Beta
Quantitative Finance glossary · Probability, Statistics & Linear Algebra
Definition
CAPM market sensitivity: β_i = (Cov(R_i, R_m))/(Var(R_m)) — the slope of R_i regressed on R_m, hence the systematic (non-diversifiable) risk loading. To compare firms with different capital structures, unlever observed equity beta: β_U = (β_L)/(1 + (1-t),D/E) and relever at the target structure. Rolling beta is non-stationary; Blume and Vasicek shrinkage estimators correct the upward bias in extreme betas toward 1.
Beta in plain English
Beta measures how much a single stock tends to swing when the whole market swings — its sensitivity to the market's ups and downs. A beta of 1 means it moves in step with the market; 2 means it tends to move twice as hard (up and down); 0.5 means it's calmer than the market. This matters because the market-wide part of the risk can't be erased by owning lots of different stocks, so investors want to know how exposed they are. Like a boat on the ocean: some boats barely rock in the waves (low beta), others get tossed around a lot (high beta) — beta tells you which kind you're holding.
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