MFAA Chapter 12 Laboratory

Real Asset Cash-Flow Engine (book §12.9)

Value layered real-asset claims: lease ladders on market-rent dynamics, regime cap rates, development options. ‘Slow numerator, fast denominator.’ Seed 20261200.

import sys, numpy as np, matplotlib.pyplot as plt
sys.path.insert(0,'..')
from engine import ch12
from dataclasses import replace

1. E1 / Ex 12.10 — Slow numerator, fast denominator (Proposition 12.4)

The rent roll low-passes market rent; g(κℓ) drops from 0.5677 (ℓ=5) to 0.3773 (ℓ=10).

for ell in (5.0, 10.0):
    print(f"lease term {ell}y: low-pass ratio g(kappa*ell) = {ch12.lowpass_ratio(0.4, ell):.4f}")
sim = ch12.rent_roll_simulation(ch12.RealAssetParams(M=2000))
t = sim['tgrid']
plt.plot(t, sim['market_rent'].mean(axis=1), label='market rent (mean)')
plt.plot(t, sim['rent_roll'].mean(axis=1), label='rent roll (mean)')
plt.fill_between(t, np.quantile(sim['market_rent'],.05,axis=1), np.quantile(sim['market_rent'],.95,axis=1), alpha=.15)
plt.legend(); plt.title('The ladder low-passes the market'); plt.xlabel('years')

lease term 5.0y: low-pass ratio g(kappa*ell) = 0.5677
lease term 10.0y: low-pass ratio g(kappa*ell) = 0.3773

Text(0.5, 0, 'years')

2. The value fan under regime cap rates

Value volatility is dominated by the fast-moving denominator.

vf = ch12.value_fan(ch12.RealAssetParams(M=4000))
t = vf['tgrid']
plt.plot(t, vf['value'].mean(axis=1), 'C0-')
plt.fill_between(t, np.quantile(vf['value'],.05,axis=1), np.quantile(vf['value'],.95,axis=1), alpha=.2)
plt.title('Value fan V = NOI / cap rate'); plt.xlabel('years')
print(f"variance share: numerator {vf['numerator_var_share']:.2f}, denominator {vf['denominator_var_share']:.2f}")

variance share: numerator 0.35, denominator 0.65

3. Ex 12.12 — The development option (Proposition 12.6)

β=1.406, V*=3.46K at σ=0.25, ρ=6%, μ=3%. The NPV rule builds too early.

do = ch12.development_option(ch12.RealAssetParams(dev_sigma=0.25, dev_rho=0.06, dev_mu=0.03), V=1.2)
print(f"beta = {do['beta']:.3f}, V* = {do['V_star_over_K']:.2f}K")
print(f"land value at V=1.2K: {do['land_value_over_K']:.3f}K (optimal), NPV rule: {do['npv_rule_value']:.3f}K")
print(f"value lost by NPV rule: {do['value_lost_fraction']*100:.0f}%")

beta = 1.406, V* = 3.46K
land value at V=1.2K: 0.555K (optimal), NPV rule: 0.200K
value lost by NPV rule: 64%

4. Validation checks

v = ch12.validation_checks()
for k,d in v.items():
    if isinstance(d,dict): print(k, 'PASS' if d['pass_'] else 'FAIL')
print('ALL:', v['all_pass'])

V1_lowpass PASS
V2_development PASS
V3_development_mc PASS
V4_lowpass_monotone PASS
V5_hurdle_in_sigma PASS
V6_reproducible PASS
ALL: True