# 5 the steeper the capital allocation line the better

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5. The steeper the capital allocation line, the better the investment opportunities to a risk-averse investor. True: The steeper the CAL, the better the reward-to-variability ratio, and thus the better the return for any level of risk. That is, the better the investment opportunities. 6. Consider Figure 1. If the curve MV F represents the minimum-variance frontier, then a portfolio such as portfolio A cannot exist. False: If there exists a risk free asset and its return, r f , allows it, then portfolio A can 2

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be a combination of a risky portfolio and the risk-free asset. That is, A cannot be a portfolio composed entirely of risky assets, since these portfolios are all to the right of the MV F curve. It can nevertheless can be a combination of portfolio P , for instance, and the risk-free asset, as shown in Figure 2. σ E [ r ] MV F A Figure 1: The minimum-variance frontier. Part II: Problems . Answer TWO of the following problems (10 points each). 1. Margin Purchase Suppose you buy on margin 1,000 shares of company XYZ, currently selling at \$30 per share, with an initial margin ratio of 50%. The interest on your broker’s loan is 6% annually and the maintenance margin requirement is 30%. (a) (4 points) If the stock price of XYZ is \$35 one year from now, what will the return on the margin purchase be? Will you receive a margin call? If so, how much money will you have to deposit in your account? How does the return on the margin purchase compare with the return on the stock? Answer: The initial margin of 50% means that \$30 × 1 , 000 2 = \$15 , 000 has initially been invested and \$15,000 has been borrowed from the broker. The return on the margin purchase is then 35 × 1 , 000 - 15 , 000 × 1 . 06 - 15 , 000 15 , 000 = 27 . 33% . Since the trade was profitable, the margin ratio after can only be higher than what it was initially, i.e. it is necessarily higher than 50% and thus there cannot 3
σ E [ r ] MV F A r f P Figure 2: How to obtain portfolio A . be a margin call. We can nevertheless look at the exact value of the margin ratio after one year, which is assets - liabilities assets = 35 , 000 - 15 , 000 × 1 . 06 35 , 000 = 54 . 57% > 30% .

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• Spring '12
• Scott
• Closed-end fund, margin purchase

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