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mid-term2008[1]

# mid-term2008[1] - want to make some investment on Bonds A...

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Department of System Engineering and Engineering Management SEG3590 Investment Science Mid-Term Examination Note 1 Open book. Note 2 All calculations must be shown in details. [Total 90 minutes; 100 marks] 1. Suppose that you took a loan of \$ 200,000 to be paid back in full by 36 equal monthly installments. The nominal interest rate is 6% per annum with monthly compouding. (a) Calculate the total interest you would pay for this loan. (b) If you repay every half a month (namely, by 72 equal installments with compouding every half a month) instead, how much would you save for the interest? 2. Bond A, with a face value \$100, pays coupon semiannually with coupon rate 7% and will mature after one year. Bond B, with face value \$100, zero-coupon, will mature after three years. The last coupon of A has just been paid. The price of A is \$100. (Suppose the yield of Bond A is the market yield.) (a) What is the yield of Bond A? (b) What is the Macaulay duration of Bond A? (c) You want to buy a car two years later. And the cost is \$100,000.

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Unformatted text preview: want to make some investment on Bonds A and B above for your car plan. How much money should you invest on each of them, so that the investment can approximately support your plan, and the diﬀerence between the value of the investment and the cost of the car will not be sensitive to the change on the yield? 3. The following table list the cash ﬂows and prices of 3 U.S. treasury securities. Bond A B C Maturity (year) 1 3 3 Coupon rate 5% 10% Face value(\$) 100 100 100 Price(\$) 95.24 96.92 110.35 Suppose all the securities pay the coupon (if they pay) annually. Use these data to determine the current spot rate s 1 , s 2 and s 3 . 1 4. Consider three uncorrelated stocks, with variance 2,2,4, and the mean rate of returns 1,2,2, respectively. Suppose shorting is allowed. (a) Determine the mean-variance eﬃcient portfolio in terms of the mean return rate of the portfolio,¯ r . (b) Find the eﬃcient portfolio that achieves the minimum-variance point. 2...
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• Spring '10
• LiDuan
• equal monthly installments, System Engineering and Engineering Management SEG3590 Investment Science, Investment Science Mid-Term

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