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Relative-Value Yield Curve Trading

Strategies for the US IR Market

Most Yield Curve analyses are based on par curves and/or

zero-coupon curves. Placing trading positions based on

par curves creates exposure across the entire yield curve

up to the term of the traded instrument. The use of

Treasuries (Bonds, Notes, Bills, Zeroes, etc.) and Vanilla IR

swaps may be undesirable when the intended position is

meant to profit from an expected change in a forward

section of the yield curve.

The availability of Eurodollar futures goes a long way in

solving this problem and allows a trader to place bets on

his view of expected forward 3-month Libor rates. At this

time, Euros are traded out to 10 years, though only the

contracts out to five years are relatively liquid.

Previously, to place yield curve trades required the useeuro futures combined with spot and forward swaps.

These trades were restricted to funds with access to the

swap market. Trades could be placed using Treasury Bond

futures but with the risk of swap spreads fluctuating. With

the advent of IR Swap futures a few years ago, yield curve

trades became accessible to the retail investor. It is now

possible for virtually anybody to place positions with a

view of likely changes in the shape of the yield curve.

As mentioned earlier, there has been a lack of a common

yield structure to analyse and view curves, trades and

potential profit/losses. An alternative method uses theconcept of continuous forward rates. This method has the

advantage of allowing us to express the effective interest

rate portions of the yield curve which is being placed

long/short when entering into a fixed-income instrument

transaction. It also produces a more pronounced

description of forward yields with a richer structure that

may be hidden when solely depending on par or zero

curves.

My trading strategies are based on an instantaneous

forward rate curve built using the Eurodollar futures strip

combined with the 5, 10 and 30yr USD Interest Rate Swap

futures contracts. Since the Euros trade out up to 10

years, the 5 and 10 yr Swap futures are simply used to

confirm the robustness of the curve construction. The

30yr Swap futures price is used to fit the curve from 10yrsout to 30yrs.

The ongoing interventions by the Fed in maintaining an

almost zero-rated short rate while buying back treasuries

across the longer term periods has created an extremely

humped forward curve. A similar shaped forward curve

was seen in the Japanese market in the early 1990s when

the Japanese injected liquidity into its bond market by

bringing its short-term lending rate virtually to zero for an

extended period of time. This humped forward curve

remained for over five years allowing a relative value trade

to earn a regular carry income while waiting for theforward curve to return to a normal shape. This profitable

trading opportunities created by the humped shape will

eventually force the curve to return to a normal shape.

The longer it takes for the shape to normalize, the longer

we can continue earning the trades carry income.

The downside to the trade is that a trader needs to remain

cautious when putting on the intended position as market

interventions may continue to make the curve even more

humped. This situation creates even more profitable

trading opportunities, but may force the trader out of his

position if he has under-allocated margin resources to

sustain intermediate losses. In case the curve becomes

more humped and the position sustains some losses, the

beneficial consequences are that the carry income will

increase as well as the eventual profit that will be made

when the curve normalizes.

There are various trading techniques and money

management methods which can be used to minimize the

chances of being forced out of the trade while balancing

the profitability of the trading opportunity.

With this analysis system, I am able to build forward rate

curves calibrated to euro prices and swap futures prices.Different portfolios consisting of euro and swap futures

positions can be analysed for their carry income, potential

profit upon reversion to a normal curve as well as

maximum potential intermediate loss. Keep in mind that a

loss on a yield curve carry / reversion trade leads to a

greater carry income and a greater potential profit upon

reversion.

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Technical Description of Forward Curve Analysis System

My system assumes a step continuous forward rate curve

fitted to Eurodollar prices having adjusted for futures vs

forwards. The forward curve out from 10yrs to 30yrs is

smoothly fitted by a cubic spline calibrating to the 30yr

swap futures price. The 5yr and 10yr curve implied swapprices are computed and compared with the swap futures

prices. The 5yr swap rates fit within 2-3 bp and the 10yr

swap rates fit within 5-10 bp. This is well within bid offer

spreads of the euros and swap futures not any possible

arbitrage. Of course the 30yr implied swap futures price

fits exactly, as it has been used for calibration of the curve.

The forward curve is nudged by a continuous 1bp move

upward per forward date interval matching the euro

future 3mo periods. The sensitivities of the Euro future

contracts as well as the swap futures contracts are

calculated.

I have also built a theoretical curve model to analyse the

impact on portfolio positions of various curve shifts, i.e.

reversion of the forward curve to a normal curve,

diversion to a more severely humped curve, etc. This

allows for the analysis of various portfolio strategies and

how one could maximize carry income, profit from curve

reversion or minimize possible loss from curve diversion,

etc.

I have developed a simple system of computing the

portfolio exposure graphically versus the yield curve to aid

in trading strategy analysis.

These models and spreadsheets are in the development

stage, therefore I would like to apologize for their lack of

elegance and lack of usability and user protection. A few

sample pages of the spreadsheets have been attached.

I welcome any further discussion regarding any of the

calculations, techniques and assumptions used in the

development of these systems and the application of the

same to yield curve trading strategies.

Bipin C. Patel