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The current term structure is flat at 2%. You have a liability of $500,000 per year for the next five years. You decide to form an immunized portfolio.

a) Describe your exact strategy if you invest in one through five-year zero-coupon bonds.

What I did is

$$ D_{\rm funding}=w_1(1)+w_2(2)+w_3(3)+w_3(3)+w_4(5)+w_5(5) $$

but does $D_{\rm funding}$ equal to 5? what does it equal to and how do I solve this equation

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  • $\begingroup$ Your equation repeats the w3 term, and has w4*5. Are those typos? It would also help to explain what your symbols (Dfunding and wx) refer to. $\endgroup$ – Brian Romanchuk Feb 10 '18 at 13:18
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Note: This answer is preliminary, as I am unsure about some components of the question. I will note that it is a very long time since I studied portfolio immunization, and so I am describing how this would be looked at in the industry.

The simplest strategy for immunization in this case is to purchase five zero coupon bonds, each with a principal value of \$500,000. This means that your portfolio generates cash flows that exactly match the liability.

(That part of the question is unclear to me. One could attempt to duration match the liability, which would make the answer more complicated.)

The price for \$1 for the i-th zero coupon is: $\frac{1}{(1.02)^i}$, (the zero coupon price formula, using a simple interest rate convention).

The cost for the immunization is the sum of the five costs.

The market value weight of each bond is its market value divided by the sum.

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