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Homework answers / question archive / 1)Which ONE of the following bonds would have highest interest rate risk?   a

1)Which ONE of the following bonds would have highest interest rate risk?   a

Finance

1)Which ONE of the following bonds would have highest interest rate risk?

  a.

17-year zero coupon bond with $1,000 face value.
  b.

5-year 10% annual coupon bond with $1,000 face value.
  c.

12-year 4% annual coupon bond with $1,000 face value.
  d.

12-year 7% annual coupon bond with $1,000 face value.
  e.

17-year 5% annual coupon bond with $1,000 face value.

2)

A $5,000 bond with a coupon rate of 6.4% paid semi-annually has four years to maturity and a yield to maturity of 6.2%. If interest rates fall and the yield to maturity decreases by 0.8%, what will happen to the price of the bond?

  a.

Fall by $40.49.
  b.

Rise by $142.78.
  c.

Rise by $84.46.
  d.

Fall by $98.64.
  e.

None of the answers are correct.

 

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1)Interest rate risk is defined by duration of bond, and duration is higher for bonds with longer maturity and less coupon rate,

So,

Option A is correct

17 year zero coupon bond with $1,000

2)

Answer)

Given

Interest Rate

= 6.2% / 2

= 3.1%
Coupon

= (0.064 X 5000) / 2

=$160
n

= 4 X 2

= 8 YEARS

Price = Coupon x [1 - 1 / (1 + r)n] / r + FV / (1 + r)n

Price = 160 x [ 1 - 1 / (1.031)8] / 0.031 + 5000 / (1 + 0.031)8

= 160 x 6.85 + 3937

= $5035

Interest Rate

= 6.2% - 0.8%

= 5.4%
Coupon

= (0.064 X 5000) / 2

=$160
n

= 4 X 2

= 8 YEARS
Rate

= 5.4% / 2

= 2.7%

Price = Coupon x [1 - 1 / (1 + r)n] / r + FV / (1 + r)n

Price = 160 x [ 1 - 1 / (1.027)8] / 0.0327 + 5000 / (1 + 0.027)8

= 160 x 7.09 + 4042

= $ 5177

Change in price = $5177 - $5035

= $142

Price has fallen by $142.

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