Volatility Calculator
Calculate historical volatility, implied volatility, and measure investment risk
Calculate Volatility
Calculation Method
Enter closing prices in chronological order (oldest to newest)
For annualization factor calculation
Volatility Results
Statistical Summary
Return Range
Interpretation
Very High Risk: Extreme volatility, very risky asset
💡 An annualized volatility of 63.32% means that, based on historical data, the asset's returns typically deviate by this percentage from the mean return over a year.
Formula used: σ_annualized = σ_period × √(periods_per_year)
Where: σ = Standard Deviation, N = 9 observations, Annualization Factor = √252
Risk Assessment
Example Calculation
Stock Price Volatility
Daily Closing Prices: $100, $102, $98, $105, $103, $107, $104, $109, $106, $110
Time Frame: Daily (252 trading days per year)
Returns Calculated: 10 price points → 9 returns
Calculation Steps
1. Calculate log returns: ln(P_t / P_(t-1)) × 100
2. Compute mean return: μ = Σr / n
3. Calculate variance: σ² = Σ(r - μ)² / (n-1)
4. Find standard deviation: σ = √variance
5. Annualize: σ_annual = σ × √252
Result: Period volatility = 3.45%, Annualized = 54.77%
Volatility Reference
Volatility Tips
Higher volatility means higher risk AND higher potential returns
Use at least 20-30 data points for reliable volatility estimates
Compare implied vs. historical volatility for trading opportunities
Volatility clustering: high volatility tends to persist
VIX index measures S&P 500 implied volatility (fear gauge)
Understanding Volatility
What is Volatility?
Volatility measures the degree of variation in an asset's price or returns over time. It's the most common way to quantify investment risk. Higher volatility means prices fluctuate more dramatically.
Types of Volatility
- •Historical Volatility: Calculated from past price movements
- •Implied Volatility: Derived from option prices, reflects future expectations
- •Realized Volatility: Actual volatility that occurred over a period
Volatility Formulas
Historical Volatility
σ = √[Σ(r - μ)² / (n-1)]
σ_annual = σ_period × √T
Where:
- σ: Standard deviation (volatility)
- r: Periodic return
- μ: Mean return
- n: Number of observations
- T: Periods per year
Annualization
Volatility is typically annualized for comparison purposes. The annualization factor depends on your data frequency:
Using Volatility in Investing
Risk Management
- • Position sizing based on volatility
- • Stop-loss placement
- • Portfolio diversification
- • Value at Risk (VaR) calculations
Trading Strategies
- • Options pricing and trading
- • Volatility arbitrage
- • Mean reversion strategies
- • Trend following with vol filters