# Understanding Inverse Price/Yield Relationship in Bonds

The investors in bonds face interest rate risk because the price of the bond is inversely proportional to the changes in interest rates. So, if interest rates rise, the bond’s price will fall and if interest rates fall, bond’s price will rise.

But why this inverse relationship? Let’s understand this with the help of an example. Let’s say that an investor purchases a $100 8% coupon 5 year maturity bond at par. Since the bond is selling at par, the yield from the bond is the same as its coupon, i.e., 8%. Let’s say the interest rates rise to 8.5%. At the same time, the investor decides to sell the bond. Any new investor would expect a yield of 8.5% and if he has to purchase a par bond, he will expect the bond to pay a coupon of 8.5%. However, in our bond, the coupon is fixed at 8%. The investor cannot change that. So, how will he convince the new investor who wants 8.5% yield from this bond. The only way to do so is to adjust the price downwards so that the new investor can make up for the loss of 0.5% in the coupon. Using bond valuation, the price at which the new investor would be willing to buy this bond at$98.03 which will then provide him a yield of 8.5%.

Similarly, if the interest rates had fallen to 7.5% (instead of rising), then the new investor will be very happy to buy this bond at par as it is providing higher yield. However, the current investor holding the bond knows that the market is offering only 7.5%, not 8%. Since his bond is providing a higher yield, he will increase the price of the bond, so that effectively provides a yield of 7.5%. In this case, he will increase the price to \$102.02.

This inverse relationship can be summarized as below:

• The bond trades at par when its coupon rate is equal to the required yield.
• If required yield is greater than the coupon rate, then the bond price will be below par (sell at a discount)
• If required yield is lower than the coupon rate, then the bond price will be above par (sell at premium)