when a bond is trading at a premium its market price is above its par or face value typically this happens when the bond s coupon rate is higher than similar bonds current market interest rates the outcomes for a roll down return strategy might differ from those for bonds at par or at a discount 
suppose you buy a bond trading at a premium as the bond approaches maturity its ytm will gradually decrease toward the current market rates for shorter dated bonds assuming a stable or declining interest rate environment this decrease in ytm can still lead to price appreciation as the bond s remaining time to maturity shortens if its yield aligns with those of similar shorter maturity bonds in an upward sloping yield curve 2however for a premium bond another factor to consider is the amortization of the premium this refers to the gradual decrease in the bond s price premium as it moves toward its par value at maturity the bond s price will converge with its par value as maturity approaches with the premium being amortized throughout the bond s life this amortization effectively reduces the bond s total return as part of the premium paid upfront is not recouped directly but is offset by receiving higher coupon payments than the market average the roll down return for a bond trading at a premium includes potential capital gains because of the bond s price appreciation as it rolls down the yield curve and the effects of premium amortization the total return for the investor will be a combination of the coupon payments the capital gains or losses from selling the bond before maturity and the results of premium amortization 