Final answer:
The yield of a bond trading at a discount is higher than its coupon rate because the investor gets the full face value at maturity while paying less for the bond. This difference between the purchase price and the face value plus interest payments results in a yield that includes capital gains and interest income, which is higher than the coupon rate alone.
Step-by-step explanation:
The yield of a bond that trades at a discount exceeds the bond's coupon rate because the investor is buying the bond at a price lower than its face value and will still receive the full face value at maturity. For example, if an investor buys a bond with a face value of $1,000 and a coupon rate of 8%, they would expect to receive $80 in interest payments annually.
However, if the bond is purchased for $964 and it still pays the $80 yearly until maturity, the investor's yield would be greater than the coupon rate. Here's a step-by-step explanation: When an investor buys a discounted bond for $964 and the bond matures at $1,000, plus the $80 last year's interest payment, the return on investment can be calculated as (($1,000 + $80) - $964)/$964 = 12%.
The bond yield, which represents the total return, includes not just the coupon payments but also the capital gains realized when the bond is redeemed for its full face value, despite the investor having paid less for it. As a result, when interest rates rise and new bonds are issued paying higher interest, existing bonds with lower rates become less attractive and therefore sell for less, causing the yield on these older bonds to increase for new investors buying them at a discount.