For a bond traded at par, what relationship exists between its basis and coupon rate?

When a bond is traded at par, its price is equal to its face value. In this scenario, the basis, which refers to the yield to maturity of the bond, is directly related to the coupon rate. Since the bond is priced exactly at par, the yield (or basis) reflects the coupon payments that the bondholder will receive. Therefore, the yield to maturity must be equal to the coupon rate because there are no premium or discount adjustments to account for.

This means that if you hold the bond until maturity, the annual income derived from the coupon payments will exactly match the yield, thus resulting in an identical relationship between the basis and coupon rate when the bond is trading at par.