From the July 01, 2012 issue of Futures Magazine • Subscribe!

Convexity analysis in fixed income

Price adjustment

Because of the convexity advantage held by a fixed-income security over eurodollar futures used in a hedge, an adjustment is made by the market — increasing the yield and decreasing the price of eurodollar futures at each maturity relative to comparative T-note, U.S. Treasury securities and interest rate swap futures. 

One way to look at the necessary adjustment in yield is to measure the change in yield required to make the interest rate swap price equal to the eurodollar price at each market yield. “Yield differences” (below) shows the yield changes necessary to move the swap futures price down to equal the eurodollar futures price at selected market yields. The largest adjustments are 22.6 and 17.3 basis points at the plus and minus 200 basis point variations from the current market yield.

A less restricted definition of convexity is to use the term in reference to any nonlinear price — yield relationships. For example, eurodollar futures are marked to market daily. These may be hedged against futures on fixed-income securities that have no intermediate cash flows and thus have an advantage over eurodollar futures in terms of margin requirements. Increasing rates result in higher margin, while decreasing rates mean investing excess margin at lower rates.

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