Question

"Why is there so much variation in the coupon rates and prices
of these various bonds?" asks one of Jill's wealthiest clients.
How should Jill respond?

Answer 1

The bonds bear fixed interest rate or coupon which is locked throughout the life of the bonds. These coupons are static in nature and insensitive to current market interest rate. Current market interest rates are also called yields.

The prices of bond keep on changing based on yield of particular category of bond. The static coupon or fixed coupon are cash flows and those cash flows are divided by yield e.g; CFn / (1+Yield)^Year , though the bond coupons are static in nature they are discounted by current yield.

Hence, mathematically higher the yield lower the bond price and lower the yield higher the bond price, because yield appears in denominator of the formula [ CFn / (1+Yield)^Year ]. Hence, we see variation in the coupon rates and prices of those bonds.

Example:

Lets take two different yields for same bond say 8% yield and 10% yield.

Maturity time 1 year

Bond face value 100

Coupon 10%

Price of the bond = ?

If we apply 8% yield:

Price of bond = 110 / 1.08^1 = 101.85

If we apply 8% yield:

Price of bond = 110 / 1.10^1 = 100

Hence we can see for same coupon the change in yield has impacted the price of bond for higher yield (10%) the price of bond is lower and Price of bond is higher when yield is lower (8%)