09 — Duration, DV01, Convexity and Curve Risk¶

Free learning pack¶

1. PIMCO Fixed Income Education Center
   https://www.pimco.com/ca/en/resources/education-center/fixed-income
2. PIMCO Understanding Duration
   https://www.pimco.com/us/en/resources/education/understanding-duration
3. MIT Finance Theory I fixed-income materials
   https://ocw.mit.edu/courses/15-401-finance-theory-i-fall-2008/
4. resources/fixed_income.md

Core approximations¶

dP/P ≈ -D_mod*dy DV01 ≈ D_mod*P*0.0001 dP/P ≈ -D*dy + 0.5*C*dy^2

HAND CALCULATION¶

For price 100 and modified duration 5:

• approximate P&L for +10 bp
• +100 bp
• -100 bp

In [ ]:

# MANUAL FIRST
price = 100.0
modified_duration = 5.0
shock_bp = 100

# Convert bp -> decimal yield change and calculate approximate price change.

# MANUAL FIRST price = 100.0 modified_duration = 5.0 shock_bp = 100 # Convert bp -> decimal yield change and calculate approximate price change.

Curve vocabulary¶

front end, belly, long end, 2s10s, 5s30s, steepener, flattener, twist, butterfly.

Key-rate duration¶

Use: dP/P ≈ -sum(KRD_k * dy_k)

After manual work inspect: convexity() in duration.py computes the second-order term above. src/pm/fixed_income/duration.py src/pm/fixed_income/curve.py

ORAL CHECK¶

How can two portfolios both have duration 5 and react differently to a steepener?