Twist
Also written Yield curve twist · Twist in the yield curve
A steepening or flattening of the yield curve in which short-term and long-term rates move in opposite directions — as distinct from a convexity change, where they move the same way by different amounts or one stays put.
In plain language
When the gap between long and short interest rates changes, the curve is either steepening (the gap widens) or flattening (the gap narrows). The workbook asks a further question: how did the gap change?
There are three ways, and they get two names:
- Both rates move in opposite directions — this is a twist.
- Both rates move in the same direction but by different extents — a convexity change.
- One rate stays constant and the other moves — also a convexity change.
So a twist is the case where the curve pivots: one end goes up while the other goes down. It is the most dramatic kind of reshaping, because the short end and the long end of a bond portfolio are being pushed in opposite directions at the same time.
How it works
The workbook frames every shift by the moves of the long-term rate (LR) and short-term rate (SR):
| Shift | Description |
|---|---|
| Steepening | Difference between LR and SR widens; the curve shifts anti-clockwise |
| Flattening | Difference between LR and SR narrows; the curve shifts clockwise |
| Parallel | All rates move in the same direction by the same extent |
From its table, starting at SR 7.00%, LR 8.00%:
| After SR | After LR | Spread | Classification | Why |
|---|---|---|---|---|
| 6.90% | 8.10% | +1.20% | Steepening — twist | SR down, LR up |
| 7.10% | 7.90% | +0.80% | Flattening — twist | SR up, LR down |
| 7.10% | 8.20% | +1.10% | Steepening — convexity change | Both up, LR more |
| 6.90% | 8.00% | +1.10% | Steepening — convexity change | LR constant |
| 7.20% | 8.10% | +0.90% | Flattening — convexity change | Both up, SR more |
And from a flat 8.00% / 8.00% curve, a move to SR 7.90%, LR 8.10% is a steepening twist, while 8.00% / 8.10% is a steepening convexity change.
The classification takes two steps: first the spread tells you steepening or flattening; then the directions of the two rates tell you twist or convexity change.
Traders who expect the curve to steepen or flatten can express the view with an inter-bond spread — a long-short position in futures on two different GOI bonds, typically of the same expiry.
A worked example
Classification drill, then an illustrative portfolio. Durations are assumed; price changes use the duration approximation.
Classify each move from SR 7.00%, LR 8.00%:
| Move | Spread change | Directions | Answer |
|---|---|---|---|
| SR 6.80%, LR 7.90% | +1.00 → +1.10 (wider) | Both down, SR more | Steepening — convexity change |
| SR 7.10%, LR 7.90% | +1.00 → +0.80 (narrower) | Opposite | Flattening — twist |
| SR 7.00%, LR 7.90% | +1.00 → +0.90 (narrower) | SR constant | Flattening — convexity change |
| SR 7.10%, LR 8.10% | Unchanged | Same, same extent | Parallel |
What a twist does to a book. A dealer holds Rs 25 crore of a 2-year bond (modified duration 1.8) and is short enough 10-year futures to be duration-neutral overall. The curve flattens by a twist: SR up 10 bp, LR down 10 bp.
- The 2-year bond's yield rises: −1.8 × 0.10% × Rs 25 crore = −Rs 4,50,000.
- The short 10-year futures lose too, because long yields fell and bond prices at the long end rose.
Both legs lose at once. A parallel shift would have made one leg's loss the other's gain; a twist pushes the two ends of the position in opposite directions, and "duration-neutral" gives no protection.
Why NISM asks about it
Chapter 1 (Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Markets) defines twist and convexity change in its section on term structure shifts, with the before-and-after table of short and long rates. Chapter 5 (Strategies using Interest Rate Derivatives) introduces the inter-bond spread as the tool for a view that the curve will steepen or flatten. Expect a question that gives two pairs of rates and asks for the classification, where the trap is calling a same-direction move a twist.
Common exam traps
- Twist = short and long rates move in opposite directions. That is the only case.
- Same direction, different extent is a convexity change, not a twist — even though it also steepens or flattens.
- One rate unchanged is also a convexity change.
- Steepening = spread widens (anti-clockwise); flattening = spread narrows (clockwise). Decide this first.
- A twist can be a steepening or a flattening. The label always has two parts.
- Duration-neutral positions are exposed to twists, because duration assumes parallel moves.
Check yourself
1.The short rate moves from 7.00% to 6.90% while the long rate moves from 8.00% to 8.10%. How is this shift in the term structure classified?
- a)Steepening – twist
- b)Steepening – convexity change
- c)Flattening – twist
- d)Parallel shift
Show the answer
Answer: (a) Steepening – twist
Apply the two-step test. Step 1 — the spread. It was +1.00% (8.00 − 7.00) and is now +1.20% (8.10 − 6.90). The gap between the long and short rate has widened, so this is a steepening (the curve rotates anti-clockwise). Step 2 — how did they move? The short rate fell while the long rate rose — opposite directions, which the workbook labels a twist. Had both moved in the same direction by different amounts, or had one stayed constant, it would have been a convexity change instead. A parallel shift would require the spread to be unchanged.
2.The short-term rate moves from 7.00% to 7.20% and the long-term rate moves from 8.00% to 8.10%. How does the workbook classify this shift in the term structure?
- a)Flattening – convexity change
- b)Flattening – twist
- c)Steepening – convexity change
- d)Parallel shift
Show the answer
Answer: (a) Flattening – convexity change
The spread (long rate minus short rate) was +1.00% before and is +0.90% after. The spread has narrowed, so this is flattening. The workbook says flattening means the "Difference between LR and SR falls or narrows" and the curve shifts clockwise.
Both rates moved in the same direction (both rose) but by different amounts. The workbook says: "both rates move in opposite direction... is called 'twist' and the last two [same direction by different extent; one constant] are called 'convexity change'." So this is Flattening – convexity change, exactly as in the workbook's table (7.00%/8.00% → 7.20%/8.10%).
Why the others are wrong:
- Twist needs the two rates to move in opposite directions, for example SR 7.00→7.10 with LR 8.00→7.90.
- Steepening would need the spread to widen. Here it narrowed.
- Parallel needs "All rates move in the same direction by same extent". Here one rate moved 20 bps and the other 10 bps.
Where this is taught
Free preparation for NISM Series IVRelated terms
- Modified DurationMacaulay's duration divided by (1 + yield) — the percentage by which a bond's price moves for a one percentage point change in interest rates, and so the standard measure of interest rate risk.
- Duration-based hedge ratioThe number of interest rate futures that drives a bond portfolio's duration to zero — portfolio modified duration times market value, divided by futures modified duration times futures price over par.
- Inter-bond spreadA long-short position in futures on two different GOI bonds, usually of the same expiry, taken to express a view on how the yield curve will steepen or flatten.
- Parallel shiftA change in the term structure in which all rates move in the same direction by the same extent, leaving the spread between short and long rates unchanged — the only kind of move duration handles well.
- Term structure of interest ratesInterest rate plotted against term — one curve per credit quality, with the risk-free curve as the base and every other borrower quoted as a spread over it.
- Term spreadThe difference in yield between two bonds of the same issuer at different maturities — the workbook's own example is the gap between a 10-year and a 2-year G-Sec.
- Three S's of the yield curveThe workbook's own name for the three ways a yield curve can move — Shift, Slope and Shape — that a fixed income manager watches when taking an interest-rate view.