Investments Course Home Work

Problem #1

A nine-year bond has a yield-to-maturity of 10 percent and a modified Duration of 6.54 years. If the market yield changes by 50 basis points, what is the change in the bond's price?

Problem #2

A nine-year bond has a yield-to-maturity of 10 percent and Duration of 7.194 years. If the market yield changes by 75 basis points, what is the change in the bond's price? What is new price?

Problem #3

Find the duration of a 7% coupon bond making annual coupon payments if it has 3 years until maturity and has a yield to maturity to maturity of 7%. What is the duration if the yield to maturity is 10%?

Problem #4

Find the duration of the bond in the previous problem if the coupons are paid semiannually.

Problem #5

An insurance company must make payments to a customer of $15 million in 1 year and $4 million in 4 years. The yield curve is flat at 9.5%.

a) If it wants to fully fund and immunize its obligation to this customer with a single issue of a zero-coupon bond, what maturity bond must it purchase?

b) What must be the face value and market value of that zero-coupon bond?

Problem #6

Make a ranking of the durations or effective durations of the following pairs of bonds:

a) Bond A is a 20- year noncallable coupon bond with a coupon rate of 8%, selling at par. Bond B is a 20-year callable bond with a coupon rate of 9%, also selling at par.

b) Bond A is an 8% coupon bond, with a 20-year time to maturity selling at par value. Bond B is an 8% coupon bond, with a 20-year maturity time selling below par value.

Problem #7

You will be paying $10,000 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%.

a) What is the present value and duration of your obligation?

b) What maturity zero-coupon bond would immunize your obligation? (Find its PV and Face value also)

c) Suppose you buy a zero-coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 9%....