
Risk will increase as the amount of borrowing increases
Financial leverage
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The New Efficient Set
Risk-free investing and borrowing creates a new set of
expected return-risk possibilities
Addition of risk-free asset results in
A change in the efficient set from an arc to a straight line tangent to the
feasible set without the riskless asset
Chosen portfolio depends on investors risk-return preferences
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Portfolio Choice
The more conservative the investor the more is placed in risk-free
lending and the less borrowing
The more aggressive the investor the less is placed in risk-free
lending and the more borrowing
Most aggressive investors would use leverage to invest more in portfolio T
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Market Portfolio
Most important implication of the CAPM
All investors hold the same optimal portfolio of risky assets
The optimal portfolio is at the highest point of tangency between RF and
the efficient frontier
The portfolio of all risky assets is the optimal risky portfolio Called the market portfolio
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CML & SML
CML : equilibrium relationship between expected return and
risk for efficient portfolio
SML : equilibrium relationship between expected return and
systematic risk
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Capital Market Line
Line from RF to L iscapital market line (CML)
y = risk premium = E(RM)
- RF x = risk = M Slope = y/x
= [E(RM) - RF]/M y-intercept = RF
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E(RM)
RF
RiskM
L
M
x
y
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The Separation Theorem
The investment decision (which risky portfolio to hold) is separatefrom the financing decision (how to allocate investable funds
between risk-free & risky assets)
Pg. 238
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Important points about CML
Consist of RF and M portfolio
Always upward sloping (ex ante)
Can be downward sloping (ex post)if return on RF assets >
return on market portofolio
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Capital Market Line
Slope of the CML is the market price of risk for efficient
portfolios, or the equilibrium price of risk in the market
Relationship between risk and expected return for portfolio P
(Equation for CML):
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pM
Mp
RF)E(RRF)E(R
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Security Market Line
Equation for expected return for an individual stock
Beta measures systematic risk
Measures relative risk compared to the market portfolio of all stocks
Volatility different than market
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RF)E(RRF)E(R Mii
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Security Market Line
Beta = 1.0 implies as risky
as market
Securities A and B are
more risky than the market Beta >1.0
Security C is less risky than
the market
Beta
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CAPMs Expected Return-Beta Relationshi
Required rate of return on an asset (ki) is composed of
risk-free rate (RF)
risk premium (i[ E(RM) - RF ])
Market risk premium adjusted for specific security
ki= RF +i[ E(RM) - RF ] The greater the systematic risk, the greater the required return
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Arbitrage Pricing Theory
APT is not critically dependent on underlying market portfolioas is the CAPM, which predicts than only market risksinfluences E(R)
Based on the Law of One Price
Two otherwise identical assets cannot sell at different prices Equilibrium prices adjust to eliminate all arbitrage opportunities
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Assumptions
CAPM
Single period investment horizon
Absence of taxes
Borrowing and lending at rate of RF
Investor selects portfolios on the basis of expected return and variance
Investor have homogenous beliefsInvestor are risk averse utility maximizers
Markets are perfect
Return are generated by a factor model
APT4 terakhir
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Factor Models
Major factors in economy that affect large number of securities
APT assumes returns generated by a factor model
Factor Characteristics
Each risk must have a pervasive influence on stock returns
Risk factors must influence expected return and have nonzero prices
Risk factors must be unpredictable to the market
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APT Model
The expected return-risk relationship for the APT can be
described as:
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2(risk premium for
factor 2) + +bin(risk premium for factor n)
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Soal UTS 2007/2008 (20 poin)
a. Berdasarkan teori portofolio Markowitz, jelaskan
bagaimana proses penentuan portofolio investasi yangterdiri dari aset bebas risiko dan sejumlah aset berisiko.
Bagaimana peran tingkat risk aversion investor dalam
menentukan portofolio investasinya? Gunakan grafik.
b. Berikut adalah informasi mengenai saham A dan B:Saham A Saham B
Harga sekarang Rp 5.000 Rp 1.500
Estimasi harga tahun depan Rp 5.500 Rp 1.725
Estimasi pembayaran div. Rp 300 Rp 0
Beta 2 0,5
Tingkat bunga bebas risiko 7%, E(Rm) = 13%.
Tentukan saham mana yang sebaiknya dibeli dan
dijual.