# Relationship of duration with yield to maturity and coupon rate

Coupon tells you what the bond paid when it was issued, but the yield to maturity tells you how much it will pay in the future, and that's. A bond’s coupon rate is the amount of interest income it earns each year based on its face value. Investors base investing decisions and strategies on yield to maturity more so than coupon shizutetsu.infoe a bond has a \$1, face value and issues semi-annual interest payments of. All the bonds have coupon interest rate, sometimes also referred to as coupon rate or What is the relationship between YTM and the discount rate of a bond?.

Duration is Approximate Duration is a linear approximation of a nonlinear relationship. Duration is more accurate as the change in the interest rate becomes smaller.

### coupon rate vs. duration | AnalystForum

Duration can increase or decrease given an increase in the time to maturity but it usually increases. You can look at this relationship in the upcoming interactive 3D app.

• Duration: Understanding the relationship between bond prices and interest rates
• An Introduction to Duration

For a review of bond coupon rates and yields see these presentations: Average of Time Payments are Received Duration can be thought of as the weighted average of when the bondholder receives payment. Check that the way the weights react is consistent with the relationships on the previous slide. This will give you an intuitive understanding of how these variables affect duration. Interactive App With the following app, you can set the maximum yield-to-maturity, and time to maturity, and see the resulting 3D duration surface.

You can also change the coupon rate and see the effect on the duration surface. You can move the 3D surface around, and zoom in and out, with your mouse.

### shizutetsu.info: Learn Finance Fast - Duration

Can you see the case where duration is decreasing with an increased time to maturity? The most common and most easily understood risk associated with bonds is credit risk. Credit risk refers to the possibility that the company or government entity that issued a bond will default and be unable to pay back investors' principal or make interest payments.

Bonds issued by the U. However, Treasury bonds as well as other types of fixed income investments are sensitive to interest rate risk, which refers to the possibility that a rise in interest rates will cause the value of the bonds to decline.

Bond prices and interest rates move in opposite directions, so when interest rates fall, the value of fixed income investments rises, and when interest rates go up, bond prices fall in value. If rates rise and you sell your bond prior to its maturity date the date on which your investment principal is scheduled to be returned to youyou could end up receiving less than what you paid for your bond.

Similarly, if you own a bond fund or bond exchange-traded fund ETFits net asset value will decline if interest rates rise. 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. 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.

## coupon rate vs. duration

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.