8. Ms. Scott purchased a 7-year, 4% annual coupon bond with the YTM of 4%. Ms. Lee invested in a 10-year, 6% annual coupon bond with the YTM of 4%. If interest rates go up by 2 percentage points due to inflation (that is, the YTM becomes 6%), who will have more capital loss? Why? Explain
To determine who will have more capital loss when interest rates increase, we first need to understand the relationship between bond prices and interest rates.
When interest rates rise, the prices of existing bonds tend to fall. This is because newly issued bonds offer higher yields, making existing bonds with lower yields less attractive to investors. Bond prices and yields have an inverse relationship, meaning that as yields increase, prices decrease, and vice versa.
Now let's analyze the two bonds:
1. Ms. Scott's 7-year, 4% annual coupon bond with a YTM of 4%:
- This bond has a lower coupon rate (4%) compared to the yield to maturity (YTM) of 4%. Therefore, it is sold at a discount.
- When interest rates increase by 2 percentage points to 6%, the bond's YTM matches its coupon rate. In this case, there is no significant impact on the bond price, as the coupon rate and YTM are the same.
2. Ms. Lee's 10-year, 6% annual coupon bond with a YTM of 4%:
- This bond has a higher coupon rate (6%) compared to the YTM of 4%. Hence, it is sold at a premium.
- When interest rates increase by 2 percentage points to 6%, the bond's YTM matches its coupon rate. This means the bond's price will decrease, as investors can now find similar yields in newly issued bonds and are less likely to pay a premium for an older bond.
Therefore, Ms. Lee, who invested in the 10-year bond with a higher coupon rate and premium price, will experience more capital loss when interest rates go up by 2 percentage points. The bond's price will decline due to the revaluation of its yield in relation to the newly issued bonds, resulting in a higher loss compared to Ms. Scott's bond, which is already sold at a discount.
In conclusion, the capital loss will be higher for Ms. Lee due to the larger impact of interest rate changes on premium bonds compared to discount bonds.