Causal Macro-Financial Stress Indices, Cross-Sectional Stress Betas, and Regime Conditioning in quarcc-risk-regime

This post accompanies our research paper, Causal Macro-Financial Stress Indices, Cross-Sectional Stress Betas, and Regime Conditioning in quarcc-risk-regime (quant-fund/papers/risk-regime/), documenting the packages/risk-regime and packages/factor-primitives Rust crates.

The resulting 327-month reference panel (reference/risk_regime_monthly.csv) powers the regime-attribution tables on our live strategy pages—QUARCC Market Neutral US Quant Fund and QUARCC US Long-Short Equities—and in our updates on QUARCC LinkedIn.

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1. Fifteen Causal Monthly Risk & Regime Indicators

Conditioning equity portfolios on macro-financial stress requires strictly point-in-time indicators that never leak future sample moments or unannounced macro releases. The quarcc-risk-regime crate (packages/risk-regime) maps daily S&P 500 OHLC bars, daily CBOE VIX closes, monthly ICE BofA High Yield and Investment Grade Option-Adjusted Spreads, weekly Thursday AAII Bearish survey readings, and publication-lagged FINRA margin debt into a 15-column monthly panel:

1. Multi-Horizon Returns & 12–1 Momentum (src/price.rs): ret_1m, ret_3m, ret_6m, and Fama–French skipped-month momentum mom_12_1 $= P_{t-1}/P_{t-13} - 1$ (Cooper, Gutierrez, and Hameed, 2004).
2. Moving-Average Distances (src/price.rs): dist_ma_6m and dist_ma_10m $= P_t / \mathrm{MA}_{k,t} - 1$ for $k \in \{6, 10\}$ inclusive of month $t$.
3. Normalised 14-Day Wilder ATR (src/atr.rs): Daily Wilder (1978) Average True Range $\mathrm{ATR}_d = \mathrm{ATR}_{d-1} + (\mathrm{TR}_d - \mathrm{ATR}_{d-1})/14$ divided by month-end close (atr) and its 1-month change (atr_chg_1m).
4. Online Welford Expanding Z-Scores (src/expanding.rs): Using Welford’s (1962) single-pass online recurrence from panel inception ($N_t \ge 2$, sample denominator $N_t - 1$), the engine standardises:
   • Credit spreads: hy_zscore ($z_t^{\text{HY}}$) and ig_zscore ($z_t^{\text{IG}}$) on ICE BofA US High Yield and Corporate OAS (Gilchrist and Zakrajšek, 2012; Friewald, Wagner, and Zechner, 2014).
   • Intramonth volatility range: vix_range_zscore ($z_t^{\text{VIX}}$) on the within-month VIX close range $\max_{d \in m(t)} \mathrm{VIX}_d - \min_{d \in m(t)} \mathrm{VIX}_d$ (Ang et al., 2006; Moreira and Muir, 2017).
   • Investor sentiment: aaii_bearish_zscore ($z_t^{\text{AAII}}$) on the final Thursday AAII Bearish survey reading in month $t$ (Baker and Wurgler, 2006).
   • Publication-lagged margin debt: Enforce a 1-month publication lag over a 6-month change window (md_6m_chg_pct $= 100(\mathrm{MD}_{t-1}/\mathrm{MD}_{t-7} - 1)$ and md_6m_chg_zscore $= z_t^{\text{MD}}$), capturing broker-dealer funding contractions (Brunnermeier and Pedersen, 2009; Adrian and Shin, 2010).
5. Composite Stress Index (src/composite.rs):

$$S_t = 0.2\left(z_t^{\text{HY}} + z_t^{\text{IG}} + z_t^{\text{VIX}} + z_t^{\text{AAII}} - z_t^{\text{MD}}\right).$$

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2. Cross-Sectional Stress Betas and Companion Primitives

To measure whether an individual equity or long–short portfolio is exposed to funding and volatility shocks independently of its market beta, src/exposure.rs estimates a bivariate OLS regression for each asset $i$ over $T \ge 4$ months ($df = T - 3$), extending Ang, Chen, and Xing (2006) and Agarwal, Ruenzi, and Weigert (2017):

$$r_{i,t} = \alpha_i + \beta_i^m r_{m,t} + \beta_i^s \Delta S_t + \varepsilon_{i,t}, \qquad \Delta S_t = S_t - S_{t-1}.$$

The crate also provides conditional stress-up betas ($\Delta S_t > 0$), upper-tail stress betas ($\Delta S_t \ge Q_p(\Delta S)$), prior shrinkage $\tilde{\beta}_i^s = \omega \hat{\beta}_i^s + (1-\omega)\beta_{\text{prior}}^s$, sector stress aggregation (src/portfolio.rs), bivariate scenario PnL $\sum_i w_i(\beta_i^m \delta_m + \beta_i^s \delta_s)$, and book/alpha conditioning operators (src/conditioning.rs):

$$g(S_t) = \mathrm{clip}\!\big(1 - \lambda\max(S_t - \tau, 0),\, g_{\min},\, g_{\max}\big), \qquad \tilde{\alpha}_{i,t} = \alpha_{i,t} - \big(\pi_0 + \kappa\max(S_t, 0)\big)\beta_i^s.$$

In packages/factor-primitives, these monthly operators are paired with daily and cross-sectional primitives: Markov transition powers and entropy (markov.rs), Baum–Welch/Viterbi Gaussian HMMs (hmm.rs), variance-targeted GARCH(1,1) / GJR-GARCH(1,1) (garch.rs), the multiplicative two-component MF2-GARCH-rw-m model of Conrad and Engle (2025) (mf2_garch.rs), and RiskMetrics/Newey–West/Vasicek/HAR-RV/QLIKE factor-risk estimators (risk/).

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3. Computational Reproduction vs. In-Sample Diagnostics

A core methodological discipline of our paper is separating deterministic software verification from in-sample investment diagnostics:

A. Deterministic Verification (327 Months, July 1999 – September 2026)

• Golden Fixture (tests/first_year.rs): All 15 metrics match the 12-month golden fixture (1999-07 to 2000-06) to within $< 10^{-9}$.
• Full 327-Month Public Reconstruction (repro/reproduce.py): Across all 327 months from July 1999 to September 2026, all price, momentum, moving-average, ATR, and FINRA margin-debt series match the reference CSV to $10^{-7}$–$10^{-5}$; minor deviations in credit and VIX z-scores reflect historical FRED ICE BofA OAS revisions and a single July 2002 VIX close vendor revision ($r = 0.999$).

B. Production Fact-Sheet Attribution & In-Sample Strategy Diagnostics

1. Live Fact-Sheet Regime Attribution (live-strategies/factsheet.py): Partitioning monthly returns of our live QUARCC Market Neutral US Quant Fund and QUARCC US Long-Short Equities books across S&P 500 up/down months, dist_ma_10m trend terciles, and lagged vix_range_zscore terciles provides transparent, zero-tuning performance attribution.
2. In-Sample A-030 Stress Attribution & Overlay Diagnostic (T = 68 months, 2021–2026): Regressing A-030 monthly returns on $r_{m,t}$ and $\Delta S_t$ confirms near-zero realised stress beta ($\hat{\beta}^s = -0.0049, t = -0.37$), while holdings-based sector attribution reveals a small $+0.002$ active sector stress tilt from net long Financials ($+9.7\%$) and IT ($+5.2\%$) against short Health Care ($-8.6\%$). Applying $g(S_{t-1})$ with $\lambda = 0.1$ raises in-sample Sharpe from $4.10$ to $4.45$, but only 9 of the 68 months have $S_{t-1} \ge 0.5$—making this strictly an in-sample diagnostic, not an out-of-sample alpha proof.
3. In-Sample v4b-monthly Factor-Risk Port (T = 116 months, 2017–2026): Replacing the untuned monthly port ($0.55\%$ excess return, $-22.80\%$ max drawdown) with the factor-primitives WLS/EWMA/shrunk-specific risk stack raises 2017–2026 excess return to $6.96\%$ and cuts max drawdown to $-10.39\%$ (evaluated in-sample across the full 116-month window).

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Read the Full Paper & View Live Regime Attribution

• Paper PDF: papers/risk-regime/risk-regime-2026.pdf
• LaTeX Source: papers/risk-regime/risk-regime-2026.tex
• Crate Source: packages/risk-regime
• Live Strategy Fact Sheets: QUARCC Market Neutral US Quant Fund & QUARCC US Long-Short Equities