MFAA Chapter 6 Laboratory

NAV Unsmoothing and Hidden-Value Reconstruction (book §6.9)

Reconstruct latent value by Kalman filtering with credible bands; report marks as posterior distributions. The habit: never quote a private-asset moment without stating the filtration and the band. Seed 20260600.

import sys, numpy as np, matplotlib.pyplot as plt
sys.path.insert(0,'..')
from engine import ch06
from dataclasses import replace

1. E2 — the committee’s three volatilities (Proposition 6.3)

Reported variance understates latent by (1−α)/(1+α); autocorrelation is αᵏ.

p = ch06.FilterParams(alpha=0.6, n=20000)
m = ch06.smoothing_moments(p)
print(f"variance ratio: sample {m['var_ratio_sample']:.4f}, theory {m['var_ratio_theory']:.4f}")
print(f"lag-1 autocorrelation: sample {m['rho1_sample']:.4f}, theory {p.alpha}")
print(f"variance-correction factor (1+α)/(1−α): {m['correction_factor']:.4f}")

variance ratio: sample 0.2487, theory 0.2500
lag-1 autocorrelation: sample 0.5971, theory 0.6
variance-correction factor (1+α)/(1−α): 4.0000

2. Kalman reconstruction with credible bands

kf = ch06.kalman_filter(ch06.FilterParams(n=300, sigma_eps=0.02))
t = np.arange(len(kf['truth']))
plt.plot(t, kf['truth'], 'k-', lw=1, label='latent truth')
plt.plot(t, kf['y'], color='grey', alpha=.5, label='reported NAV')
plt.plot(t, kf['filtered'], 'C0-', label='filtered')
sd = np.sqrt(kf['filtered_var'])
plt.fill_between(t, kf['filtered']-2*sd, kf['filtered']+2*sd, alpha=.2)
plt.legend(); plt.title('Filtered latent value with 95% band');

3. E4 — Overcorrection stress (Section 6.8)

Naive Geltner inversion with a misestimated α̂ manufactures volatility.

import pandas as pd
pd.DataFrame(ch06.overcorrection_stress(ch06.FilterParams(sigma_eps=0.03)))

	alpha_hat	inverted_vol	true_vol	noise_amp_theory
0	0.4	0.099174	0.102738	0.00780
1	0.5	0.120721	0.102738	0.01260
2	0.6	0.154613	0.102738	0.02205
3	0.7	0.213049	0.102738	0.04380
4	0.8	0.332572	0.102738	0.10980

4. Validation checks

v = ch06.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_moments PASS
V2_geltner_exact PASS
V3_correction_factor PASS
V4_smoother_tighter PASS
V5_whiteness PASS
V6_reproducible PASS
ALL: True