BKM Chapter 10

Question 1

Modified single-factor model

BKM - 10

Answer 1

R = E[R] + beta * F + e

replaces the market factor from the single-factor model with F

F = macroeconomic surprise = deviation of common factor from expected value of 0

*e’s = residual, are uncorrelated with F and b/w stocks

Question 2

Use for the modified single-factor model

BKM - 10

Answer 2

risk management (example: measure exposure and hedge specific risks)

Question 3

Main idea of multifactor models

BKM - 10

Answer 3

model systematic risk as a combination of factors instead of a single factor (F)

Question 4

Example multifactor model (GDP & IR)

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Answer 4

R = E[R] + beta(GDP) * GDP + beta(IR) * IR + e

measures 2 macroeconomic forces:

1. unanticipated GDP growth
2. interest rate changes

Question 5

Factor betas in multifactor models

BKM - 10

Answer 5

beta coefficients that measure the sensitivity of the firm’s excess returns to each macroeconomic factor

Question 6

Advantage of multifactor models

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Answer 6

captures differences in sensitivity to each macroeconomic factor

Question 7

Arbitrage

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Answer 7

ability to earn riskless profits with zero net investment

Question 8

Assumptions of the Arbitrage Pricing Theory (APT) model (3)

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Answer 8

1. security returns can be described with a factor model
2. there are enough securities to diversify away non-systematic risk
3. arbitrage opportunities DNE in well-functioning markets

Question 9

Law of one price

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Answer 9

two economically equivalent assets should have identical prices

Question 10

General arbitrage strategy

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Answer 10

long (buy) the cheaper asset and short (sell) the more expensive one

Question 11

Fundamental concept of capital market theory

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Answer 11

idea that market prices will move to rule out arbitrage opportunities

(e.g. prices of cheaper assets are bid up and prices of more expensive assets are forced down until equilibrium position is reached)

Question 12

Difference between market equilibrium under CAPM and APT

BKM - 10

Answer 12

CAPM: many investors making small trades (aka risk-return dominance argument)

APT: few investors making extremely large trades

Question 13

Excess returns (R(P)) under a well-diversified portfolio (APT)

(BKM - 10)

Answer 13

R = E[R] + beta * F

b/c e goes to 0 with diversification

Question 14

Variance (sigma^2(P)) under a well-diversified portfolio (APT)

(BKM - 10)

Answer 14

sigma^2(P) = beta(P)^2 * sigma^2(F) + sigma^2(e(P))

first term = systematic risk, second term = firm-specific risk

Question 15

Expected return for well-diversified portfolios with the same beta (APT)

(BKM - 10)

Answer 15

well-diversified portfolios with the same beta must produce the same expected return (o/w arbitrage)

Question 16

SML, arbitrage, and well-diversified portfolios (APT)

BKM - 10

Answer 16

all well-diversified portfolios must live on the SML with slope F (o/w arbitrage!)

exploiting arbitrage opportunities forces all portfolios to the SML

Question 17

SML for APT vs. CAPM (& rationale)

BKM - 10

Answer 17

SML of CAPM also applies to well-diversified portfolios b/c of the no arbitrage assumption of APT

Question 18

Advantages of APT over CAPM (2)

BKM - 10

Answer 18

1. APT does not rely on an “impossible to observe” market portfolio - instead provides a mean-beta relationship that works for a well-diversified portfolio
2. APT does not require all investors to be mean-variance optimizers

Question 19

Disadvantages of APT vs. CAPM (2)

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Answer 19

1. only assumes the mean-beta relationship holds for nearly all securities (vs. all securities)
2. relies on holding a well-diversified portfolio that eliminates firm-specific risk, but this is practically difficult

Question 20

Reason it is difficult to completely eliminate all firm-specific risk

(BKM - 10)

Answer 20

empirical evidence that it is hard to hold a large enough number of securities to have a negligible amount of firm-specific risk

Question 21

Similarities between APT and CAPM (2)

BKM - 10

Answer 21

Both:

1. produce the same SML
2. make the distinction between systematic and firm-specific risk

Question 22

Implication of imperfectly diversified portfolios for APT

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Answer 22

means there is some amount of residual, or firm-specific risk, which means that arbitrage cannot exist (b/c of riskless profit condition)

Question 23

Single-index model (aka Treynor-Black or TB model) vs. APT

BKM - 10

Answer 23

T-B model is more flexible because it responds to the practical limitations of diversification

Question 24

Additional factors in multi-factor APT model (aka factor or tracking portfolios)

(BKM - 10)

Answer 24

each factor is a different source of systematic risk

each factor portfolio has a beta = 1 for one of the risk factors (perfect correlation) and beta = 0 (uncorrelated) for the other risk factor

Question 25

Fama-French (FF) three factor model excess returns (R(i))

BKM - 10

Answer 25

R = alpha + beta(M) * R(M) + beta(SMB) * SMB + beta(HML) * HML + e

SMB = small minus big = difference in XS returns based on firm-size

HML = high minus low = difference in XS returns based on book-to-market ratio

Question 26

Reason high book-to-market ratios and firm size are intuitive for predicting average stock returns

(BKM - 10)

Answer 26

high book-to-market ratio can signal distress

small firms are more sensitive to changes in business conditions

Question 27

Ways to interpret the Fama-French (FF) model (2)

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Answer 27

1. model may signify a departure from rational equilibrium (b/c there is no theoretical reason for preferences due to firm size or book-to-market ratio)
2. firm characteristics such as firm size and book-to-market ratio are correlated with other risk factors (proxies for unidentified risk factors)

Question 28

Risk-return dominance argument of CAPM

BKM - 10

Answer 28

if there is a mis-priced security, many investors will shift their portfolios to capitalize on the mis-pricing & restore the equilibrium price

Question 29

Expected return, E[r], for the multifactor APT model

BKM - 10

Answer 29

E[r] = risk-free rate + sum(beta(j) * risk premium for factor j)

Question 30

Arbitrage portfolio for multifactor APT model

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Answer 30

select a complimentary portfolio by choosing portfolio w/constant relativity to arbitrage portfolio betas across all betas

create new portfolio w/weight 1 / relativity in the selected complimentary portfolio and 1 - 1 / relativity in the risk-free asset

buy portfolio w/higher return and short portfolio w/lower return