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Explain what it means for a rate curve to flatten or steepen, and outline a trade that would express a view that it will do either.

FRM® Part I · Valuation and Risk Models · Interest Rates · FRM1.VR.10.g

The idea

A curve flattens when the spread between long and short maturity rates narrows, for example the 10-year minus 2-year spread falling, and steepens when that spread widens. This can happen with rates rising or falling. A bull flattener has long rates falling more than short rates, a bear flattener has short rates rising more than long rates, a bull steepener has short rates falling more, and a bear steepener has long rates rising more. To trade a steepening view, buy the short-maturity bond and sell the long-maturity bond. For a flattening view do the opposite. Weight the legs by DV01, the dollar value of one basis point, not by face amount, otherwise the position is exposed to parallel shifts. A DV01-neutral steepener profits when the spread widens, whatever the level of rates, to a first-order approximation.

Formulas

Face amount for a DV01-weighted hedge or curve trade leg

Fh = Fp × DV01p ÷ DV01h

Fh
the face amount of the hedge or second leg
Fp
the face amount of the position being matched
DV01p
the DV01 per 100 of face of that position
DV01h
the DV01 per 100 of face of the hedge instrument

Shorter bonds have a smaller DV01 per 100 of face, so more face is needed. Matching face amounts leaves exposure to parallel shifts.

A practice question

From the question bank, with the reason each wrong option is wrong.

A yield curve is said to steepen when:

  1. all rates rise by the same amount.Why not: Describes a parallel shift, which leaves the slope unchanged.
  2. short-maturity rates rise above long-maturity rates.Why not: Describes inversion of the curve, not steepening.
  3. the spread between long-maturity and short-maturity rates narrows.Why not: Describes flattening, the opposite of steepening.
  4. the spread between long-maturity and short-maturity rates widens. - correct

Steepening means the slope, for instance the 10-year minus 2-year yield, increases. It can occur with yields rising or falling.

A harder one

The 2-year yield rises by 5 basis points while the 10-year yield rises by 25 basis points. This curve move is best described as a:

  1. bull steepener.Why not: Bull moves involve falling yields; here both yields rise.
  2. bear flattener.Why not: A flattener needs the short yield to rise by more than the long yield.
  3. bear steepener. - correct
  4. bull flattener.Why not: Bull moves involve falling yields, and flattening would need the long yield to move less.

The 10-2 spread widens from X to X + 20 bp, so the curve steepens; yields rise, so it is a bear move. A bear steepener has long rates rising more than short rates.

The hardest tier

A trader holds a DV01-neutral steepener: long a 2-year bond position with a DV01 of USD 20,000 and short a 10-year bond position with a DV01 of USD 20,000. The 2-year yield rises 10 basis points and the 10-year yield rises 30 basis points. The trade's profit or loss is closest to:

  1. a loss of USD 400,000.Why not: Gets the sign reversed, treating the move as a flattening for a steepener.
  2. a profit of USD 400,000. - correct
  3. zero, because the position is DV01-neutral.Why not: A DV01-neutral position is protected against parallel moves, not against changes in the spread.
  4. a profit of USD 800,000.Why not: Adds the two yield moves, ignoring that the long leg loses when its yield rises.

Long 2-year loses 20,000 x 10 = 200,000 and the short 10-year gains 20,000 x 30 = 600,000, net +400,000, which is DV01 x the 20 bp spread widening. DV01-neutral means no exposure to parallel shifts.

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