Using Multi-Factor Models Flashcards
What is a single factor model formula and name?
- CAPM
- E (Rp) = Rf + B * (Rm - Rf)
E (Rp) = Expected return of portfolio/security
Rf = risk-free rate
B = beta (sensitivity of asset/portfolio to market risk)
Rm = expected return of market
equity risk premium = (Rm-Rf)
What is the formula for arbitrage pricing model or multi-factor model for a portfolio and the different components?
E (Rp) = Rf + (Bp1 * J1) + (Bp2 * J2)….
E (Rp) = expected return of portfolio
Rf = risk free rate
Bp = sensitivity of portfolio to the factor
J = number of factors and expected reward for bearing risk (aka factor risk premium)
According to CAPM what type of risk should an investor expect compensation for?
- compensation for bearing assets non-diversifiable risk/systematic risk
What does arbitrage pricing theory (APT) claim?
- claims that expected return of an asset can be expressed as a linear function to multiple systematic risk factors priced by the market
What are the 3 types of multi-factor models?
- macroeconomic factor models
- statistical factor models
- fundamental factor models
What is the formula for macroeconomic factor model?
Ri = E (Ri) + (bi1 * F1) + (bi2 * F2) + ei
Ri = return on asset
E (Ri) = expected return on asset
bi = difference in surprise sensitivities of asset
F = difference in surprise in factors
ei = firm specific surprise, which is unrelated to macro factors p
P
What are 4 examples of macroeconomic factors?
- inflation
- economic growth
- interest rates
- exchange rates
What is the formula for fundamental factor models?
Ri = ai + (Bi1 * F1) + (Bi2 * F2) + ei
Ri = return of stock
ai = intercept
Bi = standardized sensitivities for stock to factor
F = returns for factor
ei = portion of stock return not explained by factor model
What are 4 examples of fundamental factors?
- firm size
- book to market ratio
- P/E ratio
- financial leverage
What is arbitrage?
- opportunity to earn expected positive net profit without risk and with no net investment of money
What is the Carhart Multi Factor Model formula ?
Rp - Rf = ap + (bp1 * RMRF) + (bp2 * SMB) + (bp3 * HML) + (bp4 * WML) + ep
Rp & Rf = return portfolio & risk free rate
ap = alpha or return of portfolio in excess of expected given portfolio level of systematic risk
bp = sensitivity of portfolio to given factor
RMRF = value weighted equity index return in excess of one-month T-Bill
SMB = average return on 3 small cap portfolios - average return on 3 large cap portfolios (aka small minus big cap)
HML = average return on 2 high book-to-market portfolios - average return on 2 low book-to-market portfolios (aka high minus low)
WML = return on portfolios past year winners - return on portfolios past year losers (aka momentum factor)
ep = error term, portion of return to portfolio not explained by the model
What is the Carhart Multi Factor Model formula ?
Rp - Rf = ap + (bp1 * RMRF) + (bp2 * SMB) + (bp3 * HML) + (bp4 * WML) + ep
Rp & Rf = return portfolio & risk free rate
ap = alpha or return of portfolio in excess of expected given portfolio level of systematic risk
bp = sensitivity of portfolio to given factor
RMRF = value weighted equity index return in excess of one-month T-Bill
SMB = average return on 3 small cap portfolios - average return on 3 large cap portfolios (aka small minus big cap)
HML = average return on 2 high book-to-market portfolios - average return on 2 low book-to-market portfolios (aka high minus low)
WML = return on portfolios past year winners - return on portfolios past year losers (aka momentum factor)
ep = error term, portion of return to portfolio not explained by the model
What are the 3 assumptions of arbitrage pricing theory (APT)? ANI
- asset returns can be explained using systematic factors
- no arbitrage opportunities exist in well diversified portfolios
- investors can eliminate specific risks from portfolios through diversification
What’s the difference between variance and covariance?
- variance: the spread of a data set or how far each number in a data set is from the average value or mean
- covariance: the measure of the directional relationship between two random variable speed
What is the difference between factor analysis models and principal component models?
- factor analysis models: factors that best explain historical covariances (aka direction)
- principal component models: factors that best explain historical variances (aka why it didn’t perform as well as the average value)
What’s the difference between return attribution and risk attribution?
- return attribution: set of techniques used to identify sources of excess return against a benchmark
- risk attribution: sources of volatility and risk
Which 2 asset classes benefit from low inflation and low growth?
- cash
- government bonds
Which 3 asset classes benefit from high inflation and low growth?
- inflation linked bonds
- commodities
- infrastructure
Which 2 asset classes benefit from low inflation and high growth?
- equity
- corporate debt
Which asset class benefits from high inflation and high growth?
- real assets (RE, timberland, energy, etc.)
What is active return and formula?
- active return: return on portfolio above return on benchmark
- active return = Rp - Rb
Rp: return on portfolio
Rb: return on benchmark
What is active return and formula?
- active return: return on portfolio above return on benchmark
- active return = Rp - Rb
Rp: return on portfolio
Rb: return on benchmark
What is active risk (aka tracking error) and formula?
- active risk: standard deviation of returns, or how much return for given amount of risk
- active risk = S (Rp - Rb)
S = sample standard deviation of the difference between return of portfolio & benchmark
Rp = return of portfolio
Rb = return of benchmark
What is the difference between a high tracking risk and low tracking risk, and what would be considered high and low tracking error?
- low tracking risk: portfolio is closely following the benchmark
- high tracking risk: portfolio is volatile relative to the benchmark and moving away from benchmark
- 0-2 is low tracking risk
- 2 or more is high tracking risk
What is information ratio and formula?
- information ratio: managers ability to earn excess returns after taking volatility into account (mean active returns per unit of active risk)
- information ratio: (average Rp - average Rb) / S (Rp - Rb)
average Rp: average return of portfolio
average Rb: average return of benchmark
S: standard deviation of the difference in returns
Rp: return of portfolio
Rb: return of benchmark
S (Rp-Rb): tracking error
What are 3 main reasons multi-factor models are used for?
- return attribution
- risk attribution
- portfolio construction
What are 2 ways active returns are decomposed?
- security selection
- factor return
What does security selection and factor returns arise from?
- security selection: arises from managers choice of different weights for specific securities compared to those in the benchmark
- factor return:. arises from managers decision to take on factor exposures different from those of a benchmark
What is the factor return formula?
Factor return = (Bpi - Bbi) * Fi
Bpi = factor sensitivity for factor i in active portfolio
Bbi = factor sensitivity for factor i in benchmark portfolio
Fi = factor risk premium for factor i
What is security selection return formula?
- security selection return = active return - factor return
active return: Rp (return of portfolio) - Rb (return of benchmark)
factor return: (Bpi - Bbi) Fi
Bpi = factor sensitivity for factor i in active portfolio
Bbi = factor sensitivity for factor i in benchmark portfolio
Fi = factor risk premium for factor i
What is active risk ^2 (aka active risk squared) and formula?
- methodology used to decompose total risk of a portfolio into smaller units
-active risk ^2 = active factor risk + active specific risk
What is the difference between active factor risk and active specific risk?
- active factor risk: a portfolios deviations or weights toward factors relative to the benchmark
- active specific risk: a portfolios weight towards individual assets relative to the benchmark
What is active factor risk and formula?
- active factor risk: a portfolios deviations of weights toward factors relative to the benchmark
active factor risk = (active risk)^2 -active specific risk
What is active specific risk and formula?
- active specific risk: a portfolios weight towards individual assets relative to the benchmark
active specific risk = ((Wpi - Wbi)^2 ) standard deviation^2 ei
Wpi = Weight of asset in portfolio
Wbi = Weight of asset in benchmark
standard deviation^2 ei = residual risk in asset unexplained by factors (aka the error term)
What is a factor portfolio?
- portfolio with unit sensitivity to a single factor and zero sensitivity to other factors
