Correlation vs BTC

The Pearson correlation coefficient is the covariance of two return series divided by the product of their standard deviations: ρ = Cov(coin, BTC) / (σ_coin × σ_BTC). +1 means the coin moves in lockstep with Bitcoin, −1 means perfectly opposite, and 0 means no linear relationship.

For diversification, correlation is the key number. Holding coins highly correlated with BTC (near +1) gives little risk reduction — they rise and fall together. Lower or negative correlation means a coin's swings are more independent of Bitcoin, which can smooth overall portfolio volatility even if each asset is individually volatile.

Correlation is related to but distinct from Beta vs BTC. Correlation measures the strength and direction of co-movement (a unitless −1-to-+1 figure); beta measures magnitude — how much the coin moves per BTC move — and equals ρ × (σ_coin / σ_BTC). Two coins can share a correlation but have very different betas if one is far more volatile.

Worked example: two coins each correlate 0.8 with Bitcoin, but one runs 120% annualized volatility and the other 60% (against BTC's 60%). Same correlation, very different betas: 0.8 × (1.20 ÷ 0.60) = 1.6 versus 0.8 × (0.60 ÷ 0.60) = 0.8. Correlation says both track BTC equally closely; beta says the first swings twice as hard.