You Think You're Diversified? Check With Correlation

4-section structure: Concept / How We Compute / How to Read / Caveats.

1. Concept

"Don't put all your eggs in one basket." But what counts as different baskets?

Not "many stocks" — few stocks with low correlation.

If you hold TSMC, UMC, ASE, and Silergy-KY, you hold 4 different companies but essentially one semiconductor sector bet. They rise and fall together. Your "diversified" portfolio is functionally a levered semi ETF.

The correlation coefficient quantifies how similarly two stocks move:

ρ = +1 → perfectly in sync
ρ = 0 → unrelated
ρ = −1 → perfectly opposite

A truly diversified portfolio has average ρ close to zero (or negative).

2. How We Compute

Input

Watchlist / portfolio holdings
Daily close → simple daily returns
252 trading-day window (configurable)

Two Correlations Side-by-Side

Metric	Nature	Strength
Pearson ρ	Linear; assumes normality	Industry standard
Spearman ρ	Rank-based; distribution-free	Robust to extremes

When Pearson and Spearman diverge significantly, non-linearity or outliers are present — worth attention.

Key Outputs

Symmetric correlation matrix (diagonal = 1)
Average ρ (upper triangle mean, excluding diagonal)
Diversity score:
- avg ρ < 0.3 → 🟢 High
- 0.3 ≤ avg ρ < 0.6 → 🟠 Medium
- avg ρ ≥ 0.6 → 🔴 Low
High-correlation warnings: any pair with ρ ≥ 0.85
Max / Min pairs

TW and US Computed Separately

Different trading sessions, currencies, holiday calendars — mixing them introduces timezone bias. Shown in two matrices.

Client Cache

Same portfolio composition not recomputed for 15 minutes
Adding a stock triggers immediate recomputation

3. How to Read

Watchlist: Diversity Badge

Summary bar shows:

Diversity [High / Med / Low]  [⚠ 3]

Middle = avg ρ verdict
Right red dot + number = count of high-correlation warning pairs
Click to expand: avg ρ, sample size, warning list, max/min pairs

Portfolio: Full Heatmap

Portfolio page now shows a correlation matrix below Rolling Sharpe.

Heatmap Color Coding

Deep red → strong positive correlation
Deep green → strong negative (rare but valuable)
Grey → near zero (ideal diversification)

Reading the Matrix

Look for greens and greys, not reds:

All red → highly coupled, no real diversification
Mixed → partial diversification
Grey/green dominant → genuine diversification

Warning List

Below the heatmap, all pairs with ρ ≥ 0.85 are listed. These represent pairs acting as essentially one position. Consider:

Removing one of the pair
Treating them as a single position and rebalancing

4. Caveats

⚠️ Pearson's Two Assumptions Are Often Violated

Linearity
Normality

Stock returns frequently violate both. We provide Spearman alongside as a robustness check. When they diverge noticeably, tail events are likely in the data.

⚠️ Sample Length Matters

N < 60 days → highly unstable estimates, UI shows red ⚠ Sample < 60 warning
N = 252 days → industry standard, reliable
N > 500 days → may include structural shifts; can dilute recent relationships

Default 252; user-adjustable.

⚠️ Correlation Is Not Causation

High correlation doesn't mean "A causes B." Could be:

Same sector: both ride the same business cycle
Same issuer: TSMC (2330) vs TSM — literally the same company
Common factor: both react to USD index

Identify the reason before acting. Same ADR → drop one; common factor → consider hedging instead of dropping.

⚠️ Multiple Testing Problem

20 holdings → C(20,2) = 190 pairs. Even with true independence, ~10 pairs will look "significantly correlated" by chance at α = 0.05.

1–2 warnings may be noise
More than 5 — seriously reconsider the portfolio

We currently don't apply multiple-testing correction (Bonferroni etc.); that's a planned enhancement.

⚠️ This Is Not Complete Risk Analysis

Correlation tells you co-movement, but not:

Volatility magnitude
Tail risk (correlations tend to ~1 during crashes — "correlation collapse")
Fundamental quality (two weak stocks with low ρ don't cancel each other's weakness)

Correlation is necessary but not sufficient for diversification.

Try It

Open Watchlist — click the Diversity badge in the summary bar
Open Portfolio — scroll down to the correlation heatmap
Click 📐 for the full formula and parameters