Beta equals the covariance of the asset’s return with the market return, divided by the variance of the market return: β_i = Cov(R_i, R_m) / σ²_m. In words, it scales how much the asset moves with the market by how volatile the market itself is. Correlation form β = ρ(σ_i/σ_m) is equivalent. Using total variance of the asset in the denominator is a classic wrong formula.