Porfolio part 4

Question 1

What is Arbitrage Pricing Theory (APT)?

Answer 1

A linear model with multiple systematic risk factors priced by the market; alternative to CAPM.

Question 2

List assumptions of APT.

Answer 2

1. Unsystematic risk can be diversified away, 2. Returns are generated by a factor model, 3. No arbitrage opportunities exist.

Question 3

What is the APT Equation?

Answer 3

E(RP) = RF + βP,1(λ1) + βP,2(λ2) + … + βP,k(λk); β = factor sensitivity, λ = factor risk premium.

Question 4

What is a pure factor portfolio in APT?

Answer 4

A portfolio with sensitivity of 1 to one factor and 0 to all other factors.

Question 5

What is a major advantage of APT over CAPM?

Answer 5

APT does not require the market portfolio as a factor.

Question 6

How is CAPM related to APT?

Answer 6

CAPM is a restrictive case of APT with only one factor: the market factor.

Question 7

What is an arbitrage opportunity?

Answer 7

A risk-free, costless profit opportunity that should not exist in efficient markets.

Question 8

How do you exploit an arbitrage opportunity?

Answer 8

Construct a portfolio with the same risk (factor exposures) but higher expected return; go long the better return and short the underperformer.

Question 9

How to calculate portfolio beta?

Answer 9

Beta of a portfolio is the weighted average of the individual asset betas.

Question 10

In APT, what happens when arbitrage opportunities are exploited?

Answer 10

Asset prices adjust, expected returns align with equilibrium, and arbitrage disappears.

Question 11

General rule for arbitrage portfolios?

Answer 11

Go long assets with high return-to-factor-exposure ratio and short assets with low return-to-factor-exposure ratio.

Question 12

Formula to calculate expected return using APT?

Answer 12

Expected return = risk-free rate + sum of (factor sensitivity × factor risk premium) for each factor.

Question 13

Example: If RF = 5%, β1 = 1.5, λ1 = 3%, β2 = 2, λ2 = 1.25%, what is the expected return?

Answer 13

E(R) = 5% + 1.5×3% + 2×1.25% = 12%.

Question 14

How to find factor risk premium and risk-free rate given expected returns and betas?

Answer 14

Set up equations based on expected return = RF + β × λ and solve simultaneously.

Question 15

Example: Portfolio A (7%, β=1.0), Portfolio B (7.8%, β=1.2). Find RF and λ.

Answer 15

λ = 4%, RF = 3%.

Question 16

Is Portfolio C (6.2%, β=0.8) priced correctly if RF = 3% and λ = 4%?

Answer 16

Yes, expected return = 3% + 0.8×4% = 6.2%.

Question 17

What is a multifactor model?

Answer 17

A model that assumes asset returns are driven by more than one factor.

Question 18

What are the three classifications of multifactor models?

Answer 18

1. Macroeconomic factor models 2. Fundamental factor models 3. Statistical factor models.

Question 19

What do macroeconomic factor models assume?

Answer 19

Asset returns are explained by surprises (shocks) in macroeconomic risk factors like GDP, interest rates, and inflation.

Question 20

What do fundamental factor models assume?

Answer 20

Asset returns are explained by multiple firm-specific factors like P/E ratio, market cap, and leverage ratio.

Question 21

What do statistical factor models use?

Answer 21

Statistical methods like factor analysis and principal components to explain asset returns.

Question 22

What is a major weakness of statistical factor models?

Answer 22

The factors do not lend themselves well to economic interpretation.

Question 23

In macroeconomic models, what is a factor surprise?

Answer 23

The difference between the realized value and the predicted value of a macroeconomic factor.

Question 24

Formula for a two-factor macroeconomic model?

Answer 24

Ri = E(Ri) + bi1FGDP + bi2FQS + εi.

Question 25

What does each 'b' represent in a macroeconomic model?

Answer 25

The sensitivity of the stock to a given factor surprise.

Question 26

What does firm-specific surprise (εi) capture?

Answer 26

The part of return not explained by the model, i.e., unsystematic risk.

Question 27

What are priced risk factors?

Answer 27

Systematic risks that cannot be diversified away and are compensated by the market.

Question 28

How are factor sensitivities estimated in macroeconomic models?

Answer 28

By regressing historical asset returns on historical macroeconomic factors.

Question 29

What is a fundamental factor model formula?

Answer 29

Ri = ai + bi1FP/E + bi2FSIZE + εi.

Question 30

How are sensitivities calculated in fundamental factor models?

Answer 30

They are standardized attributes, like z-scores, not regression slopes.

Question 31

How do you calculate standardized sensitivity?

Answer 31

(Attribute value - Average attribute value) / Standard deviation of attribute.

Question 32

Example: If P/E = 15.2, average P/E = 11.9, σP/E = 6.3, what is standardized sensitivity?

Answer 32

0.52.

Question 33

What are factor returns in fundamental models?

Answer 33

Returns associated with each factor, estimated from cross-sectional regressions.

Question 34

What is the intercept in fundamental factor models?

Answer 34

It has no economic meaning; it is just a regression intercept.

Question 35

Key differences: macroeconomic vs. fundamental factor models - Sensitivities?

Answer 35

Macroeconomic: estimated by regression; Fundamental: standardized from data.

Question 36

Key differences: macroeconomic vs. fundamental factor models - Interpretation of factors?

Answer 36

Macroeconomic: surprises in macro variables; Fundamental: rates of return associated with attributes.

Question 37

Key differences: macroeconomic vs. fundamental factor models - Intercept term?

Answer 37

Macroeconomic: expected return from equilibrium pricing model; Fundamental: no economic interpretation.

Question 38

What are the main uses of multifactor models?

Answer 38

Return attribution, risk attribution, and portfolio construction.

Question 39

What is active return?

Answer 39

Difference between the portfolio return (RP) and benchmark return (RB).

Question 40

How is active return decomposed?

Answer 40

Active return = Factor return + Security selection return.

Question 41

Formula for factor return?

Answer 41

Sum over all factors of (portfolio beta – benchmark beta) × factor risk premium.

Question 42

What is security selection return?

Answer 42

Active return minus factor return.

Question 43

What is active risk (tracking error)?

Answer 43

Standard deviation of active return (RP – RB).

Question 44

How is active risk decomposed?

Answer 44

Active risk squared = Active factor risk + Active specific risk.

Question 45

What is active factor risk?

Answer 45

Risk from deviations of portfolio's factor sensitivities from benchmark's sensitivities.

Question 46

What is active specific risk?

Answer 46

Risk from deviations in security weights between portfolio and benchmark.

Question 47

Formula for active specific risk?

Answer 47

Sum over all securities of (portfolio weight – benchmark weight)^2 × residual variance.

Question 48

What is a tracking portfolio?

Answer 48

A portfolio designed to match the factor exposures of a benchmark.

Question 49

What is a factor portfolio?

Answer 49

A portfolio with sensitivity of 1 to one factor and zero to all others.

Question 50

What is the Carhart four-factor model?

Answer 50

E(R) = RF + β1RMRF + β2SMB + β3HML + β4WML.

Question 51

What are the Carhart model factors?

Answer 51

Market risk (RMRF), size (SMB), value (HML), and momentum (WML).

Question 52

What does SMB represent in the Carhart model?

Answer 52

Small cap minus big cap returns.

Question 53

What does HML represent in the Carhart model?

Answer 53

High book-to-market minus low book-to-market returns.

Question 54

What does WML represent in the Carhart model?

Answer 54

Winners minus losers returns (momentum factor).

Question 55

Why consider multiple risk dimensions?

Answer 55

Helps investors choose risks they are better suited to bear and create more efficient portfolios.

Question 56

What is the information ratio (IR)?

Answer 56

Average active return divided by standard deviation of active return (tracking risk).

Question 57

Formula for information ratio?

Answer 57

IR = (Average RP – Average RB) / σ(RP – RB).

Question 58

Interpretation of a high information ratio?

Answer 58

Manager earns more active return per unit of active risk.

Question 59

Difference between IR and Sharpe ratio?

Answer 59

IR uses a benchmark portfolio return; Sharpe uses the risk-free rate.