Multifactor Models
READING 36
USING MULTIFACTOR MODELS
EXAM FOCUS
Factor models are important in understanding risk exposures and in asset selection. Be able to construct arbitrage portfolios and be familiar with different multifactor models (and their differences), how they can be used, and their advantages over the Capital Asset Pricing Model (CAPM). Also understand the application of multifactor models to return and risk decomposition and the use of multifactor models in portfolio construction, including the use of factor portfolios in making bets on a specific risk factor.
MODULE 36.1: MULTIFACTOR MODELS
LOS 36.a: Describe arbitrage pricing theory (APT), including its underlying assumptions and its relation to multifactor models.
Arbitrage pricing theory (APT) was developed as an alternative to the CAPM. APT is a linear model with multiple systematic risk factors that are priced by the market. Unlike CAPM, APT does not specify exactly which risk factors drive returns nor does it require a particular number of factors. APT explains expected returns for well-diversified portfolios as a function of exposures to multiple systematic factors and the associated factor risk premiums.
Assumptions of Arbitrage Pricing Theory (APT)
- Unsystematic risk can be diversified away in a portfolio. Investors have access to a large number of assets so that unsystematic (asset-specific) risk can be eliminated by forming diversified portfolios. This is supported by empirical evidence.
- Returns are generated using a factor model. Asset returns follow a multifactor model. APT itself provides little guidance on which factors to use-this lack of specific factor identification is a major practical weakness.
- No arbitrage opportunities exist. An arbitrage opportunity is an investment with zero net investment, zero risk and a positive profit. If such opportunities existed, arbitrageurs would take unbounded positions and force prices to adjust immediately to equilibrium.
The asset pricing relationship implied by APT is called the arbitrage pricing model.
The APT Equation
The APT describes the equilibrium relationship between expected returns for well-diversified portfolios and their multiple sources of systematic risk.
E(RP) = RF + βP,1(λ1) + βP,2(λ2) + ... + βP,k(λk)
In this equation:
- RF is the risk-free rate.
- Each λj is the expected risk premium associated with factor j; λj is the risk premium for a pure factor portfolio that has sensitivity 1 to factor j and zero sensitivity to all other factors.
- Each βP,j is the sensitivity (beta) of portfolio P to factor j.
Each factor in the APT is priced: the factor risk premium is statistically and economically significant. Unlike CAPM, the APT does not require that one factor be the market portfolio; CAPM can be viewed as a special case of APT with one factor equal to market return.
PROFESSOR'S NOTE
The CAPM can be considered a special restrictive case of the APT in which there is only one risk factor and that factor is the market portfolio.
LOS 36.b: Define arbitrage opportunity and determine whether an arbitrage opportunity exists.
The APT framework describes how arbitrage opportunities can be exploited by forming long and short portfolios so that the net exposure to systematic factors is zero while earning a positive net return.
EXAMPLE: Exploiting an arbitrage opportunity
Suppose your investment firm uses a single-factor model to evaluate assets. Consider the following data for Portfolios A, B, and C:
Calculate the arbitrage opportunity from the data provided.
Answer:
By allocating 50% of our funds to Portfolio A and 50% to Portfolio B, we can obtain a Portfolio (D) with beta equal to the Portfolio C beta (1.5):
Beta for Portfolio D = 0.5(1) + 0.5(2) = 1.5
While the betas for Portfolios D and C are identical, the expected returns are different:
Expected return for Portfolio D = 0.5(0.10) + 0.5(0.20) = 0.15 = 15%
Therefore, we have created Portfolio D that has the same risk as Portfolio C (beta = 1.5) but has a higher expected return than Portfolio C (15% versus 13%). By purchasing Portfolio D and short-selling Portfolio C, we expect to earn a 2% return (15% - 13%).
PROFESSOR'S NOTE
Recall that a portfolio beta equals the weighted average of the individual asset betas, and, likewise, the portfolio expected return equals the weighted average of the individual asset expected returns.
The portfolio that is long Portfolio D and short Portfolio C is called the arbitrage portfolio. We have invested nothing upfront because we use proceeds of the short sale on Portfolio C to buy Portfolio D, and we have undertaken no net systematic risk. The overall beta of our investment equals the difference in betas between our long and short positions: 1.5 - 1.5 = 0. As investors exploit the arbitrage opportunity, prices of assets in Portfolio C will drop and the expected return for Portfolio C will rise to its equilibrium value.
PROFESSOR'S NOTE
Generally, we want to go long assets that have a high ratio of return per unit of factor exposure, and short assets that have a low return-to-factor-exposure ratio.
The APT assumes there are no market imperfections that prevent investors from exploiting arbitrage opportunities. Consequently, extreme long and short positions are permitted and mispricing disappears immediately; arbitrage opportunities are eliminated promptly.
LOS 36.c: Calculate the expected return on an asset given an asset's factor sensitivities and the factor risk premiums.
Given a portfolio's factor exposures (betas) and factor risk premiums, compute the portfolio's expected return using the APT formula.
EXAMPLE: Calculating expected returns from the arbitrage pricing model
An investment firm employs a two-factor APT model. The risk-free rate equals 5%. Determine the expected return for the Invest Fund using the following data:
Answer:
Using the two-factor APT model, the expected return for the Invest Fund (IF) equals:
E(RIF) = 0.05 + 1.5(0.03) + 2(0.0125) = 0.12 = 12%
We can also use factor models to compute parameter values given expected returns and factor exposures.
EXAMPLE: Calculating APT parameters given expected returns
Given a one-factor model and the following information, calculate the risk-free rate and the factor risk premium.
Verify that Portfolio C with an expected return of 6.2% and factor sensitivity of 0.8 is priced correctly.
Answer:
Expected return = risk-free rate + factor sensitivity × risk premium
Therefore, given the information for portfolios A and B:
0.07 = Rf + 1.0 × λ; Rf = 0.07 - λ
Substituting this information for Portfolio B:
0.078 = (0.07 - λ) + 1.2λ;
λ = 0.04 or 4%
Rf = 0.07 - λ = 0.07 - 0.04 = 0.03 or 3%
Expected return for Portfolio C = 0.03 + (0.8 × 0.04) = 6.2%. Hence, Portfolio C is correctly priced.
MODULE QUIZ 36.1
1. Which of the following least accurately identifies an assumption made by the APT?
A. Asset returns are described by a factor model.
B. Unsystematic risk can be diversified away.
C. Arbitrage will force risk premiums on systematic risk to be zero.
2. Eileen Bates, CFA has collected information on the following three portfolios:
An arbitrage strategy would most likely involve a short position in which portfolio?
A. Portfolio A.
B. Portfolio B.
C. Portfolio C.
3. Catalyst Fund uses a two-factor model to analyze asset returns.
Given that the risk-free rate equals 5%, the expected return for the stock A is closest to:
A. 4.2%.
B. 8.7%.
C. 9.2%.
MODULE 36.2: MACROECONOMIC FACTOR MODELS, FUNDAMENTAL FACTOR MODELS, AND STATISTICAL FACTOR MODELS
LOS 36.d: Describe and compare macroeconomic factor models, fundamental factor models, and statistical factor models.
The CAPM can be described as a one-factor model because it assumes returns are explained by the market portfolio. Multifactor models assume returns are driven by more than one factor. There are three broad classifications:
- Macroeconomic factor models: Asset returns are explained by surprises (or "shocks") in macroeconomic variables such as GDP growth, interest rates, and inflation. A factor surprise is the realized value minus the consensus expected value.
- Fundamental factor models: Asset returns are explained by multiple firm-specific characteristics such as P/E ratio, market capitalisation, leverage, and earnings growth.
- Statistical factor models: Factors are derived using multivariate statistical methods. Two common approaches are factor analysis and principal component analysis (PCA). In factor analysis, factors explain covariance among returns; in PCA, factors explain variance. A major weakness of statistical factors is limited economic interpretability-these are often called "mystery factors".
Because macroeconomic and fundamental models are widely used, the following sections expand on each.
MACROECONOMIC FACTOR MODELS
A typical two-factor macroeconomic model might explain stock returns from surprises in GDP growth and credit quality spreads. A generic form is:
Ri = E(Ri) + bi,1 · F1 + bi,2 · F2 + ... + εi
In this equation:
- Each F is a factor surprise (realised minus expected).
- Each b is the sensitivity of the asset to that surprise.
- The firm-specific surprise εi captures unsystematic risk (company-specific events like strikes or fires).
EXAMPLE: Compute a stock return using a macroeconomic factor model
The two-factor model for Media Tech (MT) is given as:
RMT = E(RMT) + bMT,1 · FGDP + bMT,2 · FQS + εMT
The expected return for Media Tech equals 10%. Over the past year, GDP grew 2 percentage points higher than expected, and the quality spread was 1 percentage point lower than expected. Media Tech's sensitivity to GDP equals 2, and its sensitivity to quality spread equals -0.5. Over the past year, Media Tech also experienced a 2% company-unique surprise return. Construct the model and calculate the return for the year.
Answer:
The two-factor model for Media Tech is:
RMT = 0.10 + 2 · (+0.02) + (-0.5) · (-0.01) + 0.02
Calculate each term:
2 · (+0.02) = +0.04
(-0.5) · (-0.01) = +0.005
Now sum the components:
RMT = 0.10 + 0.04 + 0.005 + 0.02 = 0.165 = 16.5%
The Media Tech return was higher than originally expected because MT benefited from stronger-than-expected GDP growth, a narrower-than-expected credit quality spread, and a positive company-specific surprise.
PROFESSOR'S NOTE
Be careful with signs. A decrease in the quality spread is good news for MT if MT has a negative sensitivity to that factor. When credit quality spreads increase, MT's return falls; when credit quality spreads decrease, MT's return rises.
Priced Risk Factors
Systematic factors affect many assets and cannot be diversified away; therefore, they are priced-investors expect compensation for exposure to them. Unsystematic risks that affect only a few assets are diversifiable and are not priced in equilibrium.
Factor Sensitivities
Different assets have different sensitivities to macroeconomic surprises. Sensitivities are typically estimated by regressing historical asset returns on historical macroeconomic surprises. For example, retail stocks are usually more sensitive to GDP surprises than grocery chains, because retail spending depends more on income.
FUNDAMENTAL FACTOR MODELS
A typical fundamental factor model has the form:
Ri = ai + bi1 · F1 + bi2 · F2 + ... + εi
In fundamental models, the sensitivities are often standardised attributes (e.g., z-scores) rather than regression slopes. Standardisation allows mixing of variables measured in different units (for example, P/E ratios versus dividend yields).
Standardised sensitivities
The standardised sensitivity for P/E is calculated as:
Standardised sensitivity = (P/Ei - mean(P/E)) / stddev(P/E)
This measures how many standard deviations a firm's attribute is from the mean. For example, a sensitivity of 2.0 means the firm is two standard deviations above the mean.
EXAMPLE: Calculating a standardised sensitivity
The P/E for stock i is 15.20, the average P/E is 11.90 and the standard deviation is 6.30. Calculate the standardised sensitivity.
Answer:
Standardised sensitivity = (15.20 - 11.90) / 6.30
Standardised sensitivity = 3.30 / 6.30 = 0.5238 ≈ 0.52
Therefore, the stock's P/E is 0.52 standard deviations above the average.
Factor returns (e.g., FP/E, FSIZE) are the returns associated with factor portfolios (for example, the return difference between low and high P/E stocks). In practice, factor returns are estimated as slopes from cross-sectional regressions where dependent variables are stock returns and independent variables are standardised sensitivities.
Intercept term (ai) In a fundamental factor regression, factors are not surprises and generally have non-zero expected values. The regression intercept is not interpreted as expected return from equilibrium; it is simply the intercept required by the regression.
The macroeconomic model vs the fundamental model
- Sensitivities: In fundamental models the standardized sensitivities are computed directly from attributes and are not regression slopes. In macroeconomic models sensitivities are typically estimated regression slopes.
- Interpretation of factors: Macroeconomic factors are surprises; fundamental factors are factor returns (estimated rates of return associated with firm attributes).
- Intercept term: In macroeconomic models the intercept equals the asset's expected return (given consensus expectations for macro variables); in fundamental models the intercept has no economic interpretation beyond the regression intercept.
MODULE QUIZ 36.2
1. Jones Brothers uses a two-factor macroeconomic factor model to evaluate stocks and has derived the following results for the stock of AmGrow (AG):
Expected return: 10%
GDP factor sensitivity: 2
Inflation factor sensitivity: -0.5
Over the past year, GDP grew at a rate that was two percentage points lower than expected, and inflation rose two percentage points higher than expected. AG also experienced a large unexpected product recall causing a firm-unique surprise of -4% to its stock price. Based on the information provided, the rate of return for AG for the year was closest to:
A. 1%.
B. 2%.
C. 3%.
MODULE 36.3: MULTIFACTOR MODEL RISK AND RETURN
LOS 36.e: Describe uses of multifactor models and interpret the output of analyses based on multifactor models.
Multifactor models are useful for return attribution, risk attribution, and portfolio construction.
Return Attribution
Active return equals the difference between a managed portfolio and its benchmark:
Active return = RP - RB
Active return can be decomposed into:
- Factor return: Return from taking different factor exposures than the benchmark (factor tilts).
- Security selection return: Return from selecting specific securities with different weights than in the benchmark.
Security selection return equals:
security selection return = active return - factor return
EXAMPLE: Return decomposition
Glendale Pure Alpha Fund returned 11.2% while the benchmark returned 11.8% over 12 months. Given a two-factor fundamental factor model, attribute the cause of the difference and describe the manager's skill.
Answer:
Difference between portfolio return and benchmark return = 11.20% - 11.80% = -0.60%
Return from factor tilts (computed previously) = -1.16%
Return from security selection = -0.60% - (-1.16%) = +0.56%
The manager's factor bets cost -1.16% relative to the benchmark, but security selection added +0.56%, giving a net active return of -0.60%.
Risk Attribution
Active risk (tracking error) is the standard deviation of active return:
Active risk = σ(RP - RB)
Active risk (variance) can be decomposed into:
active risk squared = active factor risk + active specific risk
- Active factor risk: Risk from deviations in factor exposures relative to benchmark.
- Active specific risk: Risk from idiosyncratic asset weight differences after controlling for factor differences.
Active factor risk is computed as the residual:
active factor risk = active risk squared - active specific risk
Examples:
- Active factor risk: overweighting a particular industry versus the benchmark changes industry factor sensitivities and contributes to active factor risk.
- Active specific risk: overweighting a particular stock within an industry contributes active specific risk even if industry exposures match the benchmark.
EXAMPLE: Risk decomposition
Steve Martingale, CFA, analyses three actively managed funds with a two-factor model. The risk decomposition results are shown in a table. Questions:
1. Which fund assumes the highest level of active risk?
2. Which fund assumes the highest level of style factor risk as a proportion of active risk?
3. Which fund assumes the highest level of size factor risk as a proportion of active risk?
4. Which fund assumes the lowest level of active specific risk as a proportion of active risk?
Answer:
The proportional contributions of various sources of active risk are computed as each source divided by total active risk squared. For example, style factor contribution for the Alpha fund = 12.22 / 21.69 = 56%.
1. The Gamma fund has the highest level of active risk (6.1%).
2. The Alpha fund has the highest exposure to style factor risk (56% of active risk).
3. The Gamma fund has the highest exposure to size factor risk (47% of active risk).
4. The Alpha fund has the lowest exposure to active specific risk (15% of active risk).
Uses of Multifactor Models
Multifactor models are useful for:
- Passive management: Constructing tracking portfolios intended to match benchmark factor exposures.
- Active management: Making directional bets on specific factors while remaining neutral to others using factor portfolios. A factor portfolio has sensitivity 1 to one factor and 0 to other factors; it is useful for speculation or hedging.
- Rules-based/algorithmic strategies: Mechanically tilting factor exposures to construct alternative indices or systematic strategies.
Carhart Model
The Carhart four-factor model extends the Fama-French three-factor model by adding momentum to market, size and value factors. The four Carhart factors typically are:
- RMRF - market excess return
- SMB - size (small minus big)
- HML - value (high book-to-market minus low)
- WML - momentum (winners minus losers)
EXAMPLE: Factor portfolios
Sam Porter evaluates three portfolios with exposures to the four Carhart factors. Which strategy is most appropriate if the manager expects:
1. RMRF will be higher than expected.
2. Large-cap stocks will outperform small-cap stocks.
Answer:
1. The manager would go long the Eridanus portfolio because it is constructed to have exposure only to RMRF; it is a pure bet on market risk.
2. Expecting large-cap outperformance implies shorting a pure SMB factor portfolio (i.e., go short on a portfolio like Scorpius that is a pure bet on SMB) because SMB is small minus big; shorting it expresses a view that big will outperform small.
LOS 36.f: Describe the potential benefits for investors in considering multiple risk dimensions when modeling asset returns.
Under CAPM, investors combine the market portfolio and the risk-free asset depending on risk tolerance. Multifactor models incorporate additional risk dimensions, allowing investors to:
- Target risks they have a comparative advantage in bearing (for example, a long-term pension fund may accept liquidity risk for a liquidity premium).
- Better describe actual return drivers when multiple factors matter, which may lead to more efficient portfolio selection.
LOS 36.g: Explain sources of active risk and interpret tracking risk and the information ratio.
The Information Ratio
Active return by itself does not show consistency. Two managers can have the same average active return but very different volatility of active returns. The information ratio (IR) measures average active return relative to its volatility:
Information ratio = average active return / tracking risk
Tracking risk is the standard deviation of active return over the evaluation period.
EXAMPLE: Calculating the information ratio
Imagine the portfolio and benchmark returns for twelve months are given in a table. Using the monthly active returns, compute the average active return and the standard deviation of active returns (tracking risk). Then compute the information ratio.
Answer:
The higher the IR, the more active return the manager earned per unit of active risk. For example, an IR of 0.27 indicates roughly 27 basis points of active return per 1% of active risk.
PROFESSOR'S NOTE
The information ratio is analogous to the Sharpe ratio. The Sharpe ratio uses the risk-free rate as the benchmark and uses the standard deviation of total portfolio returns in the denominator; the IR uses a portfolio benchmark and the standard deviation of active returns in the denominator.
MODULE QUIZ 36.3
1. A multifactor model to evaluate style and size exposures (e.g., large cap value) of different mutual funds would be most appropriately called a:
A. systematic factor model.
B. fundamental factor model.
C. macroeconomic factor model.
2. A portfolio that has the same factor sensitivities as the S&P 500, but does not hold all 500 stocks in the index, is best described as a:
A. factor portfolio.
B. tracking portfolio.
C. market portfolio.
3. A portfolio with a factor sensitivity of one to the yield spread factor and a sensitivity of zero to all other macroeconomic factors is best described as a:
A. factor portfolio.
B. tracking portfolio.
C. market portfolio.
4. Factor Investment Services, LLC manages a tracking portfolio that claims to outperform the S&P 500. The active factor risk and active specific risk for the tracking portfolio are most likely to be described as:
A. high active factor risk and high active specific risk.
B. high active factor risk and low active specific risk.
C. low active factor risk and high active specific risk.
5. Relative to the CAPM, the least likely advantage of multifactor models is that multifactor models help investors to:
A. target risks that the investor has a comparative advantage in bearing.
B. select an appropriate proportion of the portfolio to allocate to the market portfolio.
C. assemble more efficient and better diversified portfolios.
KEY CONCEPTS
LOS 36.a
The arbitrage pricing theory (APT) describes the equilibrium relationship between expected returns for well-diversified portfolios and their multiple sources of systematic risk. APT makes three key assumptions:
- Unsystematic risk can be diversified away in a portfolio.
- Returns are generated using a factor model.
- No arbitrage opportunities exist.
LOS 36.b
An arbitrage opportunity is an investment that bears no risk and has no cost but yields a positive profit. Arbitrage is implemented by forming long and short portfolios financed by short sale proceeds; factor sensitivities of the long and short positions are equal so net systematic exposure is zero and the difference in returns is the arbitrage return.
LOS 36.c
Expected return = risk-free rate + ∑ (factor sensitivity) × (factor risk premium)
LOS 36.d
A multifactor model extends the one-factor market model by incorporating multiple factors. The three types of multifactor models are:
- Macroeconomic factor models: use surprises in macro variables.
- Fundamental factor models: use firm-specific attributes and returns on attribute-based factor portfolios.
- Statistical factor models: use statistical methods (factor analysis, PCA) to identify factors explaining covariation in returns; factors may lack economic interpretation.
LOS 36.e
Multifactor models are useful for return attribution (splitting active return into factor return and security selection return) and risk attribution (decomposing active risk into active factor risk and active specific risk).
active risk squared = active factor risk + active specific risk
active factor risk = active risk squared - active specific risk
Multifactor models also support portfolio construction: passive managers use tracking portfolios; active managers use factor portfolios for bets or hedges. A factor portfolio has sensitivity 1 to a single factor and zero to others; a tracking portfolio has a specified set of factor sensitivities that match a benchmark.
LOS 36.f
Multifactor models allow investors to target risks they can bear and avoid those they cannot, and they often explain returns better than single-factor CAPM models, enabling improved portfolio efficiency.
LOS 36.g
Active return is RP - RB. Active risk is the standard deviation of active return. Active risk is driven by active factor tilts and active asset selection. The information ratio is active return divided by active risk.
ANSWER KEY FOR MODULE QUIZZES
Module Quiz 36.1
1.
C The assumptions of APT include (1) unsystematic risk can be diversified away in a portfolio, (2) returns can be explained by a factor model, and (3) no arbitrage opportunities exist. However, arbitrage does not cause the risk premium for systematic risk to be zero. ((<>)LOS 36.a)
2.
C An arbitrage portfolio comprises long and short positions such that the net return is positive yet the net factor sensitivity is zero. In this question, the low expected return of Portfolio C per unit of factor sensitivity indicates that Portfolio C should be shorted. Suppose that we arbitrarily assign Portfolio C a 100% short weighting and, furthermore, we assign a weighting of w to Portfolio A and a weighting of (1 - w) to Portfolio B. Because the weighted sum of long and short factor sensitivities must be equal, we develop the following equation: w × 1.20 + (1 - w) × 2.00 = 1.00 × 1.76. Solving algebraically for w gives a 30% long weight on Portfolio A, a 70% long weight on Portfolio B, and a 100% short weight on Portfolio C. The factor sensitivity of this portfolio will be (0.3)(1.20) + (0.7)(2.0) - (1)(1.76) = 0. The expected return on this zero risk, zero investment portfolio will be (0.3)(10) + (0.7)(20) - (1)(13) = 4%. ((<>)LOS 36.b)
LOS 36.c
3. B Using the two-factor APT model, the expected return for stock A equals:
E(RIF) = 0.05 + (0.88) × (0.03) + (1.10) × (0.01) = 0.0874 = 8.74%
Module Quiz 36.2
1.
A The two-factor model for AG is:
RAG = 0.10 + 2(-0.02) + (-0.5)(0.02) + (-0.04) = 0.01 = 1%
The AG return was less than originally expected because AG was hurt by lower-than-expected economic growth (GDP), higher-than-expected inflation, and a negative company-specific surprise. ((<>)LOS 36.d)
Module Quiz 36.3
1.
B Style (e.g., value versus growth) can be evaluated based on company-specific fundamental variables such as P/E or P/B ratio. Size is generally proxied by market capitalisation. A fundamental factor model is appropriate when the underlying variables are company-specific. ((<>)LOS 36.e)
2.
B A tracking portfolio is a portfolio with a specific set of factor sensitivities. Tracking portfolios are often designed to replicate the factor exposures of a benchmark index like the S&P 500-in fact, a factor portfolio is just a special case of a tracking portfolio. One use of tracking portfolios is to attempt to outperform the S&P 500 by using the same factor exposures as the S&P 500 but with a different set of securities than the S&P 500. ((<>)LOS 36.e)
3.
A A factor portfolio is a portfolio with a factor sensitivity of 1 to a particular factor and zero to all other factors. It represents a pure bet on that factor. For example, a portfolio manager who believes GDP growth will be greater than expected, but has no view of future interest rates and wants to hedge away the interest rate risk in her portfolio, could create a factor portfolio that is only exposed to the GDP factor and not exposed to the interest rate factor. (LOS 36.e)
4.
C A tracking portfolio is deliberately constructed to have the same set of factor exposures to match (track) a predetermined benchmark. The strategy involved in constructing a tracking portfolio is usually an active bet on asset selection (the manager claims to beat the S&P 500). The manager constructs the portfolio to have the same factor exposures as the benchmark, but then selects superior securities (subject to the factor sensitivities constraint), thus outperforming the benchmark without taking on more systematic risk than the benchmark. Therefore, a tracking portfolio, with active asset selection but with factor sensitivities that match those of the benchmark, will have little or no active factor risk, but will have high active specific risk. ((<>)LOS 36.e)
5.
B Multifactor models enable investors to zero in on risks that the investor has a comparative advantage in bearing and avoid the risks that the investor is unable to take on. Multifactor models are preferred over single-factor models like CAPM in cases where the underlying asset returns are better described by multifactor models. Allocation of an investor's portfolio between the market portfolio and the risk-free asset is part of CAPM, not multifactor models. (LOS 36.f)
