(i) Let {C} denote a series of cash flows at times tk for k = 1, 2, ..., n. (ii) (a) Define the volatility of the cash flow series, and derive a formula expressing the volatility in terms of tk, {C} and v. (b) Define the convexity of the cash flow series, and derive a formula expressing the convexity in terms of tk, {C} and v. An investment company has future liabilities of £8 million due in 5 years' time and £15 million due in 10 years' time and assets consisting of 3 zero-coupon bonds, one paying £6.3 million in 2 years' time, another paying £9.7 million in 7 years' time and another paying £9.8332 million in 25 years' time. Assuming that the current interest rate is 6% per annum effective: (a) Show that Redington's first two conditions for immunization against small changes in the rate of interest are satisfied for this company. (b) Determine the profit or loss, expressed as a present value, which the insurance company will make if the interest rate decreases immediately to 5.5% per annum effective. (c) Explain briefly why you would have anticipated whether a profit or loss would be made in (b) without even carrying out the calculations.
(i) Let {C} denote a series of cash flows at times tk for k = 1, 2, ..., n. (ii) (a) Define the volatility of the cash flow series, and derive a formula expressing the volatility in terms of tk, {C} and v. (b) Define the convexity of the cash flow series, and derive a formula expressing the convexity in terms of tk, {C} and v. An investment company has future liabilities of £8 million due in 5 years' time and £15 million due in 10 years' time and assets consisting of 3 zero-coupon bonds, one paying £6.3 million in 2 years' time, another paying £9.7 million in 7 years' time and another paying £9.8332 million in 25 years' time. Assuming that the current interest rate is 6% per annum effective: (a) Show that Redington's first two conditions for immunization against small changes in the rate of interest are satisfied for this company. (b) Determine the profit or loss, expressed as a present value, which the insurance company will make if the interest rate decreases immediately to 5.5% per annum effective. (c) Explain briefly why you would have anticipated whether a profit or loss would be made in (b) without even carrying out the calculations.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
Using formulas, no tables
correct answers:
ii) (a) PV(A)(6%)= 14.349 ≈ PV(L)(6%)= 14.354
PV'(A)(6%)= 113.649 ≈ PV'(L)(6%)= 113.649
Alternatively, T(A)(6%) ≈ T(L)(6%) ≈ 7.92
(b) P(5.5%) = 0.004450
Transcribed Image Text:(i)
Let {C} denote a series of cash flows at times tk for k = 1, 2, ..., n.
(ii)
(a) Define the volatility of the cash flow series, and derive a formula expressing the
volatility in terms of tk, {C} and v.
(b) Define the convexity of the cash flow series, and derive a formula expressing the
convexity in terms of tk, {C} and v.
An investment company has future liabilities of £8 million due in 5 years' time and
£15 million due in 10 years' time and assets consisting of 3 zero-coupon bonds, one
paying £6.3 million in 2 years' time, another paying £9.7 million in 7 years' time and
another paying £9.8332 million in 25 years' time. Assuming that the current interest
rate is 6% per annum effective:
(a) Show that Redington's first two conditions for immunization against small
changes in the rate of interest are satisfied for this company.
(b) Determine the profit or loss, expressed as a present value, which the insurance
company will make if the interest rate decreases immediately to 5.5% per annum
effective.
(c) Explain briefly why you would have anticipated whether a profit or loss would be
made in (b) without even carrying out the calculations.
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