From the July 01, 2011 issue of Futures Magazine • Subscribe!

Government bond yields and forward rates

Comparing yields

The Eurodollar yield curve is higher than the U.S. Treasury yield curve because of the risk differential between risk-free government securities and 90-day dollar deposits, and the need for Eurodollar futures to offset their lack of convexity — a straight-line price change at $25 per basis point compared to the convex bond price curve. On "Two yield curves" (below) the risk/convexity spread of Eurodollar yields over Treasury yields is approximately 50 basis points on April 19, 2011.

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"Two yield curves" shows how closely correlated the Eurodollar yield curve is with the U.S. Treasury yield curve. Each Eurodollar quarterly rate must be in its proper place for the two curves to fit together, and a shift in Treasury yields must be reflected in Eurodollar rate and yield changes. At the same time, the Treasury yield curve immediately determines, through arbitrage, the yields and prices of other interest rate futures, including two-, five- and 10-year T-note futures and futures contacts on interest rate swaps.

Just as the Eurodollar yield curve can be used to describe the shape and individual quarterly yields along the U.S. Treasury yield curve, the 90-day interest rate futures of non-U.S. markets should respond to their individual government security yield curves. For example, "Short sterling rates and yields" (below) shows 90-day short sterling futures rates and the yield curve that is created from quarterly sterling rates. The risk-convexity spread between the yield curves is 50 basis points for most of 16 quarters of futures delivery dates.

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Similar to the implied forward rates computed from the U.S. Treasury yield curve, forward rates for the United Kingdom can be found by reversing back down the government yield curve. The implied forward rates approximately are parallel to — and slightly lower than — the short sterling rates. The government yield curve in each country or market is the determinant of short-term interest rate futures as well as the forward rates on government interest-bearing securities.

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