# Duration and yield to maturity relationship

### jingle-bells.info: Learn Finance Fast - Duration

Calculating duration rather involved, taking into account yields, bond coupons and that final maturity payment. The calculation essentially. All, Can someone refresh my memory and simply explain the relationship between YTM and Duration? Why is Duration higher at lower YTMs?. Conversely, bonds with shorter maturity dates or higher coupons will have shorter If interest rates were to fall, the value of a bond with a longer duration would.

FMRCo Of course, duration works both ways.

## What’s the Difference Between Duration and Maturity?

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.

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.

Keep in mind that duration is just one consideration when assessing risks related to your fixed income portfolio. Credit risk, inflation risk, liquidity risk, and call risk are other relevant variables that should be part of your overall analysis and research when choosing your investments.

Viewing and using duration data on Fidelity. Take a test drive by signing up for Guest Access. Managing the duration of your portfolio Accessing the duration of an individual investment Plot the duration of your fixed income holdings using Fidelity's Guided Portfolio SummarySM GPS to see at a glance the weighted average duration of your fixed income holdings at Fidelity. The duration of your fixed income investments is also plotted on a grid in comparison to the benchmark. Use the Interest Rate Sensitivity Illustrator to calculate the impact of interest rate changes on the value of your bond and bond fund holdings.

View duration in the Fixed Income Analysis tool to see the duration of your bonds, CDs, and bond funds.

• An Introduction to Duration
• Relationship between YTM vs. Duration

Also, model the hypothetical addition to your portfolio of new bonds to see how they might impact the duration of the overall portfolio. An example should drive the concept home.

Macaulay Duration

Keep in mind the image of a see-saw on a playground conveying the idea that when interest rates go up, bond prices go down and the opposite is true. As noted earlier, duration is more of a concept that estimates the impact to the bond when interest rates change.

## Duration: Understanding the relationship between bond prices and interest rates

Ultimately, market participants determine price, but keep in mind market participants would probably be using models to calculate duration in an attempt to determine supply selling and demand buying. You may have noticed the duration example had the term listed as years.

That is the norm used to note duration and also the probable reason why it is can be easily confused with maturity. Recall that the formula s for duration measured how long it took for the cash flows to repay the initial investment.

### Duration vs. Maturity and Why the Difference Matters

Now, the bottom line of the bottom line. Two bonds may have the same maturities, but their sensitivity to interest rate changes may be different.

Investors and portfolio managers not only can diversify holdings in regards to when the holdings may expire or mature, but now can diversify holdings in regards to the possible volatility or impacts to bond price movements as interest rates change. Take high yield bonds for example — according to the iShares website www. The bonds within these portfolios have, on average, a relatively similar period of time until the principal is assumed to be paid as shown by the average maturities.

However, high yield bonds are implied to have greater insulation to changes in interest rates versus the year Treasuries. Floating rate, as the name implies, has the characteristic of periodically adjusting their interest rate payouts making them even less susceptible to rate changes than the other two.

An investor or fund manager may be comparing these potential investments in their due diligence process. Using Duration Specifically, the steps in using duration are: The Macaulay Duration is: These are weights and sum to 1. Duration cannot exceed the number of periods to maturity of the bond. The Duration of a zero-coupon bond is the number of years until maturity. Also note, we can calculate the duration of a bond portfolio as the weighted average of the duration of all of the individual the bonds in the portfolio.

You can check your answers with the interactive app on the following slide. All bonds have annual payments in the interactive app.