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Workshop 7

Questions from prior examinations

1.   Security A has a beta of 1.0 and an expected return of 12%. Security B has a beta of 0.75 and an expected return of 11%. The risk-free rate is 6%. Explain the arbitrage opportunity that     exists; explain how an investor can take advantage of it. Give details about how to form the   portfolio, including what to buy and what to sell.

2.   Suppose that a well-diversified Portfolio A is priced based on two factors, F1  and F2 . Portfolio A’s beta on F1  is 1. 1, and its beta on F2  is 0.45. Furthermore, the expected return on F1 is 11%, and 17% on F2 . The risk-free rate of return is 5.2%. Use the APT relationship to answer the following:

(i)     What is the risk premium on each of the two factors, F1 and F2?

(ii)    What is the risk premium on portfolio A, due to its exposure to each of the two factors?

(iii)   What is the total risk premium and total expected return on portfolio A?

3.  You currently hold two bonds that mature in 5 years. The first is a zero coupon bond that pays $1,000 at maturity, and the second is a 7% coupon bond, which pays coupons semi-annually. Your tax rate is 35% on ordinary income, and 25% on capital gains income. The yield to maturity is presently 7% p.a.

Required:

(i)     Calculate the prices of the two bonds now, assuming they are priced to yield 7% p.a.

(ii)    What is the price of each of your two bonds in one year, assuming that the yield

to maturity will be 7% p.a. at that time? What is your pre-tax and after-tax holding period return over the year?

(iii)   Recalculate your answer to ii. above, but instead assume that the yield to maturity

will be 6% p.a. one year from today.