This dashboard presents a purely descriptive empirical analysis of historical joint tail behaviour across a universe of 136 financial assets spanning equities, crypto, fixed income, commodities, FX, and volatility indices. No parametric model is fitted; all quantities are computed directly from the empirical distribution of observed price increments over overlapping windows. The analysis makes no out-of-sample predictions — it characterises what has historically co-occurred in the data.

Symbols used throughout the framework. Note that q_Y applies uniformly to all 136 predicted assets regardless of asset class — it is a quantile of that asset's own empirical increment distribution, not a fixed price level.

How the τ-day increment is defined for each asset class, and whether that class is used as a predicted variable Y:

For predicted asset Y, predictor X, look-back window τ_p, forward window τ_f, and quantile thresholds q_X, q_Y, the pairwise Conditional Probability of Exceedance (CPE) is:

where the increments are:

• Δ^(τ)Y_t = ln(P^Y_t+τ / P^Y_t) — τ-day log return of Y from t (forward-looking)
• Δ^(τ)X_t = ln(P^X_t / P^X_t−τ) — τ-day log return of X ending at t (backward-looking)

For the bearish direction, both inequalities are reversed (lower tail conditioning predicts lower tail outcome):

The empirical estimator counts co-exceedance events over all overlapping windows:

Overlapping windows are used throughout. Each calendar date t constitutes one observation regardless of window overlap with adjacent dates, maximising the number of conditioning events especially at large τ values.

Lift measures how much the conditioning event amplifies the exceedance probability relative to its unconditional value:

• Lift = 1.0 — conditioning provides no information; CPE equals base rate
• Lift = 1.5 — conditioning increases exceedance probability by 50%
• Lift = 2.0 — conditioning doubles the exceedance probability

All signals satisfy CPE ≥ 0.80, Lift ≥ 1.5, and n ≥ 100.

Joint CPE generalises pairwise CPE to a set of K predictors {X₁, …, X_K}, each with their own look-back window τ_p,k and quantile threshold q_Xk:

The joint conditioning event is the intersection of all K individual conditioning events — all predictors must simultaneously exceed their respective thresholds. Different predictors may have different look-back windows.

Greedy predictor selection: Starting from the single predictor with the highest pairwise CPE, at each step the predictor is added that maximises joint CPE while maintaining n_joint ≥ 100 and Lift ≥ 1.5. Each ticker appears at most once (deduplication enforced). The algorithm terminates when no further predictor can be added satisfying the constraints, or when K = K_max = 10.

Statistical discipline: The minimum joint conditioning sample size n_joint ≥ 100 is enforced at all set sizes identically to the pairwise minimum and is never relaxed for larger K. If no predictor can be added while maintaining n_joint ≥ 100, the algorithm stops. This ensures all reported joint CPE values have genuine statistical support.

All price data sourced from Yahoo Finance via the yfinance Python library. Adjusted closing prices are used for all equity and commodity ETFs (split- and dividend-adjusted). Futures series use front-month contracts. FX rates are mid-price quotes.

The following assets are excluded from the predicted set (Y) to avoid mechanically implied signals:

• Leveraged/inverse ETFs: SSO, SDS, TQQQ, TMF, TBT, TBF, UVXY, SVXY, VIXY, VIXM, VXX — returns are deterministic functions of their underlying assets
• Managed/pegged currencies: THBUSD=X, CNYUSD=X, KRWUSD=X — heavy central bank intervention compresses increment distributions, generating spurious quantile exceedances

VIX-family and Treasury yield indices are included as predictors only, using level changes (not log returns).

Quantile thresholds r_q are estimated using the full historical sample for each (asset, τ) pair. This is appropriate for a purely descriptive analysis — no out-of-sample forecasting is claimed.