Final answer:
The statement is true: a bond trades at a premium when its yield to maturity is less than its coupon rate because it offers a more attractive interest rate than currently available in the market.
Step-by-step explanation:
The statement that a bond trading at a premium when the yield to maturity is less than the coupon rate is indeed true. When the yield to maturity (YTM) is below the coupon rate, the bond offers more periodic interest payments than the prevailing market rates, which makes it more valuable. Therefore, the price of the bond increases above its face value, leading to a premium. Conversely, if the YTM were higher than the coupon rate, the bond would be less attractive because it pays lower interest compared to the market, and it would trade at a discount (below face value).
This concept is integral to understanding bond pricing and interest rate movements. For instance, if a bond with no risk pays $80 annually (an 8% coupon rate) and is approaching maturity while overall market interest rates have risen to 12%, the bond price must decrease to provide a similar yield, causing the bond to trade at a discount. On the other hand, if market interest rates were to fall, the bond's higher coupon rate would lead to it trading at a premium.
In summary, a bond's pricing above or below face value is a direct reflection of how its coupon rate compares to current market rates, thus affecting its yield to maturity.