MFAA Chapter 1 Laboratory

Taxonomy, Cash-Flow Visualization, and the Liquidity-Adjusted Valuation Sandbox (book §1.9)

This notebook drives the same engine.ch01 module that powers the webapp and the Excel workbook — identical seeds, identical numbers. Laboratory seed: 20260100.

import sys, numpy as np, matplotlib.pyplot as plt
sys.path.insert(0, '..')
from engine import ch01
from engine.ch01 import SandboxParams, template
from dataclasses import replace

1. Taxonomy (A1)–(A5)

Classify each asset along the five dimensions of Definition 1.2 and read the implied modeling choices.

import pandas as pd
pd.DataFrame([{**{'asset': a['asset']}, **a['profile'], 'note': a['note']} for a in ch01.TAXONOMY])
asset A1 A2 A3 A4 A5 note
0 Listed REIT share False False False False False All five fail for the share itself: a liquid w...
1 Direct commercial property True True True True True All five hold; the smoothing model of Section ...
2 Interval fund (private credit) True True True True False Hybrid: liquidity exists only at periodic wind...
3 Music-royalty stream True True True True False Cash flows observed on quarterly statements; l...
4 Litigation-finance contract True True True True True Nearest thing to a pure unspanned claim; legal...
5 Gold futures False False False False False Classical asset: the clean negative case. 
ch01.IMPLIED_CHOICES
{'A1': 'liquidity states constrain admissible actions (Chs. 5, 13, 14)',
 'A2': 'two filtrations; filtering and de-smoothing (Ch. 6)',
 'A3': 'price bounds, SDF selection, nonlinear operators (Chs. 3, 4, 7)',
 'A4': 'contractual payoff maps: waterfalls, covenants (Chs. 8-12)',
 'A5': 'optimal stopping and control (Ch. 14)'}

2. The LDCF sandbox: from number to distribution

Base configuration; the output is a valuation distribution, not a number.

p = SandboxParams()   # or template('buyout'), template('private_credit'), ...
out = ch01.sandbox(p)
print(f"mean {out['mean']:.5f}  se {out['se']:.5f}")
out['quantiles']
mean 1.25369  se 0.00841
{'q01': 0.27912603234898725,
 'q05': 0.3940524194387659,
 'q25': 0.6540933020989765,
 'q50': 0.9469358156256389,
 'q75': 1.4204142223294345,
 'q95': 3.04465658961917,
 'q99': 5.9496673711501975}
plt.hist(out['values'], bins=60, color='#1F3864', alpha=.85)
plt.axvline(out['mean'], color='crimson', label=f"mean {out['mean']:.3f}")
plt.xlabel('discounted value'); plt.ylabel('paths'); plt.legend(); plt.title('Valuation distribution (seed 20260100)');

3. Experiments E1–E4 (assignable before any theory)

E1 — From number to distribution. Freeze everything, verify the deterministic DCF, then release risks one at a time.

for fz, label in [(("cash","rate","timing","liquidity"),'deterministic'),
                  (("rate","timing","liquidity"),'cash-flow risk only'),
                  (("timing","liquidity"),'+ rate risk'),
                  (("liquidity",),'+ timing risk'), ((), 'all risks')]:
    s = ch01.summarize(ch01._simulate(p, frozenset(fz))['values'])
    print(f"{label:24s} mean {s['mean']:.4f}  std {s['std']:.4f}  q05 {s['quantiles']['q05']:.4f}  q95 {s['quantiles']['q95']:.4f}")
deterministic            mean 1.3557  std 0.0000  q05 1.3557  q95 1.3557
cash-flow risk only      mean 1.3568  std 0.3265  q05 0.8859  q95 1.9453
+ rate risk              mean 1.3470  std 1.1134  q05 0.3900  q95 3.3315
+ timing risk            mean 1.2598  std 1.1860  q05 0.4099  q95 3.0299
all risks                mean 1.2537  std 1.1898  q05 0.3941  q95 3.0447

E2 — Covariation and premia. Vary ρ with λ fixed; the direction of the change in expected value is the covariation argument of §1.7.

for rho in [-0.6,-0.3,0.0,0.3,0.6]:
    s = ch01.summarize(ch01._simulate(replace(p, rho=rho, M=8000))['values'])
    print(f"rho {rho:+.1f}  mean {s['mean']:.4f}")
rho -0.6  mean 1.4218
rho -0.3  mean 1.3590
rho +0.0  mean 1.3003
rho +0.3  mean 1.2429
rho +0.6  mean 1.1863

E3 — Liquidity as timing risk. Slow I→Liq and watch the left tail.

for nu in [3.0, 1.5, 0.75, 0.3]:
    s = ch01.summarize(ch01._simulate(replace(p, nu_il=nu, M=8000))['values'])
    print(f"nu_IL {nu:4.2f}  q05 {s['quantiles']['q05']:.4f}  q01 {s['quantiles']['q01']:.4f}  mean {s['mean']:.4f}")
nu_IL 3.00  q05 0.4009  q01 0.2807  mean 1.2673
nu_IL 1.50  q05 0.3882  q01 0.2748  mean 1.2619
nu_IL 0.75  q05 0.3631  q01 0.2457  mean 1.2493
nu_IL 0.30  q05 0.2965  q01 0.1783  mean 1.2153

E4 — The opening problem, first pass. Configure the buyout template at a residual six-year horizon: at what fraction of the sandbox mean would you transact? Retain your answer for Chapters 6, 7, 13.

pb = replace(template('buyout'), T=6.0)
sb = ch01.sandbox(pb)
print(f"buyout, 6y residual: mean {sb['mean']:.4f}; q25 {sb['quantiles']['q25']:.4f} = {sb['quantiles']['q25']/sb['mean']:.0%} of mean")
buyout, 6y residual: mean 0.9680; q25 0.5006 = 52% of mean

4. Validation checks V1–V4

A simulation that has not passed its anchors is not evidence of anything (LOS 1.7).

val = ch01.validation_checks()
for k, d in val.items():
    if isinstance(d, dict): print(k, 'PASS' if d['pass_'] else 'FAIL')
print('ALL:', val['all_pass'])
V1_deterministic PASS
V2_lambda0 PASS
V3_stability PASS
V4_antithetic PASS
ALL: True

5. Risk-source decomposition (Exercise 1.10) and smoothing (Exercises 1.7, 1.11)

rows = ch01.risk_decomposition(template('private_credit'), mode='isolated')
pd.DataFrame([{ 'config': r['config'], 'std': r['std'], **(r['quantiles'] or {})} for r in rows])
config std q01 q05 q25 q50 q75 q95 q99
0 all risks 0.399917 0.071619 0.094570 0.165618 0.270453 0.463367 1.054202 1.998970
1 cash risk only 0.048906 0.318532 0.343642 0.385664 0.416904 0.450475 0.504697 0.544334
2 rate risk only 0.215086 0.147163 0.188149 0.278304 0.373058 0.510600 0.832168 1.180421
3 timing risk only 0.240162 0.095460 0.109918 0.187962 0.323412 0.529051 0.930700 0.930700
4 liquidity risk only 0.001317 0.413260 0.416265 0.419348 0.419587 0.419587 0.419587 0.419587
5 interaction (all-risks std minus sum of isolated) -0.105555 NaN NaN NaN NaN NaN NaN NaN 
sm = ch01.simulate_smoothing()
print(f"variance ratio {sm['variance_ratio_sample']:.4f} (theory {sm['variance_ratio_theory']:.4f})")
print(f"rho1           {sm['rho1_sample']:.4f} (theory {sm['rho1_theory']:.4f})")
plt.plot(sm['latent'][:200], lw=.8, alpha=.7, label='latent')
plt.plot(sm['reported'][:200], lw=1.4, label='reported')
plt.legend(); plt.title('Smoothing recursion (seed 20260111)');
variance ratio 0.2456 (theory 0.2500)
rho1           0.5899 (theory 0.6000)