22 — Pass-Throughs, Prepayment, and WAL¶

Free learning pack¶

1. resources/fixed_income.md
2. reference/fixed_income/pass_throughs.md, prepayment_models.md

Do not search for more material until these are insufficient.

PREDICT¶

A mortgage pool has a 30-year scheduled amortization. If every borrower prepays faster than scheduled (CPR > 0), does the pool's actual weighted average life (WAL) end up longer or shorter than 30 years?

Formula¶

Scheduled (no prepayment) amortization: standard level-payment formula.

SMM = 1 - (1-CPR)^(1/12)

TotalPrincipal_t = ScheduledPrincipal_t + (BeginningBalance_t - ScheduledPrincipal_t) * SMM

WAL = sum(t_i * Principal_i) / sum(Principal_i)

In [ ]:

import numpy as np

balance = 1_000_000.0
annual_rate = 0.06
months = 360

# MANUAL FIRST:
# build the scheduled amortization: beginning balance, scheduled
# principal, interest, ending balance for each of the 360 months.
# (payment = balance * r / (1 - (1+r)^-months), r = annual_rate/12)
beginning = None
scheduled_principal = None
print(beginning[:3] if beginning is not None else None)

import numpy as np balance = 1_000_000.0 annual_rate = 0.06 months = 360 # MANUAL FIRST: # build the scheduled amortization: beginning balance, scheduled # principal, interest, ending balance for each of the 360 months. # (payment = balance * r / (1 - (1+r)^-months), r = annual_rate/12) beginning = None scheduled_principal = None print(beginning[:3] if beginning is not None else None)

PREDICT (PSA)¶

At 100% PSA, when does the pool reach its fastest prepayment speed — immediately, or after a ramp-up period?

In [ ]:

psa_multiplier = 1.5  # 150% PSA

# MANUAL FIRST:
# for each month 1..360, compute the PSA CPR (ramps 0% to 6%*multiplier
# over the first 30 months, then flat), convert to SMM, then overlay it
# on `beginning`/`scheduled_principal` to get total principal per month.
# Finally compute the WAL of the resulting principal cash flows and
# compare it to the WAL of the no-prepayment schedule.
wal_with_prepay = None
wal_scheduled = None
print(wal_with_prepay, wal_scheduled)

psa_multiplier = 1.5 # 150% PSA # MANUAL FIRST: # for each month 1..360, compute the PSA CPR (ramps 0% to 6%*multiplier # over the first 30 months, then flat), convert to SMM, then overlay it # on `beginning`/`scheduled_principal` to get total principal per month. # Finally compute the WAL of the resulting principal cash flows and # compare it to the WAL of the no-prepayment schedule. wal_with_prepay = None wal_scheduled = None print(wal_with_prepay, wal_scheduled)

Experiment¶

Re-run at 300% PSA. How much shorter does WAL get, and does it keep shrinking proportionally, or is there a floor?

Reference¶

reference/fixed_income/pass_throughs.md
reference/fixed_income/prepayment_models.md

Promote¶

Use src/pm/fixed_income/mbs.py (mortgage_amortization_schedule, single_monthly_mortality, psa_cpr, apply_prepayment, weighted_average_life) only after your own implementation.

Test¶

pytest tests/test_mbs.py

ORAL CHECK¶

Explain to a PM why a 30-year MBS pool's actual average life is almost never close to 30 years, and what assumption drives the gap.

Try /tutor fixed-income prepayment for an adaptive walkthrough.