Reading 69: Introduction to the Measurement of Interest R

答案和详解如下：

1.Assume that the current price of a bond is 102.50. If interest rates increase by 0.5 percent the value of the bond decreases to 100 and if interest rates decrease by 0.5 percent the price of the bond increases to 105.5. What is the effective duration of the bond?

A)   5.37.

B)   5.48.

C)   5.50.

D)   5.85.

The correct answer was A)

The duration is computed as follows:

2.Consider an annual coupon bond with the following characteristics:

§       Face Value of $100

§       Time to Maturity of 12 years

§       Coupon Rate of 6.50%

§       Issued at Par

§       Call Price of 101.75 (assume the bond price will not exceed this price)

For a 75 basis point change in interest rates, the bond's duration is:

A)   5.09 years.

B)   8.17 years.

C)   8.79 years.

D)   5.80 years.

The correct answer was A)

3.Calculate the effective duration for a 7-year bond with the following characteristics:

§       Current price of $660

§       A price of $639 when interest rates rise 50 basis points

§       A price of $684 when interest rates fall 50 basis points

A)   6.8.

B)   3.1.

C)   6.5.

D)   6.1.

The correct answer was A)

4.A non-callable bond with 18 years remaining maturity has an annual coupon of 7 percent and a $1,000 par value. The current yield to maturity on the bond is 8 percent. Which of the following is closest to the effective duration of the bond?

A)   9.63.

B)   11.89.

C)   8.24.

D)   12.72.

The correct answer was A)

First, compute the current price of the bond as:  FV=$1000, PMT=$70, N=18, I/Y=8%, compute PV= –$906.28.  Then compute the price of the bond if rates rise by 50 basis points to 8.5% as: FV=$1000, PMT=$70, N=18, I/Y=8.5%, compute PV= –$864.17.  Then compute the price of the bond if rates fall by 50 basis points to 7.5% as: FV=$1000, PMT=$70, N=18, I/Y=7.5%, compute PV= –$951.47.  The formula for effective duration is: (V_-–V₊)/(2V₀Δy).  Therefore, effective duration is:
($951.47 – $864.17)/(2 x $906.28 x 0.005) = 9.63.

5.A bond with a yield to maturity of 8.0% is priced at 96.00. If its yield increases to 8.3% its price will decrease to 94.06. If its yield decreases to 7.7% its price will increase to 98.47. The effective duration of the bond is closest to:

A)   7.66.

B)   4.34.

C)   2.75.

D)   27.53.

The correct answer was A)

The change in the yield is 30 basis points.

Duration = (98.47-94.06)/(2*96.00*0.003) =7.6563.