As of 12/31/2013, an insurance company has a known obligation to pay 1,000,000 on 12/31/2017. To fund this liability, the company immediately purchases 4-year 5% annual coupon bonds totaling 822,703 of par value. The company anticipates reinvestment interest rates to remain constant at 5% through 12/31/2017. The maturity value of the bond equals the par value.

Consider two reinvestment interest rate movement scenarios effective 1/1/2014. Scenario A has interest rates drop by 0.5%. Scenario B has interest rates increase by 0.5%.

Determine which of the following best describes the insurance company’s profit or (loss) as of 12/31/2017 after the liability is paid.

• Scenario A – 6,610, Scenario B – 11,150
• Scenario A – (14,760), Scenario B – 14,420
• Scenario A – (18,910), Scenario B – 19,190
• Scenario A – (1,310), Scenario B – 1,320
• Scenario A – 0, Scenario B – 0

Joe must pay liabilities of 1,000 due 6 months from now and another 1,000 due one year from now. There are two available investments:

Bond I: A 6-month bond with face amount of 1,000, an 8% nominal annual coupon rate convertible semiannually, and a 6% nominal annual yield rate convertible semiannually;

Bond II: A one-year bond with face amount of 1,000, a 5% nominal annual coupon rate convertible semiannually, and a 7% nominal annual yield rate convertible semiannually.

Calculate the amount of each bond that Joe should purchase to exactly match the liabilities.

• Bond I – 1, Bond II – 0.97561
• Bond I – 0.93809, Bond II – 1
• Bond I – 0.97561, Bond II – 0.94293
• Bond I – 0.93809, Bond II – 0.97561
• Bond I – 0.98345, Bond II – 0.97561

Joe must pay liabilities of 2000 due one year from now and another 1000 due two years from now. He exactly matches his liabilities with the following two investments:

Mortgage I: A one year mortgage in which X is lent. It is repaid with a single payment at time one. The annual effective interest rate is 6%.

Mortgage II: A two-year mortgage in which Y is lent. It is repaid with two equal annual payments. The annual effective interest rate is 7%.

Calculate X + Y.

• 2600
• 2682
• 2751
• 2825
• 3000

Joe must pay liabilities of 1,000 due one year from now and another 2,000 due three years from now. There are two available investments:

Bond I: A one-year zero-coupon bond that matures for 1000. The yield rate is 6% per year

Bond II: A two-year zero-coupon bond with face amount of 1,000. The yield rate is 7% per year.

At the present time the one-year forward rate for an investment made two years from now is 6.5%

Joe plans to buy amounts of each bond. He plans to reinvest the proceeds from Bond II in a one-year zero-coupon bond. Assuming the reinvestment earns the forward rate, calculate the total purchase price of Bond I and Bond II where the amounts are selected to exactly match the liabilities.

• 2584
• 2697
• 2801
• 2907
• 3000

An insurance company must pay liabilities of 99 at the end of one year, 102 at the end of two years and 100 at the end of three years. The only investments available to the company are the following three bonds. Bond A and Bond C are annual coupon bonds. Bond B is a zero-coupon bond.

All three bonds have a par value of 100 and will be redeemed at par.

Calculate the number of units of Bond A that must be purchased to match the liabilities exactly.

• 0.8807
• 0.8901
• 0.8975
• 0.9524
• 0.9724

Determine which of the following statements is false with respect to Redington immunization

• Modified duration may change at different rates for each of the assets and liabilities a time goes by.
• Redington immunization requires infrequent rebalancing to keep modified duration ofassets equal to modified duration of liabilities.
• This technique is designed to work only for small changes in the interest rate.
• The yield curve is assumed to be flat.
• The yield curve shifts in parallel when the interest rate changes.

Aakash has a liability of 6000 due in four years. This liability will be met with payments of A in two years and B in six years. Aakash is employing a full immunization strategy using an annual effective interest rate of 5%.

Calculate [math]|A-B|[/math].

• 0
• 146
• 293
• 586
• 881

Trevor has assets at time 2 of A and at time 9 of B. He has a liability of 95,000 at time 5. Trevor has achieved Redington immunization in his portfolio using an annual effective interest rate of 4%.

• 0.7307
• 0.9670
• 1.0000
• 1.0132
• 1.3686

Which of the following statements regarding immunization are true?

• If long-term interest rates are lower than short-term rates, the need for immunization is reduced.
• Either Macaulay or modified duration can be used to develop an immunization strategy.
• Both processes of matching the present values of the flows or the flows themselves will produce exact matching.

• I only
• II only
• III only
• I, II and III
• The correct answer is not given by (A), (B), (C), or (D).

Determine which of the following statements regarding asset-liability management techniques is true.

• Redington immunization requires that the convexity of the liabilities is greater than the convexity of the assets.
• An advantage of the Redington immunization technique over the cash-flow matching technique is that the portfolio manager has more investment choices available.
• Both Redington immunization and full immunization are based on the assumption that the yield curve has higher yields for longer term investments.
• A fully immunized portfolio ensures that the present value of assets will exceed the present value of liabilities with non-parallel shifts in the yield curve.
• A cash-flow matched portfolio requires less rebalancing than a Redington immunized portfolio, but more rebalancing than a fully immunized portfolio.