Duration and convexity relationship tips

Duration: Understanding the Relationship Between Bond Prices and Interest Rates - Fidelity using duration. Duration can also be approximated by the following formula: Maturity = Date in quotes when bond matures. Coupon = Nominal Diagram of modified duration and convexity and the price-yield curve of a bond. Although. In this post, we discuss convexity of a bond, non-linear relationship between the price and yield of the bond, formula, risk management with examples. definitions of duration and convexity without due care; and second, the traditional . show the relationship between bond price, duration and duration. convexity. .. Journal of Livingston, Douglas G., , Bond Risk Analysis: A Guide to.

The duration of a zero bond is equal to its time to maturity but as there still exists a convex relationship between its price and yield, zero coupon bonds have the highest convexity and its prices most sensitive to changes in yield.

In the above graph Bond A is more convex than Bond B even though they both have the same duration and hence Bond A is less affected by interest rate changes. Convexity is a risk management tool used to define how risky a bond is as more the convexity of the bond, more is its price sensitivity to interest rate movements. A bond with a higher convexity has larger price change when the interest rate drops than a bond with lower convexity.

Hence when two similar bonds are evaluated for investment with similar yield and duration the one with higher convexity is preferred in a stable or falling interest rate scenarios as price change is larger. In a falling interest rate scenario again a higher convexity would be better as the price loss for an increase in interest rates would be smaller. Positive and Negative Convexity Convexity can be positive or negative. A bond has positive convexity if the yield and the duration of the bond increase or decrease together, i. The yield curve for this typically moves upward. This typical is for a bond which does not have a call option or a prepayment option. Bonds have negative convexity when the yield increases the duration decreases i. These are typically bonds with call optionsmortgage-backed securities and those bonds which have a repayment option.

If the bond with prepayment or call option has a premium to be paid for the early exit then the convexity may turn positive. The coupon payments and the periodicity of the payments of the bond contribute to the convexity of the bond. 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. 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.

Convexity of a Bond | Formula | Duration | Calculation

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. Portfolio Duration Duration is an effective analytic tool for the portfolio management of fixed-income securities because it provides an average maturity for the portfolio, which, in turn, provides a measure of interest rate risk to the portfolio. The duration for a bond portfolio is equal to the weighted average of the duration for each type of bond in the portfolio: Minimize Duration Risk When yields are low, investors, who are risk-averse but who want to earn a higher yield, will often buy bonds with longer durations, since longer-term bonds pay higher interest rates.

Duration & Convexity: The Price/Yield Relationship

But even the yields of longer-term bonds are only marginally higher than short-term bonds, because insurance companies and pension funds, who are major buyers of bonds, are restricted to investment grade bonds, so they bid up those prices, forcing the remaining bond buyers to bid up the price of junk bondsthereby diminishing their yield even though they have higher risk.

Indeed, interest rates may even turn negative. In Junethe year German bond, known as the bund, sported negative interest rates several times, when the price of the bond actually exceeded its principal. Interest rates vary continually from high to low to high in an endless cycle, so buying long-duration bonds when yields are low increases the likelihood that bond prices will be lower if the bonds are sold before maturity.

This is sometimes called duration risk, although it is more commonly known as interest rate risk. Duration risk would be especially large in buying bonds with negative interest rates.