Question

Consider a bond with a coupon rate of 9%, face value of $1,000, term to maturity of 4 years, and yield to maturity of 5%. Without doing any calculations, which of the price and duration pairings below can be true for this bond?

a. Price = $800, MacD = 6.6 years
b. Price = $1,250, MacD = 3.7 years
c. Price = $800, MacD = 4 years
d. Price = $800, MacD = 3.7 years
e. Price = $1,250, MacD = 4 years

Answer 1

When interest rates rise, the price of a bond decreases. Based on this information, the correct pairing for the bond is Price = $800, MacD = 4 years.

Step-by-step explanation:

When interest rates rise, the price of a bond decreases. This is because the bond will pay a lower interest rate compared to newer bonds in the market, making it less attractive for investors. Therefore, the price of the bond will be below its face value of $1,000.

Based on this information, we can determine the correct pairings:

1. Price = $800, MacD = 6.6 years: False. The price should be lower than $1,000.
2. Price = $1,250, MacD = 3.7 years: False. The price should be lower than $1,000.
3. Price = $800, MacD = 4 years: True. The price can be lower than $1,000, and the Macaulay duration can remain the same.
4. Price = $800, MacD = 3.7 years: False. The Macaulay duration should be higher.
5. Price = $1,250, MacD = 4 years: False. The price should be lower than $1,000.