In “Waiting for Godot,” by Samuel Beckett, there are two characters, Vladimir and Estragon, waiting endlessly for someone named Godot.

A real-life counterpart exists in the financial world. This is the long wait for the Federal Reserve to raise U.S. interest rates. The wait extended over a period of approximately six years, from 2009 to November 2015. The expectation of a rate increase in December 2015 — which was met with a quarter-point increase in the target rate — was rampant, and if it had not been raised, it certainly would have equaled the comedic content of the stage play.

The recent history (February 2007 through November 2015) of Eurodollar futures and U.S. Treasury interest rates and yields is shown in the charts “Yields and Rates” (below). Rates are quarterly interest rates (90 days in maturity) that link up through their successive geometric means to equal a yield at the end of each quarterly period.

For example, the yield on five-year U.S. Treasury securities is the geometric mean of 20 quarterly rates leading up to the end of five years. Thus, the five-year yield is not a forecast of interest rates or yields at the end of five years. It, like all maturities of Eurodollar futures and Treasury yields, is an average (the geometric mean) of previous shorter-term rates.

Throughout this brief history, it is clear that Eurodollar quarterly rates must continuously adjust to make the resulting Eurodollar yield curve match the curve of U.S. Treasury yields. At times, this adjustment has been difficult. For example, in February 2007, when the Fed increased short-term rates to control an overheated economy, Eurodollar quarterly rates quickly descended from 5.4% to 5.0% in an effort to pull the Eurodollar yield curve closer to U.S. Treasury yields.

A year later, in November 2008, with the Fed now reducing short-term rates in the face of a financial crisis, the Eurodollar yield curve was back in place — parallel with the U.S. Treasury yield curve and approximately 100 basis points higher. During that year, the two-year Treasury yield fell from approximately 5% to 1.5%. The short-term Eurodollar rates — attempting to keep the yield curve in proper relationship — were still slightly below their related Eurodollar yields.

In July 2008, the Eurodollar yield curve was in a more normal position with Treasury yields. Eurodollar quarterly rates were equal to or above Eurodollar yields and the Eurodollar yield curve was parallel to the Treasury yield curve and approximately 100 basis points higher. The shorter-term Eurodollar rates were again shown to increase rapidly through the first 12 quarters to lift the Eurodollar yield curve to its final height above the U.S. Treasury yield curve. At this time, the shortest rates were approximately 3%.

### Waiting begins

Quantitative Easing began in December 2008 and by September 2009, the Fed was deeply involved in rescuing the U.S. economy by adding liquidity — not only reducing the shortest-term interest rates to near zero — by purchasing longer-term U.S. agency securities as well as Treasury debt. The spread between the Eurodollar yield curve and U.S. Treasury yields edged slightly lower than 100 basis points. From this time until November 2015, the shortest rates have been held near zero while the Fed applied the alternative strategy of adding liquidity to intermediate- and longer-term interest rate markets.

The charts show that Federal Reserve operations affect yields at all maturities. Eurodollar futures and options provide ways to study the Fed because of the close ongoing relationship between Eurodollar futures and U.S. Treasury yields.

### Forecast by the market

Eurodollar futures are futures on interest rates, rising in price when rates fall and falling when rates increase. This means that the usual relation between puts and calls as analyzed by the log-log parabolic (LLP) pricing model is reversed. Application of the model to Eurodollar options results in puts being priced as calls because the underlying is an interest rate.

“June 2016 Eurodollar options” (below) is an example of pricing puts by regression analysis that includes seven strike rates and put market prices. The resulting formula is accurate enough to hold the largest variation from predicted prices to approximately $5.00 while delta values extend from 0.030 to 0.710.

Potential high and low interest rates based on the Eurodollar futures rate of 0.785% on Nov. 27, 2015 are 1.122% and 0.599% at the 0.75% strike rate. The rate spread of plus 42% and minus 23% from the current Eurodollar futures interest rate shows the options’ market forecast of rates from November 2015 through June 2016. Because rates are already low, the bias is toward rising rates.

Interest rate ranges during the period to expiration are shown for three Eurodollar futures with March, June and September 2016 expiration dates on “Potential Eurodollar futures rates” (below). The lower rates for each month are relatively level as the underlying rate moves from far out-of-the-money to the point at which the underlying futures rate equals the strike rate.

Meanwhile, the line of higher prices descends in a shallow curve that provides the narrowest spread at-the-money before it moves up again as the futures rate increases and puts move toward being further in-the-money. The curve is a picture of the “volatility smile.”

The potential rate spreads are much lower as time to expiration grows shorter. Again, typical of other options, shrinkage of the spread between expiration months accelerates and the spread between March and June is smaller than the spread between June and September. Forecasts of rates between November 2015 and September 2016 vary between 0.50% and 2.00% with June in the middle with approximately 0.60% to 1.50% when the current futures rate is 0.78%.

### Effect of rates-to-yields

“Eurodollar rates-to-yields” (below) shows the effect of low short-term rates on the relationship between rates and yields at Eurodollar futures maturities over 40 quarters. As shown above, Eurodollar futures rates work to coordinate the Eurodollar yield curve with the U.S. Treasury yield curve. On Nov. 25, 2015, the two yield curves are almost equal. This not only shows that there is no convexity or risk difference separating Eurodollar yields and U.S. Treasury yields, but also that the ratio of rates-to-yields for Eurodollar futures options peaks at approximately 1.5 near the two-year maturity.

A shift by the Fed to higher short-term rates should have the effect of flattening the yield curve, allowing the Eurodollar yield curve to match the U.S. Treasury curve with less effort on the part of short-term Eurodollar rates. This change may result in a reduction of the rates-to-yields ratios. Because interest rate swaps and Treasury-note futures are not concerned with this adjustment of yield curves, it is possible for Eurodollar rates to increase less than the rise in swap rates or Treasury-note rates when the looked-for rate increase occurs.

In this way, a change in Fed policy may help traders who spread Eurodollar rates against interest rate swaps or Treasury-note futures, providing a potential 10 to 15 basis points advantage to Eurodollar futures.

Now that the Federal Reserve Open Market Committee has decided to allow interest rates to increase, it will be interesting to compare the results with the thoughts and assumptions reported here.