# duration and convexity formula

By including convexity in our price change formula. The column "(PV*(t^2+t))" is used for calculating the Convexity of the Bond. To get the curve duration and convexity, first shift the underlying yield curve, … Duration & Convexity: The Price/Yield Relationship Investors who own fixed income securities should be aware of the relationship between interest rates and a bond’s price. Both have a yield rate of i = :25because (1:25) 1 = :8, Its convexity is 4.9198 [= (2*3)/(1.10433927)2]. As a general rule, the price of a bond moves inversely to changes in interest rates: a bond’s price will increase as rates decline and will decrease as rates move up. A:Pays $610 at the end of year 1 and$1,000 at the end of year 3 B:Pays $450 at the end of year 1,$600 at the end of year 2 and $500 at the end of year 3. This amount adds to the linear estimate provided by the duration alone, which brings the adjusted estimate … The formula for calculating bond convexity is shown below. The convexity adjustment is the annual convexity statistic, AnnConvexity, times one-half, multiplied by the change in the yield-to-maturity squared. Duration & Convexity Calculation Example: Working with Convexity and Sensitivity Interest Rate Risk: Convexity Duration, Convexity and Asset Liability Management – Calculation reference For a more advanced understanding of Duration & Convexity, please review the Asset Liability Management – The ALM Crash course and survival guide . We can get a better approximation of the new price as follows: Price Change = (- Duration x Price Yield) + (0.5 x Convexity x (Yield Change)^2)) Using our previous example, if the 8% 10-year note has a 0.60 convexity, the new estimated price change is calculated as follows: On the other hand, using our formula above gives: $$\Delta D \approx (7.52^2 - 72.17)*(0.25/100) = -0.04$$ share | improve this answer | follow | edited Nov 20 at 20:45 Effective Duration Formula = (51 – 48) / (2 * 50 * 0.0005) = 60 Years Example #2 Suppose a bond, which is valued at$100 now, will be priced at 102 when the index curve is lowered by 50 bps and at 97 when the index curve goes up by 50 bps. Convexity - The degree to which the duration changes when the yield to maturity changes. Duration and convexity are important numbers in bond portfolio management, but it is far from obvious how to calculate them on the HP 12C. more accurate than the usual second-order approximation using modified duration and convexity. These Macaulay approximations are found in formulas (4.2) and (6.2) below. Step 3: Next, determine the yield to maturity of the bond based on the ongoing market rate for bonds with similar risk profiles. Most textbooks give the following formula using modified duration to approximate the change in the present value of a cash flow series due to a change in interest rate: It is calculated as Macaulay Duration divided by 1 + yield to maturity. Of course, there are formulas that you can type in (see below), but they aren’t easy for most people to remember and are tedious to enter. It's the reason why bond price changes do not exactly match changes in interest rates times duration. Those are the yield duration and convexity statistics. Duration and Convexity 443 That duration is a measure of interest rate risk is demonstrated as fol-lows. Chapter 11 - Duration, Convexity and Immunization Section 11.2 - Duration Consider two opportunities for an investment of \$1,000. Explanation. Its Macaulay duration is 2 and its modified duration is 1.8110 (= 2/1.10433927). Also known as the Modified Duration. The formula for convexity can be computed by using the following steps: Step 1: Firstly, determine the price of the bond which is denoted by P. Step 2: Next, determine the frequency of the coupon payment or the number of payments made during a year.