Standard deviation quantifies the dispersion of returns around the average. A lower value means more predictable returns, while higher values indicate greater uncertainty.
Formula
σₚ = √(Σᵢ Σⱼ wᵢwⱼσᵢσⱼρᵢⱼ)Methodology
Volatility (standard deviation) is the foundational risk measure in Modern Portfolio Theory. It captures the total dispersion of returns - both upside and downside.
For a portfolio, we use the Markowitz formula which accounts for correlations between assets. This is crucial because diversification reduces portfolio volatility below the weighted average of individual volatilities.
The formula involves a double summation over all asset pairs: σₚ² = Σᵢ Σⱼ wᵢwⱼσᵢσⱼρᵢⱼ
Where wᵢ is weight, σᵢ is individual volatility, and ρᵢⱼ is the correlation between assets i and j.
When historical volatility data is unavailable, we estimate individual stock volatility using: σ_stock ≈ β × σ_market × 1.3, where the 1.3 factor accounts for idiosyncratic risk.
How to Interpret
| Range | Label | Meaning |
|---|---|---|
| ≥ 25 | Very High | Very high volatility - expect large swings in value |
| 18 to 25 | High | High volatility - significant year-to-year variation |
| 12 to 18 | Moderate | Moderate volatility - typical of balanced portfolios |
| 6 to 12 | Low | Low volatility - relatively stable returns |
| < 6 | Very Low | Very low volatility - highly predictable returns |
Data Source
Calculated using the Markowitz mean-variance framework. Individual stock volatilities from historical data; correlations from sector-based model.
Reference
Markowitz, H. (1952). Portfolio Selection. Journal of Finance, 7(1), 77-91
Limitations
Volatility is backward-looking and assumes returns are normally distributed. It treats upside and downside volatility equally.
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For Educational Purposes Only
This analysis is not investment advice. Results are based on simplified models using historical data. Past performance does not guarantee future results. All investments carry risk of loss. Consult a qualified financial advisor before making investment decisions.