Exam 25: Portfolio Theory and Asset Pricing Models

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For markets to be in equilibrium (that is,for there to be no strong pressure for prices to depart from their current levels),

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Arbitrage pricing theory is based on the premise that more than one factor affects stock returns,and the factors are specified to be (1)market returns, (2)dividend yields,and (3)changes in inflation.

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The CAPM is a multi-period model which takes account of differences in securities' maturities,and it can be used to determine the required rate of return for any given level of systematic risk.

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You plan to invest in Stock X,Stock Y,or some combination of the two.The expected return for X is 10% and σ\sigma X = 5%.The expected return for Y is 12% and σ\sigma Y = 6%.The correlation coefficient,rXY,is 0.75. a. Calculate rp and σ\sigma p for 100%, 75%, 50%, 25%, and 0% in Stock X. b. Use the values you calculated for rp and σ\sigma p to graph the attainable set of portfolios. Which part of the attainable set is efficient? Also, draw in a set of hypothetical indifference curves to show how an investor might select a portfolio comprised of Stocks X and Y. Let an indifference curve be tangent to the efficient set at the point where rp = 11%. c. Now suppose we add a riskless asset to the investment possibilities. What effects will this have on the construction of portfolios? d. Suppose rM = 12%, σ\sigma M = 4%, and rRF = 6%. What would be the required and expected return on a portfolio with σ\sigma P = 10%? e. Suppose the correlation of Stock X with the market, rXM, is 0.8, while rYM = 0.9. Use this information, along with data given previously, to determine Stock X's and Stock Y's beta coefficients. f. What is the required rate of return on Stocks X and Y? Do these stocks appear to be in equilibrium? If not, what would happen to bring about an equilibrium?

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Which of the following statements is CORRECT?

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If investors are risk averse and hold only one stock,we can conclude that the required rate of return on a stock whose standard deviation is 0.21 will be greater than the required return on a stock whose standard deviation is 0.10.However,if stocks are held in portfolios,it is possible that the required return could be higher on the low standard deviation stock.

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Which of the following statements is CORRECT?

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You are given the following returns on "the market" and Stock F during the last three years.We could calculate beta using data for Years 1 and 2 and then,after Year 3,calculate a new beta for Years 2 and 3.How different are those two betas,i.e.,what's the value of beta 2 - beta 1? (Hint: You can find betas using the Rise-Over-Run method,or using your calculator's regression function.) Year Market Stock F 1 6.10\% 6.50\% 2 12.90\% -3.70\% 3 1620\% 2171\%

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Which of the following statements is CORRECT?

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It is possible for a firm to have a positive beta,even if the correlation between its returns and those of another firm are negative.

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Your mother's well-diversified portfolio has an expected return of 12.0% and a beta of 1.20.She is in the process of buying 100 shares of Safety Corp.at $10 a share and adding it to her portfolio.Safety has an expected return of 15.0% and a beta of 2.00.The total value of your current portfolio is $9,000.What will the expected return and beta on the portfolio be after the purchase of the Safety stock? rp bp

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The SML relates required returns to firms' systematic (or market)risk.The slope and intercept of this line can be influenced by managerial actions.

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A stock you are holding has a beta of 2.0 and the stock is currently in equilibrium.The required rate of return on the stock is 15% versus a required return on an average stock of 10%.Now the required return on an average stock increases by 30.0% (not percentage points).The risk-free rate is unchanged.By what percentage (not percentage points)would the required return on your stock increase as a result of this event?

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In portfolio analysis,we often use ex post (historical)returns and standard deviations,despite the fact that we are interested in ex ante (future)data.

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You hold a portfolio consisting of a $5,000 investment in each of 20 different stocks.The portfolio beta is equal to 1.12.You have decided to sell a coal mining stock (b = 1.00)at $5,000 net and use the proceeds to buy a like amount of a mineral rights company stock (b = 2.00).What is the new beta of the portfolio?

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