What is the approximate change in capital on the investment

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Reference no: EM133363982

Question: Mr John retires at the age of 65 with £1,000,000 in his account. He decides to invest the sum for the next 15 years, and will consider only Treasury Gilts because of his risk profile (and age).

Assume that the yield curve derived from zero coupon bonds is flat at 3% per annum. There is a 15 year old Treasury that has a coupon rate of 3%. There is also a 6-months zero (another Treasury) that will yield 3% per annum.

a) Assume that Mr John is planning to live only on the interests earned from his investments.

i) If interest rates fall from 3% to 2%, explain which bond is more appealing?

ii) Calculate the duration of the coupon paying bond.

What is the approximate change in capital on the investment in the coupon paying bond if interest rates increase to 5%? Is this change in capital of any consequence to Mr John?

b) Suppose Mr John decides to purchase an annuity from Maya Inc, a financial institution. Maya Inc pays Mr John £41,639.19 every six months for 15 years in exchange of the £1,000,000 deposit.

i) Show that the figure paid to Mr John comes from the present value of a stream of cash flows, discounted at 1.5% every six months that sum to £1,000,000.

ii) Calculate the duration of Maya Inc's obligation (i.e. the annuity payment), assuming the flat rate of 3% per annum.

iii) If Maya Inc will immunize this portfolio by investing in 2-year zeros and the 15 year Treasury, determine the weight of its investment in each bond.

iv) What does it need to do periodically to maintain an immunized portfolio?

c) Suppose Maya Inc. has to make a payment of £1,612,179 in 15 years' time to a younger colleague of Mr John who preferred to invest his £1,000,000 for fifteen years at a rate of 3.23% p.a. Current interest rates are still 3% p.a., and there is a 20 year old bond that pays semi-annual coupons at a rate of 3.21% p.a. and has face value £1,000,000. Show how Maya Inc. can immunize its portfolio by investing in this bond. What happens to the final value of the financial institution's portfolio if interest rates drop to 2%? And if interest rates increase to 5%?

Reference no: EM133363982

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