16 — Swaps, Swap DV01, and Swap Spreads¶

Free learning pack¶

1. PIMCO Education Center — Understanding Duration
2. resources/fixed_income.md
3. reference/fixed_income/swap_dv01.md, swap_spread.md

Do not search for more material until these are insufficient.

PREDICT¶

A PM wants to add 5 years of duration to a portfolio without buying more cash Treasuries. They enter a 5-year receive-fixed swap. Does this increase or decrease the portfolio's DV01? What if they pay fixed instead?

Approximation¶

Treat the swap's fixed leg as a par bond: coupon = swap rate, priced at par, ytm = swap rate. Then swap DV01 is just bond DV01 on that proxy bond. See reference/fixed_income/swap_dv01.md for what this approximation ignores (floating-leg resets, discounting basis).

In [ ]:

import pandas as pd

curve = pd.read_csv("../../data/mock_curve.csv")
five_year = curve.loc[curve.tenor_years == 5].iloc[0]
notional = 50_000_000

print(five_year)

# MANUAL FIRST:
# treat the 5Y swap_rate as coupon = ytm on a par "bond" with this notional,
# 5-year maturity, semiannual frequency. Compute its DV01 by hand using
# the modified-duration and DV01 formulas (don't call src yet).
swap_dv01_5y = None
print(swap_dv01_5y)

import pandas as pd curve = pd.read_csv("../../data/mock_curve.csv") five_year = curve.loc[curve.tenor_years == 5].iloc[0] notional = 50_000_000 print(five_year) # MANUAL FIRST: # treat the 5Y swap_rate as coupon = ytm on a par "bond" with this notional, # 5-year maturity, semiannual frequency. Compute its DV01 by hand using # the modified-duration and DV01 formulas (don't call src yet). swap_dv01_5y = None print(swap_dv01_5y)

PREDICT (swap spread)¶

If bank funding stress widens swap spreads across the curve, does a PM who is long Treasuries and short swaps (pay-fixed) gain or lose?

Formula¶

swap_spread = swap_rate - treasury_yield

In [ ]:

# MANUAL FIRST:
# compute the swap spread at every tenor in `curve` (swap_rate minus
# treasury_par_yield), and identify which tenor has the widest spread.
spreads = None
print(spreads)

# MANUAL FIRST: # compute the swap spread at every tenor in `curve` (swap_rate minus # treasury_par_yield), and identify which tenor has the widest spread. spreads = None print(spreads)

Experiment¶

Shock every swap_rate in the curve up 20bp while leaving treasury_par_yield unchanged (a pure swap-spread-widening scenario). Recompute swap DV01 P&L for the 5Y position above.

Reference¶

reference/fixed_income/swap_dv01.md
reference/fixed_income/swap_spread.md

Promote¶

Use src/pm/fixed_income/swaps.py (swap_dv01, swap_spread) only after your own implementation.

Test¶

pytest tests/test_fixed_income.py

ORAL CHECK¶

Explain to a PM why swap DV01 computed this way is a proxy, and name one concrete scenario where it would be noticeably wrong.

Try /tutor fixed-income swap dv01 for an adaptive walkthrough.