# Cpn Rate - Current Yield - YTM

Refering to the question below, if a bond is selling at a discount, its coupon rate (cpn/face value) is obviously lower than its current yield (annual cpn/price). I was mainly wondering other people’s thought process as to why the current yield is less than the YTM for a bond selling at a discount? I was thinking the current yield does not account for the increased reinvestment income while the YTM does? Also for a bond selling at a premium whould the relationship be coupon rate>current yield>YTM. A bond is selling at a discount relative to its par value. Which of the following relationships holds? A) coupon rate < current yield < yield to maturity. B) yield to maturity < coupon rate < current yield. C) current yield < coupon rate < yield to maturity. Your answer: A was correct! When a bond is selling at a discount, it means that the bond has a larger YTM (discount rate that will equate the PV of the bond’s cash flows to its current price) than its current yield (coupon payment/current market bond price) and coupon payment.

Yes, for a bond selling at a premium the relation would be Coupon rate>current yield>YTM A bond will be selling at a premium if the coupon rate is higher than YTM. Thus Coupon rate>YTM For a bond selling at premiun, the current yield would be- Coupon rate/bond price since the bond is selling at a premium the denominator would be higher leading to a lower current yield. Thus curren yieldcurrent yield Now when we calculate the current yield and YTM the numerator would be coupon rate and present value of coupon rate respectively. since the numerator is lower in YTM, the relation would be Current yield> YTM So, Coupon rate>current yield>YTM when bonds are trading at premium.