You are to design for a small pension fund a bond portfolio to fund a $10 millio

Question

You are to design for a small pension fund a bond portfolio to fund a $10 million obligation due in
4 years. The fund managers would like to use a 2-year zero along with an 8-year zero to fund the
obligation. Currently, the yield curve is flat at around 5% for all maturities.
a. Design a bond portfolio that will protect the pension fund from fluctuations in interest
rates.
b. Suppose that immediately after you set up the portfolio, the yield curve shifts to 6% at all
maturities. Calculate what you expect the future value of the investment in the two bonds
to be in year 4. Do you exactly meet the obligation of the fund? Explain any difference.

Explanation / Answer

The duration of a Zero coupon bond is its maturity

and for loan immunization the weighted duration of bond portfolio should match against loan maturity

let weights of 2 year bond is W so weights of 8 year bond is 1-W

4=2W+(1-W)8

W=.67

1-W=.33

so he should invest 10,000,000*67=6,700,000 maturity value in 2 year bonds and

10,000,000*.33=3,300,000 maturity value in 8 year bond

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