A company owes 1000 one year from now and 1000 two years from now. Which of the following demonstrates a strategy to use exact cash-flow matching between assets and liabilities?

• The company purchases a one-year zero-coupon bond and a two-year zero-coupon bond, each with a face amount of 1000.
• The company deposits 1859.41 into an account that currently earns an annual effective interest rate of 5% that is subject to change in one year.
• The company purchases an asset that has the same duration as the liabilities and a larger convexity.

• 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 conditions are necessary for an immunization strategy.

• The present value of the cash inflow from the assets is equal to the present value of the cash outflow from the liabilities.
• The price sensitivity to changes in interest rates is greater for assets than for liabilities.
• The convexity of assets is less than the convexity of liabilities.

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

A company has liabilities of 402.11 due at the end of each of the next three years. The company will match the duration of its liabilities by investing a total of 1000 in one-year and three-year zero-coupon bonds. The annual effective yield of both bonds is 10%.

Calculate the amount the company will invest in one-year bonds.

• 366
• 402
• 442
• 500
• 532

A company is required to pay 500,000 ten years from now and 500,000 fifteen years from now. The company needs to create an investment portfolio using 5-year and 20-year zero-coupon bonds, so that, using a 7% annual force of interest, the present value and Macaulay duration of its assets match those of its liabilities.

Calculate the amount invested today in each bond.

• 211,631 for the 5-year bond and 211,631 for the 20-year bond
• 217,699 for the 5-year bond and 217,699 for the 20-year bond
• 223,852 for the 5-year bond and 199,410 for the 20-year bond
• 229,857 for the 5-year bond and 205,540 for the 20-year bond
• 248,293 for the 5-year bond and 174,969 for the 20-year bond

A construction firm is facing three liabilities of 1000, due at times 1, 2, and 3 in years. There are three bonds available to match these liabilities, as follows:

Bond I: A bond due at the end of period 1 with a coupon rate of 1% per year, valued at a annual effective yield rate of 14%.

Bond II: A bond due at the end of period 2 with a coupon rate of 2% per year, valued at a annual effective yield rate of 15%.

Bond III: A zero-coupon bond due at time 3 valued at a periodic effective yield rate of 18%.

Calculate the face value of each bond that should be purchased to exactly match the liabilities.

An institute has provided an early retirement incentive package to a 60-year-old retiree that pays 12,000 per year at the end of each year up to and including age 65, plus a lump sum payment of 150,000 at age 65. All payments are guaranteed whether or not the retiree is alive at age 65. The institute will create a portfolio of two five-year bonds to exactly match the payments under this package. The first bond has a face amount of 100,000 and an annual coupon rate of 10%.

Determine which of the following second bonds will exactly match the liability.

• A bond with a price of 42,015, an annual coupon rate of 4% and annual effective yield of 8%.
• A bond with a price of 50,000, an annual coupon rate of 4% and annual effective yield of 8%.
• A bond with a price of 41,588, an annual coupon rate of 8% and annual effective yield of 10%.
• A bond with a price of 50,000, an annual coupon rate of 8% and annual effective yield of 10%.
• A bond with a price of 55,451, an annual coupon rate of 8% and annual effective yield of 10%.

Three asset-liability cash flows are given in the following table where a positive amount is an asset cash flow and a negative amount is a liability due at the corresponding time

Determine which set of cash flows is Redington immunized for an annual effective interest rate of i = 25%.

• X only
• Y only
• Z only
• X, Y, and Z
• The correct answer is not given by (A), (B), (C) or (D)

Determine which of the following statements regarding the Redington immunization technique is false.

• This technique assumes that the yield curve is flat.
• This technique assumes that only parallel shifts in the yield curve are allowed.
• This technique is designed to work only for small changes in the interest rate.
• The modified duration of the assets must equal the modified duration of the liabilities.
• The convexity of the assets must equal the convexity of the liabilities.

A company is required to pay 190,000 in 20.5 years. The company creates an investment portfolio using three bonds with annual coupons, so that its position is Redington immunized based on an annual effective interest rate of 7%. The table below shows the Macaulay duration for each of the bonds.

The company invests twice as much money in Bond C as in Bond B.

Calculate the amount the company invests in Bond A.

• 6,640
• 8,630
• 11,075
• 13,308
• 14,240

A company created a portfolio in order to protect its position using Redington immunization. Under which of the following changes in the yield rate is the immunization strategy guaranteed to be effective?

• Only a small decrease in the yield rate
• Only a small increase in the yield rate
• Only a small change in the yield rate
• Any decrease in the yield rate
• Any change in the yield rate