ABC Corp. expects to make payment of one time lump sum cash flow of $10 million in 10 years. The firm would like to immunize its liability by investing in two different securities: an annuity paying $1 million for the next 5 years annually and a perpetuity paying $50,000 annually forever. Each of the securities has a 5% yield.

2. Find the Macaulay's duration for (i) the lump sum liability, (ii) the 5-year annuity and, (iii) the perpetuity. Show calculations.
4. Calculate the convexity for each of the three securities. Show calculations.
6. If yields change from 5% to 8%, what will be the best estimate for the percentage change in price of the 5-year annuity? Compare this to the actual percentage change in the price of the 5-year annuity. Are the two percentage changes in prices identical?
8. How much of each of the two securities (in market value) will ABC Corp. want to hold to fully immunize its obligation?
10. Now suppose that interest rates immediately rises from 5% to 8%. What happens to the net position, that is, to the difference between the value of asset and liability?

Answer rating: 100% (QA)

To calculate the Macaulays duration for each security we need to consider the present value of the cash flows and the timing of those cash flows i Lump sum liability Since the lump sum liability is a ... View the full answer