BUS403_Investments_Prof. Chung 0

Part II : PORTFOLIO THEORY

o Risk and Return

o Efficient Diversification

o CAPM and APT

o Efficient Markets

o Behavioral Finance and Technical Analysis

BUS403_Investments_Prof. Chung 1

CAPM and APT

BUS403_Investments_Prof. Chung 2

요인모형(factor model): 자산의 수익률 변동을 어떤 공통요인의 변동에 의해 설명하고자 하는 수익생성모형(return generating model)

ㅇ 단일요인모형(Single Factor Model): 자산의 수익률이 어떤 하

나의 공통요인(예, GDP성장률)의 변동과 관련

Ri = ai + βi * F + ei……(1)

Ri: 자산 i 초과수익률(= ri–rf); F: 요인의 가치; ai: 요인의 기대가

치가 0일 때 자산 i 초과기대수익률; βi: 자산 i 수익률의 요인 값

에 대한 민감도; ei: 잔차항(고유요인 변동에 의한 수익률 변동)

(가정) E(ei)=0, Cov(F, ei)=0, Cov(ei, ej)=0, ij

(예) Ri=0.03+1.5*F+ei, F: GDP성장률

i) F=0%, 자산 i 초과기대수익률=3%

ii) F=5%, 자산 i 초과기대수익률=10.5%

CAPM and Multifactor Models

BUS403_Investments_Prof. Chung 3

ㅇ 단일요인모형(Single Factor Model)(계속)

E(Ri) = ai + βi*E(F)……(2)

i2 = βi

2 F2 + ei

2,

F2: 요인 F의 분산; ei

2: 잔차항의 분산

식(1)-식(2)

Ri = E(Ri) + βi*(F-E(F)) + ei……(3)

Risks on a security come from two sources

– Common macro-economic factor

– Firm specific events

Possible common macro-economic factors

– Gross Domestic Product Growth

– Interest Rates

– Inflation, etc.

Unexpected change; shock; innovation

CAPM and Multifactor Models

BUS403_Investments_Prof. Chung 4

ㅇ 다요인모형(Multi-Factor Model): 2개 이상의 공통요인에

의해 자산수익률의 변동을 설명

1) 두 요인모형(Two-factor model)

Ri=ai + βi1*F1 + βi2*F2 + ei

Ri: 자산 i 초과수익률; F1, F2: 요인1, 2의 가치

ai: 두 요인의 기대가치가 0일 때 자산 i 초과기대수익률

βi1: 자산 i 수익률의 요인F1 값에 대한 민감도

βi2: 자산 i 수익률의 요인F2 값에 대한 민감도

ei: 잔차항 (고유요인의 변동에 의한 수익률 변동)

(가정)E(ei)=0, Cov(F1,ei)=0, Cov(F2,ei)=0, Cov(F1,F2)=0, Cov(ei, ej)=0, ij

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CAPM and Multifactor Models

BUS403_Investments_Prof. Chung 5

ㅇ 다요인모형(Multi-Factor Model) (cont’d)

2) Fama-French Three-Factor Model

Returns are related to factors other than market returns

Size

Book value relative to market value

CAPM and Multifactor Models

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BUS403_Investments_Prof. Chung 6

• Stephan A. Ross(1976)

• Roll’s critique on CAPM

– No such a market portfolio

• The APT proposes that the relationship between risk and return is more complex and may be due to multiple factors such as GDP growth, expected inflation, tax rate changes, and dividend yield, etc.

– No arbitrage profit condition

– Factor (Multifactor) model

– Well-diversified portfolio instead of market portfolio

Arbitrage Pricing Theory (APT)

BUS403_Investments_Prof. Chung 7

A factor model describing security returns

Sufficient securities to diversify away idiosyncratic risk

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Three key propositions

BUS403_Investments_Prof. Chung 8

※ Well-Diversified Portfolios

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BUS403_Investments_Prof. Chung 9

No arbitrage condition * Arbitrage - arises if an investor can

construct a zero investment portfolio with a sure profit. Since no investment is required, an investor can create large positions to secure large levels of profit.

– Zero net investment

(self-financing)

– No systematic risk

– No return in equilibrium 0

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Three key propositions (cont’d)

BUS403_Investments_Prof. Chung 10

fj = required rate of return on a factor portfolio having a unit

sensitivity only to economic factor j and zero sensitivities to all

other factors. (fi-rf: risk premium for factor portfolio i)

βij = sensitivity of stock i to factor j.

Required Return for Stock i under the APT

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BUS403_Investments_Prof. Chung 11

Required Return for Stock i under the APT

BUS403_Investments_Prof. Chung 12

APT with 3 factors of inflation, industrial production and

the aggregate degree of risk aversion (=iTB – iBB)

rf=8%

RRR is 13% on a portfolio with unit sensitivity to

inflation and zero sensitivities to two other factors

RRR of factor (IP) portfolio : 10%

RRR of factor (ADRA) portfolio: 6%

Factor sensitivities of Stock i: 0.9 to inflation FP, 1.2 to

IP FP, and -0.7.

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Required Return for Stock i under the APT

BUS403_Investments_Prof. Chung 13

APT and CAPM Compared

• Both are equilibrium asset pricing models.

• APT can be extended to multifactor models.

– CAPM assumes a single factor of market portfolio.

• APT is more general in that it gets the expected return and

beta relationship without the assumption of the market

portfolio

– No special role for the market portfolio in the APT, whereas the

CAPM requires the market portfolio be efficient.

• APT does not specify relevant factors.

• APT applies only to well-diversified portfolios whereas

CAPM applies to all assets without reservation.