Question

Prob 3.1 (A-D) 4 parts

Reminder: Duration is always calculated using PV dollars. Show all work and label all numbers with units.

1. (3 points) Assume 2 securities have the following annual Cash Flows (CFs):

            CF1                CF2                CF3   

A:        $200               $350               $500

B:        $500               $350               $200

a. If the appropriate interest rate (R) is 5.0%, calculate the present value of each of the individual CFs. Calculate the price (PV) of these securities using an interest rate of 5.0%.

B. Calculate the duration of each security.

C. Which security has a lower duration? Explain why in an essay and refer specifically to your results above.

D. If interest rates increase to 6.00%, calculate the new price (in dollars) of each security using the Duration formula below:

           

            %Price = -D x    ? R          

                                             1 + R

Answer 1

Security B has lower duration.

Duration is basically the effect of change in rates on the price of the security. If you see in security B, higher cash flows are getting generated at intial period of time. So these cash flows will have lower senstivity to the interest rates (because of lower discounting). So that is why, overall, security B will has less senstivity towards interest rate as compared to B.

%change in price = - duration*change in rates

using this formula and duration calculated above, following are the new prices.