# How to Adjust Modified Duration for Convexity

Investors purchase bonds for several reasons. A bond provides a regular income stream for the investor. Investors face less risk with bonds because the company incurs a legal obligation to repay the face value of the bond. Bonds typically last for many years. Interest rates fluctuate during those years, changing the value of the bond. Analysts use the modified duration to estimate the change in the bond’s price and the risk of a decline in value as a result of bond valuation changes. Adjusting the modified duration for convexity makes the valuation more accurate.

1. Add the bond price to the bond price when the interest rate is incremented. Multiply the bond price when the interest rate is decremented by two and subtract. This equals the numerator used to calculate convexity.

2. Multiply the bond price by the change in the interest rate squared. Multiply this answer by two. This equals the denominator used to calculate convexity.

3. Divide the numerator by the denominator. This equals convexity.

4. Multiply the convexity by 100 by the change in the interest rate squared. This equals the convexity adjustment.

5. Multiply the bond’s modified duration by the change in the yield of the bond. Divide by the convexity adjustment. This equals the modified duration adjusted for convexity.

#### Tips

• Understand the impact that a change in yield makes on the bond’s cash flows. If a yield change impacts the cash flows of the bond, the modified duration will be inaccurate.
• Bond prices typically change in the opposite direction as yield changes. For instance, if the market interest rate increases, the bond price decreases. This causes the bond’s yield to equal the market interest rate. Convexity can be negative. This means that the bond’s price would move in the same direction as the yield.

#### Warning

• Investors often choose bond securities because they believe that these securities pose less risk. In many cases, this is true. The bond creates a legal obligation for the company. Bonds do not come without risk, however. Companies suffering financial struggles may default on the money owed to the bondholders. These bondholders lose their entire investment when this occurs.

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