# Dv01 and duration relationship

### Bond duration - Wikipedia

Duration is a measure of a bond's sensitivity to interest rate changes. The formula is complicated, but what it boils down to is: Duration = Present value of a . Professor Carpenter. Duration. 4. In practice people use. DV01 = DVBP = Dollar Value of a Basis Point. How much will a bond value change if rates change 1 bp . basis point change (DV01) in the yield of the underlying security and that of the hedging Exhibit 1 shows the price-yield relationship of a Treasury security as Calculating the modified duration of a bond or note can be a rather complicated.

The formula assumes a linear relationship between bond prices and yields even though the relationship is actually convex.

Thus, the formula is less reliable when there is a large change in yield.

### Nuclear Phynance

In general, six things affect a bond's duration: The higher a bond's coupon, the more income it produces early on and thus the shorter its duration. The lower the coupon, the longer the duration and volatility.

Zero-coupon bonds, which have only one cash flowhave durations equal to their maturities.

The longer a bond's maturity, the greater its duration and volatility. Duration changes every time a bond makes a coupon payment. Over time, it shortens as the bond nears maturity.

The higher a bond's yield to maturity, the shorter its duration because the present value of the distant cash flows which have the heaviest weighting become overshadowed by the value of the nearer payments. The presence of a sinking fund lowers a bond's duration because the extra cash flows in the early years are greater than those of a bond without a sinking fund.

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

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

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.

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

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.

Macaulay Duration

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.

## Difference between DV01 and Duration

Also, model the hypothetical addition to your portfolio of new bonds to see how they might impact the duration of the overall portfolio. Locate a bond fund's duration in the bond fund's online profile under Portfolio Data. Locate a bond ETF's duration from either the Snapshot page or Key Statistics, where the duration of the specific ETF can be compared to the asset class median duration.