Answers to text problems

[Adam Gehr]

First you need to calculate the present value of the liability. This is
$10 million so you know you need that amount of bonds. Then you calculate
the duration of the liability, which is 11 years. You know you must mix 5
and 20 year bonds to have a weighted average duration of 11 years, i.e.:
5x+20(1-x)= 11. 
Now you need to solve for the weights. Finally multiply the weights times
$10 million to get the current market value of the bonds you will buy.


On Tue, 4 Mar 2003, Ofelia Sanchez wrote:

> 
> Hi,
> Can someone help me figure out problem 12.   I am not sure how to get the weights for the 5 yr. zeros and the 20 yr zeros.  
> Thank-you, 
> Ofelia
>  Adam Gehr <agehr at mozart.depaul.edu> wrote:Here are the answers to the problems I assigned in class last week.
> 
> 1) -3.27%
> 
> 2) a. 2.833 years
> b. 2.824 years
> 
> 3) 1.952 years
> 
> 6) a. B is shorter duration
> b. A has longer duration
> 
> 7) Ranking from longest to shortest Duration: C D A B E.
> 
> 8) a. Modified duration is 9.26 years
> b. Duration takes into account size and timing of all cash flows as
> well as the level of interest rates.
> c. i. Higher coupon implies lower duration
> ii. Duration decreases as maturity decreases.
> 
> 10) a. Duration of obligation 1.16/.16 = 7.25 years.
> PV of obligation $12.5 million
> put 6.7 million in the 5-year bond and 5.8 million in the 20-year
> bond.
> 
> b. 14.25 million
> 
> 12) a. market value: $6 million in 5-year zeros and $4 million in 20
> years.
> 
> b. Face value $9.66 million in 5-year bonds and $26.91 in 20-year
> bonds. 
> 
> 
> 
> 
> 
> ---------------------------------
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