Beta Coefficient Calculator
From asset and market volatility and correlation, compute the beta and CAPM expected return.
輸入資料
計算結果
重點速覽：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.
計算公式
Beta = Cov(Ra,Rm) / Var(Rm)。
E[R] = Rf + β(Rm − Rf)。
β=1 同步；>1 放大；<1 減弱。
使用說明
- Enter the asset-market correlation and the two volatilities.
- Enter the risk-free rate and expected market return.
- View the beta and the CAPM expected return.
理財情境案例
資產 5,-2,8,3,6；市場 3,1,5,0,4
算得 Beta ≈ 1.05（略高於大盤）。
E[R] = 4 + 1.05×(9−4) = 9.25%。
常見問題
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.
相關工具
參考資料
內容審核：香港計算器科學團隊。Beta 協方差/變異數與 CAPM 公式驗證。