All questions
Question 1
Many of the empirical critiques of the CAPM, such as the size and value effects, show that certain stock characteristics beyond beta have predictive power for returns. These findings are a direct challenge to the validity of the:
- Capital Market Line (CML), because it implies portfolios exist that offer a better risk-return trade-off.
- Efficient Market Hypothesis (EMH), as these anomalies may represent predictable profit opportunities.
- Two-Fund Separation Theorem, because it suggests investors should hold more than just the market portfolio and the risk-free asset.
- Security Market Line (SML), because it implies that systematic risk factors other than market covariance are being priced. (correct answer)
Explanation: When you encounter questions about empirical anomalies in asset pricing, focus on understanding what each model actually predicts and how violations challenge those specific predictions.
The CAPM's Security Market Line (SML) makes a precise claim: only systematic risk (beta) should be priced in expected returns. The equation E(Ri)=Rf+βi[E(Rm)−Rf] says that beta fully captures all risk factors that affect expected returns. When empirical studies show that size, value, or other characteristics predict returns even after controlling for beta, this directly contradicts the SML's fundamental assumption that beta alone explains the risk premium.
Answer D is correct because these anomalies reveal that additional systematic risk factors beyond market covariance are being priced by investors, violating the SML's core prediction.
Answer A is wrong because the Capital Market Line relates to efficient portfolios of risky assets combined with the risk-free asset, not individual stock characteristics. Answer B misses the target—while these anomalies might challenge market efficiency, the question specifically asks about CAPM critiques, and the EMH is a separate theory about information processing, not asset pricing models. Answer C incorrectly focuses on the Two-Fund Separation Theorem, which deals with optimal portfolio construction rather than the pricing of individual securities' risk characteristics.
Remember: CAPM anomalies specifically challenge the completeness of beta as a risk measure. When you see empirical evidence of additional pricing factors, think immediately about how this contradicts the Security Market Line's prediction that beta captures all systematic risk. Question 2
An analyst conducts an empirical test of the CAPM using the S&P 500 as a proxy for the market portfolio. The test results show a weak, statistically insignificant relationship between average returns and beta across a wide range of stocks. According to Roll's Critique, what is the most valid conclusion the analyst can draw from this finding?
- The CAPM is definitively false as a theory of asset pricing because its main prediction is not supported.
- The S&P 500 is not a mean-variance efficient portfolio, and a different proxy should be used.
- The test results are inconclusive regarding the validity of the CAPM itself. (correct answer)
- Beta is not a relevant measure of systematic risk for the assets that were tested in the sample.
Explanation: Roll's Critique argues that any test of the CAPM is a joint test of two hypotheses: (1) the CAPM model is correct, and (2) the market portfolio proxy used is mean-variance efficient. If the test fails (as in this case), it is impossible to know which of the two hypotheses is false. The model might be wrong, the proxy might be inefficient, or both. Therefore, the test is inconclusive about the validity of the CAPM theory itself.
Question 3
A financial analyst constructs two portfolios, P-Small and P-Large. P-Small contains stocks in the lowest market capitalization decile, and P-Large contains stocks in the highest decile. Over a long-term study period, the analyst finds that P-Small consistently generates a positive and statistically significant Jensen's alpha, while P-Large's alpha is close to zero. This finding is a direct challenge to which aspect of the CAPM?
- The assumption that investors can borrow and lend at the risk-free rate.
- The conclusion that beta is the sole determinant of expected excess returns. (correct answer)
- The theoretical requirement of a single-period investment horizon for all investors.
- The proposition that the market portfolio lies on the efficient frontier.
Explanation: Jensen's alpha measures the return of a portfolio above or below that predicted by the CAPM. A persistent positive alpha for a group of stocks (small-cap stocks) suggests that there is a factor other than beta (in this case, size) that explains returns. This directly contradicts the central tenet of the CAPM, which is that beta is the single, sufficient measure of systematic risk that determines expected returns.
Question 4
A researcher argues that the well-documented "value premium" (high book-to-market stocks earning higher returns than CAPM predicts) does not necessarily invalidate the CAPM. Instead, the researcher suggests the anomaly might be an artifact of using a poor proxy for the market portfolio. This argument relies on the logic that:
- High book-to-market stocks have betas that are inherently unstable and difficult to measure accurately.
- The true, unobservable market portfolio might have risk characteristics that are proxied by the book-to-market ratio. (correct answer)
- Investors in value stocks have different, systematically biased expectations compared to investors in growth stocks.
- The single-period framework of the CAPM is insufficient to capture the long-term nature of the value premium.
Explanation: This argument connects Roll's Critique to empirical anomalies. If the proxy for the market portfolio (e.g., a stock index) is not the true market portfolio, it might be missing important risk factors. It is possible that the book-to-market ratio is correlated with these missing risk factors from the true market portfolio (which includes assets like human capital, real estate, etc.). In this view, the value premium isn't a new risk factor, but rather a proxy for systematic risks that are not being captured by the flawed market index proxy.
Question 5
Empirical studies have observed that portfolios of low-beta stocks have historically generated higher risk-adjusted returns than portfolios of high-beta stocks, a phenomenon known as the "low-beta anomaly." This finding directly contradicts which fundamental prediction of the CAPM?
- All investors hold a combination of the risk-free asset and the market portfolio.
- The Security Market Line (SML) accurately describes the expected return for any given level of systematic risk. (correct answer)
- Unsystematic risk can be eliminated through diversification and thus earns no expected return.
- The market portfolio is mean-variance efficient and contains all traded assets.
Explanation: The Security Market Line (SML) is the graphical representation of the CAPM, showing a positive, linear relationship between an asset's beta and its expected return. The low-beta anomaly finds that low-beta stocks often plot above the SML (positive alpha) and high-beta stocks plot below it (negative alpha). This means the empirical relationship is 'flatter' than the SML predicted by the theory. This directly contradicts the idea that the SML correctly prices assets based on their systematic risk.
Question 6
The CAPM's reliance on beta as the sole risk measure is theoretically justified if investment returns are normally distributed or if investors have quadratic utility. If returns are, in fact, skewed or exhibit fat tails (kurtosis), why does this present a limitation for the CAPM?
- Beta can no longer be estimated accurately using standard ordinary least squares regression.
- The risk-free rate becomes undefined in the presence of non-normal returns.
- Investors may care about higher moments of the return distribution, not just mean and variance. (correct answer)
- The market portfolio can no longer be considered well-diversified if returns are not normal.
Explanation: The CAPM is based on mean-variance optimization, which assumes investors are only concerned with two things: expected return (mean) and risk (variance). If returns are not normally distributed, other characteristics of the distribution, such as skewness (asymmetry) and kurtosis (fat tails), become important. Investors might prefer positive skewness (lottery-like payoffs) or be averse to high kurtosis (extreme events). The CAPM's focus on variance alone as the measure of risk is insufficient to capture these preferences.
Question 7
A mutual fund manager's portfolio has a beta of 1.4 and consists primarily of high-momentum stocks. Over the past year, the fund generated a significant positive alpha when measured against the CAPM's Security Market Line. A critic argues this alpha is not evidence of skill. Which CAPM limitation provides the strongest basis for this critique?
- The CAPM fails to account for momentum, a systematic factor that may explain the fund's excess returns. (correct answer)
- The fund's high beta indicates excessive risk-taking, which invalidates the alpha calculation.
- The single-period nature of the CAPM is inappropriate for evaluating performance over a one-year horizon.
- The true market portfolio is unobservable, meaning the beta and the SML are likely mis-specified.
Explanation: When evaluating portfolio performance using CAPM, you're testing whether a manager generated excess returns beyond what their systematic risk (beta) would predict. However, CAPM's single-factor model has well-known limitations that can create misleading alpha measurements.
The correct answer is A because momentum is a documented systematic risk factor that CAPM ignores. Academic research shows momentum stocks tend to outperform over certain periods due to behavioral biases and market inefficiencies. Since this fund holds high-momentum stocks and generated positive alpha, the excess returns might simply reflect exposure to the momentum factor rather than manager skill. A more sophisticated model like the Fama-French three-factor model or Carhart four-factor model (which includes momentum) would likely explain away much of this alpha.
Answer B is wrong because high beta doesn't invalidate alpha calculations—CAPM specifically adjusts for systematic risk through beta. The alpha measurement already accounts for the fund's 1.4 beta.
Answer C misunderstands CAMP's application. While CAPM is a single-period model theoretically, it's routinely and appropriately used for multi-period performance evaluation. One year is a standard evaluation horizon.
Answer D, while technically true that the true market portfolio is unobservable, doesn't specifically address why this momentum-focused fund's alpha might be misleading. This limitation affects all CAPM applications equally, not just this particular case.
Study tip: When you see performance evaluation questions involving specialized strategies (momentum, value, etc.), consider whether missing risk factors could explain apparent outperformance better than manager skill.
Question 8
The CAPM assumes that all investors have homogeneous expectations, meaning they all agree on the expected returns, variances, and covariances of all assets. In reality, investors have diverse opinions. What is the most direct theoretical consequence of relaxing this assumption?
- The market portfolio would no longer be considered the single optimal risky portfolio for all investors. (correct answer)
- The Security Market Line (SML) would become downward-sloping for high-beta assets.
- Unsystematic risk would become a priced factor in determining expected returns.
- The beta of an asset would become completely irrelevant for portfolio construction decisions.
Explanation: The Two-Fund Separation Theorem, a key building block of the CAPM, states that all investors will hold some combination of the risk-free asset and a single optimal risky portfolio (the market portfolio). This result depends on all investors perceiving the same efficient frontier, which requires homogeneous expectations. If expectations are heterogeneous, each investor will perceive a different efficient frontier and thus a different optimal risky portfolio. The idea of a single market portfolio that is optimal for everyone breaks down.
Question 9
The theoretical market portfolio in the CAPM includes all assets, including non-traded ones like human capital and private businesses. Why does the exclusion of these assets from empirical proxies (like stock market indices) pose a significant limitation to testing the model?
- It causes the estimated risk-free rate to be biased upwards, leading to incorrect SML calculations.
- It introduces significant unsystematic risk into the market proxy, which should ideally be fully diversified.
- It makes it impossible to verify if the chosen market proxy is actually mean-variance efficient. (correct answer)
- It violates the assumption of normally distributed returns, as human capital returns are highly skewed.
Explanation: This is a core element of Roll's Critique. The CAPM's predictions are conditional on using the true, all-encompassing market portfolio, which must be mean-variance efficient. Any proxy we use in the real world, such as the S&P 500, is necessarily incomplete because it excludes vast categories of assets. Since the proxy is not the true portfolio, we have no way of knowing if it is mean-variance efficient. Therefore, any test using this proxy cannot truly validate or invalidate the CAPM.
Question 10
The CAPM assumes investors can borrow and lend unlimited amounts at a single risk-free rate. In practice, the borrowing rate (rb) is typically higher than the lending rate (rl). What is the primary theoretical effect of introducing this market friction?
- It causes the Security Market Line (SML) to become a curve instead of a straight line.
- It invalidates the concept of beta as a measure of systematic risk.
- It leads to a range of optimal risky portfolios instead of a single market portfolio. (correct answer)
- It implies that all investors will hold portfolios consisting solely of risky assets.
Explanation: When the borrowing and lending rates differ, the clean logic of the single Capital Market Line (CML) breaks down. Lenders (who are more risk-averse) will combine the risk-free lending asset with one optimal risky portfolio. Borrowers (who are less risk-averse) will leverage up by borrowing at a higher rate and will combine this with a different optimal risky portfolio. This violates the Two-Fund Separation Theorem and means there is no longer a single 'market portfolio' that is optimal for all investors.
Question 11
An investment committee is reviewing its use of the CAPM. A member raises a concern, stating: "Our historical beta calculations for various industry sectors seem to change significantly depending on whether we use a 3-year or a 10-year lookback period. Furthermore, our chosen market index, a domestic large-cap index, ignores international assets and private equity, which are increasingly large parts of the global investment landscape." These two concerns highlight, respectively, which pair of CAPM limitations?
- Homogeneous expectations and the size effect.
- Non-normal returns and the low-beta anomaly.
- The single-period horizon and the value effect.
- Beta instability and the market portfolio proxy problem. (correct answer)
Explanation: When you encounter CAPM criticism questions, focus on identifying which specific theoretical assumptions or practical implementation challenges are being highlighted.
The committee member's concerns point to two fundamental CAPM problems. First, the observation that beta calculations "change significantly" between 3-year and 10-year periods directly illustrates beta instability - the empirical reality that betas are not constant over time as CAPM assumes. This instability makes it difficult to reliably estimate future systematic risk from historical data.
Second, the concern about using a "domestic large-cap index" that "ignores international assets and private equity" highlights the market portfolio proxy problem. CAPM theory requires the "true" market portfolio containing all risky assets globally, but in practice, we use imperfect proxies like the S&P 500. This creates measurement errors and biases in risk-return calculations.
Answer D correctly identifies both limitations. Answer A is wrong because homogeneous expectations refers to investors sharing identical beliefs about returns, and the size effect involves small-cap stocks outperforming large-cap stocks - neither matches the described concerns. Answer B is incorrect as non-normal returns address return distribution shapes, and the low-beta anomaly involves low-beta stocks earning higher risk-adjusted returns than predicted. Answer C misses the mark because the single-period horizon refers to CAPM's static one-period framework, and the value effect involves value stocks outperforming growth stocks.
Remember: CAPM limitation questions often contrast theoretical assumptions with real-world implementation challenges. Beta instability and market portfolio proxy issues are among the most practically relevant criticisms you'll encounter.
Question 12
In their seminal 1992 paper, Fama and French presented evidence showing that, over their study period, there was no significant positive relationship between beta and average stock returns when other factors were considered. This empirical result is a powerful critique of the CAPM because it suggests that:
- The risk-free rate used in tests of the model was likely mismeasured.
- The market risk premium was effectively zero or negative during the study period.
- The primary risk factor identified by the model is not empirically priced by the market. (correct answer)
- Transaction costs for small and value stocks are high enough to explain their excess returns.
Explanation: The core prediction of the CAPM is that assets with higher systematic risk (beta) should have higher expected returns. In other words, beta is the risk factor that the market 'prices'. The Fama-French finding that beta had little to no explanatory power over returns was a direct and powerful challenge to this central prediction. It suggested that beta was not the risk that investors were being compensated for, and that other factors (size and value) were more important.
Question 13
A portfolio manager is using the CAPM to estimate the expected return for a manufacturing firm that recently completed a major acquisition of a software company, fundamentally altering its business mix and leverage. The manager uses a beta calculated from the past five years of historical data. Which limitation of the CAPM is most likely to lead to a significant error in the expected return calculation in this scenario?
- The assumption of homogeneous investor expectations about the firm's future.
- The non-stationarity of the beta coefficient over time. (correct answer)
- The omission of non-traded assets like human capital from the market portfolio.
- The model's failure to account for the value premium in stock returns.
Explanation: The firm has undergone a major structural change. Its systematic risk profile is likely very different after the acquisition than it was before. Using a beta estimated from historical data that predates this change assumes the beta is stable (stationary) over time. In reality, betas are non-stationary and can change significantly with shifts in a company's fundamentals, making the historical beta a poor predictor of future beta. This instability is a major practical limitation.
Question 14
If the 'low-beta anomaly' is true, where low-beta stocks earn higher returns than predicted by CAPM and high-beta stocks earn lower returns than predicted, what would a plot of realized average returns against beta for a large cross-section of stocks look like relative to the theoretical Security Market Line (SML)?
- The plotted points would form a line with a steeper slope than the theoretical SML.
- The plotted points would show no discernible pattern, indicating beta is entirely unrelated to returns.
- The plotted points would form a U-shaped curve, with both very low and very high beta stocks earning high returns.
- The plotted points would form a line with a flatter slope and a higher intercept than the theoretical SML. (correct answer)
Explanation: When you encounter questions about market anomalies and the CAPM, focus on how empirical evidence deviates from theoretical predictions. The low-beta anomaly is a well-documented violation of the Capital Asset Pricing Model that shows the Security Market Line is "too steep" in reality.
The low-beta anomaly means that low-beta stocks earn higher returns than CAPM predicts, while high-beta stocks earn lower returns than expected. If you plot actual average returns against beta, this creates a line that's flatter than the theoretical SML. Additionally, since low-beta stocks are earning more than predicted, the entire empirical line shifts upward, creating a higher intercept. This confirms answer D is correct.
Answer A suggests a steeper slope, which would mean high-beta stocks earn even higher returns than CAPM predicts – the opposite of the low-beta anomaly. Answer B implies beta has no relationship with returns at all, but the anomaly still shows a positive beta-return relationship, just weaker than CAPM suggests. Answer C describes a U-shaped relationship where extreme betas earn high returns, which isn't what the low-beta anomaly describes – it's specifically about the linear relationship being flatter than expected.
Remember this pattern: when market anomalies show "convergence" toward average performance (low-risk assets doing better than expected, high-risk assets doing worse), the empirical relationship will always be flatter than theory predicts. This appears in many finance contexts beyond just the low-beta anomaly.
Question 15
A CFO is using the CAPM to determine the cost of equity for a small-cap, high-growth startup. An advisor cautions that the standard CAPM may significantly underestimate the true cost of equity for this firm. Which of the following CAPM limitations is the most likely reason for the advisor's concern?
- The empirical finding that small-capitalization stocks have historically earned returns greater than predicted by their beta. (correct answer)
- The inability of the model to incorporate personal taxes into the asset pricing framework.
- The theoretical assumption that all assets are perfectly divisible and liquid.
- The difficulty in finding a truly risk-free asset to use in the CAPM formula.
Explanation: When evaluating CAPM's limitations for specific types of companies, you need to consider how well the model's assumptions match real-world market behavior, especially for firms with unique characteristics like small-cap startups.
The advisor's concern stems from the well-documented "small firm effect" or "size premium" in financial markets. Empirical studies have consistently shown that small-capitalization stocks earn returns significantly higher than what CAPM predicts based solely on their systematic risk (beta). This anomaly suggests that small firms face additional risk factors not captured by beta, such as higher information asymmetry, lower liquidity, greater financial distress risk, and limited access to capital markets. For a small-cap startup, CAPM would likely underestimate the required return by ignoring these size-related risk premiums, making option A correct.
Option B is wrong because personal taxes, while not explicitly modeled in CAPM, don't systematically bias cost of equity estimates for small firms specifically. Option C incorrectly identifies divisibility and liquidity assumptions as the primary concern—while liquidity matters for small caps, this choice doesn't capture the systematic underestimation problem. Option D misses the mark because finding a risk-free rate affects all CAPM applications equally, not just small firms.
Study tip: Remember that CAPM works reasonably well for large, established companies but often underestimates required returns for small-cap firms. When you see questions about CAPM limitations for specific company types, think about what empirical anomalies affect those firms—the size effect is one of the most robust findings in finance research.
Question 16
The CAPM is a single-period model, which assumes investors make decisions for one period and do not consider future periods. How does this assumption limit the model's applicability for long-term investors?
- It prevents the model from incorporating the effects of taxes and transaction costs, which accumulate over time.
- It ignores investors' desires to hedge against unfavorable changes in future investment opportunities. (correct answer)
- It incorrectly implies that the beta of an asset must remain constant across all future periods.
- It cannot account for investors' preferences for assets with skewed return distributions.
Explanation: In a multi-period world, investors care about more than just the value of their portfolio at the end of the current period. They also care about the investment opportunities available in the future. For instance, they may wish to hold assets that perform well when future investment opportunities worsen (e.g., when expected market returns fall). This desire to hedge against changes in the investment opportunity set is ignored by the single-period CAPM. Models like the Intertemporal CAPM (ICAPM) were developed to address this limitation.
Question 17
An analyst is evaluating the stock of a large consulting firm. A significant portion of the firm's value is tied to the human capital of its employees. How does the nature of this key asset present a problem for applying the standard CAPM?
- The returns on human capital are likely to be negatively correlated with the stock market, making beta an unreliable risk measure.
- The consulting firm's stock will exhibit higher unsystematic risk than predicted by the model due to its reliance on key personnel.
- The firm's human capital is a major non-traded asset, making the firm's covariance with a standard market index an incomplete measure of its true systematic risk. (correct answer)
- The value of human capital cannot be determined, so the firm's book-to-market ratio is meaningless for multifactor model analysis.
Explanation: This is an application of the market portfolio proxy problem. The true market portfolio should include all sources of wealth, including human capital. A firm whose value is heavily dependent on human capital will have returns that covary with the returns on aggregate human capital in the economy. A standard stock market index ignores this massive asset class. Therefore, a beta calculated against such an index provides an incomplete picture of the firm's total systematic risk relative to the true, all-encompassing market portfolio.
Question 18
An analyst observes that, after controlling for beta, stocks with lower trading volume and higher bid-ask spreads consistently earn higher average returns. This evidence suggests a limitation of the standard CAPM because it implies that:
- The market portfolio proxy used to estimate beta is likely inefficient.
- Investors demand compensation for bearing a risk factor other than market risk. (correct answer)
- Transaction costs are a significant driver of unsystematic risk for most assets.
- The assumption of homogeneous expectations is violated in illiquid markets.
Explanation: The standard CAPM posits that only systematic market risk, measured by beta, is priced by the market. If another characteristic, such as illiquidity (proxied by trading volume and bid-ask spreads), can predict returns even after accounting for beta, it means that illiquidity is a priced risk factor. Investors demand a higher expected return (a liquidity premium) as compensation for the costs and risks of holding assets that are difficult to trade. This suggests the single-factor CAPM is incomplete.
Question 19
A portfolio manager observes that over a 10-year period, small-cap value stocks consistently generated returns 3% higher than predicted by CAPM, while maintaining the same systematic risk as predicted. Large-cap growth stocks performed exactly as CAPM predicted. If CAPM were a complete model, what should the manager's optimal response be, and why might this response fail in practice?
- Increase allocation to small-cap value stocks, but this may fail because the observed outperformance could reflect compensation for systematic risk factors not captured by market beta alone (correct answer)
- Maintain current allocations since CAPM assumes markets are efficient and apparent mispricings will disappear, but this may fail because CAPM's single-factor approach oversimplifies complex risk-return relationships
- Decrease allocation to large-cap growth stocks since they show no alpha generation, but this may fail because CAPM ignores transaction costs and liquidity differences between asset classes
- Arbitrage the difference by shorting large-cap growth and buying small-cap value, but this may fail because CAPM assumes unlimited borrowing capacity at the risk-free rate
Explanation: The correct answer is A. If CAPM were complete, persistent outperformance with identical systematic risk would represent pure alpha, justifying increased allocation. However, this response may fail because CAPM's limitation is its single-factor approach - the outperformance likely reflects exposure to systematic risk factors (size, value) not captured by market beta. Choice B incorrectly suggests maintaining allocations when alpha exists. Choice C misidentifies the problem as lack of alpha in large-caps rather than unexplained alpha in small-caps. Choice D incorrectly focuses on borrowing constraints rather than CAPM's factor limitations.
Question 20
A pension fund manager notices that CAPM consistently underestimates required returns for utility stocks and overestimates required returns for technology stocks, even after adjusting for differences in market beta. The manager hypothesizes this occurs because utility stocks tend to perform poorly during economic downturns while technology stocks often maintain growth. What does this pattern most likely indicate about CAPM's limitations?
- CAPM's assumption of constant correlation between assets over time fails to capture the changing relationships during different market cycles
- CAPM's reliance on historical data fails to incorporate forward-looking risk assessments that distinguish between cyclical and defensive sectors
- CAPM's single-factor approach fails to account for systematic risks beyond market risk, such as sensitivity to economic cycles or business conditions (correct answer)
- CAPM's assumption of rational investors fails to account for behavioral biases that cause systematic mispricing of growth versus value characteristics
Explanation: The correct answer is C. The pattern described suggests that utilities and technology stocks have different sensitivities to systematic risk factors beyond market beta - specifically, economic cycle sensitivity. CAPM's single-factor limitation means it cannot capture these additional systematic risk dimensions. Choice A focuses on correlation changes rather than additional risk factors. Choice B incorrectly emphasizes the historical vs. forward-looking distinction when the issue is factor completeness. Choice D mischaracterizes the problem as behavioral/mispricing rather than missing systematic risk factors.