Question

Explain why fixed-rate bond prices vary inversely with interest rates (i.e., why bond prices and yields move in opposite directions).

Answer 1

Bond Price is the Accumulated present value of all the cash flows or the income that the bond is going to generate over the years that is Coupon payment and the face vaue at it's maturity.

The Discount rate that is used to bring the cash flows in present value is the market interest rate which is the yield to maturity, and if the bond Yield is higher than the coupon rate then it means there will be higher discounting of cash flows than it's actual coupon rate leading to lesser present value. Thus, The accumulated present value will fall below the face value showing the opposite relation or inverse relation between the bond price and the yield.

Similarly, If the interest rate is lower then coupon rate, then it would be lesser discounting of cash flows leading to higher present value, and the accumulated value of cash flows will be higher than the face value.