Question

You are the investment manager for the Stevens Life Insurance Company (SLIC) that specializes in Guaranteed Investment Contracts. A pension plan, which is a customer of your company, deposits $1,000,000 with you, in a contract that guarantees 5% per annum for the next two years. The pension plan will withdraw half of the account balance at the end of the first year, and the rest at the end of two years, You have two assets available for your company’s investments: a one-year risk-free zero coupon bond yielding 5.5% per annum, and a two-year zero-coupon bond yielding 6% per annum. Build a cash flow matching strategy that ensures the client guaranteed income and determine your profit.

Answer 1

All financials below are in $.

Amount deposited by Pension fund, A = $ 1,000,000

Guaranteed return, R = 5% per annum

Account balance after year 1 = A x (1 + R) = 1,000,000 x (1 + 5%) =  1,050,000

Amount to be withdrawn by the pension fund at then end of year 1 = Half the account balance= 1,050,000 / 2 =  525,000

Maturity amount to pension fund after year 2 = Balance amount + 5% return = (1,050,000 - 525,000) x (1 + 5%) = 551,250

Hence, the liability of SLIC is crystallized as:

End of year 1: $ 525,000

End of year 2: $ 551,250

In order to match these liabilities, SLIC should:

• Invest present value of $ 525,000 in Zero coupon bond (ZCB) maturing in 1 year with yield of y1 = 5.5% per annum. Hence amount to be invested in 1 year ZCB = 525,000 / (1 + y1) = 525,000 / (1 + 5.5%) = $  497,630.33 . This will take care of SLIC's liability at the end of year 1.
• Invest the balance amount = 1,000,000 -  497,630.33 =  502,369.67 in 2 year ZCB yielding y2 = 6%.

Maturity amount of 2 years ZCB, after year 2 =  502,369.67 x (1 + y2)² =  502,369.67 x (1 + 6%)² =  564,462.56

Profits of SLIC = Maturity amount of 2 years ZCB - Liability at the end of year 2 = 564,462.56 - 551,250 = $ 13,212.56