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
22
2
2
2
2
1
2
1
2
222111
2211
))(())(()(
)()()(
eiFiFii
iiiii
iiii
eFEFFEFRER
FEFEaRE
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
ratio B/M low shigh versu a with firmsbetween returnsin difference :
firms large and smallbetween returnsin difference :
)(
HML
SMB
HMLHMLSMBSMBfMMifi
r
r
rrrrarr
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
i
s
mim
s
i
s
iii FFFRER 2211)(
ii
s
mimi
s
ii
s
iiii
i
s
mim
s
i
s
iiiii
wFwFwFwREw
FFFREwRwRp
2211
2211
)(
))((
Three key propositions
BUS403_Investments_Prof. Chung 8
※ Well-Diversified Portfolios
N
j
jjp
N
j
jjp
p
s
ppp
wwwhere
FRER
11
,,
)(
2
1
22
3
2
2
2
12
2
2
1
222
1
22222
111
,/1
][
NNNN
NwLet
ww
N
i
N
ip
i
N
i
iiF
N
i
iipFpp
FppFpp
s
ppp whereFRER 222,,)(
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
0
,0
1
1
iip
N
i
iji
N
i
i
RwR
jw
w
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
iinii
ii
i
e
e
])E(F-F[])E(F-[F])E(F-[F)E(r r
])E(r-[r)E(r r
]r-)[E(rr )E(r:SML
nn222111ii
mmii
fmfi
inii )r-f()r-f()r-(fr )E(r fn2f21f1fi
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.
16.3%8%)(-0.7)-(6%8%)1.2-(10%8%)0.9-(13%8%
)r-f()r-f()r-(fr )E(r 3f32f21f1fi
iii
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.