# Drift and the Long Bond, by Victor Niederhoffer

October 20, 2006 |

I recently reviewed a paper which drew my attention to the long term rise of the US Treasury long bond future (continuously adjusted with all contract shifts), showing a price rise from 78-20 to 114-06 from 1977 to present. The question we are batting around the office is whether there is any economic reason for there to be a long term upward drift in prices. Such a drift would be related to the normally rising structure of the yield curve, with long term yields higher than short term. The upward shape is supposed to occur because of increased price variability of the long term bond vs. short term and liquidity preference; the desire to have your money sooner rather than later because your risk on holding the investment until it expires is greater. Liquidity would also seem to relate to the ability to trade the issue at tight spreads. Any educated comments on the subject would be welcomed.

Prof. Charles Pennington replies:

I assert that Treasury futures will have a long term upward drift if and only if long term bonds outperform short term in total return, over the long term.

Suppose that a bond maturing in 30 years is trading at price 100, and let’s assume that long term yield are 10% and short term yields are 2%.

Consider a futures contract on 30-year bonds that settles in one year, and suppose that this contract is trading at price P.

We could construct a risk-free portfolio consisting of a long position in treasury bonds and a short position in the treasury bond futures contract. This should earn the short term risk-free rate (and let me assume that 1 year is close enough to being “short term”).

Let’s also suppose that after one year, the price of the 30-year Treasury, which will also be the settlement price of our futures contract, has risen by \$1 to a value of 101.

The final value of our portfolio, which cost 100 initially, is:

101 + 10 + (Pi-101)

(The “10″ is the dividend, and “Pi-101″ is the gain or loss on the short sale.)

This final value should be equal to 102, since we should earn the risk-free return. From that, we can solve Pi and get 92.

So in this example, the total return of a Treasury bond was 11% (10% dividend and 1% capital gain). The total return that we would have had by going long the futures contract would have been (101-92)=9, or 9% of the notional value. That’s equal to the total return that we would have had from holding the bond minus 2%, the short term rate.

In other words, the return from the futures contract is “as if” we had borrowed at the short term rate and bought the long term bond.

If that strategy makes money over the long term, then the continuous futures contract will show a long term upward drift. The Siegel book indicates that that strategy was about breakeven from 1802 through about 1980 and then did quite well since then.

Paul DeRosa Responds:

It is true that the bond future trades at a discount to its delivery value equal to the positive carry on the cash bond. If that carry is negative, the future will trade at a premium. There are hundreds if not thousands of traders who spend their days bent over desks enforcing that condition. It doesn’t necessarily imply the price of the futures contract will drift upward over time. They drift upward only within each quarter. So in the example you give, the contract will start each quarter at a discount of 2% to its maturity value. If the level of market interest rates were to stay at 10%, the next contract also would start the quarter at a 2% discount, but it would have the same maturity value as its predecessor. I would add one caveat, which sounds like a technicality but who overlooking as been the cause of tens if not hundreds of millions of dollars in trading losses during the past 30 years. The 2% discount I alluded to can be reliably captured only by owning the contract and being short the so called “deliverable” bond. At any point in time, several different bonds can satisfy the delivery conditions against the contract, only one of which is cheapest to deliver. Being long the contract and short the wrong bond can lead to any one of several outcomes.

George Zachar replies:

Yes. The accretion of the forward months should be identical to the positive carry one would receive by owning the underlying bond outright and financing it at the overnight/repo rate. You can make the money by carrying the “cash” or buying the forward, but the dollar amounts should be the same. This is carry and not drift/true price appreciation.

There is very slight positive carry on bond futures now:

USZ6 Dec06 110-18
USH7 Mar07 110-17
USM7 Jun07 110-16

The two-year future shows the impact of negative financing/curve inversion, where holding the instrument costs money (as your asset yields less than its cost to carry).

TUZ6 Dec06 101-28 3/4
TUH7 Mar07 102-02 s

The carry/deliverables/basis on these contracts is perhaps the most “crowded” trade on the planet.

“In the day”, one could make money in the forward mortgage market, when lenders would sell their production forward at a discount to carry. Those glorious days are long gone.

Carry hogs, er, traders have been known to “ride the Japanese curve” with enough leverage to make your eyes tear.

JBZ6 Dec06 133.56
JBH7 Mar07 132.83

They’d buy the forward Japanese bond, and pocket the carry, enduring the interest rate, yield curve and currency risks along the way.

The takeaway here is that one must be aware of all this when looking at fixed income debt futures prices. To evaluate long term interest rates cleanly, it is best to look at yields of relevant “constant maturity” indices.

Earlier posters observed that very long-term secular trends of dampened reported inflation and declining risk premia since the financial shocks of the Volcker era account for the observed trend toward lower yields and higher bond prices. I wholeheartedly second that analysis.

Stocks, famously, have unlimited long-term upside. Fixed income has the “zero bound” on rates, and central banks who have shown themselves willing to ensure that Deflation is rarely seen. Therefore, with an assurance that there’ll always be a little inflation, debt instruments are effectively capped out when their yields reach the low single digits.

Michael Cohn responds:

I would recommend everyone find a way to get “Rolling Down the Yield Curve” by Martin Leibowitz, circa early 1980s. Few articles as clear about how bonds work. I stopped trading basis myself in 1989 when four JGB basis-traders for what was then Mitsubishi Bank took me out to lunch one day in Japan.

Very little can go wrong when you are long the cheapest to deliver and short the future. Depending upon the set-up it was also a way to play changes in yield curve shape but now there are so many instrument, such as swaps, to play it an explicitly.

Jon Corzine made his name at Goldman by trading the delivery options and the dead period after the US bond contract stopped trading each delivery cycle. The legendary trader Mark Winkleman at Goldman made his name buy buying the bond basis and funding it cheaper. He had it to himself and our friends at Salomon. The old days were relatively easy.

You need to have a firm grasp of reverse repo rates for the deliverable bonds, and yield curve volatilities, to play from short side where you are short the bond and long the future. I recall the programs at my firm for modeling the change in deliverables to be extensive, as I use to play the bund basis, but with no apparent skill as I did not control the collateral, as could a German insurance company.

Dr. Alex Castaldo responds:

The question that started this thread was: is there an upward drift in fixed income markets like there is in equities?

The article by Vesilind claimed that this is so, and this drift arises from the fact that the yield curve is (on average) upward sloping due to the “liquidity preference hypothesis” and/or the “preferred habitat hypothesis”. In other words the “expectation hypothesis” of interest rates does not hold and there is a non-zero “term premium” embedded in interest rates.

Certainly there have been plenty of academic articles in recent years saying the expectation hypothesis does not hold. But I am more interested in the practical money-making potential here.

A simple strategy to capture the drift, that works well according to Vesilind, is to be long the “fourth nearmost eurodollar future”. I decided to test an even simpler strategy: each September buy the eurodollar future with one year to expiration and hold it until expiration.

You can think of it as a test of the good old “Keynesian normal backwardation hypothesis”: is the price of the future one year before expiration biased low compared to the expectation of what the settlement price will be.

Here is the data:

Contract       Date      Price      ExpDate  Price    Chg

EDU6 06 9/19/2005 95.690 9/18/2006 94.610 -1.080
EDU5 05 9/13/2004 97.045 9/19/2005 96.080 -0.965
EDU4 04 9/15/2003 98.165 9/13/2004 98.120 -0.045
EDU3 03 9/16/2002 97.535 9/15/2003 98.860 1.325
EDU2 02 9/17/2001 96.425 9/16/2002 98.180 1.755
EDU1 01 9/18/2000 93.470 9/17/2001 96.890 3.420
EDU0 00 9/13/1999 93.755 9/18/2000 93.340 -0.415
EDU9 99 9/14/1998 95.040 9/13/1999 94.490 -0.55
EDU8 98 9/15/1997 93.825 9/14/1998 94.500 0.675
EDU7 97 9/16/1996 93.700 9/15/1997 94.281 0.5812
EDU6 96 9/18/1995 94.260 9/16/1996 94.440 0.18
EDU5 95 9/19/1994 93.180 9/18/1995 94.190 1.01
EDU4 94 9/13/1993 96.070 9/19/1994 94.940 -1.13
EDU3 93 9/14/1992 96.140 9/13/1993 96.810 0.67
EDU2 92 9/16/1991 93.550 9/14/1992 96.870 3.32
EDU1 91 9/17/1990 91.670 9/16/1991 94.500 2.83

Avg 0.724

T Stat 1.940

At first the results look impressive: there is a 72.4bp per year gain, with a t-statistic near 2. However, much of the result is driven by the first two years (1991 and 1992) when interest rates were dropping rapidly. Without these two years the gain is only 39 basis points with a t-statistic of 1.15.

As mentioned by others, it is difficult to distinguish the term premium from the general interest rate decline after 1990.

The Vesilind paper is an excellent and reasonably accessible overview of mechanistic currency trading systems that execute carry trades based on yield differentials, and volatility (implied riskiness).

The authors find, retrospectively, that during a period of irregularly declining rates and risk premia (1993-2006), rotating capital between currency pairs offering high yield spreads at times of high perceived risk earned worthwhile alpha.

The carry/risk aversion trade is a standard formula for speculating in currencies, and the authors “kept it simple”, making evaluation of their strategy relatively easy.

The study’s charts neatly show the performance of different strategies as the cycles change.

I must, however, disagree with the chair that currency pairs trading per se can be said to showcase “drift”. The time period involved was particularly favorable to yield chasers, and the regular shifting of positions from one set of underlyings to another strikes me as antithetical to the notion of passive drift.

That said, I believe there is a different speculative lesson to be drawn from this study, and that is the seeking of relative value within the confines of a large, complex set of related instruments.

Relative value among currency pairs based on yield/return vs. vol/risk strikes me as analagous to relative value within the stock market between sectors and individual stocks. There’s no shortage of relaive value measures with which to “count” fundamental and performance dispersion in stocks. Ditto risk/vol.

The paper at hand provides a nice introductory framework for setting up relative value/risk matrices.

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