Step 2 — DCC(1,1) scalar:
Qt = (1 − a − b) · S̄ + a · εt−1ε't−1 + b · Qt−1
Rt = diag(Qt)^{−½} · Qt · diag(Qt)^{−½}
α_DCC
0.0194
shock reaction speed
β_DCC
0.8509
correlation persistence
α + β
0.8702
half-life ≈ 5 days
21 pairs · 7 stocks
631
daily obs · Jan 2024–Jun 2026
GARCH(1,1) parameter estimates — real Bloomberg log-returns
The DCC half-life of 5 days is notably shorter than in Engle (2002), who found near-integrated correlations (α+β ≈ 0.997, HL ~350d) for equities. With only 2.5 years of Bloomberg data dominated by two sharp shock-and-recovery episodes, the model estimates a fast-reverting correlation process — an artefact of the sample period. TSLA is the exception: its GARCH β = 0.973 implies a 157-day volatility half-life, consistent with its persistent high-vol regime. GOOGL and AMZN show low persistence (HL ≈ 2d), driven by their large, transient return spikes (AMZN −9.4% on Apr 3).
NVDA peak vol
95.9%
Apr 2025 tariff shock
AAPL peak vol
84.4%
Apr 9 pause bounce
TSLA avg vol
57.6%
persistently elevated
NVDA Sharpe
1.26
best risk-adj return
GARCH(1,1) conditional volatility — annualised %
MSFT
AAPL
NVDA
GOOGL
AMZN
META
TSLA
Annual performance (full sample Jan 2024–Jun 2026)
Pair selector
DCC (Engle 2002)
Unconditional S̄
Avg Δρ · DeepSeek
−0.0067
correlations fell · idiosyncratic
Avg Δρ · Tariffs
+0.0931
correlations spiked · systemic
Top pair S2
META↔TSLA
Δρ = +0.129 · fear trade
Systemic ratio
14×
tariff avg Δρ ÷ DeepSeek
DeepSeek shock · all 21 pairs · Δρ
Tariff shock · all 21 pairs · Δρ
All 21 pairs — Δρ comparison chart
Equal-weighted Mag-7 portfolio — annualised vol: DCC-implied vs constant correlation
DCC vol
Constant-corr vol
1-day 99% VaR — DCC vs constant correlation
Min-variance weights across regimes (long-only)
During the tariff shock, min-variance drops AAPL weight to near zero (its GARCH vol spiked to 84%) and concentrates into MSFT and GOOGL as the lower-vol safe havens. NVDA and TSLA receive zero weight throughout — their high idiosyncratic variance dominates the optimisation. The DCC VaR substantially exceeds the CCC VaR during both shocks, confirming that ignoring time-varying correlations would have led to significant risk underestimation.
CI_t vs Mag-7 → SPX average ρ · dashed lines = signal thresholds
Within-Mag-7 CI_t
Mag-7 → SPX avg ρ
τwarn
τalert
Individual ρ(stock, SPX) — fan of 7 series
Proactive framing: CI_t crossed tau_warn 22 trading days before the DeepSeek onset (Dec 19 2024 to Jan 20 2025) and 60 trading days before the tariff shock onset (Jan 8 to Apr 2 2025). A reactive framework — waiting for price drawdowns — would have missed both windows entirely. The gap between CI_t and the Mag-7 to SPX series narrows sharply during the tariff shock, confirming crowding was first a within-group phenomenon before it transmitted to the broader index. Thresholds calibrated on pre-shock baseline (Jan 2024 – Jan 2025): mu = 0.3999, sigma = 0.0170.
Reactive benchmark trigger:
Reduce by 30% when 5-day portfolio return < -5% · Re-enter after 5-day recovery > +2%
Position multiplier w_t — proactive DCC rule (CI_t on right axis)
w_t (position mult.)
tau_warn
tau_alert
Reduction periods — proactive (blue) vs reactive (amber)
The proactive rule was active — days (—% of sample) vs — days for the reactive strategy. The proactive rule fires earlier and holds the reduced position longer — trading some upside for protection before the dislocation rather than after. The 5-day re-entry lag matches the DCC half-life, creating a natural symmetry between correlation reversion speed and position restoration speed.
Proactive total return
—
DCC signal + capital rule
Static total return
—
no adjustment
Proactive max drawdown
—
vs static
Proactive Sharpe
—
vs static
Cumulative return: proactive vs reactive vs static — Jan 2024 to Jun 2026
Proactive (DCC rule)
Reactive (price trigger)
Static (no adjustment)
Drawdown: proactive (DCC) catches the tariff shock earlier
Core thesis: The proactive strategy reduces peak drawdown from -31.4% (static) to — — a saving of — percentage points — by acting on the correlation signal before prices dislocate. The reactive strategy achieves similar drawdown reduction but misses the first 5-10 days of the tariff selloff, reducing from a higher starting loss. The cost is modest: proactive gives up —pp of total return over the full period due to being underinvested during some upside days. The Sharpe ratio improves from — (static) to — (proactive).
Average Δρ across all 21 pairs in the tariff shock — 14× larger than the DeepSeek shock. The macro nature of Liberation Day tariffs propagated through all names simultaneously.
−0.67pp
Average Δρ in the DeepSeek shock. Correlations actually fell — the AI disruption caused differentiation, not contagion. The market rotated rather than sold en masse.
+12.9pp
META↔TSLA is the biggest mover in the tariff shock. Two of the most sentiment-driven names in the group — investors fled both simultaneously as "risk-off" dominated.
5 days
DCC half-life of correlation shocks (α+β = 0.870). Correlations reverted quickly post-shock — consistent with the V-shaped market recovery after the Apr 9 tariff pause.
2.65→3.57
Effective number of independent bets fell from 3.49 pre-shock to 2.65 at the tariff peak — then recovered to 3.57 post-shock. Diversification within Mag-7 collapsed briefly but fully recovered.
+6.1pp
NVDA↔GOOGL was the top-moving pair in DeepSeek (+6.1pp) — both directly impacted by the AI competitive threat. The one statistically meaningful correlation spike that day.