Stock Beta Calculator
Compute a stock's beta from its correlation with the market and the two return volatilities.
輸入資料
計算結果
重點速覽：Beta = correlation x (stock volatility / market volatility), equivalent to covariance / market variance. Beta = 1 moves with the market; >1 amplifies; <1 calmer; negative is inverse. In Hong Kong, proxy the market with the Hang Seng Index. WARNING: Beta is history-based, sensitive to period/frequency/index; it captures only systematic risk; past beta may not persist.
計算公式
β = 相關係數 × (股票回報標準差 ÷ 市場回報標準差)。
等價於 β = 協方差(股票, 市場) ÷ 市場變異數。
$$\beta = \rho_{i,m} \times \dfrac{\sigma_i}{\sigma_m} = \dfrac{\text{Cov}(r_i, r_m)}{\sigma_m^2}$$$$\text{要求回報} = r_f + \beta (r_m - r_f) \quad (\text{CAPM})$$使用說明
- Enter the correlation between the stock and the market.
- Enter the stock and market volatilities (annualised standard deviation).
- View the stock's beta.
市場標準差固定 20% 時，不同相關係數與股票波動率對應的貝塔
| 相關係數 | 股票標準差 | 市場標準差 | 貝塔 (β) | 風險屬性 |
|---|---|---|---|---|
| 0.6 | 15% | 20% | 0.45 | 防守型 (< 1) |
| 0.8 | 25% | 20% | 1.00 | 本工具預設，與大市同步 |
| 1.0 | 20% | 20% | 1.00 | 完全同向、同波幅 |
| 0.9 | 30% | 20% | 1.35 | 進取型 (> 1) |
| −0.4 | 18% | 20% | −0.36 | 與大市反向 (避險特性) |
理財情境案例
案例一：估算股票貝塔
某股票與恒指的相關係數 0.8，股票回報年化標準差 25%，恒指標準差 20%。β = 0.8 × (25 ÷ 20) = 0.8 × 1.25 = 1.00。
貝塔約為 1，代表該股整體與大市同步波動 — 大市升約 10%，它大致也升 10%。這數字可直接作為 CAPM 的輸入。
案例二：用貝塔算 CAPM 要求回報
延續上例 β = 1.0。假設香港無風險利率 (如政府債券孳息) 為 3.5%，市場預期回報 9.5%，則 CAPM 要求回報 = 3.5% + 1.0 × (9.5% − 3.5%) = 9.5%。
若換成一隻進取型高貝塔股 β = 1.35，要求回報升至 3.5% + 1.35 × 6% = 11.6% — 承受更高市場風險，理論上就該要求更高回報。這正是貝塔連結風險與估值的橋樑。
常見問題
What is a high beta stock?
Beta above about 1.2 is high (swings more than the market); below 0.8 is defensive. Hong Kong's property and some tech names often run above 1; utilities and telecoms below 1.
Does beta change over time?
Yes. Beta differs by sample period, frequency (daily/monthly) and benchmark. It is typically estimated from 1-5 years of monthly data against the Hang Seng Index.
What is a negative beta?
The stock tends to move opposite the market (some hedges, gold, shorts). Negative beta can rise when the market falls, offering diversification value in downturns.
Does beta = 0 mean risk-free?
No. Beta = 0 means no correlation with the market (zero systematic risk), but the stock may still carry company-specific (unsystematic) risk. Diversification removes unsystematic risk, not the business risk itself.
How do I interpret beta for Hong Kong stocks?
Use the Hang Seng Index as the market proxy and Exchange Fund Bill yields as the risk-free proxy in CAPM. Note that HK market beta estimates can be noisier for small caps and China-related names; treat beta as one input, not a verdict, and combine with fundamentals, liquidity and policy risk.
相關工具
參考資料
內容審核：香港計算器財經團隊。計算邏輯與公式參考香港金融管理局（HKMA）及投資者及理財教育委員會（IFEC）之個人理財計算指引，結果僅供參考，實際以相關機構公佈為準。