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Portfolio Management > Using Multi-Factor Models > Flashcards

Using Multi-Factor Models Flashcards

1
Q

What is a single factor model formula and name?

A
  • 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)

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2
Q

What is the formula for arbitrage pricing model or multi-factor model for a portfolio and the different components?

A

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)

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3
Q

According to CAPM what type of risk should an investor expect compensation for?

A
  • compensation for bearing assets non-diversifiable risk/systematic risk
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4
Q

What does arbitrage pricing theory (APT) claim?

A
  • claims that expected return of an asset can be expressed as a linear function to multiple systematic risk factors priced by the market
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5
Q

What are the 3 types of multi-factor models?

A
  • macroeconomic factor models
  • statistical factor models
  • fundamental factor models
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6
Q

What is the formula for macroeconomic factor model?

A

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

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7
Q

What are 4 examples of macroeconomic factors?

A
  • inflation
  • economic growth
  • interest rates
  • exchange rates
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8
Q

What is the formula for fundamental factor models?

A

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

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9
Q

What are 4 examples of fundamental factors?

A
  • firm size
  • book to market ratio
  • P/E ratio
  • financial leverage
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10
Q

What is arbitrage?

A
  • opportunity to earn expected positive net profit without risk and with no net investment of money
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11
Q

What is the Carhart Multi Factor Model formula ?

A

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

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12
Q

What is the Carhart Multi Factor Model formula ?

A

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

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13
Q

What are the 3 assumptions of arbitrage pricing theory (APT)? ANI

A
  • 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
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14
Q

What’s the difference between variance and covariance?

A
  • 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
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15
Q

What is the difference between factor analysis models and principal component models?

A
  • 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)
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16
Q

What’s the difference between return attribution and risk attribution?

A
  • return attribution: set of techniques used to identify sources of excess return against a benchmark
  • risk attribution: sources of volatility and risk
17
Q

Which 2 asset classes benefit from low inflation and low growth?

A
  • cash
  • government bonds
18
Q

Which 3 asset classes benefit from high inflation and low growth?

A
  • inflation linked bonds
  • commodities
  • infrastructure
19
Q

Which 2 asset classes benefit from low inflation and high growth?

A
  • equity
  • corporate debt
20
Q

Which asset class benefits from high inflation and high growth?

A
  • real assets (RE, timberland, energy, etc.)
21
Q

What is active return and formula?

A
  • active return: return on portfolio above return on benchmark
  • active return = Rp - Rb

Rp: return on portfolio

Rb: return on benchmark

22
Q

What is active return and formula?

A
  • active return: return on portfolio above return on benchmark
  • active return = Rp - Rb

Rp: return on portfolio

Rb: return on benchmark

23
Q

What is active risk (aka tracking error) and formula?

A
  • 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

24
Q

What is the difference between a high tracking risk and low tracking risk, and what would be considered high and low tracking error?

A
  • 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
25
Q

What is information ratio and formula?

A
  • 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

26
Q

What are 3 main reasons multi-factor models are used for?

A
  • return attribution
  • risk attribution
  • portfolio construction
27
Q

What are 2 ways active returns are decomposed?

A
  • security selection
  • factor return
28
Q

What does security selection and factor returns arise from?

A
  • 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
29
Q

What is the factor return formula?

A

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

30
Q

What is security selection return formula?

A
  • 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

31
Q

What is active risk ^2 (aka active risk squared) and formula?

A
  • methodology used to decompose total risk of a portfolio into smaller units

-active risk ^2 = active factor risk + active specific risk

32
Q

What is the difference between active factor risk and active specific risk?

A
  • 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
33
Q

What is active factor risk and formula?

A
  • active factor risk: a portfolios deviations of weights toward factors relative to the benchmark

active factor risk = (active risk)^2 -active specific risk

34
Q

What is active specific risk and formula?

A
  • 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)

35
Q

What is a factor portfolio?

A
  • portfolio with unit sensitivity to a single factor and zero sensitivity to other factors

Portfolio Management (6 decks)

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