- A stock has a beta of 0.8 and a standard deviation of 30%. The market portfolio has a standard deviation of 15%, the risk-free rate is 3%, and the expected return on the market is 11%. The stock is priced in accordance with the capital asset pricing model. Which of the following statements about the stock is true?
Answer: The stock plots on the security market line and below the capital market line.
Under the capital asset pricing model, a stock priced in accordance with the model plots on the security market line: its beta of 0.8 gives a required return of 3% + 0.8 x (11% - 3%) = 9.4%. The capital market line, however, relates expected return to total risk and applies only to efficient portfolios; at a 30% standard deviation the CML would require 3% + (11% - 3%) x (30% / 15%) = 19%, so the stock plots well below the CML. The statement that it plots on the CML is wrong because the CML describes only efficient combinations of the market portfolio and the risk-free asset, not individual securities. The statement that it plots above the SML is wrong because CAPM compensates only systematic risk, and the stock was given no alpha. The statement that it plots below the SML and above the CML gets both relationships backwards.
An investment adviser backtests a moving-average crossover rule using only historical prices and volume. The backtest shows average annual returns 3 percentage points above the market over 20 years, before trading costs and taxes.
Under the weak form of the efficient market hypothesis, the most appropriate conclusion is that: Answer: If the excess return remains after trading costs, taxes, and risk adjustment, the result would be inconsistent with weak-form efficiency.
Under weak-form efficiency, current prices already reflect historical price and volume data, so a technical trading rule should not produce persistent abnormal returns after adjusting for risk and costs. Because the backtest return is before trading costs and taxes and is not risk-adjusted, the reported edge does not by itself establish a violation; it would do so only if it survived those adjustments. The claim that using historical prices and volume disproves weak-form efficiency skips those required adjustments. The claim that the result is consistent because weak-form efficiency covers all public information misstates the weak form, which concerns historical market data rather than all public information. The claim that weak-form efficiency applies only to fundamental information is backwards; it is specifically about historical price and volume data.
- Which of the following statements regarding the capital market line (CML) and the market portfolio is true?
Answer: The market portfolio is the tangency portfolio where the CML touches the efficient frontier, and it bears only systematic risk.
Under the capital asset pricing model, the CML is the straight line from the risk-free asset tangent to the efficient frontier, and the tangency portfolio is the market portfolio, which is fully diversified and therefore carries only systematic risk. The statement that the market portfolio is the minimum-variance portfolio is wrong: the minimum-variance portfolio is the leftmost point on the efficient frontier and is generally not the tangency portfolio, and the CML is upward sloping, not horizontal. The statement that the CML measures risk by beta is wrong: the CML uses total risk (standard deviation) and applies only to efficient portfolios; it is the security market line that uses beta and prices individual securities. The statement that the CML's slope equals the market risk premium is half right: the market portfolio is value-weighted, but the CML's slope is the market risk premium divided by the market's standard deviation, not the market risk premium alone.
An IAR is estimating required returns under the CAPM. Expected inflation rises by 1 percentage point, and investor risk aversion increases so that the market risk premium rises by 0.25 percentage point. The risk-free rate moves one-for-one with expected inflation. A stock has a beta of 2.0.
By how much should the stock's required return increase? Answer: 1.50 percentage points
Under the CAPM, the change in a stock's required return equals the change in the risk-free rate plus beta times the change in the market risk premium: 1 percentage point + 2(0.25 percentage point) = 1.50 percentage points. The 1.25 percentage-point figure is the increase in the expected return on the market portfolio (1 + 0.25) and would be the required-return increase only for a stock with beta of 1.0. The 2.50 percentage-point figure incorrectly multiplies the entire increase in the expected market return by the stock's beta. The 1.00 percentage-point figure reflects only the higher risk-free rate and ignores the increased market risk premium.
- Which of the following statements regarding the capital asset pricing model (CAPM) is true?
Answer: Investors have homogeneous expectations, borrow and lend at the risk-free rate without limit, and choose portfolios using expected return and standard deviation.
The capital asset pricing model assumes homogeneous expectations, unlimited borrowing and lending at the risk-free rate, and mean-variance optimization; these assumptions justify the market portfolio and the single-factor security market line. The statement that investors are compensated for unsystematic risk contradicts the model's central insight: unsystematic risk is diversifiable, so only systematic risk is priced. The statement that returns are driven by multiple systematic factors describes the arbitrage pricing theory, not the CAPM's single-factor beta model. The statement that the efficient frontier is a straight line connecting the risk-free asset to the minimum-variance portfolio misidentifies the tangency point of the capital market line (CML): the CML is tangent to the risky-asset frontier at the market portfolio, not at the minimum-variance portfolio.
An adviser is comparing two possible additions to a client's portfolio. The portfolio would be invested 50% in a market index fund with an expected return of 8% and a standard deviation of 20%, and 50% in whichever candidate is selected. Candidate X has an expected return of 9%, a standard deviation of 20%, and a correlation of +0.4 with the index fund. Candidate Y also has an expected return of 9% and a standard deviation of 20%, but a correlation of -0.4 with the index fund.
Which statement is correct under modern portfolio theory? Answer: Candidate Y produces a portfolio standard deviation of about 10.95%, lower than the 16.73% produced with Candidate X.
Under modern portfolio theory, for two assets, σp² = w1²σ1² + w2²σ2² + 2w1w2ρσ1σ2. With 50/50 weights and 20% standard deviations, Candidate X (correlation +0.4) gives 100 + 100 + 80 = 280, or about 16.73%. Candidate Y (correlation -0.4) gives 100 + 100 - 80 = 120, or about 10.95%. The negative correlation offsets some of the index fund's fluctuations, so the correct statement is that Candidate Y produces the lower standard deviation. The 14.14% figure is the zero-correlation result; it does not apply to Candidate Y or to both candidates at the stated correlations, and saying Candidate X produces 14.14% ignores the positive correlation's contribution to X's variance.
A client shows an IAR a newsletter that has beaten the S&P 500 in 8 of the last 10 years by trading only on published earnings announcements. The client asks whether this performance disproves semi-strong market efficiency.
Which response is most consistent with the efficient market hypothesis? Answer: It would be evidence against semi-strong efficiency only if the returns are risk-adjusted, after costs, and persistent; otherwise the record may reflect luck or compensation for risk.
Semi-strong efficiency holds that current prices reflect all public information, so a strategy based on published earnings announcements should not generate persistent abnormal returns after risk adjustment and costs. An observed 8-of-10 record does not by itself disprove the hypothesis; the apparent outperformance may reflect higher risk, may disappear once costs are deducted, or may simply be luck. The outright-disproof answer is too absolute; the strong-form answer misapplies strong-form efficiency, which would also rule out gains from nonpublic information; the 'not relevant' answer inverts the theory because published information is central to semi-strong efficiency.
An IAR at a state-registered adviser is reviewing a large-cap stock. The risk-free rate is 2.4%, the expected return on the market portfolio is 10.2%, and the stock's beta is 1.25. The IAR's independent forecast is a 13.4% annual return for the stock.
Using the capital asset pricing model, which conclusion is correct? Answer: The CAPM required return is 12.15%, so the stock plots above the security market line and is undervalued.
Capital Asset Pricing Model: required return = risk-free rate + beta x (expected market return - risk-free rate) = 2.4% + 1.25 x (10.2% - 2.4%) = 12.15%. Because the IAR's forecast of 13.4% is above the security market line, the stock has a positive alpha of 1.25% and is undervalued. The 15.15% answer treats the expected market return as if it were the market risk premium; the 9.75% answer computes the risk premium but omits the risk-free rate. Stating that the stock is overvalued with the same 12.15% required return reverses the comparison between forecast and required return.
- A researcher finds that stocks whose earnings announcements beat analysts' expectations earn abnormal returns for several weeks after the announcement, even after trading costs. Assuming the finding is genuine and not a statistical artifact, which form of the efficient market hypothesis is most directly contradicted?
Answer: The semi-strong form, because the public earnings news is not fully reflected in stock prices at the announcement.
Under the efficient market hypothesis, the semi-strong form holds that all publicly available information is reflected in stock prices immediately. Because the abnormal returns come from trading on a public earnings announcement and persist after transaction costs, the finding most directly contradicts the semi-strong form. The weak form covers only information in past prices and returns, so calling the drift a weak-form violation misstates the information set. The claim that the EMH applies only to long-term returns over full market cycles is not part of any form of the hypothesis. The strong-form explanation is wrong because the strategy does not use nonpublic information; the earnings figures were publicly announced, so the information set involved is public, not private.
A state-registered adviser is building a two-stock portfolio. Omega is 60% of the portfolio and has a beta of 1.4. Delta is 40% of the portfolio and has a beta of 0.6. The correlation between Omega and Delta is +0.3. The expected return on the market is 8%, and the risk-free rate is 3%.
Under the CAPM, what is the portfolio's expected return? Answer: 8.4%
The portfolio beta is a weighted average of the component betas: portfolio beta = 0.6 x 1.4 + 0.4 x 0.6 = 1.08. Therefore, expected return = 3% + 1.08 x (8% - 3%) = 8.4%. The correlation between the two stocks affects portfolio variance and diversification, but it does not change the CAPM expected return once beta is known. The 11.6% answer treats the expected market return as if it were the market risk premium; 8.0% uses equal weights; 7.6% reverses the portfolio weights.
An IAR is analyzing a stock with a beta of 1.8 and a total standard deviation of 45%. The market portfolio has a standard deviation of 15%.
Under the capital asset pricing model, approximately what percentage of the stock's total variance is systematic? Answer: 36%
Beta is defined as beta = correlation x (stock standard deviation / market standard deviation), so the correlation is 1.8 x (15% / 45%) = 0.6. The fraction of the stock's variance explained by the market is the correlation squared, 0.6 x 0.6 = 0.36, or 36%; the remaining 64% is unsystematic. The 60% answer is the correlation rather than the explained variance; 64% is the diversifiable portion; 27% is the systematic standard deviation, not the percentage of variance.
- A portfolio is invested equally in Fund X and Fund Y. Fund X has a standard deviation of 30%, Fund Y has a standard deviation of 20%, and the correlation between the two funds' returns is 0.3. The portfolio's standard deviation is closest to:
Answer: 20.4%
Under modern portfolio theory, the variance of a two-asset portfolio is w12 x s12 + w22 x s22 + 2 x w1 x w2 x s1 x s2 x rho = 0.25 x 900 + 0.25 x 400 + 2 x 0.50 x 0.50 x 30 x 20 x 0.30 = 225 + 100 + 90 = 415, so the standard deviation is the square root of 415, about 20.4%. The 25.0% answer is the simple average of 30% and 20%, which ignores squared weights and correlation. The 18.0% answer omits the covariance term, which is equivalent to assuming the two funds are uncorrelated. The 25.5% answer applies the 50/50 weights directly to the variances rather than to the squared weights and also omits the covariance term. - An investor places 60% of a portfolio in a stock with a beta of 1.6 and a standard deviation of 28%, and the remaining 40% in Treasury bills yielding 3%. The expected return on the market is 11%. Under the capital asset pricing model, the portfolio's expected return is closest to:
Answer: 10.7%
Under the capital asset pricing model, only systematic risk is priced, so the stock's 28% standard deviation is a distractor. The portfolio beta is the weighted average of the component betas: 0.60 x 1.6 + 0.40 x 0 = 0.96, and the CAPM return is 3% + 0.96 x (11% - 3%) = 10.68%, or about 10.7%. The 15.8% figure uses the stock's full beta of 1.6 and ignores the 40% allocated to T-bills. The 13.6% figure uses the correct 0.96 beta but treats the market's 11% expected return as the risk premium (3% + 0.96 x 11%). The 7.8% figure weights the market return and the T-bill rate by the portfolio weights (0.60 x 11% + 0.40 x 3%) and ignores beta entirely.
An IAR uses a three-factor arbitrage pricing model (APT) to evaluate a stock. The risk-free rate is 2.0%. The stock has factor sensitivities of 1.2 to industrial production, -0.5 to inflation, and 0.8 to the term premium. The factor risk premiums are 3.0%, 2.0%, and 1.0%, respectively. The IAR's own forecast for the stock is an 8.0% return.
Based on the APT model, the stock is best described as: Answer: Underpriced, because the APT expected return is 5.4% and the forecast return exceeds it by 2.6%.
Arbitrage Pricing Theory: E(R) = Rf + sum of (factor sensitivity x factor risk premium) = 2% + 1.2(3%) - 0.5(2%) + 0.8(1%) = 5.4%. Because the IAR's 8.0% forecast exceeds the APT expected return, the stock has a positive expected alpha and is underpriced; buying should raise the price until the expected return falls toward the model rate. The 7.4% answer treats the inflation sensitivity as positive, and calling the stock overpriced also reverses the sign of the alpha. The 8.0% answer adds the factor risk premiums to the risk-free rate without applying the sensitivities. The 3.8% answer misapplies the sign of the term-premium sensitivity.
