Baran

 

7、A 12-year, 8 percent annual coupon bond with $100 par value currently sells at par. The bond is callable at 102. What is the effective duration of the bond assuming interest rates change by 100 basis points?

A) 5.85.  

B) 4.58. 

C) 7.55.  

D) 10.50.

Baran

 

The correct answer is B

 

Since the bond is selling at par, its yield = coupon rate = 8%.

V0 = Par = 100.

I/Y = 7.00; FV = 100; N = 12; PMT = 0.08 x 100 = 8; PV = V- = 107.94.

Since the call price is 102 which is lower than 107.94, we use V- = 102

I/Y = 9.00; FV = 100; N = 12; PMT = 0.08 x 100 = 8; PV = V+ = 92.84     

D = Duration = (V- - V+)/2V0(Δy)         

                     = (102-92.84)/(200x0.01)

                     = 4.58

Baran

 

8、Duration of a bond can be defined as the:

A) sensitivity of the value of the bond to a change in maturity.  

B) sensitivity of the value of the bond to a change in interest rates. 

C) weighted-average maturity of a bond portfolio.  

D) sensitivity of the value of the bond to a change in the value of market portfolio.

Baran

 

The correct answer is B

 

Duration is the first derivative of price with respect to yield and hence measures the sensitivity of the value of the bond to a change in interest rates. Weighted average maturity does not take into account cash flows or yield. Sensitivity of the value of an asset to change in maturity is not defined; and sensitivity of the value of an asset to change in the value of the market portfolio is defined as beta.

Baran

 

5、A 12-year, 5 percent semiannual coupon bond with $100 par value currently yields 8.00 percent. What is the duration of the bond given a 100 basis point increase and decrease in yield?

A) 7.80.  

B) 12.56. 

C) 16.78.  

D) 8.38.

Baran

 

The correct answer is D

 

I/Y = 8/2=4; FV = 100; N = 24; PMT = 0.05/2 x 100 = 2.50; PV = V0 = 77.13

I/Y = 7/2=3.50; FV = 100; N = 24; PMT = 0.05/2 x 100 = 2.50; PV = V- = 83.94

I/Y = 9/2=4.50; FV = 100; N = 24; PMT = 0.05/2 x 100 = 2.50; PV = V+ = 71.01

D = effective duration = (V- - V+)/2V0(Δy)

= (83.94-71)/(2x77.13x0.01)

= 8.38 years

Baran

 

6、Which of the following statements regarding duration is FALSE?

A) Duration is unitless.  

B) Duration is a measure of percentage change in price for a given change in yield.

C) Duration of a portfolio of bonds is equal to the market value weighted average of the duration of individual bonds in the portfolio.

D) Other things equal, bonds with longer durations tend to have higher yields.

Baran

 

The correct answer is A

 

Duration is a measure of percentage change in price for a given change in yield. Hence it is not unitless like beta. Since duration is a measure of risk for bonds, bonds with higher duration tend to have a higher yield (other things being equal). Portfolio duration can be computed as simply market-value weighted durations of individual bonds in the portfolio.

Baran

 

The correct answer is B

Baran

 

Given your answers to the two prior questions, the percentage price change associated with a 20-basis-point increase in yield is closest to a:

A) decrease of 1.56%.   

B) decrease of 1.60%.  

C) decrease of 1.58%.   

D) decrease of 1.54%.