Question

1. Give an example of the effect of interest rate changes on a fixed coupon bond, what factors cause the relationship discussed in answer 1 (relationship between interest rates and bond prices).
2. How can the same bond sell at par, at a discount, and at a premium over its life?

Answer 1

1)there exists a close relationship between the interest rates and bond prices. if the interest rates fall in general the bonds will become attractive and hence the demand for the bonds will go up causing and increase in price. if the interest rates goes up , then the fixed interest bearing bonds will become less attractive and hence the price will fall. thus there is an inverse relationship between bond price and interest rates.

2)

assume that an investor bought a $10,000 5% bond that matures in 5 years. Over the next couple of years, the market interest rates fall so that new $10,000, 10-year bonds only pay a 2% coupon rate. The investor holding 5% bond has a better position compared to the one with 2% . therefore the investor holding the 5% bond will sell the bond only at a premium amount in the secondary market. i.e when in interest falls , higher yielding bonds become more attractive and hence are sold at a premium.

conversly, as interest rates rise, new bonds will be issued at higher rates pushing those bond yields up in comparison to the bond which were previously issued. hence the older bond with lower yields will become less attractive in the secondary market and hence will be sold at a discount.

a bond will be sold at par when  the yield to the investor is equal to the coupon amount.

hence , the same bond may sold at premium ,par or discount ,depending on the relative position of its coupon rate against the market interest rate .