We know that a bond’s price is inversely related to the yield. How sensitive a bond price is to yield depends on the various features of the bond such as its maturity, coupon rate, and any embedded options in the bond. Let’s look at how these factors influence the impact of interest rate changes on a bond’s price.

**Maturity**

In general, the longer the maturity, the higher the interest rate sensitivity. This means that for a given change in interest rates, everything else remaining the same, the price of a bond with higher maturity will change more compared to another similar bond with lower maturity. This happens because a higher number of cash flows need to be discounted.

**Coupon Rate**

All other factors remaining the same, the lower the coupon, the higher is the interest rate sensitivity. This happens because when the bond has lower coupon, its value is more dependent on the par amount to be received at maturity. In other words, it takes longer for a bondholder to get back its capital when the interest rates are low. On the other hand, a bond with high coupon rate has higher cash flows in the beginning which reduces its dependency on the maturity value. In this sense, zero-coupon bonds have highest interest rate sensitivity compared to a similar coupon paying bond.

**Embedded Bonds**

Some bonds can have embedded options such as a call option attached to it. For a callable bond, the bond can be called back by the issuer. Such an option also affects the interest rate sensitivity of the bond. All other factors remaining the same, a bond with embedded call option will be less sensitive to interest rate changes. This happens because the price of a callable bond is lower than a similar non-callable bond by an amount equal to the value of the option.

Price of Callable Bond = Price of Non-callable Bond – Price of Embedded Option

The price is reduced because the call option is a benefit for the issuer. The opposite will be true for a puttable bond which provides the right to the investor to return the bond to the issuer.

When interest rates rise, the price of the embedded call option declines. Therefore, the overall effect on the decline in the price of the bond is less.

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