Final answer:
The yield on a bond that is trading at a discount increases because the investor gains both the coupon payments and capital gains upon maturity, resulting in a total return higher than the bond's coupon rate.
Step-by-step explanation:
When a bond is trading at a discount, it means the bond is selling for less than its face value. This situation generally occurs when the market interest rates have risen above the bond's coupon rate, making newer issues more attractive and causing existing bonds with lower rates to decrease in price to yield a competitive return.
Let's say an investor buys a bond with a face value of $1,000 and a coupon rate of 8% for $964, and one year later the bond matures and they receive the face value of $1,000 plus the last year's interest payment of $80. The yield on this bond can be calculated as (($1,080 - $964) / $964) = 12%. Therefore, while the bond's coupon rate remains unchanged at 8%, the investor's total return includes both the interest payments and the capital gains from purchasing the bond at a discount, driving the yield up.
To summarize, when a bond trades at a discount, it can produce a higher yield than the stated coupon rate. This illustrates a fundamental principle of bond investing - bond prices and yields are inversely related; as bond prices decrease, yields increase, and vice versa.