Protecting Yourself from A Steeper Yield Curve

The Chicago Board of Trade's Keith Schap explains a more flexible approach to a classic problem

A common defensive tactic portfolio managers use when they anticipate a steepening of the yield curve (longer-term yields rising relative to shorter-term yields) involves either liquidating the longer-term holding and parking the money in overnight or commercial paper, or neutralizing it with futures.

In the event of an adverse interest rate change accompanied by a yield curve slope change, those moves could allow them to outperform their benchmarks. But it seems possible to improve performance further, and to adopt a more flexible approach with regard to choosing which risks to manage, through the use of the recently introduced Chicago Board of Trade yield curve spread (YCS) futures or options.

A Sample Portfolio

To illustrate a few of the possibilities, suppose you hold a portfolio with crucial interest rate sensitivities at the 5-year and 10-year sectors of the yield curve. It probably contains a variety of instruments that cluster around each focal point, but for ease of exposition, assume the portfolio contains 5-year and 10-year on-the-run Treasuries and has these characteristics:

Coupon	Maturity	Price	Yield	Duration	DV01	Par Value (millions)
6 1/4	Oct 31, 01	100-20+	6.10	4.22	0.0424	10
6 1/2	Oct 15, 06	101-05+	6.34	7.23	0.0734	5.804

The par amounts give each holding the same sensitivity to parallel shifts in the yield curve, but these holdings will react differently to twists in the shape of the yield curve.

The Yield Curve Spread Contracts

Discussions of duration-based hedging always stress that duration-neutral cash-futures structures perform well assuming small parallel shifts in the yields involved. Of course, parallel shifts are hardly the norm. For that reason, the Chicago Board of Trade has introduced a family of YCS contracts that can help risk managers overcome that limitation.

YCS futures and options track the spreads between pairs of on-the-run U.S. Treasury yields. Essentially equivalent to duration-weighted cash positions that change value only with shifts in yield curve slope, these spreads allow you to isolate the exposure of a portfolio to slope changes and take defensive action without also taking a directional position. This family of contracts includes the following spreads:

2-year to 3-year	3-year to 10-year
2-year to 5-year	3-year to 30-year
2-year to 10-year	5-year to 10-year
2-year to 30-year	5-year to 30-year
2-year to 5-year	10-year to 30-year

Put and call options are available on each spread.

Basically, a position long 5-10 YCS futures will benefit whenever the 5-year to 10-year segment of the U.S. Treasury yield curve steepens. The 10-year yield must increase relative to the 5-year, but that can result from the 10-year increasing more than the 5-year or decreasing less. The spread result will be the same in either case. Conversely, a short position will benefit from a flattening of the relevant portion of the yield curve. Because a self-adjusting feature is built into these contracts, they eliminate concerns about convexity.

YCS futures pricing is simple. The basis point value for one contract is $250. Because these spread contracts cash-settle, you need only be concerned with changes in the spread from initiation to settlement. For example, suppose your view includes a steepening of the yield curve, so you go long the 5-10 spread with that spread at 25 basis points. If the slope in that sector steepens 10 bp, to 35 bp, you will gain $2,500 a contract.

Basis point				Spread value
change	x	250	=	change
10	x	250	=	2,500

Similarly, you can easily locate the appropriate hedge ratio for yield curve hedges. You simply find the value of a 1 bp spread change for the portfolio and divide that by the YCS bp value, which is $250.

Isolating Curve Shift Effect

A simple scenario analysis serves to identify the effect of shifts in the slope of the yield curve on a given portfolio. Assume, for example, a +10 bp parallel shift in the yields of the sample portfolio. With rising interest rates, both positions will suffer losses-$42,461 on the 5-year holding, $42,436 on the 10-year holding. The portfolio will suffer an $84,897 loss.

	Yield Change	Initial Price	New Price	Dollar Change
6 1/4 Oct. 31, 01	+10	100-20+	100-07	-42,461
6 1/2 Oct. 15, 06	+10	101-05+	100-14	-42,436
				-84,897

Next, assume the 10-year yield rises 15 basis points. That increases the loss in that sector to $63,510 and the loss of the entire portfolio to $105,971.

	Yield Change	Initial Price	New Price	Dollar Change
6 1/4 Oct. 31, 01	+10	100-20+	100-07	-42,461
6 1/2 Oct. 15, 06	+15	101-05+	100-02	-63,510
				-105,971

The difference between the total loss for the parallel shift and the total loss from the steepening amounts to $21,074 given these data. That can be regarded as the dollar value to this portfolio of a 5-bp steepening of the 5-10 yield curve segment.

Finding the YCS hedge ratio that will protect against such a shift effect requires finding, first, the value of a 1 bp steepening for this portfolio and dividing the result by $250 (the DV01 for YCS futures). If you hold the 5-year yield constant and change the 10-year yield by 1 basis point (from 6.34 to 6.35 or to 6.33), you will discover a $4,261 value change. Thus the hedge ratio is 17.

4,261/250 = 17.04, round to 17

You must go long 17 of the 5-10 YCS futures contracts to protect this portfolio against a steepening yield curve.

To check on that, recall that the YCS payout formula multiplies 250 times the basis point spread change times the number of contracts:

250 x 5 x 17 = 21,250

But suppose the yield curve steepened 10 basis points, not 5. The hedge ratio holds, as it should. For example, if the 5-year yield rose 10 basis points and the 10-year yield rose 20 basis points, that 10-bp steepening would result in a $42,052 curve shift effect.

	Yield Change	Dollar Change	Yield Change	Dollar Change	Curve Shift Effect
6 1/4 Oct 31, 01	+10	-42,461	+10	-42,461
6 1/2 Oct 15, 06	+10	-42,436	+20	-84,488
		-84,897		-126,949	42,052

And in this case, the 17 long 5-10 YCS contracts would return $42,500 (250 x 10 x 17 = 42,500).

Evaluating Performance

If your benchmark is to outperform a position long these amounts of the 5-year and 10-year securities, then overlaying the YCS position will help you achieve that goal. In the case of the 10-bp shift, your performance will be $42,500 better than the benchmark loss of $126,949-a 33 percent performance improvement.

In that context, liquidating the 10-year and parking the cash at overnight rates might seem more attractive, until you think about the transaction costs or about the difficulties inherent in moving some of the non-treasury paper you hold.

An alternative way to isolate the 5-year holding from interest rate change is to use conventional futures to take its duration to zero. The usual hedge ratio arithmetic shows that going short 67 March 10-year Treasury note futures contracts will give that portion of the portfolio zero sensitivity to interest rate change. That conventional hedge plus the YCS hedge can limit the losses from rising interest rates and a 5-bp steepening of the yield curve to $20,795.

	Yield Change	Dollar Change	Futures Change	Hedged Profit & Loss
6 1/4 Oct 31, 01	+10	-42,461	-	-42,461
6 1/2 Oct 15, 06	+15	-63,522	+63,938	+416
17 YCS futures	+5	-	+21,250	+21,250
		-105,983	+85,188	-20,795

Obviously, such a portfolio with futures significantly outperforms the benchmark cash holding. Further, this example makes no mention of the coupon income that will accrue during the holding period of the strategy. That is another advantage of neutralizing the 10-year security with futures as opposed to liquidating and earning only overnight rates.

A third set of tactics is possible. Suppose your view encompasses both rising interest rates and a steepening yield curve, and, for whatever reasons, you want to protect your holding from both effects. A hedge using only conventional 5-year Treasury note futures will perform well for parallel shifts, but the results of such a hedge will be less than happy if the yield curve steepens.

Given your view and your need to be fully hedged, you might construct a hedge using both conventional futures and YCS contracts. The conventional contracts, ratioed to the weighted-average duration of the portfolio will protect against, say, a 10-bp parallel shift. The overlay of 5-10 YCS contracts will protect against a steepening yield curve.

On the conventional side, you will discover the need to go short 200 March 5-year Treasury note contracts. In the case of a 10-bp parallel shift, that hedge almost exactly balances the cash loss. But in the case of a 5-bp steepening in addition to the 10-bp upward shift, the conventional hedge underperforms significantly to leave the portfolio with a $21,047 loss.

	Yield Change	Dollar Change	Yield Change	Dollar Change
6 1/4 Oct. 31, 01	+10	-42,461	+10	-42,461
6 1/2 Oct. 15, 06	+10	-42,436	+15	-63,510
-200 5 yr futures		+84,924		-84,897
		+27		-21,047

That $21,047 loss seems little different from the $20,795 loss that results from combining YCS contracts with 10-year Treasury futures. You might well ask why not just use the simpler hedge. The reason to entertain the new possibility becomes clear if you consider the effect, in each case, of a 10-bp steepening. In the case of the combination hedge, the wider steepening generates a $634 gain.

	Yield Change	Dollar Change	Futures Change	Hedged Profit & Loss
6 1/4 Oct. 01	+10	-42,461	-	-42,461
6 1/2 Oct. 06	+20	-84,504	+85,099	+595
17 YCS	+5	-	+42,500	+42,500
		-126,965	+127,599	+634

In the case of the simple 5-year hedge, the wider steepening results in a $42,041 loss.

	Yield Change	Dollar Change	Futures Change	Hedged Profit & Loss
6 1/4 Oct. 01	+10	-42,461	+10	-42,461
6 1/2 Oct. 06	+20	-42,436	+20	-84,504
-200 5 yr futures		+84,924		+84,924
		+27		-42,041

That should make it clear that over a range of scenarios the two hedges are not equivalent.

Further, consider the results that come from adding the 17 contract 5-10 YCS position to that portfolio. In the case of the parallel shift, the YCS position adds nothing, but in the case of the 5-bp steepening, the use of the extra hedge element completes the protection.

	Yield Change	Dollar Change	Futures Change	Hedged Profit & Loss
6 1/4 Oct. 01	+10	-42,461	+10	-42,461
6 1/2 Oct. 06	+15	-42,436	+15	-63,510
-200 5 yr futures		+84,924		+84,924
+17 5-10 YCS		0		+21,250
				+203

Most important, although these seem to be extremely view-driven tactics, the possibilities illustrated show that adding the new YCS contracts to your risk management toolbox provides additional flexibility. You can isolate the interest rate risk of either or both of your portfolio segments, as before, and you can isolate the effect of changes in yield curve shape. Better, these contracts allow you to deal with any or all of those aspects of interest rate risk in an efficient and cost-effective way.