Fiedler Network Risk Indicators

Key Finding: High Aggregate λ₂ = Momentum, NOT Risk

All aggregate Fiedler eigenvalue indicators are positively correlated with forward S&P 500 returns. High theme synchronization reflects healthy market momentum, not systemic danger. Risk requires derived measures — decline breadth, concentration, and historical extremes.

Aggregate λ₂ — Momentum Signal

Best Correlation

+0.212

median λ₂ → fwd 20d

Q5 fwd 20d Return

+2.32%

Highest λ₂ quintile

Q1 fwd 20d Return

-0.13%

Lowest λ₂ quintile

Q5-Q1 Spread

+2.45%

20-day forward spread

Spearman Correlations: Aggregate λ₂ vs Forward S&P 500

Indicator	5d ρ	10d ρ	20d ρ	60d ρ
median_l2	+0.117	+0.174	+0.212	+0.149
mean_l2	+0.100	+0.155	+0.195	+0.154
pct_above3	+0.108	+0.161	+0.210	+0.184
pct_above5	+0.091	+0.143	+0.206	+0.211
p90_l2	+0.076	+0.120	+0.166	+0.137
std_l2	+0.044	+0.079	+0.101	+0.067

📈 All correlations are positive across every horizon. Higher aggregate λ₂ → higher forward returns. This is a momentum signal.

Quintile Forward Returns (20d) by Aggregate λ₂

Derived Risk Indicators — What Actually Predicts Downside

US — Spearman Correlations: Derived Indicators vs Forward Returns & Drawdowns

Indicator	Description	5d ρ	10d ρ	20d ρ	60d ρ	MDD20 ρ	Risk Score
l2_decline_pct	% themes with λ₂ declining over 20d	-0.081	-0.159	-0.195	-0.163	+0.031	0.629
l2_cv	CV of λ₂ across themes	-0.083	-0.095	-0.087	+0.056	+0.116	0.325
l2_hhi	Herfindahl index of λ₂ shares	-0.081	-0.094	-0.087	+0.058	+0.119	0.323
l2_skew	Skewness of λ₂ distribution	-0.027	-0.040	-0.040	-0.015	+0.194	0.316
l2_pct252	Percentile rank vs 1yr history	+0.029	+0.048	+0.032	-0.074	-0.207	0.280
l2_z60	Z-score vs 60d rolling mean	+0.067	+0.113	+0.115	+0.116	-0.064	-0.347
l2_roc20	Rate of change (20d)	+0.077	+0.148	+0.194	+0.200	-0.025	-0.594

🚨 l2_decline_pct is the best US risk indicator (score 0.629). When >65% of themes lose synchronization, forward 20d returns average -0.57%. l2_pct252 is the best drawdown predictor (ρ = -0.207 with MDD20).

US l2_decline_pct Quintile Returns

US Extreme Conditions — Top/Bottom 10%

Composite Risk Indicator

Composite Risk Quintile Analysis

Composite = mean(decline_pct_rank, cv_rank, hhi_rank, skew_rank)

Composite Risk Correlations

Target	Spearman ρ	p-value	Significance
fwd_5d	-0.085	0.0036	**
fwd_10d	-0.120	<0.0001	**
fwd_20d	-0.125	<0.0001	**
fwd_60d	-0.024	0.4043	ns
fwd_MDD20	+0.134	<0.0001	**

📊 Composite captures both return prediction (ρ = -0.125 with fwd_20d) and drawdown prediction (ρ = +0.134 with MDD20). Statistically significant at p<0.01 for horizons up to 20d.

US vs KRX — Different Markets, Different Risk Signals

US Best Risk Indicator

l2_decline_pct

ρ = -0.195 (fwd 20d) | Q5-Q1: -2.30%

KRX Best Risk Indicator

l2_hhi

ρ = -0.143 (fwd 20d) | Q5-Q1: -2.04%

Economic Logic

Different Mechanisms

US: breadth | KRX: concentration

KRX l2_hhi Quintile — KOSPI Forward Returns

KRX Risk Indicator Correlations vs KOSPI

Indicator	5d ρ	10d ρ	20d ρ	60d ρ	MDD20 ρ
l2_hhi	-0.103	-0.115	-0.143	-0.199	-0.006
l2_cv	-0.049	-0.051	-0.074	-0.026	+0.057
l2_skew	-0.028	-0.024	-0.059	-0.032	+0.069
l2_decline_pct	-0.037	-0.075	-0.092	+0.013	-0.063
l2_pct252	+0.054	+0.063	+0.078	-0.000	+0.042

💡 US: When many themes lose sync simultaneously → broad weakness. KRX: When λ₂ concentrates in few dominant themes → fragile structure. Different mechanisms, both valid.

Cross-Market Network Spillover

KRX → US fwd 20d

-0.127

p < 0.0001 | KRX leads US

US → KRX fwd 20d

-0.047

p = 0.077 | Not significant

Decline Breadth Corr

+0.229

US-KRX decline_pct co-movement

Cross-Market Lead-Lag Discovery

🇮🇷 KRX network stress predicts US weakness (ρ = -0.127, p<0.0001). KRX is a more sentiment-sensitive market that picks up global risk signals earlier.

🇺🇸 US does NOT reliably predict KRX (ρ = -0.047, p=0.077). The lead-lag relationship is asymmetric — smaller markets lead larger ones in network stress.

🔗 Network decline breadth co-moves at ρ = +0.229. When themes break down, it tends to happen across both markets, but KRX breaks first.

Current Network Risk Readings

US as of 2026-03-02

✅ US network has already collapsed (λ₂ at 2nd percentile, z-score -2.6). Historically, this extreme is closer to a rebound zone than continued risk. Composite risk at 7th percentile.

KRX as of 2026-02-06

📊 KRX HHI at 7th percentile (dispersed λ₂) is historically positive. Decline breadth at 65th pctl is moderate. Data lags US by ~1 month — March turmoil not yet reflected.

Methodology & Data

Data Sources

US Themes	128 WorldThemeClassification themes
KRX Themes	222 Naver Finance themes
US Period	2019-12-27 to 2026-03-02 (1,551 days)
KRX Period	2015-07-17 to 2026-02-06 (2,592 days)
US Benchmark	SPY ETF (S&P 500 proxy)
KRX Benchmark	KOSPI Index (^KS11)
Graph	60d rolling correlation, positive adjacency

Indicator Definitions

l2_decline_pct	Fraction of themes where λ₂ fell over 20 days
l2_hhi	Herfindahl index of λ₂ shares across themes
l2_cv	Coefficient of variation of λ₂ cross-sectionally
l2_pct252	Percentile rank of median λ₂ vs trailing 252d
l2_z60	Z-score of median λ₂ vs 60d rolling mean/std
l2_skew	Cross-sectional skewness of λ₂ distribution
Composite	Mean percentile rank of top-4 risk indicators