Arizona State University - FIN 421 / FIN421 Lecture 6 Practice Questions

Lecture 6 Practice Questions 1. The variance of a portfolio of risky securities is . A) the sum of the securities’ covariances with the portfolio B) the sum of the securities’ variances C) the weighted sum of the securities’ covariances with the porfolio D) the weighted sum of the securities’ variances E) none of the above Answer: C 2. According to the capital asset pricing model, . A) all securities must lie on the capital market line B) all securities must lie on the security market line C) underpriced securities lie below the security market line D) overpriced securities lie above the security market line E) all of the above Answer: B The SML plots expected returns against betas. All securities should lie on this line. If a security lies above the line, its expected return is higher than implied by the CAPM, therefore the security will be underpriced. 3. A security’s beta coefficient will be negative if A) its returns are negatively correlated with market index returns B) its returns are positively correlated with market index returns C) its stock price has historically been very stable D) its returns have been on average negative for a while E) market demand for the firm’s shares is very low Answer: A Beta is the ratio of covariance to the market variance. Since variances are always positive, a negative beta is equivalent to a negative correlation. 14. Consider the CAPM. The risk-free rate is 5% and the expected return on the market is 15%. What is the beta on a stock with an expected return of 12%? A) .5 B) .7 C) 1.2 D) 1.4 E) None of the above Answer: B :12 − :05 = β × (:15 − :05); or β = 0:7 5. The risk-free rate is 4%. The expected market rate of return is 11%. If you expect stock X with a beta of .8 to offer a rate of return of 12 percent, then according to the CAPM you should . A) buy stock X because it is overpriced B) buy stock X because it is underpriced C) sell short stock X because it is overpriced D) sell short stock X because it is underpriced E) None of the above Answer: B :04 + 0:8(:11 − :04) :12; ! α 0: A positive α means the security is underpriced. 6. Which is NOT a true statement regarding the market portfolio. A) All securities in the market portfolio are held in proportion to their market values B) It includes all assets of the universe C) It is the tangency point between the capital market line and the indifference curve D) It lies on the efficient frontier E) All are true Answer: C The market portfolio is the tangency portfolio, but not every investors indifferent curve will touch the CML in this point. Investors will combine the market portfolio with the risk-free asset to find their highest utility. 27. Suppose the Capital Asset Pricing Model (CAPM) assumptions hold. The market portfolio consists of only 2 risky assets, which are in positive net supply. The expected rate of return of assets A and B are 10% and 13% respectively, their market betas are 0.5 and 0.8 respectively, and the risk free rate is 5%. Is this economy in equilibrium? A) Yes, both assets lie on the SML, satisfying the optimality of the market. B) No, asset A is held in negative amount in the tangency portfolio in contrast to supply=demand condition. C) No, asset B is held in negative amount in the tangency portfolio in contrast to supply=demand condition. D) It is impossible to tell without further information about the correlation between the two assets E) None of the above Answer: B The elegant answer is: Both assets have betas less than one! Since the market must have a beta of one, it will consist of a short position in asset B: wAβA + (1 − wA)βB = 1; or 0:5wA + (1 − wA)0:8 = 1; or wA = −2=3: You can get to the same conclusion by computing the expected market return: 10% − 5% = 0:5 × (µM − 5%), or µM = 15. The equation for the other stock holds as well. But, both stocks have expected returns lower than the market, therefore a short position would be necessary. 8. Security A has an expected rate of return of 12% and a beta of 1.10. The market expected rate of return is 8% and the risk-free rate is 5%. The alpha of the stock is . A) -1.7% B) 3.7% C) 5.5% D) 8.7% Answer: B E(r) = :05 + 1:1(:08 − :05) = :083; and therefore α = :12 − :083 = :037 9. The beta of a security is A) The covariance between the security and the market returns divided by the variance of the market returns. B) The covariance between the security and the market returns divided by the variance of the security’s returns. 3