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Calculate the convexity for the three securities

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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.

- Find the Macaulay's duration for (i) the lump sum liability, (ii) the 5-year annuity and, (iii) the perpetuity. Show calculations.

- Calculate the convexity for each of the three securities. Show calculations.

- 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?

- How much of each of the two securities (in market value) will ABC Corp. want to hold to fully immunize its obligation?

- 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?

Reference no: EM133114207

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