Curve trades: betting on the shape, not the level
Most rate views are about the shape of the curve. Buy one maturity, sell another, and size the legs so their DV01s match: a parallel move then makes nothing, and the P&L depends only on the spread between them.
- Size a DV01-neutral 2s10s steepener or flattener
- Compute its P&L from the moves in the two yields
- Size the legs for a target dollars-per-basis-point of spread, and the spread move a dollar target needs
- Say what an equal-face "curve trade" is really exposed to
The intuition
You think the central bank will cut sooner than the market expects, pulling two-year yields down much further than ten-year yields. That is a view on the spread between them, not on the level of rates. A steepener expresses it: buy two-year notes, sell ten-year notes. But a ten-year note carries several times the rate risk of a two-year per dollar of face, so the legs must be sized in DV01, not face. Short $25 million of ten-years with a DV01 of $850 per million is $21,250 a basis point; matching that with two-years at $190 per million takes about $112 million of face.
Now a parallel move cancels: the long two-year loses $21,250 per basis point and the short ten-year makes $21,250. What survives is the difference. If ten-year yields rise 10 bp and two-year yields fall 5, the spread widens 15 bp and the steepener makes $21,250 × 15 = $318,750. Set the trade up with equal face instead and the two-year leg carries only $4,750 a basis point: the position is mostly an outright short of ten-years, and its P&L is mostly about the level.
Two-year face = ten-year face × DV01₁₀ ÷ DV01₂. Steepener P&L = DV01 per leg × (Δ10-year yield − Δ2-year yield). For a target $/bp of spread, each leg's face = target ÷ its DV01 per $1. Spread move for a dollar goal = goal ÷ DV01 per leg. Which leg is long is set by which yield you expect to fall relatively.
Why it works
- The conventions here: a 2s10s Treasury curve trade. DV01s are dollars per basis point per $1M face and are held constant; no convexity, carry, roll or repo. A steepener is long two-year notes and short ten-year notes, DV01-neutral; a flattener is the reverse. The spread is the ten-year yield minus the two-year yield, in basis points. The equal-face comparison uses the same face on both legs.
- Why it is called a steepener when you are long the short end. It makes money when the curve steepens: two-year yields falling relative to ten-year yields lifts the two-years you own more than the ten-years you are short. Which yield you expect to fall relatively decides which leg is long.
- The P&L is the spread change times one leg's DV01. Long two-years: −DV01 × Δ2y. Short ten-years: +DV01 × Δ10y. With equal DV01s the sum is DV01 × (Δ10y − Δ2y), and the level drops out.
- Bull, bear and twist. The average of the two moves says whether yields fell (bull) or rose (bear) overall; the difference says whether the curve steepened or flattened. A DV01-neutral trade cares only about the second.
- The equal-face mistake. With equal face the two-year DV01 is a fraction of the ten-year's, so the net DV01 is a large short. The trade is mostly a bet that yields rise; the curve view is a small part of the P&L.
- The risk that remains. Neutral to parallel moves, not to the wrong kind of shape change. A steepener put on for cuts loses if the long end rallies on growth fears instead, a bull flattening.
| Ten-year leg DV01: 25 × $850 | $21,250 a basis point |
| Two-year face to match: $21,250 ÷ $190 per $1M | $111.8M |
| Ten-year yields +10 bp, two-year yields −5 bp: spread change | +15 bp |
| Steepener P&L: $21,250 × 15 | $318,750 |
| Equal face instead: two-year DV01 25 × $190 | $4,750 |
| Equal-face P&L: 4,750 × 5 + 21,250 × 10 | $236,250, and net DV01 $16,500 short |
| Spread widening needed to make $100,000: 100,000 ÷ 21,250 | 4.7 bp |
The formulas
Match dollars per basis point, not face.
The level cancels; the spread change remains.
Each leg carries the target on its own.
The backwards reading.
Worked example
Each leg's P&L from its own yield move, with the short leg's sign flipped, then the sum. The follow-up asks whether the move was bull or bear, and what the position cared about.
See it move
Same trade. Change the ten-year face, each note's DV01 per million, and how each yield moves.
- Raise the ten-year move. The spread change and the steepener P&L rise one DV01 per basis point, and so does the equal-face P&L.
- Raise the two-year move. The spread change and the steepener P&L fall; the equal-face P&L falls too, but by less, because its two-year leg is small.
- Raise the ten-year DV01. The DV01 per leg and the two-year face rise. Raise the two-year DV01 instead and the two-year face falls, because each million of it now carries more risk.
- Raise the ten-year face. The DV01 per leg and the two-year face rise in proportion, and both P&Ls scale with them.
Run it backwards
Your PM wants a DV01-neutral flattener that makes a stated amount for every basis point the spread narrows. What face of each note do you trade?
Each leg must carry the target DV01 on its own: face = target ÷ DV01 per dollar of face, for the ten-year you buy and the two-year you sell. The two-year face comes out several times larger.
A flattener profits when the ten-year yield falls relative to the two-year. Owning the ten-year and being short the two-year gains from exactly that, and being DV01-neutral, ignores the overall level.
Traps
Say it in the interview
“You expect the central bank to cut sooner than priced. How do you trade it without a view on the level of rates?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- Match DV01s, not face; the shorter leg needs several times the face.
- Steepener P&L = DV01 per leg × (Δ10y − Δ2y): the level drops out.
- The leg you expect to rally relatively is the long leg.
- Equal face is mostly an outright bet on the longer bond.