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Beta Coefficient Calculator

From asset and market volatility and correlation, compute the beta and CAPM expected return.

Input Data

Correlation
Asset Vol
%
Market Vol
%
Risk Free Rate
%
Market Return
%

Results

Sensitivity of the asset to the market.
1
CAPM expected return for the asset.
9%

At a glance:Beta = rho x (sigma_a / sigma_m), equivalent to covariance / market variance. CAPM expected return = risk-free + beta x (market - risk-free). Beta = 1 moves with market; >1 amplifies; <1 calmer; negative is inverse. In Hong Kong, use Exchange Fund Bills / govt bond yields as the risk-free proxy and the Hang Seng Index as the market proxy. WARNING: Beta is history-based, sensitive to period/frequency/index; it captures only systematic risk; past beta may not persist.

Formula

Beta = Covariance(asset returns, market returns) / Variance(market returns).

Equivalently: β = ρ × (σ_asset / σ_market), where ρ is the correlation.

How to Use

  1. Enter the asset-market correlation and the two volatilities.
  2. Enter the risk-free rate and expected market return.
  3. View the beta and the CAPM expected return.

FAQ

What is a high beta?

Beta above about 1.2 is high (swings more than the market); below 0.8 is low (defensive). Utilities/telecoms often sit below 1; tech/biotech often above 1.

Does beta change?

Yes. Beta differs by period, frequency (daily/monthly) and benchmark index. It is typically estimated from 1-5 years of monthly data against the Hang Seng or S&P.

What is negative beta?

The asset moves opposite the market (some hedges, gold, shorts). Negative beta can rise in a crash, offering diversification value.

Does beta = 0 mean risk-free?

Statistically it means no correlation with the market. But beta = 0 is not risk-free — it may still carry unsystematic risk; it only means zero systematic risk.

Is CAPM accurate?

It is an academic benchmark with known limits (the market portfolio is unobservable; single factor). Useful for a rough required return; precise pricing needs multi-factor models. Pair with fundamentals and other risk metrics.

How does beta relate to the Sharpe ratio?

Sharpe measures return per unit of total risk; beta/CAPM measures the required return for systematic risk. They are complementary: Sharpe assesses past performance, CAPM sets the expected return.

Related Tools

References

Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.

Found a problem with the results?

If this calculator's result is wrong, or you have any question about the calculation logic, please let us know. You are viewing:Beta Coefficient Calculator（/finance/beta）。