Volatility Calculator
Calculate the volatility of investment returns using standard deviation and variance. Enter your return data to measure price fluctuation and risk levels.
Volatility Results
Statistical Analysis
Volatility Benchmarks
Low Volatility: < 10%
Moderate: 10-20%
High Volatility: 20-30%
Very High: > 30%
Note: Annualized figures
Understanding Volatility
Volatility measures the degree of variation in investment returns over time. It quantifies the risk of price fluctuations and helps investors understand the stability of their investments.
Standard Deviation Formula
The standard deviation of returns is calculated as:
s = v[S(R_i - R_avg)² ÷ (n - 1)]
Where: R_i = individual return, R_avg = average return, n = number of observations
Variance vs. Standard Deviation
- Variance: Average of squared deviations from the mean
- Standard Deviation: Square root of variance (more interpretable)
- Units: Variance in squared units, standard deviation in original units
- Usage: Standard deviation more commonly used for volatility measurement
Interpreting Volatility Levels
| Volatility Level | Annual Standard Deviation | Typical Investments | Risk Level |
|---|---|---|---|
| Very Low | < 5% | Treasury bills, money market | Very Low |
| Low | 5-10% | Bonds, blue-chip stocks | Low |
| Moderate | 10-20% | Large-cap stocks, balanced funds | Moderate |
| High | 20-30% | Small-cap stocks, emerging markets | High |
| Very High | > 30% | Cryptocurrencies, options | Very High |
Historical Volatility Examples
- S&P 500: ~15-20% annual volatility
- US Treasury Bonds (10-year): ~5-10% annual volatility
- Gold: ~15-25% annual volatility
- Bitcoin: ~50-100% annual volatility
- Individual Stocks: Often 30-50% annual volatility
Applications
- Risk Assessment: Quantify investment risk levels
- Portfolio Diversification: Balance high and low volatility assets
- Option Pricing: Key input for Black-Scholes model
- Risk Management: Set position sizes and stop losses
- Performance Evaluation: Compare risk-adjusted returns
Types of Volatility
- Historical Volatility: Past price fluctuations
- Implied Volatility: Market expectations of future volatility
- Realized Volatility: Actual volatility experienced
- Conditional Volatility: Volatility under specific conditions
Volatility Clustering
Volatility tends to cluster - high volatility periods are often followed by more high volatility, and low volatility periods tend to persist.
- Market Crashes: Followed by continued high volatility
- Bull Markets: Often characterized by low volatility
- Behavioral Factors: Investor psychology amplifies volatility clustering
- Risk Management: Important to consider in portfolio construction
Limitations
- Past Performance: Historical volatility may not predict future
- Normal Distribution: Assumes returns follow normal distribution
- Black Swan Events: Extreme events not captured by standard measures
- Time Varying: Volatility changes over time
- Sample Size: Needs sufficient data for reliable estimates
Tip: Volatility is a double-edged sword - it represents both risk and opportunity. Higher volatility can mean higher potential returns, but also higher potential losses. Use volatility measures to understand your risk tolerance and construct appropriately diversified portfolios.