15 — Curve Trades and Scenario Analysis¶

Free learning pack¶

1. PIMCO Education Center — Understanding Duration
2. resources/fixed_income.md
3. reference/fixed_income/curve_trades.md, key_rate_duration.md

Do not search for more material until these are insufficient.

PREDICT¶

Two portfolios both have aggregate DV01 of $100,000. Portfolio A is all 10-year notes; Portfolio B is half 2-year / half 30-year (a "barbell"). Under a 2s10s steepener (2Y yields fall, 10Y+ yields rise), which portfolio does better, and why might that not be obvious from DV01 alone?

Construction¶

A DV01-neutral 2-leg curve trade sizes the second leg with:

units_leg2 = hedge_ratio(dv01_leg1, dv01_per_unit_leg2)

so the combined position has ~zero net DV01 while still expressing a view on curve shape (steepening/flattening), not the level of rates.

In [ ]:

# 2s10s steepener: long $10mm 2Y notes, short an offsetting DV01 in 10Y notes.
dv01_2y_per_100mm = 19_000   # $ per bp for $100mm face of 2Y notes
dv01_10y_per_100mm = 85_000  # $ per bp for $100mm face of 10Y notes

long_2y_face = 10_000_000
dv01_2y_leg = dv01_2y_per_100mm * (long_2y_face / 100_000_000)

# MANUAL FIRST:
# use hedge_ratio(dv01_2y_leg, dv01_per_unit) to size the offsetting 10Y
# face amount so the trade is DV01-neutral. dv01_per_unit is the 10Y DV01
# per $1 face (derive it from dv01_10y_per_100mm).
short_10y_face = None
print(short_10y_face)

# 2s10s steepener: long $10mm 2Y notes, short an offsetting DV01 in 10Y notes. dv01_2y_per_100mm = 19_000 # $ per bp for $100mm face of 2Y notes dv01_10y_per_100mm = 85_000 # $ per bp for $100mm face of 10Y notes long_2y_face = 10_000_000 dv01_2y_leg = dv01_2y_per_100mm * (long_2y_face / 100_000_000) # MANUAL FIRST: # use hedge_ratio(dv01_2y_leg, dv01_per_unit) to size the offsetting 10Y # face amount so the trade is DV01-neutral. dv01_per_unit is the 10Y DV01 # per $1 face (derive it from dv01_10y_per_100mm). short_10y_face = None print(short_10y_face)

PREDICT (scenario)¶

Given the trade above, if 2Y yields fall 25bp and 10Y yields rise 15bp (a steepener), is the trade's P&L positive or negative? Estimate the sign before computing.

In [ ]:

from pm.scenarios import Scenario

steepener = Scenario(
    name="2s10s Steepener",
    curve_bp={"2Y": -25, "10Y": 15},
)

# MANUAL FIRST:
# using key_rate_return_approximation (or DV01 * yield change directly for
# each leg), compute the P&L contribution from the 2Y leg, the 10Y leg,
# and the total.
total_pnl = None
print(total_pnl)

from pm.scenarios import Scenario steepener = Scenario( name="2s10s Steepener", curve_bp={"2Y": -25, "10Y": 15}, ) # MANUAL FIRST: # using key_rate_return_approximation (or DV01 * yield change directly for # each leg), compute the P&L contribution from the 2Y leg, the 10Y leg, # and the total. total_pnl = None print(total_pnl)

Experiment¶

Re-size the trade as a butterfly (add a 5Y belly leg) so it's DV01-neutral against both a steepener and a pure twist. What breaks first — the DV01-neutrality or your ability to reason about the position by hand?

Reference¶

reference/fixed_income/curve_trades.md
reference/fixed_income/key_rate_duration.md

Promote¶

Use src/pm/fixed_income/duration.py::hedge_ratio and src/pm/fixed_income/curve.py::key_rate_return_approximation only after your own implementation.

Test¶

pytest tests/test_fixed_income.py

ORAL CHECK¶

Explain to a PM how two portfolios with identical aggregate DV01 can have opposite P&L under the same curve shock.

Try /tutor fixed-income curve trades for an adaptive walkthrough.