Investment Committee Risk Memo: Multi-Asset Regime Contagion & Tail-Risk Allocation sdfgdsfg

Mandate Summary. This memorandum evaluates the proposed $100M institutional multi-asset allocation (45% US Equities, 25% 10Y Treasuries, 12% Gold Bullion, 13% Commercial Real Estate / REITs, and 5% Digital Assets) against a traditional 60/40 Stock–Bond Benchmark across 2,520 daily historical observations (10 years, 2016–2026) and 10,000 correlated Student-$$t$$ Monte Carlo paths over a 5-year horizon.

Under the unconditional full-cycle baseline, transitioning from the 60/40 benchmark to the proposed Multi-Asset mandate lifts expected annualized return from 7.20% to 8.12%, improves the portfolio Sharpe ratio from 0.32 to 0.37 (a +0.05 uplift), and raises 5-year median terminal wealth from $140.3M to $146.3M. Over the 10-year historical tape, $100 indexed in the multi-asset sleeve compounded to $203.9 vs. $177.4 for 60/40 while trimming realized peak-to-trough drawdown from 22.7% to 21.5%.

Open the interactive portfolio allocation & stress-test simulator on the Stage

1. Regime-Switching Covariance Breakdown

Standard single-regime mean–variance models assume a static covariance matrix $$\Sigma$$. In practice, cross-asset correlations and volatilities shift sharply across macroeconomic regimes. Across our 2,520-day sample, 360 trading days (14.3% of the tape) occurred inside stressed inflationary rate-shock or systemic liquidity-crisis windows.

For a portfolio weight vector $$w \in \mathbb{R}^5$$ satisfying $$\sum_{i=1}^5 w_i = 1$$, the regime-conditional annualized variance under state $$s \in {\text{normal}, \text{rate_shock}, \text{liquidity_crisis}}$$ is:

$$ \sigma_p^2(w \mid s) = w^\top \Sigma_s w = \sum_{i=1}^{5} \sum_{j=1}^{5} w_i w_j \sigma_{i,s} \sigma_{j,s} \rho_{ij,s} \tag{1} $$

Two structural correlation breaks dominate portfolio tail risk:

1. Stock–Bond Correlation Sign Flip in Inflationary Rate Shocks: During expansionary regimes, 10Y Treasuries hedge equity drawdowns with a negative pairwise correlation of $$\rho_{\text{eq,bond}} = $$ -0.25. In an inflationary rate-hike regime (such as 2022), discount-rate repricing drives simultaneous stock and bond selloffs, flipping equity–bond correlation to +0.60 while doubling Treasury volatility from 5.7% to 11.4%.
2. Cross-Asset Contagion in Liquidity Crises: During systemic deleveraging, average off-diagonal correlation across all five asset classes surges from 0.14 in normal markets to 0.30 in rate shocks and 0.34 in liquidity crises. Equity–REIT correlation rises to 0.82, equity–crypto correlation climbs to 0.76, and annualized equity volatility expands from 14.1% to 30.9%.

Table 1: Regime-conditional asset volatility and correlation parameters estimated by regime_covariance.py.

2. Fat-Tailed Monte Carlo Engine & Conditional Value-at-Risk (CVaR)

Because financial asset returns exhibit excess kurtosis (leptokurtic tails), Gaussian Value-at-Risk systematically understates extreme loss severity. In scripts/monte_carlo_sim.py, we simulate $$M = $$ 10,000 monthly return paths over $$T = 60$$ months (5 years) using Cholesky factorizations $$L_s L_s^\top = \Sigma_s$$ coupled with multivariate Student-$$t$$ innovations ($$\nu = 6$$ degrees of freedom, variance-normalized by $$\sqrt{(\nu - 2)/\nu}$$):

$$ R_{t,s} = \mu_s \Delta t + L_s \sqrt{\Delta t} , \frac{Z_t}{\sqrt{\chi_\nu^2 / \nu}} \sqrt{\frac{\nu - 2}{\nu}}, \qquad Z_t \sim \mathcal{N}(0, I_5) \tag{2} $$

Following Rockafellar and Uryasev, let $$L_p = -(W_{1\text{Y}} / W_0 - 1)$$ denote the 1-year percentage loss random variable. The $$\alpha$$-level Value-at-Risk ($$\text{VaR}\alpha$$) and Conditional Value-at-Risk ($$\text{CVaR}\alpha$$, or Expected Shortfall) at $$\alpha = 95%$$ are defined as:

$$ \text{VaR}\alpha(w) = \inf \left{ \ell \in \mathbb{R} : \mathbb{P}(L_p \le \ell) \ge \alpha \right}, \qquad \text{CVaR}\alpha(w) = \mathbb{E}!\left[ L_p ;\middle|; L_p \ge \text{VaR}_\alpha(w) \right] \tag{3} $$

Comparative Performance Across Institutional Allocations

Table 2 compares all four institutional allocations under the Full-Cycle Baseline and Stressed Regimes on our $100M mandate.

Table 2: Monte Carlo Risk, Tail Shortfall, and 5-Year Terminal Wealth Summary Across Allocations and Regimes.

3. Stress-Test Findings & Investment Committee Guardrails

Table 3 isolates how the proposed IC Multi-Asset Mandate behaves across each macroeconomic regime when correlation assumptions are stressed.

Table 3: Regime Stress-Test Decomposition for the IC Proposed Multi-Asset Mandate ($100M Initial Capital).

Approved Risk Guardrails

1. Inflationary Rate-Shock Resilience via Real Assets: Because the 12% Gold Bullion sleeve maintains a near-zero correlation to both equities and Treasuries during rate shocks, the Multi-Asset portfolio sustains a positive expected drift (+1.14%) and trims 1-year 95% CVaR from 30.16% (60/40) to 29.88% (-0.28% improvement) while preserving $99.6M in 5-year median capital.
2. Digital Asset Variance Budget Cap (5% Hard Ceiling): Although a 5% Bitcoin sleeve contributes meaningfully to full-cycle Sortino (0.57) and Sharpe (0.37), its high annualized volatility and +0.76 crisis equity correlation cause marginal risk contribution to spike during liquidity stress. We enforce a strict 5.0% rebalance cap whenever 21-day realized portfolio volatility exceeds 16.0%.
3. Dynamic De-Risking Trigger: If rolling 63-day equity–bond correlation exceeds $$+0.40$$ and 1-year 95% CVaR breaches 24.30%, the mandate automatically shifts toward the All-Weather Risk-Parity weights (30/35/20/15/0), which limits Liquidity Crisis 95% CVaR to 32.94%. Test these allocations interactively on the Stage.