Beta

Beta (β) measures how much a portfolio moves when the benchmark moves. A portfolio with β = 1.2 against the S&P 500 is expected to move 1.2% when SPX moves 1%, in either direction. Beta is the foundational input for CAPM and the workhorse of every equity factor model.

Formula

β = Cov( R_p, R_b ) / Var( R_b )

In practice β is estimated by OLS regression of portfolio returns on benchmark returns: R_p = α + β · R_b + ε. The standard window is 36 or 60 monthly observations; daily betas are noisier but more responsive.

Interpretation

• ·β = 0 — independent of benchmark (cash, market-neutral hedge funds).
• ·β = 1 — moves in lockstep on average (broad equity index funds).
• ·β > 1 — amplifies benchmark (high-beta sectors: tech, small-caps, levered ETFs).
• ·β < 0 — moves opposite to benchmark (long volatility, gold in equity-stress regimes).

Stale beta and rolling beta

A single full-period β collapses regime changes into one number. The 36-month β of a tech-heavy portfolio looks reassuringly close to 1 because half the window covers the 2020-2021 bull run; in 2022 the realised beta was 1.4. Rolling β (typically 63 or 252 days) shows how the relationship evolves and is the more honest reporting standard.

How MEDGE Capital uses Beta

Beta is reported in every Compare report against the user-selected benchmark, alongside the full regression diagnostics (α, R², Tracking Error). Rolling 63-day β is plotted as a ribbon so changes in regime become visible at a glance.