Question 1: A financial institution has the following liabilities
which it is trying to immunize against a change in interest rates (all
are priced to yield 8%):
- 5-year (annual payments) 8% coupon bonds with a total par value of $38 million.
- Three payments of $24 million, each one due at the end of the next three years.
- 12-year (annual payments) 12% coupon bonds with a total par value of $20 million.
Available
for the purpose of immunization each year are a 1-year zero coupon bond
(a rolling issue, new ones each year) and consol (perpetual) bonds with
a 11% coupon, both yielding 10% to maturity. Assuming that you
re-balance the portfolio each year immediately after any payments are
made, what is the dollar amount of each hedging instrument you will hold
at t=0 and t=1 to completely neutralize the institution’s exposure to
interest rate changes over the coming year?
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