Correlation and concentration

EN source master · P06-L05 · 30 minutes estimated · needs_review

Offline formative study. No wallet connection, real funds, private keys, signatures, live trade or personal portfolio inputs. Visuals are specifications. This source master remains needs_review; completing the formative exercise does not issue certification.

Several different asset labels may share one collateral, venue or liquidity dependency.

Correlation is a sample association

Linear correlation compares paired deviations from their means [CORR]. For nonconstant samples, r=sum((A−meanA)(B−meanB))/sqrt(sum(A−meanA)^2×sum(B−meanB)^2). Values near+1 describe aligned supplied variation; they do not prove causation. A constant sample makes the denominator zero.

Use like periods and units

Our fictional return series A=[−1,0,+1]% and B=[−2,0,+2]% are aligned observation pairs. Price levels and returns are different inputs. Mixing timestamps or intervals destroys the paired interpretation. Three points are a demonstration, not a robust estimate.

Concentration follows dependencies too

The original desk assigns weights40%,35%,25% to A/B/C. A and B share a fictional custodian and redemption route; combined75% therefore has that operational dependency. Token count alone does not measure independent exposure. C has a separate route, but no safety is implied.

Stress is distinct from correlation

An estimated historical correlation can change with regime or simultaneous liquidity pressure. A scenario loss=sum(weight×assigned adverse return) is a declared stress, not a probability forecast. Opposing three-point samples cannot establish reliable future hedging. Record common factors, lookback and stress assumptions, then leave unmeasured future dependence UNKNOWN.

• Paired returns: same-period changes compared together.
• Correlation: normalized sample linear association.
• Concentration: exposure sharing an asset or dependency.
• Factor: condition affecting multiple nominally distinct positions.

ILLUSTRATIVE paired returns A=[−1,0,+1]%, B=[−2,0,+2]%, C=[+1,0,−1]%. Desk weights40/35/25%. A/B share fictional routeR. Separate stress returns A−30%, B−20%, C−5%; no scenario probability supplied.

Dependency graph: A/B connect to shared routeR; C separate routeS. Pair with weighted-loss table and sample-correlation labels. Edges indicate stipulated dependency, never human ownership.

Supplied sample associations and exposure to the stipulated shared route.

Stable future correlation, causal influence, independent custody verification or a guaranteed hedge.

• OBSERVED: FIX-P06-L05 stipulates shared routeR for A/B.
• INFERRED:75% of assigned weight depends on R.
• UNKNOWN: future joint-return distribution.
• INSUFFICIENT EVIDENCE: C reliably offsets A in stress.

• Counting names as independent diversification.
• Using price-level correlation without saying so.
• Carrying a tiny-sample negative correlation into a guarantee.

Calculate A/B and A/C correlations, routeR concentration and weighted stress loss. Explain one return-data limitation and one operational factor not represented by r.

Deliver calculations or annotations, claim/source table and limitations. Suggested allocation: study 12 minutes, exercise 8, correction/quiz 10; estimate subject to calibration.

• Pair identical periods.
• State returns versus levels.
• Map shared dependencies.
• Separate sample association and stress.

Diversification analysis combines paired-return evidence with shared operational factors; neither asset count nor sample r ensures an offset.

• Compute a simple paired-return correlation.
• Identify shared factors beyond asset names.

P06-L06 after correction review.

NONE in the authoritative catalog. The supplied offline fixture/package is sufficient; no paid feature or unverified Production capability is required. Lab/certification metadata denotes downstream associations, not access gates or live awards.

• [CORR] NIST — Linear correlation — Correlation describes association in paired data; no causal or future guarantee. Checked 2026-10-01; locator turn11view3.