Which of the following statements is NOT true for a bond trading at a premium?

When a bond is trading at a premium, it means that the bond’s market price is higher than its face value. This typically occurs when the bond's coupon rate is higher than current market interest rates, making it more attractive to investors.

The statement that the basis and coupon will be identical is false in the context of a premium bond. The basis, which is the bond's adjusted cost basis for tax purposes, will be lower than its market price because the investor paid more than the face value of the bond. As a result, the premium is gradually amortized, lowering the investor's cost basis over time until maturity.

In contrast, the bond's coupon rate remains fixed, and therefore it does not adjust to reflect the market price. Thus, the basis and the coupon cannot be the same for a bond trading at a premium. This is the key reason why the indication that they are identical is not true.

Other statements address the characteristics of premium bonds correctly: if trading at a premium, the yield will indeed be lower than the coupon rate, the basis will be lower than the market price due to the premium paid, and some investors might receive a premium if redeeming the bond before maturity, although this context is typically based on the bond being