Topic 5: International Asset Pricing Models

Question 1

Why study?

Answer 1

i) Why some strategies are profitable? Risk premium? systematic risk? Need asset pricing model to determine “systematic risk/risk premium

ii) To answer practical questions (investing into a hedge fund? A new profitable strategy? Factor investing?)

Question 2

Domestic Asset Pricing Models

Answer 2

CAPM
Fama French 3 factor model
Carhart 4 factor model
Fama French 5 factor model

Question 3

How to test CAPM

Answer 3

E(rj,t) − rf,t = βj(E(rm,t) − rf,t)

1: run regression using historical data to estimate Alpha and Beta

2: Take expectation on the regression: E(rj,t) − rf,t = αj + βj(E(rm,t) − rf,t)

3: CAPM holds when α = 0. We test this hypothesis statistically. If α ≠ 0, the CAPM doesn’t hold (so-called CAPM anomalies)

Question 4

CAPM anomalies

Answer 4

Size anomaly
Value anomaly

Question 5

Size anomaly

Answer 5

Small firm stocks tend to have higher HPRs, even after accounting for the CAPM beta risk

How to implement: buy a portfolio of small firms (S) but you finance it by short-selling a portfolio of large firms (B)

Question 6

Value anomaly

Answer 6

Value firm stocks tend to have higher returns, even after accounting for the CAPM beta risk

How to implement: buying a portfolio of value firms (H) but you finance it by short-selling a portfolio of growth firms (L) = HML

Question 7

Fama-French-3-factor model

Answer 7

(‘alpha’ become ‘beta’):
E(Rj,t) − Rf,t = βj(E(Rm,t ) − Rf,t) + Sj E(SMBt)+ HjE(HMLt)

Question 8

Fama-French Anomalies

Answer 8

Momentum Anomaly
Profitability Anomaly
Investment Anomaly

Question 9

Momentum Anomaly

Answer 9

Past winners tend to have higher HRPs, even after accounting for the FF 3F risks

How to implement: buy a portfolio of past winners (W) but you finance it by short-selling a portfolio of past losers (L)

Question 10

Profitability anomaly

Answer 10

Past profitable firms stocks tend to have higher returns, even after accounting for the FF 3F risks

How to implement: buy a portfolio of past robust profitable firms (R) but you finance it by short-selling past weak profitable firms (W)

Question 11

Investment anomaly

Answer 11

Past low investment firm stocks tend to have higher returns, even after accounting for the FF 3F risks

How to implement: buy past conservative firms (portfolio C) but you finance it by short-selling past aggressive firms (portfolio A)

Question 12

Carhart 4-Factor Model

Answer 12

(Alpha become Beta):
E(Rj,t) - Rf,t = βj(E(Rm,t ) − Rf,t) + Sj E(SMBt)+ HjE(HMLt) + WjE(WMLt)

Question 13

Fama-French 5 factor model

Answer 13

(Alpha become Beta):
E(Rj,t) - Rf,t = βj(E(Rm,t ) − Rf,t) + Sj E(SMBt)+ HjE(HMLt) + R*jE(RMWt) + CjE(CMAt)

Question 14

International Asset Pricing Models

Answer 14

World CAPM
CAPM with Partial Integration
Bakaert and Harvey (1995s) model
International APT
International APT with partial integration

Question 15

World CAPM

Answer 15

E(rj,t) − rf,t = βj(E(rw,t) − rf,t)
with fully integrated markets and no premiums for taking FX risk (real returns + RPPP holds)

Question 16

CAPM with partial integration

Answer 16

Partially integrated? Psychological barriers, Legal restrictions, Transaction costs, Tax, Political risks, FX risks, etc

Question 17

Bekaert and Harvey (1995)’s model

Answer 17

Bekaert and Harvey (1995)’s model:

E(rj,t) − rf,t = wt[βj,w(E(rw,t) − rf,t)] + (1 − wt)[βj,l(E(rl,t) − rf,t)]

Note: Weights, wt, are determined by variables that proxy for the degree of integration, like size of trade sector and equity market capitalisation to GDP

Question 18

International APT

Answer 18

(local/regional/global anomalies: LSMB (e.g., UK-SMB), RSMB (e.g., Asian-SMB), GSMB (e.g., MSCI-SMB))

Question 19

International APT with partial integration

Answer 19

Fama-French 3-factor model with partial integration:
E(rj,t) − rf,t = βj,w(E(rw,t) − rf,t) + sj,GE(GSMBt)+ hj,GE(GHMLt) + βj,l(E(rl,t) − rf,t) + sj,lE(LSMBt)+ hj,lE(LHMLt)

Repeat for Carhart 4 factor and FF-5F with partial integration

Question 20

Karolyi and Wu (2018)’s 4-Factor model

Answer 20

Carhart 4-factor model with partial integration, but with different ways to define global/local factors

Investability Restriction: Karolyi and Wu (2014,WP) define globally-accessible stocks as follows: the stocks in the globally accessible sample need to be listed in the markets which are fully open to global investors or to be secondarily cross-listed in target markets (US, UK, etc.) with minimum foreign investment restrictions and reasonably active trading in foreign cross-listed issues).

They propose and test multi-factor models (e.g., Carhart with partial integration) based on factor portfolios comprised on only globally-accessible stocks (global factors) and of locally-accessible stocks (local factors)