# What Is the Relationship Between Bond Price Volatility and the Coupon Rate?

by Jay Way ; Updated July 27, 2017While bond prices fluctuate as market interest rates change, the volatility of bond price fluctuation depends on the types of bonds as characterized by different maturity terms and coupon rates. The relationship between bond price volatility and the coupon rate is an inverse one -- the higher the coupon rate, the less volatile the bond price is to interest rate change, and vise versa. Bond investors rely on coupon payments as one of the sources to recover their bond investments. Bonds with higher coupon rates pay higher coupon payments, allowing investors to be paid back their initial investment costs sooner in terms of time value of money, and thus subjecting bond prices to interest rate change to a lesser degree.

## Coupon Rate and Bond Duration

Coupon rate is linked to bond duration, a concept used to directly measure bond price volatility. Bond duration is the average time it takes to receive all periodic cash flows as measured in their present values; that is, equivalently the number of years to recover a bond investment as if in a single payment. To calculate bond duration, the number of years to receive each cash payment is totaled and weighted by the percentage of each cash payment's present value over the sum of the present values of all cash payments, which is the investment cost.

The concept of bond duration attempts at illustrating two equivalent scenarios in terms of how long a bond investment can be recovered: receiving a number of payments over the maturity term or one payment at the end of the bond duration. The higher the coupon rate and cash payments, the faster the bond investment is recovered and thus the shorter the bond duration is.

## Bond Price Volatility and Bond Duration

Bond duration makes it possible to compare price volatility of bonds of different coupon rates and maturity terms on a single basis. The longer the bond duration, the more volatile the bond price is to changing interest rates. Bond duration is also a direct measure of how much a bond's price will change for an interest rate change of 100 basis points (1 percent). For every 1 percent change in interest rates, a bond with five years in bond duration, for example, will change by 5 percent in price.

## Coupon Rates and Rising Interest Rates

To preserve and grow the value of a bond portfolio as measured by the market prices of its various bonds, bond investors adjust a bond holdings in accordance with changing interest rates. When interest rates are likely to rise, prices of all bonds are expected to fall. Investors should unload bonds that are most volatile with prices falling more than others. Choose bonds with higher coupon rates in a rising interest rate environment, as bonds with lower coupon rates are more volatile and fall the most in prices.

## Coupon Rates and Declining Interest Rates

When interest rates are likely to decline, prices of all bonds are expected to rise and bond investors should add bonds that are most volatile with prices rising more than others. The lower the coupon rate, the more volatile the bond's price is. In a declining interest rate environment, bond investors should choose bonds with lower interest rates over bonds with higher interest rates, as bonds with higher interest rates are less volatile and rise less in prices.

## Time Value of Money Effect

The different amounts of coupon payments as determined by coupon rates have a time value of money implication to bond investors. The concept of time value of money is often figuratively supported by the "bird-in-the-hand" argument. Simply put, a bird in the hand now is worth more than a bird in the hand later. The less the coupon payments, the longer it takes to receive back all investments and the more risk exposure of a bond's price has to interest rate changes.

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