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1、Problems1.The following table lists foreign exchange rates between US dollars and British pounds during April.DateUS Dollars per GBPDateUS Dollars per GBP4/11.95644/181.7504 4/41.92934/191.7255 4/51.9144/201.6914 4/61.93744/211.672 4/71.9614/221.6684 4/81.89254/251.6674 4/111.88224/261.6857 4/121.85
2、584/271.6925 4/131.7964/281.7201 4/141.79024/291.7512 4/151.7785Which day would have been the best day to convert $200 into British pounds?Which day would have been the worst day? What would be the difference in pounds?2.Consider a bond with a 7% annual coupon and a face value of $1,000. Complete th
3、e following table:Years to MaturityDiscount RateCurrent Price35 37 67 97 99What relationship do you observe between yield to maturity and the current market value? Years to Maturity Yield to Maturity Current Price 3 5 $1,054.46 3 7 $1,000.00 6 7 $1,000.00 9 5 $1,142.16 9 9 $ 880.10 When yield to mat
4、urity is above the coupon rate, the bands current price is below its face value. The opposite holds true when yield to maturity is below the coupon rate. For a given maturity, the bonds current price falls as yield to maturity rises. For a given yield to maturity, a bonds value rises as its maturity
5、 increases. When yield to maturity equals the coupon rate, a bonds current price equals its face value regardless of years to maturity.3.You are willing to pay $15,625 now to purchase a perpetuity which will pay you and your heirs $1,250 each year, forever, starting at the end of this year. If your
6、required rate of return does not change, how much would you be willing to pay if this were a 20-year, annual payment, ordinary annuity instead of a perpetuity? Solution: To find your yield to maturity, Perpetuity value PMT/I. So, 15625 1250/I. I 0.08 The answer to the final part, using a financial c
7、alculator: N 20; I 8; PMT 1250; FV 0 Compute PV : PV 12,272.694.A bank has two, 3-year commercial loans with a present value of $70 million. The first is a $30 million loan that requires a single payment of $37.8 million in 3 years, with no other payments until then. The second is for $40 million. I
8、t requires an annual interest payment of $3.6 million. The principal of $40 million is due in 3 years. a.What is the duration of the banks commercial loan portfolio? b.What will happen to the value of its portfolio if the general level of interest rates increased from 8% to 8.5%?Solution: The durati
9、on of the first loan is 3 years since it is a zero-coupon loan. The duration of the second loan is as follows:Year123SumPayment3.603.6043.60 PV of Payments3.333.0934.6141.03 Time Weighted PV of Payments3.336.18103.83 Time Weighted PV of Payments Divided by Price0.080.152.532.76The duration of a port
10、folio is the weighted average duration of its individual securities. So, the portfolios duration 3/7 (3) 4/7 (2.76) 2.86If rates increased, 0.005DUR2.8670,000,000926,852.11.08iPPi 5.Consider a bond that promises the following cash flows. The required discount rate is 12%.Year01234Promised Payments16
11、0170180230You plan to buy this bond, hold it for 2 years, and then sell the bond. a.What total cash will you receive from the bond after the 2 years? Assume that periodic cash flows are reinvested at 12%. b.If immediately after buying this bond, all market interest rates drop to 11% (including your
12、reinvestment rate), what will be the impact on your total cash flow after 2 years? How does this compare to part (a)? c.Assuming all market interest rates are 12%, what is the duration of this bond?Solution: a.You will receive 160, reinvested that for 1.5 years, and 170 reinvested for 0.5 years. The
13、n you will sell the remaining cash flows, discounted at 12%. This gives you:1.50.5 0.51.5180230160 (1.12)170 (1.12)$733.69.1.121.12b.This is the same as part (a), but the rate is now 11%.1.50.5 0.51.5180230160(1.11)170(1.11)$733.74.1.111.11Notice that this is only $0.05 different from part (a). c.Th
14、e duration is calculated as follows:Year1234SumPayments160.00170.00180.00230.00 PV of Payments142.86135.52128.12146.17552.67 Time Weighted PV of Payments142.86271.05384.36584.68 Time Weighted PV of PaymentsDivided by Price0.260.490.701.062.50Since the duration and the holding period are the same, yo
15、u are insulated from immediate changes in interest rates! It doesnt always work out this perfectly, but the idea is important.6. You own a $1,000-par zero-coupon bond that has 5 years of remaining maturity. You plan on selling the bond in one year, and believe that the required yield next year will
16、have the following probability distribution:ProbabilityRequired Yield0.16.60% 0.26.75% 0.47.00% 0.27.20% 0.17.45%a.What is your expected price when you sell the bond?b.What is the standard deviation?Multiple Choice1.When the inflation rate is expected to increase, the real cost of borrowing declines at any given interest rate; as a result, the _D_ bonds increases and the _ curve shifts to the right.
