A construction firm is facing three liabilities of 1000, due at the end of each of the periods 1, 2,and 3. 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 period, valued at a periodic effective yield rate of 14%

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

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

Calculate the total purchase price of the three bonds required to exactly match the liabilities.

• 2182
• 2202
• 2222
• 2242
• 2283

An investor purchases two bonds having the same positive annual effective yield rate. With respect to the annual effective yield rate, their modified durations are a years and b years, with 0 < <a b . One of these two bonds has a Macaulay duration of d years, with a < d < b. Determine which of the following is an expression for the Macaulay duration of the other bond, in years.

• bd / a
• ad / b
• ab / d
• b + d – a
• a + d – b

Determine which of the following statements about immunization strategies are true.

• Redington immunization protects against any change in interest rates.
• Full immunization occurs only when the duration of the assets is greater than the duration of the liabilities.
• Immunization techniques strive to arrange the asset portfolio such that the convexity of the assets is equal to the convexity of the liabilities.

• None
• I and II only
• I and III only
• II and III only
• The correct answer is not given by (A), (B), (C), or (D)

A company is required to pay 50, 000(1.075)y in y years. The company invests 30,000 in a 28- year zero-coupon bond and 20,000 in a 35-year zero-coupon bond to Redington immunize its position against small changes in interest rates, based on an annual effective interest rate of 7.5%.

Calculate y.

• 30.80
• 31.32
• 31.50
• 31.68
• 32.20

You are given the following information regarding Company J.

1. It has a single liability of 1,750,000 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 n years.
3. At an annual effective interest rate of 7%, Company J’s position is fully immunized.

Calculate n.

• 13
• 14
• 15
• 16
• 17

A company faces the following liabilities at the end of the corresponding years:

The company can invest in the following three annual coupon bonds redeemable at par:

The company invests in each bond so that the asset and liability cash flows are exactly matched.

Calculate X.

• 1221
• 1245
• 1290
• 1318
• 1375

A liability consists of a payment of 2000 to be paid six months from now and a payment of 1500 to be paid one year from now. The only investments available are:

1. Six-month zero-coupon bonds with an annual nominal yield rate of 3.5% convertible semiannually, and
2. One-year par value bonds with an annual coupon rate of 6% payable semiannually and an annual nominal yield rate of 4.2% convertible semiannually.

Calculate the total cost of a portfolio that exactly matches the liability cash flows.

• 3393
• 3404
• 3418
• 3447
• 3463

You manage a pension fund, and your liabilities consist of two payments as follows:

Your assets are $18 million. The term structure is currently flat at 5%.

Suppose that you invest the $18 million in 1-year Treasury bills (i.e., 1-year zero-coupon bond) and in a Treasury bond with modified duration of 20. What % of your investments do you allocate to 1 year T-bills in order to avoid interest rate risk of your portfolio, which includes both assets and liabilities?

• 7%
• 9%
• 11%
• 13%
• 15%

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

As a mid-size company, you have a pension plan which pays out $10 million a year forever. The first payment is exactly one year from now. The term structure is currently flat at 5%.

Suppose that the pension plan is fully funded (i.e., the value of your assets equal the value of pension liabilities). You want to invest all your assets in bonds to avoid any interest rate risk. What should the duration of your bond portfolio be?

• 20
• 20.4
• 20.8
• 21.2
• 21.6

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.

You manage a pension fund, which provides retired workers with lifetime annuities. The fund must pay out $1 million per year to cover these annuities. Assume for simplicity that these payments continue for 20 years and then cease. The interest rate is 4% (flat term structure). You plan to cover this obligation by investing in 5- and 20-year maturity Treasury zero coupon bonds.

You decide to minimize the funds exposure to changes in interest rates. How much should you invest in the 5- and 20- year bonds? What will be the par value of your holdings of each bond?

• 5.9M in the five year bond and 12.4M in the 20 year bond
• 6.9M in the five year bond and 11.4M in the 20 year bond
• 7.9M in the five year bond and 10.4M in the 20 year bond
• 8.9M in the five year bond and 9.4M in the 20 year bond
• 11.9M in the five year bond and 8.4M in the 20 year bond

References

Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.