Explainer, in Risk & Portfolio Construction
Beta
Beta = Cov(R_p, R_m) / Var(R_m). For a single-factor model the benchmark is the market; for multi-factor it's a vector of factor betas. Beta is unbounded (negative for short strategies, can exceed 1 for leveraged exposures), and it is not the same as correlation — beta scales with relative volatility, correlation does not.
1 question. Published May 10, 2026. By AI Fin Hub Research.
Definition
Beta
Beta = Cov(R_p, R_m) / Var(R_m). For a single-factor model the benchmark is the market; for multi-factor it's a vector of factor betas. Beta is unbounded (negative for short strategies, can exceed 1 for leveraged exposures), and it is not the same as correlation — beta scales with relative volatility, correlation does not.
Why it matters
Beta is the fee compressor. Anything you can replicate by holding a benchmark with leverage is beta, and beta has been priced at near-zero cost since the rise of index ETFs. The job of any active strategy is to deliver risk-adjusted excess return that isn't explained by tradable factor exposures.
How it works
Regress periodic excess returns of the portfolio on excess returns of the benchmark. Slope = beta. Most production estimates use rolling windows (12-36 months) because beta is non-stationary — a momentum strategy's beta to the market drifts over time as the regime changes.
Example
Tech-heavy long-only fund vs S&P 500
Cov(fund, S&P)
0.0028
Var(S&P)
0.0019
β
0.0028 / 0.0019 = 1.47
Implied move on +1% S&P
+1.47%
Beta 1.47 means the fund moves 1.47x the S&P on average. A 2% S&P drop becomes a roughly 3% fund drop — leverage you may not have realized you were running.
Key takeaways
Beta is sensitivity, not correlation; high correlation with low relative vol still produces low beta.
Static (full-sample) beta hides regime-dependent factor drift — use rolling windows.
Beta to the wrong benchmark is misleading; pick the factor that matches the strategy.
Related terms
Run the numbers next
- Calculators Portfolio Correlation Matrix
Paste a multi-asset returns CSV. See the Pearson correlation heatmap, condition number, average absolute correlation, and eigenvalue concentration.
- Calculators Risk-Adjusted Returns Calculator
Paste a returns CSV. Sharpe, Sortino, Calmar, Omega, alpha, beta, tracking error, information ratio, max drawdown, and tail moments — plus.
Questions people ask next
What's the difference between beta and correlation?
Correlation is bounded between -1 and 1 and ignores relative magnitude. Beta scales with relative volatility — a strategy that moves 0.5x the market with perfect correlation has correlation 1.0 and beta 0.5.
Sources
- Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk , Sharpe (1964), Journal of Finance 19(3)
Keep the topic connected
- Learn Alpha
Alpha as risk-adjusted excess return: definition, the beta-adjustment math, and why most claimed alpha disappears once you adjust for the right factors.
- Learn Volatility
Volatility as the standard deviation of returns: realized vs implied, the annualization gotcha, and why volatility-of-volatility matters.