Final answer:
The NOT TRUE statement for a bond trading at a premium is that the basis and coupon will be identical. Bonds trading at a premium have a market price above face value, which results in a current yield lower than the nominal yield and a basis below the coupon rate.
Step-by-step explanation:
The statement that is NOT TRUE for a bond trading at a premium is D. The basis and coupon will be identical. When a bond trades at a premium, it means that its market price is above its face value, typically because the prevailing interest rates have fallen since the bond was issued and its fixed coupon rate is higher than current market rates. As a result, the bond's current yield, which is the annual coupon payments divided by the bond's market price, will be lower than the nominal or coupon yield because the investor pays more for the bond than the face value. The bond will trade at a basis (yield to maturity or YTM) below its coupon rate because the YTM takes into account not only the coupon payments but also the loss or gain if the bond is held to maturity. A bond will not have the same basis and coupon rate unless it's trading at its face value, which is not the case for a premium bond. Therefore, options A, B, and C can be true for a premium bond, but option D is not.