To calculate approximate convexity the formula here says we need to take the price of the bond if interest rates go up. So what we need to do is make an assumption that well. Okay. Let's say that interest rates go up. What will the new price on the bond be calculating that price using a present value calculation. So standard discounting calculations. We then need to say okay what happens if interest rates go down and bond prices go up, assuming the same change in yield to get to the higher interest rates and the lower interest rates for this P plus and P minus respectively. So we're moving the same direction in terms of yield away from the current yield on a bomb. We then need to subtract from this two times the current bonds price and divide everything by two times their current price times the change in yield squared. This will give us a whole number just like we have modified duration being a whole number. And if we then want to calculate how much we need to add on to the bonds new price to adjust for convexity. We could look at this on a percentage basis. So you take your convective number times it by a hundred and then multiply it by the change in yield squared or if we're looking for the dollar amount of an adjustment to make we would replace the hundred with the current bond price per hundred dollars of power value. If we're then trying to get to a comprehensive formula of what a new bond price will be using modified duration and a convexity adjustment. We start off with a current bond price. That's our P0. We then deduct from that to pick up the inverse relationship between One prices and yields so deduct from that modify duration Times by your current price Times by The Changing yield that you're modeling. And then add on to this always add on because the convexity adjustment always needs to add on to the modified duration assumed new price the convexity number times by the current bond price Times by the change in yield squared. So let's put some numbers around that let's assume that we've got a bond that's got five years maturity pays an annual coupon of 2% and has a yield to maturity of 2% This would give us a modified duration of 4.71. So for every 1% change in yields, we'll get a 4.71% change in the bonds press. If we were then to Model A changing yields to get to our connected number of 1% We then say OK. Well, if yields went up by 1% would now have yields of 3% and we'll be able to calculate a new price for the bond using present value calculations of 95.42. And then equally if interest rates went down by 1% to get that P minus would get to yields being 1% which would give us a new bond price of 104.85. With all of these numbers we can then drop them into the convexity formula. We take the price if rates go up the 95.41 add on to that the price if rates go down by the same amount the 104.85 and then deduct from this two times the current bond price that being the hundred if we then divide all this by two times the current bond price times the changing yield in One Direction that we were modeling 1% squared. That would then give us the convexity number as a whole number of 13.68. To turn this into a convexity adjustment in percentage terms to correspond to the percentage adjustment that we have for duration. We need to take the convexity Times by 100 and by the change in yield squared to give us 0.14 the way that we interpret this is that we have a 0.14% adjustment for convexity to add on for every one percent change in use. And if we try to apply it to this Bond. Assuming that we get a full in rate of 1% So what were the new price be if we had a falling rates of 1% We then need to take the current price of 100 deduct from this the modified duration 4.71 times the current one price of 100 times the change in yield that we're modeling a fall of rates of 1% in decimal form. We then need to add on to this the convexity number the 13.68 multiplied by the current bond price of a hundred multiplied by the changing yield that we're modeling of 1% Square. Working through those calculations. We'll take the hundred. We then add on to this 4.71 because the rates are falling. So if one prices are going up and then we also add on to this 0.14 for the convexity adjustment all together giving us 104.85 which matches the bond price that we got to when we calculated P minus using our present value calculations. So that was the price we got to when interest rates felt. Taking modified duration on its own would have got us to a new price of 104.71 which would be too low, but then adding on the convexity adjustment of 0.14 we get up to the price of the bond of 104.85 that we would have arrived at had. We used a present value calculation to get to the bonds price if the yield was one percent.