Question

I'm having trouble putting in words, basically I would like to explain for each bond par/discount/premium, the relationship between coupon rate, current yield and yield-to-maturity. Basically explain the relationship

Discount Bonds (Price < Par): YTM > Current Yield > Coupon Rate

but in the least math terms as possible. Any tips? thanks!

Answer 1

Ans:- Discount Bonds (Price<Par) : YTM > Current Yield > Coupon Rate

Discount bonds are the bonds that are issued at a discount from its face value or par value. For ex.- If a  10% bond having a face value of 100 is issued at a price of 90, then it is issued at a discount rate of 10.

In the above example, we can clearly see that the Price < Par i.e 90 < 100

Also, the coupon rate is 10% and the current yield will be calculated as:- Annual coupon payment/Bond price = 100*10%/90 = 0.11 OR 11%

Yield to maturity = ( Face value/Present value) -1

= (100/90) - 1

= 1.111 -1 = 0.111 Or 11.1%

In the above example, we can clearly see that YTM > Current Yield > Coupon Rate

So, it is proved that when a bond is issued at a discount it's YTM is greater than it's Current yield and Coupon rate, and it's Current yield will be greater than it's Coupon rate, in other words  Price < Par: YTM > Current Yield > Coupon Rate