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solution

A portfolio manager for a target retirement date bond
mutual fund for clients with a 6-year investment holding horizon,
would like to ensure a 5% annual compound return for the
fund. He has a choice between two bonds. Whatever
money he has to invest will be invested bonds of one type or the
other, so the difference in the prices of the two types of bonds is
not a consideration.

Find the Duration and Modified Duration for each
bond (show your work and answer the questions below)

  • Bond 1 has a 5% annual coupon rate, $1000
    maturity value, n = 6 years, YTM = 5%
    (pays a $50 annual coupon at the end of each year for each of the 6
    years and $1,000 maturity payment at the end of year
    6).
  • Bond 2 is a zero-coupon bond with a $1000
    maturity value, and n = 6 years; YTM= 5%.
    (pays no coupons; only a $1,000 maturity payment at the end of year
    6)

a. Price Bond 1
___________
Price Bond 2 _ _______

b. Duration Bond 1 ________ Duration Bond 2
_________

c. Modified Duration Bond 1 _______
Modified Duration Bond 2 ____________

(Be sure to show your work for the bond price and duration
calculations for credit).

d. Which of the two bonds should you choose for your
6-year investment horizon to duration match to ensure your desired
5% annual compound yield if you hold the bond to maturity? Explain
why.
(assume the same default risk for each
bond).

e. If interest rates go up by 1%, what will be the
% Change in the market value for each Bond’s Price? (Hint
Change in Price % = – Modified Duration x Change in Rate (expressed
as a fraction, i.e. .01).

f. Which of the 2 bonds has more price risk and
which has more reinvestment risk?

Explain why.

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