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Convexity adjustment accounts for the non-linear relationship between price and interest rate. For instance, a bond’s price may decrease at a lower rate when rates rise and increase at a faster rate when rates fall – a property called convexity. A convexity adjustment will result in a more accurate view of the change in the price of the bond with respect to a change in the interest rate – called interest rate risk. The adjustment is given by the second derivative of the price with respect to yield and is added to the interest rate risk of the bond calculated in a linear relationship with yield. A similar adjustment is made to forward rates to arrive at futures rates, where the convexity adjustment is the difference between the forward interest rate and the future interest rate.
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