Problem
Consider a $1,000 bond with a fixed-rate 10 percent annual coupon rate and a maturity (N) of 10 years. The bond currently is trading to a market yield to maturity (YTM) of 10 percent.
a. Complete the following table:
|
Change
|
|
N
|
Coupon
Rate
|
YTM
|
Price
|
$ Change in Price from Par
|
% Change in Price from Par
|
|
8
|
10%
|
9%
|
|
|
|
|
9
|
10
|
9
|
|
|
|
|
10
|
10
|
9
|
|
|
|
|
10
|
10
|
10
|
|
|
|
|
10
|
10
|
11
|
|
|
|
|
11
|
10
|
11
|
|
|
|
|
12
|
10
|
11
|
|
|
|
b. Use this information to verify the principles of interest rate-price relationships for fixed-rate financial assets.
Rule1. Interest rates and prices of fixed-rate financial assets move inversely.
Rule2. The longer is the maturity of a fixed-income financial asset, the greater is the change in price for a given change in interest rates.
Rule3. The change in value of longer-term fixed-rate financial assets increases at a decreasing rate.
Rule4. Although not mentioned in the Appendix, for a given percentage (±) change in interest rates, the increase in price for a decrease in rates is greater than the decrease in value for an increase in rates.
The following questions and problems are based on material in Appendix 9B to the chapter.
MLK Bank has an asset portfolio that consists of $100 million of 30-year, 8 percent coupon $1,000 bonds that sell at par.
a. What will be the bonds' new prices if market yields change immediately by +/ - 0.10 percent? What will be the new prices if market yields change immediately by +/ - 2.00 percent?
b. The duration of these bonds is 12.1608 years. What are the predicted bond prices in each of the four cases using the duration rule? What is the amount of error between the duration prediction and the actual market values?
c. Given that convexity is 212.4, what are the bond price predictions in each of the four cases using the duration plus convexity relationship? What is the amount of error in these predictions?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.