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

Convexity analysis in fixed income

Pricing consequences

As shown, price and yield calculations on the 10-year swap futures are computed based on the $100,000 notional principal with an annual coupon rate of 4% with interest paid semiannually. Given a listed or hypothetical price, the yield may be calculated by finding the yield resulting in a matching price or discount rate. CME Group publishes a table of price and yield changes for T-note and swap futures online. 

The pattern of eurodollar rates over 40 quarters changes shape in response to shifting yield curves of U.S. Treasury securities and proxies, such as interest rate swaps and T-note futures. In this process, eurodollar futures create their own form of convexity with changes in the curve of quarterly rates-to-yields.

“Rates-to-yields” (above) shows that on three dates in years 2007, 2009 and 2012 the ratio is smaller when yields are high and rise to top levels when yields are low. The following table includes eurodollar yields at quarters 1, 20 and 40 for maturities of 0, 5 and 10 years in addition to the U.S. Treasury yield at those dates. 

Quarter   

2/1/07

1/30/09

4/11/12

1

5.37%

1.25%

0.50%

20

5.18%

2.58%

1.29%

40

5.35%

2.64%

2.34%

Treasury

     

20

4.84%

1.88%

0.88%

Because of convexity adjustments and shifts in the pattern of rates-to-yields, future changes in market yields will produce significant changes in eurodollar rates, yields and prices. By being aware of this relationship, traders can be prepared better for future shifts in market values.

Paul Cretien is an investment analyst and financial case writer. His e-mail is PaulDCretien@aol.com.

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