Asset-Pricing and Factor Models

Introduction and Context

Investment decisions require more than estimating whether an asset will rise or fall. A professional investor must determine what compensation is justified for bearing risk, distinguish systematic exposure from security-specific information, and evaluate whether a manager’s return reflects skill or merely exposure to common risk factors. Asset-pricing models provide structured ways to perform this analysis.

The Capital Asset Pricing Model (CAPM) links an asset’s expected return to its exposure to market risk. The security market line (SML) converts this relationship into a practical benchmark for assessing expected returns. Alpha measures performance unexplained by the chosen benchmark, while beta measures sensitivity to systematic risk. Arbitrage Pricing Theory (APT) and multifactor models generalize the CAPM by allowing several economic or empirical sources of risk. Modern investment practice commonly examines size, value, momentum, quality, low-volatility and macroeconomic factors.

These models are not mechanical truth machines. They depend on assumptions, measurement choices, sample periods and portfolio-construction methods. Their professional value lies in disciplined analysis: identifying exposures, estimating risks, constructing expected-return benchmarks and testing whether apparent skill survives appropriate controls.

Learning Objectives

After completing this chapter, the reader should be able to:

1. Explain the logic, assumptions and implications of CAPM.
2. Calculate and interpret beta, expected return, alpha and the security market line.
3. Distinguish systematic risk from diversifiable risk.
4. Explain APT and compare it with CAPM.
5. Evaluate size, value, momentum, quality, low-volatility and macroeconomic factors.
6. Use multifactor models to decompose portfolio returns and risk.
7. Distinguish genuine manager skill from factor exposure.
8. Identify estimation, implementation, governance and ethical limitations of factor investing.

1. Risk, Return and the Pricing Problem

An asset’s realized return is uncertain. Investors therefore require compensation for postponing consumption, bearing inflation and accepting uncertain cash flows. Not every form of risk earns a premium. Risk that can be eliminated cheaply through diversification should not, in a competitive market, command a persistent expected-return premium. By contrast, risk that remains in a well-diversified portfolio may require compensation.

1.1 Total, systematic and idiosyncratic risk

For asset i, a simple return decomposition is:

R_i is the realized return and E(R_i) is its expected return. Systematic shocks affect many securities; idiosyncratic shocks are specific to the asset or issuer. In a diversified portfolio, idiosyncratic components may partly offset one another. Systematic exposure remains.

Variance is a common measure of total return risk:

where σ_i² is variance and Var(R_i) denotes the variance of returns. Standard deviation is σ_i = √(σ_i²). Variance and standard deviation are statistical dispersion measures, not complete definitions of economic risk. They do not by themselves distinguish upside from downside uncertainty, permanent loss, liquidity risk or model risk.

1.2 Covariance and correlation

The relationship between an asset and a market portfolio is summarized by covariance and correlation:

Covariance has squared-return units, whereas correlation is unit-free and lies between −1 and +1. Covariance is central to beta because it measures how an asset co-moves with the market.

2. The Capital Asset Pricing Model

The CAPM states that, in equilibrium, the expected return on an asset equals the risk-free rate plus compensation for its market risk:

Here:

• E(R_i) = expected return on asset i;
• R_f = risk-free return for the relevant horizon and currency;
• β_iM = asset i’s beta relative to the market portfolio;
• E(R_M) = expected return on the market portfolio;
• E(R_M) − R_f = expected market risk premium.

The equation is dimensionally consistent: every term is a return, usually expressed as a decimal or percentage per period. The model applies to expected returns over a specified period, and all inputs must use consistent horizons, currencies and compounding conventions.

2.1 Beta

Beta is defined as:

An equivalent expression using correlation is:

A beta of 1 indicates market sensitivity equal to that of the market portfolio. A beta greater than 1 indicates greater sensitivity, while a beta below 1 indicates lower sensitivity. A negative beta indicates that the asset tends, on average, to move opposite to the market.

Beta is estimated, not observed directly. Analysts commonly estimate it by ordinary least squares (OLS):

where t indexes time, α_i is the regression intercept, and ε_it is the residual. In the ideal CAPM, alpha should be zero in expectation. In practice, a non-zero intercept may reflect skill, omitted factors, measurement error, costs, luck or a misspecified benchmark.

2.2 CAPM assumptions

The traditional CAPM relies on restrictive assumptions:

• investors are rational mean–variance optimizers;
• investors have homogeneous expectations about expected returns, variances and covariances;
• investors can borrow and lend at a common risk-free rate;
• markets are frictionless, with no taxes, transaction costs or constraints;
• assets are infinitely divisible and tradable;
• investors can hold the same efficient market portfolio;
• information is available to investors and markets clear.

These assumptions help derive the model but are not realistic in their literal form. Their importance is analytical: relaxing them can generate additional risk premiums, heterogeneous portfolios and constraints.

2.3 The market portfolio

The theoretical market portfolio includes all investable assets, weighted by market value. A broad equity index is only a proxy. The choice of proxy matters because beta and alpha are benchmark-dependent. A global investor using a domestic equity index may misclassify international, currency or commodity exposure as alpha. A private-market investor cannot directly observe the return of the complete market portfolio and must rely on imperfect proxies.

3. The Security Market Line

The CAPM relationship is represented graphically by the security market line. The horizontal axis measures beta and the vertical axis measures expected return. The intercept is the risk-free rate, and the slope is the market risk premium.

Figure: The security market line relates expected return to systematic market risk, measured by beta.

The expected-return form of the SML is the CAPM equation. The excess-return form is:

An asset plotted above the SML offers a higher expected return than CAPM requires for its beta and may be considered undervalued under the model. An asset below the SML may be overvalued. This conclusion is conditional on accurate expected returns, beta, risk-free rate, market proxy and model specification.

The SML differs from the capital market line (CML). The CML relates expected return to total risk for efficient portfolios; the SML relates expected return to beta for individual assets and portfolios. Confusing the two leads to incorrect risk assessments.

Worked Example 1: CAPM expected return

Assume a one-year risk-free rate of 4%, expected market return of 10% and a stock beta of 1.3. The market risk premium is 6%.

Under CAPM, the stock’s required expected return is 11.8%. This is not a forecast that the stock will certainly earn 11.8%; it is a benchmark return conditional on the assumptions and estimates.

4. Alpha and Performance Attribution

Alpha is the return unexplained by a specified model. For a single-factor CAPM regression, Jensen’s alpha is the intercept:

For realized sample returns, a portfolio’s average alpha can be estimated as:

A positive alpha means that the portfolio’s average excess return exceeded the return predicted by its estimated beta. It does not automatically prove skill. Statistical significance, economic significance, transaction costs, survivorship bias, look-ahead bias, benchmark selection and factor omissions must be examined.

A manager may produce positive CAPM alpha by taking value, momentum or liquidity exposure that CAPM omits. A multifactor model may reduce that alpha by explaining the return through recognized factors. Thus, alpha is always relative to a model and benchmark.

Information ratio is another practical performance measure:

Active return is portfolio return minus benchmark return. Tracking-error standard deviation is the standard deviation of active returns. The information ratio is useful for assessing benchmark-relative efficiency, but it can be unstable over short samples and can reward hidden illiquidity or leverage.

5. Arbitrage Pricing Theory

APT, associated principally with Stephen Ross, begins with a factor-generating process and a no-arbitrage argument rather than the CAPM’s complete-market equilibrium. A simplified multifactor return equation is:

where F_j is an unexpected factor realization, β_ij is asset i’s sensitivity to factor j, and ε_i is an asset-specific residual. Under diversification and no-arbitrage conditions, expected returns may be expressed as:

λ_j is the risk premium associated with factor j. The factors may be macroeconomic, statistical or portfolio-based. Unlike CAPM, APT does not require one unique market portfolio, but it does not identify the factors automatically. Factor selection is an empirical and economic task.

5.1 Conditions and limitations of APT

APT is most persuasive when idiosyncratic risk can be diversified, assets are sufficiently numerous, factor exposures are reasonably stable and arbitrage opportunities are not prevented by trading costs, funding constraints or short-sale restrictions. In real markets, apparent arbitrage can persist because prices can diverge further before converging, capital can be limited and implementation can be costly.

CAPM and APT answer related but different questions. CAPM identifies market beta as the priced risk in an equilibrium framework. APT permits several priced sources of common variation but offers less guidance about which factors belong in the model. Empirical multifactor models operationalize the APT insight by defining measurable factors.

6. Empirical Factor Models

A factor is a systematic characteristic, portfolio return or economic variable that helps explain differences in asset returns. Factors can be:

• Risk-based: compensation for bearing adverse states or constrained exposures.
• Behavioral: results of investor biases, such as extrapolation or overreaction.
• Institutional: effects of mandates, leverage limits, taxation or delegated management.
• Statistical: latent portfolios that summarize common return variation.

A standard factor regression is:

This example includes market, size, value and momentum factors. SMB commonly means “small minus big,” HML means “high minus low” book-to-market portfolios, and MOM is a momentum factor. Definitions vary across providers and markets.

6.1 Size

The size factor captures the historical tendency, in some samples, for smaller companies to earn different average returns from larger companies. A conventional long–short size factor buys small-cap stocks and sells large-cap stocks, often controlling for market exposure.

Possible explanations include greater distress, illiquidity, information costs and limited financing. The effect is sensitive to micro-cap inclusion, transaction costs, market, period and portfolio weighting. A manager heavily invested in small companies may appear skilful relative to a large-cap benchmark while simply receiving size exposure.

6.2 Value

Value investing generally buys securities with low prices relative to fundamentals and sells or underweights securities with high prices relative to fundamentals. Measures include book-to-market, earnings-to-price, cash-flow-to-price and enterprise-value ratios. A simple value factor may be represented by high-minus-low fundamental valuation portfolios.

Value exposure can reflect compensation for distress or cyclical risk, investor overreaction, or both. Accounting data are backward-looking and may be distorted by intangible assets, accounting policy and industry differences. A value signal must specify the measurement date to avoid look-ahead bias.

6.3 Momentum

Momentum strategies buy recent winners and sell recent losers, usually excluding the most recent month in academic implementations to reduce short-term reversal effects. Momentum may reflect underreaction, gradual information diffusion, investor herding or compensation for crash risk.

Momentum can experience sharp, correlated losses during market reversals. Turnover, bid–ask spreads, market impact and short-sale costs are especially important. A manager with frequent trading and strong recent performance may be harvesting momentum rather than demonstrating security-selection skill.

6.4 Quality

Quality is a composite concept rather than a universally fixed variable. Common indicators include profitability, earnings stability, balance-sheet strength, accrual quality, governance and investment discipline. Quality portfolios may favor firms with high return on equity, strong cash conversion and conservative leverage.

Because quality measures are heterogeneous, analysts must inspect the exact construction. A strategy may be labelled quality but actually load on profitability, low leverage, growth or large-cap exposure. Quality signals can also be expensive when widely recognized.

6.5 Low volatility

Low-volatility or low-beta strategies invest in securities with historically lower volatility or market beta. The low-volatility anomaly describes the observation that low-risk portfolios have sometimes earned risk-adjusted returns superior to those predicted by a positive risk-return slope.

Possible explanations include leverage constraints, lottery preferences, benchmark restrictions and delegated-management incentives. Low-volatility strategies are not risk-free: they may have concentration, interest-rate, sector and valuation risks and can lag strongly in speculative bull markets.

6.6 Macroeconomic factors

Macroeconomic factor models use variables such as unexpected inflation, industrial production, interest-rate changes, credit spreads, exchange rates, commodity prices and consumption growth. The relevant factor is generally the unexpected component, not merely the observed level. For example, an asset may respond differently to an unexpected increase in inflation than to a predictable inflation rate already reflected in prices.

Macro factors are economically interpretable but difficult to estimate. Data are revised, releases occur at different frequencies and factor relationships can change across regimes. A portfolio may have significant implicit duration, inflation, credit or currency exposure even when its manager does not describe the strategy in macro terms.

7. Multifactor Risk and Return Decomposition

For a portfolio p, a multifactor model may be written as:

The model’s predicted excess return is the sum of alpha and factor contributions. Over a sample period:

If the regression includes an intercept and residuals average close to zero, observed average excess return is approximately decomposed into estimated alpha plus factor-related return. This is attribution, not proof of causation.

Portfolio factor exposure can arise intentionally or unintentionally. For example, a concentrated bank portfolio may have value, size, credit and macroeconomic exposures. A technology fund may have growth, momentum and duration-like exposures. A private-equity fund may have leverage, illiquidity and small-company exposures.

Estimation issues

OLS estimates can be affected by:

• non-stationary betas;
• correlated factors and multicollinearity;
• heteroskedastic and autocorrelated residuals;
• non-synchronous trading, especially across markets;
• omitted variables;
• structural breaks and regime changes;
• data mining and multiple testing.

Statistical inference should use appropriate standard errors, such as heteroskedasticity- and autocorrelation-consistent errors when justified. Out-of-sample testing, economic constraints and realistic costs are more informative than a highly fitted in-sample regression.

8. Distinguishing Factor Exposure from Manager Skill

The central performance question is not simply whether a manager earned a high return. It is whether the return was high after accounting for the risks and opportunities available to the manager.

A disciplined evaluation proceeds as follows:

1. Define the mandate and benchmark. Match geography, capitalization, currency, leverage, liquidity and investment universe.
2. Collect reliable return data. Use net and gross returns consistently, include cash flows correctly and avoid survivorship bias.
3. Specify economically justified factors. Do not add factors solely because they improve historical fit.
4. Estimate exposures. Use rolling or conditional models where exposures plausibly change.
5. Measure alpha net of costs. Include management fees, performance fees, trading costs, financing and taxes where relevant.
6. Test robustness. Examine alternative factor definitions, periods, markets and benchmarks.
7. Assess capacity and implementation. A paper factor premium may not be investable at the strategy’s scale.
8. Evaluate process evidence. Repeatable research, risk controls and decision discipline support—but do not guarantee—skill.

Suppose a manager earns 14% while the market earns 10%. If the portfolio has high momentum and small-cap exposure during a period when those factors perform strongly, CAPM alpha may overstate skill. A multifactor model might attribute most of the excess return to factors. Conversely, a manager may possess genuine skill but appear to have no alpha because the benchmark is too broad, the sample is short or fees consume the advantage.

Skill is also multidimensional. Security selection, asset allocation, timing, execution, risk management and access to differentiated information are different capabilities. A single alpha estimate cannot identify which capability generated performance.

9. Worked Example 2: Multifactor Attribution

Assume a portfolio has the following monthly factor exposures and realized average monthly factor returns:

The estimated contribution of each factor is exposure multiplied by factor return:

Adding contributions and alpha:

The portfolio’s estimated monthly excess return is therefore 0.86%, before any residual and estimation error. The positive alpha is 0.15 percentage points per month in this illustrative model. Annualizing by simply multiplying by 12 gives 1.80% as an approximation; exact annualization of a compounded monthly return uses (1 + 0.0015)¹2 − 1, and should not be confused with annualizing an estimated regression intercept. The example demonstrates attribution, not a claim that the manager has persistent skill.

10. Applied Case: Evaluating an Active Equity Fund

This is an illustrative case.

Background

An investment committee is considering an actively managed domestic equity fund. Over five years, the fund returned 13.2% annually, compared with 10.0% for the broad equity index. The fund’s reported CAPM alpha is 2.4% annually.

Problem

The committee must determine whether the fund’s performance reflects manager skill or systematic exposures that are absent from the broad index benchmark.

Analysis

The risk team estimates a model using market, size, value, momentum, quality and low-volatility factors. The fund has a market beta of 1.08, positive size and momentum exposures, modest negative value exposure and a positive quality exposure. Its holdings also have higher turnover and lower average market capitalization than the index.

The committee examines several concerns. First, the five-year period included a strong momentum cycle. Second, the fund’s small-company exposure generated additional returns but increased trading costs. Third, the reported return was gross of certain platform fees, while the investor would receive a lower net return. Fourth, factor definitions supplied by different vendors produce different alpha estimates. Fifth, the fund changed managers midway through the period, making the historical track record less informative about the current process.

A multifactor regression reduces estimated alpha from 2.4% to 0.7% annually. The confidence interval is wide and includes zero after correcting for estimation uncertainty. Net of fees and estimated transaction costs, the residual alpha is smaller still.

Approach and decision

The committee does not conclude that the manager has no skill. Instead, it classifies the fund as a combination of factor exposures and uncertain residual skill. It compares the fund with lower-cost factor products, requests holdings-based exposure reports, evaluates capacity and requires net-of-cost performance attribution. Continued allocation is made conditional on evidence that the current team’s process can generate differentiated returns after factor and implementation costs.

Outcome and learning points

The case illustrates five professional lessons:

• benchmark choice can materially change alpha;
• factor exposure is not necessarily intentional or stable;
• gross returns can overstate investor outcomes;
• a short or regime-specific sample is weak evidence of skill;
• factor models support due diligence but cannot replace qualitative assessment of process, governance and incentives.

11. Implementation, Governance and Ethical Considerations

Factor strategies require clear rules for universe selection, signal measurement, ranking, portfolio weighting, rebalancing, liquidity, shorting and risk limits. A factor label should be supported by transparent definitions and holdings-based evidence. Marketing should not imply that a historical premium is guaranteed or that a factor is riskless.

Investment committees should monitor unintended concentrations, turnover, leverage, derivatives, securities lending, counterparty exposure and liquidity under stress. Model governance should document data sources, revisions, estimation windows, overrides and validation results. Conflicts may arise when a manager reports a favourable benchmark or selects a factor definition after observing results. Independent oversight and consistent methodology reduce these risks.

Artificial intelligence and machine learning can help process large datasets, identify nonlinear exposures and improve monitoring. However, flexible models increase overfitting, opacity, data leakage and governance risk. A machine-learning signal should be economically interpretable where possible, tested out of sample, evaluated after realistic costs and subject to human oversight. Technology does not eliminate the need for economic reasoning.

12. Contemporary Developments and Best Practices

Current practice increasingly emphasizes:

• Dynamic exposures: factor sensitivities vary with valuation, volatility, liquidity and market regime.
• Portfolio-aware factors: signals are combined with constraints on turnover, capacity, sector and country concentration.
• Sustainability integration: environmental, social and governance data may affect risk and expected return, but definitions and data quality vary.
• Crowding analysis: popular factors can become expensive and vulnerable to synchronized liquidation.
• Alternative data: new datasets create potential information advantages but also privacy, licensing and bias concerns.
• Transaction-cost-aware construction: expected factor returns must be evaluated net of market impact and financing costs.
• Transparent attribution: investors increasingly demand holdings-based, scenario-based and net-of-fee reporting.

Best practice is to treat factor premiums as uncertain, investable hypotheses. The analyst should define the economic rationale, test the signal across markets and periods, assess costs and capacity, monitor exposures continuously and communicate uncertainty honestly.

Challenges and Limitations

No asset-pricing model fully captures markets. CAPM’s single-factor structure may omit important risks. APT does not uniquely identify factors. Empirical factors can be proxies for one another, and their premiums may weaken after publication and implementation. Historical relationships may be sample-specific. Expected returns are difficult to estimate, and small errors in risk premiums can produce large valuation differences.

Factor models also simplify nonlinear and tail risks. Options, leverage, liquidity and credit exposures may not be represented adequately by linear betas. A fund can have modest average beta yet suffer severe losses in a particular stress event. Therefore, factor analysis should be combined with scenario analysis, stress testing, drawdown analysis, liquidity assessment and qualitative due diligence.

Chapter Summary

CAPM proposes that an asset’s expected return equals the risk-free rate plus beta multiplied by the market risk premium. Beta measures covariance with the market relative to market variance and captures systematic rather than diversifiable risk. The security market line represents this relationship and provides a conditional framework for judging required returns.

Alpha is the intercept or unexplained return relative to a specified model; it is not synonymous with skill. APT extends the pricing logic to multiple sources of systematic risk, while empirical multifactor models operationalize this insight using market, size, value, momentum, quality, low-volatility and macroeconomic factors. Multifactor attribution helps identify whether returns arise from exposures or residual performance.

Professional evaluation requires suitable benchmarks, reliable data, realistic costs, robust statistical testing, capacity analysis and attention to changing exposures. Factor models are valuable analytical tools but are subject to estimation error, model uncertainty, crowding, implementation constraints and governance risks.

Key Terms

Alpha: Return unexplained by a specified asset-pricing model.

Arbitrage Pricing Theory (APT): A no-arbitrage framework in which expected returns depend on exposure to multiple systematic factors.

Beta: Sensitivity of an asset’s return to a market or factor return.

CAPM: Model linking expected return to the risk-free rate and market beta.

Capital market line: Relationship between expected return and total risk for efficient portfolios.

Covariance: Measure of joint variation between two returns.

Factor: Systematic characteristic, portfolio return or economic variable associated with return variation.

Factor premium: Expected compensation associated with exposure to a factor.

Idiosyncratic risk: Asset-specific risk that may be diversified away.

Information ratio: Average active return divided by tracking-error standard deviation.

Jensen’s alpha: CAPM-based abnormal return measure.

Market portfolio: Theoretical portfolio containing all investable assets, usually approximated by an index.

Momentum: Tendency for recent winners and losers to continue differing in performance over a specified horizon.

Multifactor model: Return model containing two or more systematic factors.

Quality factor: Exposure associated with profitability, financial strength, stability or related characteristics.

Security market line: CAPM line relating expected return to beta.

Size factor: Return exposure associated with smaller versus larger firms.

Systematic risk: Non-diversifiable risk affecting many securities.

Value factor: Exposure associated with inexpensive securities relative to fundamentals.

Volatility: Statistical dispersion of returns, commonly measured by standard deviation.

Review Questions

Short Answer Questions

1. What is the difference between systematic and idiosyncratic risk?
2. Define beta and state its covariance-based formula.
3. What does the slope of the security market line represent?
4. Why does a positive CAPM alpha not necessarily prove manager skill?
5. Distinguish the capital market line from the security market line.

Long Answer Questions

1. Explain the CAPM, its assumptions and its practical limitations.
2. Compare CAPM and APT in terms of assumptions, factors and empirical application.
3. Discuss the economic and behavioural explanations for value and momentum premiums.
4. Explain how multifactor regression can be used for portfolio performance attribution.
5. Evaluate the challenges of implementing factor strategies in institutional portfolios.

Analytical / Application Questions

1. A stock has beta 0.8, a risk-free rate of 3% and an expected market return of 9%. Calculate its CAPM expected return and interpret the result.
2. An active fund has positive CAPM alpha but strong momentum and small-cap exposures. Design an analysis to determine whether the alpha represents skill.
3. Construct a governance framework for approving an AI-assisted multifactor investment strategy, including validation, cost analysis, monitoring and disclosure.

Multiple Choice Questions with Answers

Question 1

According to CAPM, which risk is rewarded with an expected return premium?

A. Total accounting risk

B. Systematic market risk measured by beta

C. All firm-specific risk

D. Uncertainty in dividend timing only

Correct Answer: B. Systematic market risk measured by beta

Question 2

A stock has a beta of 1.2, a risk-free rate of 4% and an expected market return of 9%. What is its CAPM expected return?

A. 6.0%

B. 9.0%

C. 10.0%

D. 14.8%

Correct Answer: C. 10.0%

Question 3

Beta is calculated as:

A. Market variance divided by asset covariance

B. Asset standard deviation divided by market standard deviation

C. Covariance of asset and market returns divided by market variance

D. Asset return divided by risk-free return

Correct Answer: C. Covariance of asset and market returns divided by market variance

Question 4

What does an asset plotted above the security market line indicate under CAPM?

A. Its expected return is higher than required for its beta

B. Its total risk is zero

C. Its beta must be negative

D. Its realized return is guaranteed

Correct Answer: A. Its expected return is higher than required for its beta

Question 5

Why can CAPM alpha overstate manager skill?

A. Alpha is always equal to beta

B. CAPM may omit exposures to factors such as value or momentum

C. Risk-free rates cannot be measured

D. Market returns are never observable

Correct Answer: B. CAPM may omit exposures to factors such as value or momentum

Question 6

Which statement best describes APT?

A. It requires only one market factor

B. It links expected returns to multiple factor sensitivities under no-arbitrage conditions

C. It assumes all idiosyncratic risk is priced

D. It applies only to risk-free assets

Correct Answer: B. It links expected returns to multiple factor sensitivities under no-arbitrage conditions

Question 7

A traditional value strategy most commonly seeks exposure by:

A. Buying securities expensive relative to fundamentals

B. Buying securities inexpensive relative to fundamentals

C. Buying only securities with high recent returns

D. Holding only government bonds

Correct Answer: B. Buying securities inexpensive relative to fundamentals

Question 8

Which factor is most closely associated with recent winners continuing to outperform recent losers?

A. Momentum

B. Quality

C. Low volatility

D. Inflation

Correct Answer: A. Momentum

Question 9

In a multifactor regression, the intercept is commonly interpreted as:

A. The portfolio’s market capitalization

B. The residual return unexplained by included factors

C. The risk-free rate only

D. The factor covariance matrix

Correct Answer: B. The residual return unexplained by included factors

Question 10

Which practice best improves the credibility of a factor-investing backtest?

A. Selecting factors after observing the results

B. Ignoring transaction costs

C. Testing out of sample with realistic costs and capacity constraints

D. Using only the most successful historical period

Correct Answer: C. Testing out of sample with realistic costs and capacity constraints