Methodology

1. Log returns

All return-based metrics use continuously-compounded log returns, not simple returns:

r_t = ln(P_t / P_(t-1))

Log returns are time-additive and approximately normally distributed for short horizons, which makes correlation, β and volatility math more stable.

2. Correlation (Pearson & Spearman)

Pearson measures linear co-movement of log returns:

ρ(x,y) = Σ((x_i − x̄)(y_i − ȳ)) / √(Σ(x_i − x̄)² · Σ(y_i − ȳ)²)

Spearman is Pearson computed on ranks — captures monotonic (not just linear) relationships and is robust to outliers.

3. Beta (β) vs BTC

β = Cov(r_asset, r_BTC) / Var(r_BTC)

β = 1 means the asset moves 1:1 with BTC. β > 1 amplifies BTC moves; β < 0 is negative correlation.

4. Annualized volatility

σ_annual = σ_daily · √365

Crypto uses 365 (not 252) because markets trade 24/7.

5. Sharpe ratio

Sharpe = (r̄ − r_f) / σ

Default risk-free rate r_f is 0% for crypto (adjustable in portfolio settings).

6. Maximum drawdown

MDD = max_t ( (peak_t − P_t) / peak_t )

The largest peak-to-trough decline in the period, as a percentage of the peak.

7. Pyth confidence interval

Every Pyth price ships with a conf value. The real price is bounded by price ± conf. For risk-sensitive use cases we apply:

• Lending collateral valuation: use price − conf (conservative).
• Debt valuation: use price + conf (conservative).
• Trading displays: show raw price with conf as a secondary badge.

8. Staleness thresholds

• 🟢 Fresh: publishTime within last 2 seconds
• 🟡 Warm: 2–10 seconds old
• 🔴 Stale: older than 10 seconds — reject for trading

Equity feeds go stale outside US market hours by design.

9. Data sources

• Prices: Pyth Hermes API
• Historical OHLC: aggregated market-data API (cached)
• Solana quotes: Jupiter Aggregator
• Yields: DeFiLlama