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

Opportunities along the yield curve

These are exciting times for Treasury futures. Futures on several maturities of Treasuries should help hedge changes that will occur in a yield curve that is unusually low at present but should rise and change shape with an improving U.S. economy. Now is the time to prepare for that eventuality.

The long end of the yield curve is of particular interest at the moment because the Federal Reserve — having approached the limit of reductions in short-term interest rates — is resorting to purchases of longer-maturity bonds to push more funds into the U.S. economy. Flattening the yield curve will reduce the cost of long-term debt, encouraging investment in fixed-assets, while taking some of the downward pressure off of the dollar by allowing short-term rates to increase. It also may reduce the positive carry currently enjoyed by banks and other institutions with historically low borrowing rates.

Five Treasury futures contracts are included in the following analysis. The short-term portion of the yield curve is represented by two-year, five-year and 10-year T-note futures, while the longer maturities are covered by the 30-year classic and ultra 30-year Treasury bond futures.

Understanding treasuries

The original 30-year bond futures contract has price and yield cash flows that correspond to a 20-year fixed-income security. The ultra 30-year T-bond futures contract is so called because it has a longer maturity, at least 25 years. CME Group created the ultra to better reflect a 30-year maturity. The original bond contract specifications called for 30-year bonds with more than 15 years left to maturity. When the Treasury Department discontinued offering long bonds in 2001, the supply shrank. Because there were none offered for a seven-year period, the remaining supply reflected a shorter maturity. The ultra has cash flow characteristics that match a 30-year bond. Thus, the yield curve is covered by two-, five-, 10-, 20- and 30-year maturities.

Note that Treasury futures, as notional instruments, do not return cash payments in terms of interest and principal. Futures are held and traded primarily to take advantage of price changes before their delivery dates. Long and short Treasury futures contracts require a cash transaction on or around the delivery date because these derivatives are settled by the exchange of Treasury securities that closely match the maturity of the underlying T-note or T-bond.

Three of the Treasury futures maturities are shown on "Yields & rates" (below). The chart shows the eurodollar futures quarterly rates and yield curve, U.S. Treasury yields and T-note futures yields at two-, five- and 10-year maturities. Eurodollar yields form a smooth curve that is slightly higher and parallel to U.S. Treasury yields that are shown at eight maturities from three months to 10 years. Eurodollar yields are based on the geometric means of quarterly rates that extend over a 10-year span.


The three Treasury futures maturities shown on "Yields & rates" are two-, five- and 10-year T-notes. The T-note yields shown are slightly higher than corresponding eurodollar yields. Eurodollar futures — although representing dollar deposits that have more risk than Treasury securities — have the advantage of cash settlement at the delivery date.

Options on T-note and T-bond futures may be analyzed by using the LLP option pricing model available on Excel spreadsheets that can be downloaded from For example, an option price curve based on 12 strike prices was computed for the March 2011 five-year T-note futures on Oct. 28, 2010. A portion of the spreadsheet is shown on "Five-year T-note calls" (below).


The analysis results in call option prices predicted by a regression equation, the slope (delta value) of the option price curve at each strike price and upper and lower breakeven prices at expiration, 109 days in the future. Breakeven prices are those that would result in zero gain or loss on a delta-neutral trade between calls and underlying futures.

For the five-year T-note option with 121.00 strike price, the breakeven prices are 123,198 and 119,361. These prices imply a yield spread for the five-year T-note of 1.205% to 1.920%, while the yield on Oct. 28 was 1.665%. The price and yield spread on the measurement date shows the options market’s assessment of yield and price volatility for five-year T-bond futures through the expiration date in March 2011.


"Calls on Treasury futures" (above) shows the option price curves for the five Treasury futures on Oct. 28, 2010. Heights of the curves correspond to the maturities of the underlying note or bond. For example, calls for the 30-year ultra T-bond futures are on the highest curve because longer maturities produce the largest change in price for fixed-income securities with equal risk. As shown on "Breakeven prices & yields" (below), breakeven yield spreads for the five Treasury-based futures increase with larger underlying maturities. Because the five Treasuries have identical risk and equal times to expiration, maturities are the primary reason for different curve heights, breakeven prices and yield spreads.


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