First, for a given term to maturity and initial yield, the price volatility of a bond is greater, the there is an inverse relationship between modified duration and the . One of those risks is the higher volatility of long-term bonds. The rate vs. volatility trade-off can The Relation Between Time to Maturity & Bond Price Volatility. Duration: Understanding the relationship between bond prices and interest rates including the maturity date and coupon rate on the bond or the bonds held by act to reinforce or magnify the price volatility measure indicated by duration as .

The degree to which values will fluctuate depends on several factors, including the maturity date and coupon rate on the bond or the bonds held by the fund or ETF.

Using a bond's duration to gauge interest rate risk While no one can predict the future direction of interest rates, examining the "duration" of each bond, bond fund, or bond ETF you own provides a good estimate of how sensitive your fixed income holdings are to a potential change in interest rates.

Investment professionals rely on duration because it rolls up several bond characteristics such as maturity date, coupon payments, etc. Duration is expressed in terms of years, but it is not the same thing as a bond's maturity date.

**Explaining Bond Prices and Bond Yields**

That said, the maturity date of a bond is one of the key components in figuring duration, as is the bond's coupon rate. In the case of a zero-coupon bond, the bond's remaining time to its maturity date is equal to its duration.

When a coupon is added to the bond, however, the bond's duration number will always be less than the maturity date. The larger the coupon, the shorter the duration number becomes. Generally, bonds with long maturities and low coupons have the longest durations. These bonds are more sensitive to a change in market interest rates and thus are more volatile in a changing rate environment.

Conversely, bonds with shorter maturity dates or higher coupons will have shorter durations.

### Duration: Understanding the Relationship Between Bond Prices and Interest Rates - Fidelity

Bonds with shorter durations are less sensitive to changing rates and thus are less volatile in a changing rate environment. Why is this so?

Because bonds with shorter maturities return investors' principal more quickly than long-term bonds do.

Therefore, they carry less long-term risk because the principal is returned, and can be reinvested, earlier. This hypothetical example is an approximation that ignores the impact of convexity; we assume the duration for the 6-month bonds and year bonds in this example to be 0. Duration measures the percentage change in price with respect to a change in yield. FMRCo Of course, duration works both ways. If interest rates were to fall, the value of a bond with a longer duration would rise more than a bond with a shorter duration.

Using a bond's convexity to gauge interest rate risk Keep in mind that while duration may provide a good estimate of the potential price impact of small and sudden changes in interest rates, it may be less effective for assessing the impact of large changes in rates.

## The Relation Between Time to Maturity & Bond Price Volatility

This is because the relationship between bond prices and bond yields is not linear but convex—it follows the line "Yield 2" in the diagram below. This differential between the linear duration measure and the actual price change is a measure of convexity—shown in the diagram as the space between the blue line Yield 1 and the red line Yield 2.

Relationship between price and yield in a hypothetical bond The impact of convexity is also more pronounced in long-duration bonds with small coupons—something known as "positive convexity," meaning it will act to reinforce or magnify the price volatility measure indicated by duration as discussed earlier. Bond Price Function The price or market value of an investment bond is based on the rate of interest the bond pays -- called the coupon rate -- compared to the current market yield for similar bonds.

If a bond's coupon rate is higher than market rates, the value of the bond will be higher than the face amount to bring the yield an investor earns in line with current rates. This is called a premium bond.

- Bond Price Function
- Mutual Funds and Mutual Fund Investing - Fidelity Investments
- Coupon Rate and Bond Duration

A discount bond is priced below the face amount, because the bond's coupon rate is lower than current market rates. Bond prices move inversely to interest rate changes. Factors Affecting Price Volatility Two features of bonds affect the price volatility in response to changes in market interest rates.

### The Relation Between Time to Maturity & Bond Price Volatility | Finance - Zacks

A bond with a lower coupon rate will be more volatile than a bond with a higher coupon rate. Also, longer-term bonds are more volatile than bonds with a shorter time to maturity. Volatility in this case is the amount a bond's price changes in response to a specific change in interest rates.

Bond Duration The mathematical concept of bond duration can be used as a measure of the volatility or risk of a bond. Duration is similar to maturity but is a measure of the cash flow of a bond: