The price of a bond, which gives the owner rights over future cash flows, should be equal to the present discounted value of those cash flows. The interest rates that guarantees the equality of cash flows and price of bonds is defined as the yield rate. Bonds’ prices and yield rates are inversely related.
When a Central Bank raises short-term interest rates, the discount factor increases, which reduces the present discounted value of those cash flows. Therefore, as yield rates increases, the prices of bonds decreases.
The note available at (https://lnkd.in/g8uW-cFS) explains the relationship between coupon rates, yield rates and bonds prices.
As an example, consider the cases of one-year, three-years, and five-years bonds that pay an annual coupon rate of 4% every six months and has a face value of $100. When the interest rate is 6%, the prices of the bonds, for one-year, three-years, and five-years bonds tenors, are $98.09, $94.58, and $91.47, respectively. When interest rate rises to 8%, the prices of those bonds drop to $96.23 (-1.89%), $89.52 (-5.36%), and $83.78 (-8.41%), respectively.
Therefore, as interest rates rises, the price of bonds drops, with larger drops for longer tenor bonds, as the opportunity cost of holding bonds with fixed cash flows, increases.