investment - jones - chp 9

8/13/2019 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

9-2


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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

9-3

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

9-4


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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

9-5


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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

9-6


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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

9-7


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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

9-9

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

9-10


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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):

9-12

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

9-13

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

9-15


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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

9 18


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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

9-18

9 19


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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.

investment - jones - chp 9

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