Porfolio part 4 Flashcards
What is Arbitrage Pricing Theory (APT)?
A linear model with multiple systematic risk factors priced by the market; alternative to CAPM.
List assumptions of APT.
- Unsystematic risk can be diversified away, 2. Returns are generated by a factor model, 3. No arbitrage opportunities exist.
What is the APT Equation?
E(RP) = RF + βP,1(λ1) + βP,2(λ2) + … + βP,k(λk); β = factor sensitivity, λ = factor risk premium.
What is a pure factor portfolio in APT?
A portfolio with sensitivity of 1 to one factor and 0 to all other factors.
What is a major advantage of APT over CAPM?
APT does not require the market portfolio as a factor.
How is CAPM related to APT?
CAPM is a restrictive case of APT with only one factor: the market factor.
What is an arbitrage opportunity?
A risk-free, costless profit opportunity that should not exist in efficient markets.
How do you exploit an arbitrage opportunity?
Construct a portfolio with the same risk (factor exposures) but higher expected return; go long the better return and short the underperformer.
How to calculate portfolio beta?
Beta of a portfolio is the weighted average of the individual asset betas.
In APT, what happens when arbitrage opportunities are exploited?
Asset prices adjust, expected returns align with equilibrium, and arbitrage disappears.
General rule for arbitrage portfolios?
Go long assets with high return-to-factor-exposure ratio and short assets with low return-to-factor-exposure ratio.
Formula to calculate expected return using APT?
Expected return = risk-free rate + sum of (factor sensitivity × factor risk premium) for each factor.
Example: If RF = 5%, β1 = 1.5, λ1 = 3%, β2 = 2, λ2 = 1.25%, what is the expected return?
E(R) = 5% + 1.5×3% + 2×1.25% = 12%.
How to find factor risk premium and risk-free rate given expected returns and betas?
Set up equations based on expected return = RF + β × λ and solve simultaneously.
Example: Portfolio A (7%, β=1.0), Portfolio B (7.8%, β=1.2). Find RF and λ.
λ = 4%, RF = 3%.
Is Portfolio C (6.2%, β=0.8) priced correctly if RF = 3% and λ = 4%?
Yes, expected return = 3% + 0.8×4% = 6.2%.
What is a multifactor model?
A model that assumes asset returns are driven by more than one factor.
What are the three classifications of multifactor models?
- Macroeconomic factor models 2. Fundamental factor models 3. Statistical factor models.
What do macroeconomic factor models assume?
Asset returns are explained by surprises (shocks) in macroeconomic risk factors like GDP, interest rates, and inflation.
What do fundamental factor models assume?
Asset returns are explained by multiple firm-specific factors like P/E ratio, market cap, and leverage ratio.
What do statistical factor models use?
Statistical methods like factor analysis and principal components to explain asset returns.
What is a major weakness of statistical factor models?
The factors do not lend themselves well to economic interpretation.
In macroeconomic models, what is a factor surprise?
The difference between the realized value and the predicted value of a macroeconomic factor.
Formula for a two-factor macroeconomic model?
Ri = E(Ri) + bi1FGDP + bi2FQS + εi.
What does each ‘b’ represent in a macroeconomic model?
The sensitivity of the stock to a given factor surprise.
What does firm-specific surprise (εi) capture?
The part of return not explained by the model, i.e., unsystematic risk.
What are priced risk factors?
Systematic risks that cannot be diversified away and are compensated by the market.
How are factor sensitivities estimated in macroeconomic models?
By regressing historical asset returns on historical macroeconomic factors.
What is a fundamental factor model formula?
Ri = ai + bi1FP/E + bi2FSIZE + εi.
How are sensitivities calculated in fundamental factor models?
They are standardized attributes, like z-scores, not regression slopes.
How do you calculate standardized sensitivity?
(Attribute value - Average attribute value) / Standard deviation of attribute.
Example: If P/E = 15.2, average P/E = 11.9, σP/E = 6.3, what is standardized sensitivity?
0.52.
What are factor returns in fundamental models?
Returns associated with each factor, estimated from cross-sectional regressions.
What is the intercept in fundamental factor models?
It has no economic meaning; it is just a regression intercept.
Key differences: macroeconomic vs. fundamental factor models - Sensitivities?
Macroeconomic: estimated by regression; Fundamental: standardized from data.
Key differences: macroeconomic vs. fundamental factor models - Interpretation of factors?
Macroeconomic: surprises in macro variables; Fundamental: rates of return associated with attributes.
Key differences: macroeconomic vs. fundamental factor models - Intercept term?
Macroeconomic: expected return from equilibrium pricing model; Fundamental: no economic interpretation.
What are the main uses of multifactor models?
Return attribution, risk attribution, and portfolio construction.
What is active return?
Difference between the portfolio return (RP) and benchmark return (RB).
How is active return decomposed?
Active return = Factor return + Security selection return.
Formula for factor return?
Sum over all factors of (portfolio beta – benchmark beta) × factor risk premium.
What is security selection return?
Active return minus factor return.
What is active risk (tracking error)?
Standard deviation of active return (RP – RB).
How is active risk decomposed?
Active risk squared = Active factor risk + Active specific risk.
What is active factor risk?
Risk from deviations of portfolio’s factor sensitivities from benchmark’s sensitivities.
What is active specific risk?
Risk from deviations in security weights between portfolio and benchmark.
Formula for active specific risk?
Sum over all securities of (portfolio weight – benchmark weight)^2 × residual variance.
What is a tracking portfolio?
A portfolio designed to match the factor exposures of a benchmark.
What is a factor portfolio?
A portfolio with sensitivity of 1 to one factor and zero to all others.
What is the Carhart four-factor model?
E(R) = RF + β1RMRF + β2SMB + β3HML + β4WML.
What are the Carhart model factors?
Market risk (RMRF), size (SMB), value (HML), and momentum (WML).
What does SMB represent in the Carhart model?
Small cap minus big cap returns.
What does HML represent in the Carhart model?
High book-to-market minus low book-to-market returns.
What does WML represent in the Carhart model?
Winners minus losers returns (momentum factor).
Why consider multiple risk dimensions?
Helps investors choose risks they are better suited to bear and create more efficient portfolios.
What is the information ratio (IR)?
Average active return divided by standard deviation of active return (tracking risk).
Formula for information ratio?
IR = (Average RP – Average RB) / σ(RP – RB).
Interpretation of a high information ratio?
Manager earns more active return per unit of active risk.
Difference between IR and Sharpe ratio?
IR uses a benchmark portfolio return; Sharpe uses the risk-free rate.
