You are given the following information about a fully immunized portfolio:

1. The liability is a single payment of 600,000 due in two years.
2. The asset portfolio consists of a one-year zero-coupon bond maturing for x and a four-year zero-coupon bond maturing for y.
3. The annual effective interest rate is 4.6%.

Calculate x.

• 218,800
• 325,400
• 365,600
• 382,400
• 402,800

An insurance company aims to structure a portfolio of assets and liabilities so that:

1. Its assets and liabilities have equal present values and equal modified durations.
2. The convexity of its assets exceeds the convexity of its liabilities.

Determine which term precisely describes the company’s position.

• Diversified
• Fully immunized
• Fully leveraged
• Exactly matched
• Redington immunized

Prosperity Insurance sells a two-year annuity with equal payments at the end of each year. The price of this annuity is 9297. Prosperity Insurance creates a portfolio made up of a one-year zero- coupon bond and a two-year zero-coupon bond to immunize this annuity. The company uses an annual effective interest rate of 5% to vaue its assets and liabilities.

Calculate the amount invested today in the two-year zero-coupon bond

• 3769
• 4535
• 4762
• 5000
• 9297

An insurance company has liabilities due at the end of each of the next two years. The liability due at the end of the second year is twice that for the first year. The company uses a combination of the following two bonds to match the liabilities. The second bond has annual coupons.

Assume both bonds are redeemed at par and the company invests 9465 in the two-year bond. Calculate the amount the company should invest in the one-year bond to construct an exactly matched portfolio.

• 4245
• 4398
• 4481
• 4717
• 4953

An insurance company has a single liability due in three years. The company fully immunizes its position by purchasing one-year and four-year zero-coupon bonds. The face value of the one- year bond is 20,000 and the face value of the four-year bond is 50,000. Assume that the yield curve is flat.

• 40,000
• 55,699
• 69,624
• 73,333
• 97,500

Calculate the amount of the liability.

The table gives information about the assets and liabilities of three companies.

(I) Company U’s position is immunized against small interest rate changes.

(II) Company V’s position is immunized against small interest rate changes.

(III) Company W’s position is immunized against small interest rate changes.

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

An insurance company has a liability of 2662 that is due at the end of three years. The present value of this liability is 2000. There are two investments available: a one-year zero-coupon bond and a four-year zero-coupon bond. The company wants to find an investment plan that satisfies Redington immunization.

Calculate the amount the company invests in the one-year zero-coupon bond.

• 400
• 667
• 858
• 1,000
• There is no investment plan that satisfies Redington immunization

An insurance company has a liability of 750,000 due four years from now. To protect against interest rate risk, it decides to employ the technique of full immunization. Specifically, it decides to hold three assets, each providing a single cash flow as follows

1. Asset X provides a cash flow of A_X , exactly two years from now
2. Asset Y provides a cash flow of 250,000, exactly four years from now.
3. Asset Z provides a cash flow of A_Z , exactly five years from now.

The annual discount factor is v = 0.95

• 150,000
• 175,000
• 200,000
• 225,000
• 250,000

You are given the following information regarding Company J.

1. It has a single liability of 1.75 million to be paid 12 years from now.
2. Its asset portfolio consists of a zero-coupon bond maturing in 5 years for 242,180 and a zero-coupon bond maturing in 14 years for X.
3. At an annual effective interest rate of 7%, Company J’s position is fully immunized.

Calculate the present value of the assets less the present value of the liabilities if the annual effective interest rate immediately changes to 4%

• 5,910
• 8,871
• 11,029
• 14,746
• 17,462

A scholarship foundation is committed to make a payment of 20,000 exactly two years from today. It plans to use two zero-coupon bonds to fully immunize the liability based on a flat curve and an annual effective yield rate of 5.5%. One of the bonds will have a one-year maturity and the other will have a three-year maturity.

Calculate the face value of the one-year zero-coupon bond

• 9,479
• 9,779
• 10,079
• 10,379
• 10,679