Impact of Yield Level on Bond’s Price Sensitivity

In the previous article we learned about how maturity, coupon, and embedded options impact interest rate risk in bonds. Apart from this, the price sensitivity of a bond to interest rate change is also affected by the level of yield (interest rate). Note that other factors remaining the same, the different bonds trade at different yield because of the credit risk premium.

The rule is as follows:

The higher is the yield, the lower is the interest rate sensitivity. That is, the price of the bond will change less for a one basis point change in yield, compared to a bond with lower yield.

Consider two 5-year bonds, both paying 7% coupon, one selling at an initial yield of 7% (trading at par) and the other selling at a yield of 9% (selling at a discount). Now, if interest rates increase by 1%, let’s see how the bonds’ prices will change.

For the first bond, the initial price is $100 (as it is selling at par). When the yield increases by 1%, the price drops to $94, a drop of $4 or 4%.

For the second bond, the initial price is $92.22. When the interest rates rise by 1%, the price drops to 88.62, a drop of $3.59, or 3.89%.

When we compare the two bonds, we can conclude that bond with lower yield is more volatile and vice versa. This happened because a 1% increase in interest rates reflects a higher % increase in interest rates for a lower initial yield. A shift from 7% to 8% is an increase of 14.28% in the yield, while a shift from 9% to 10% is an increase of only 11.11% in the yield.

We can also say that bond prices are more volatile in a low interest rate environment and less volatile in a high interest rate environment.