CHAPTER 4

Test Bank

1. An interest rate is 15% per annum when expressed with annual compounding. What is the equivalent rate with continuous compounding?

i=ln(1+HPY)=ln(1.15)

i=13.98%

2. An interest rate is 8% per annum when expressed with continuous compounding. What is the equivalent rate with semiannual compounding?

e^0.08=1.08328

(1.08328-1)*100=8.33%

BEY=((1+8.33%)^(1/2)-1)*2*100=8.16%

3. An interest rate is 12% when expressed with quarterly compounding. What is the equivalent rate with semiannual compounding?

BEY=((1+(0.12/4))^2-1))*2*100=12.18%

4. The three-year zero rate is 7% and the four-year zero rate is 7.5% (both continuously compounded. What is the forward rate for the fourth year?

forward=(( (1+.075)^4 / (1+.07)^3 )-1)*100=9.0141%

5. The six-month zero rate is 8% with semiannual compounding. The price of a one-year bond that provides a coupon of 6% per annum semiannually is 97. What is the one-year continuously compounded zero rate?

ln(100/96.15)=e^(r*.5)

r= .0784

3e^-0.0784*.5 + 103e^-r = 97

e^-r = (97-2.88)/103

r=-ln(.9138)

r=.09018=9.0158%

6. The yield curve is flat at 6% per annum with semiannual compounding. What is the value of an FRA where the holder receives interest at the rate of 8% per annum for a six-month period on a principal of $1,000 starting in two years?

yield curve (4-5): 1000*1.03= 1030

FRA (4-5): 1000*1.04= 1040

FRA-yc=1040-1030=10

10e^(-0.03*5)=8.6071

7. Under liquidity preference theory, which of the following is always true (circle one)

(a) The forward rate is higher than the spot rate when both have the same maturity.

(b) Forward rates are unbiased predictors of expected future spot rates.

(c) The spot rate for a certain maturity is higher than the par yield for that maturity.

(d) Forward rates are higher than expected future spot rates.

8. When the zero curve is upward sloping, which of the following is true?

(a) The one-year zero rate is always greater than the forward rate for the period between 1 year and 1.5 years.

(b) The one-year zero rate is always less than the forward rate for the period between 1 year and 1.5 years.

(c) The one-year par yield is always greater than the one-year zero rate.

(d) None of the above

9. The short term risk-free rate usually used by derivatives traders is (circle one)

(a) The Treasury rate

(b) The LIBOR rate

(c) The repo rate

(d) The commercial paper rate

10. A company invests $1,000 in a five-year zero-coupon bond and $4,000 in a ten-year zero-coupon bond. What is the duration of the portfolio?

D = (1000/5000)*5 + (4000/5000)*10= 9