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1、.CHAPTER 4Interest RatesPractice QuestionsProblem 4.1.A bank quotes you an interest rate of 14% per annum with quarterly compounding. What is the equivalent rate with (a) continuous compounding and (b) annual compounding? (a) The rate with continuous compounding is or 13.76% per annum. (b) The rate
2、with annual compounding is or 14.75% per annum. Problem 4.2.What is meant by LIBOR and LIBID. Which is higher? LIBOR is the London InterBank Offered Rate. It is calculated daily by the British Bankers Association and is the rate a AA-rated bank requires on deposits it places with other banks. LIBID
3、is the London InterBank Bid rate. It is the rate a bank is prepared to pay on deposits from other AA-rated banks. LIBOR is greater than LIBID. Problem 4.3.The six-month and one-year zero rates are both 10% per annum. For a bond that has a life of 18 months and pays a coupon of 8% per annum (with sem
4、iannual payments and one having just been made), the yield is 10.4% per annum. What is the bonds price? What is the 18-month zero rate? All rates are quoted with semiannual compounding. Suppose the bond has a face value of $100. Its price is obtained by discounting the cash flows at 10.4%. The price
5、 is If the 18-month zero rate is, we must have which gives %. Problem 4.4.An investor receives $1,100 in one year in return for an investment of $1,000 now. Calculate the percentage return per annum with a) annual compounding, b) semiannual compounding, c) monthly compounding and d) continuous compo
6、unding. (a) With annual compounding the return is or 10% per annum. (b) With semi-annual compounding the return is where i.e., so that. The percentage return is therefore 9.76% per annum. (c) With monthly compounding the return is where i.e.so that . The percentage return is therefore 9.57% per annu
7、m. (d) With continuous compounding the return is where: i.e., so that. The percentage return is therefore 9.53% per annum. Problem 4.5.Suppose that zero interest rates with continuous compounding are as follows: Maturity (months)Rate (% per annum)38.068.298.4128.5158.6188.7Calculate forward interest
8、 rates for the second, third, fourth, fifth, and sixth quarters. The forward rates with continuous compounding are as follows toQtr 28.4%Qtr 38.8%Qtr 48.8%Qtr 59.0%Qtr 69.2%Problem 4.6.Assuming that zero rates are as in Problem 4.5, what is the value of an FRA that enables the holder to earn 9.5% fo
9、r a three-month period starting in one year on a principal of $1,000,000? The interest rate is expressed with quarterly compounding. The forward rate is 9.0% with continuous compounding or 9.102% with quarterly compounding. From equation (4.9), the value of the FRA is therefore or $893.56. Problem 4
10、.7.The term structure of interest rates is upward sloping. Put the following in order of magnitude: (a) The five-year zero rate (b) The yield on a five-year coupon-bearing bond (c) The forward rate corresponding to the period between 4.75 and years in the future What is the answer to this question w
11、hen the term structure of interest rates is downward sloping? When the term structure is upward sloping, . When it is downward sloping, . Problem 4.8.What does duration tell you about the sensitivity of a bond portfolio to interest rates? What are the limitations of the duration measure? Duration pr
12、ovides information about the effect of a small parallel shift in the yield curve on the value of a bond portfolio. The percentage decrease in the value of the portfolio equals the duration of the portfolio multiplied by the amount by which interest rates are increased in the small parallel shift. Th
13、e duration measure has the following limitation. It applies only to parallel shifts in the yield curve that are small. Problem 4.9.What rate of interest with continuous compounding is equivalent to 15% per annum with monthly compounding? The rate of interest is where: i.e., The rate of interest is t
14、herefore 14.91% per annum. Problem 4.10.A deposit account pays 12% per annum with continuous compounding, but interest is actually paid quarterly. How much interest will be paid each quarter on a $10,000 deposit? The equivalent rate of interest with quarterly compounding is where or The amount of in
15、terest paid each quarter is therefore: or $304.55. Problem 4.11.Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum with continuous compounding respectively. Estimate the cash price of a bond with a face value of 100 that will mature in 30 months and pays a coupon of 4% per annum semiannually. The bond pays $2 in 6, 12, 18, and 24 months, and $102 in 30 months. The cash price is Problem 4.12.A three-year bon
