What is the relationship between a bond's basis and its yield-to-maturity?

A bond's basis, which refers to the bond's cost basis or the price at which it was purchased, is closely tied to its yield-to-maturity (YTM). The yield-to-maturity is a measure of the total return anticipated on a bond if it is held until maturity, factoring in all interest payments and any gain or loss from the difference between the purchase price and the par value.

When a bond is purchased at a discount (below par value), its yield-to-maturity will be higher than its coupon rate because the investor will receive the full par value at maturity along with the interest payments. Conversely, if a bond is purchased at a premium (above par value), the yield-to-maturity will be lower than the coupon rate, reflecting the amount the investor will lose upon maturity. This relationship underscores that the price paid for the bond (the basis) directly affects the yield-to-maturity, making them synonymous in practical terms: as the basis changes, the YTM will adjust accordingly.

Understanding this relationship is critical for investors and financial professionals, as it affects investment decisions and the assessment of a bond's potential returns.