Standard Deviation

Standard deviation is a statistical measure that quantifies the dispersion of returns around the mean (average). In investing, it's the most common measure of volatility and risk.

Interpretation:

• Higher SD: More volatile, returns vary widely
• Lower SD: Less volatile, more consistent returns
• 68% Rule: ~68% of returns fall within 1 SD of mean
• 95% Rule: ~95% of returns fall within 2 SD of mean

Example:

• Investment A: 10% average return, 5% SD
• Investment B: 10% average return, 20% SD

Investment A is much more predictable—most years return 5-15%. Investment B could range from -30% to +50% in any year.

Calculation:

1. Calculate mean return
2. Find each return's deviation from mean
3. Square each deviation
4. Average the squared deviations
5. Take square root of average

Uses in Investing:

• Risk Comparison: Compare volatility across investments
• Sharpe Ratio: SD is the denominator
• Portfolio Optimization: Minimize SD for given return
• VaR Calculation: Estimate worst-case scenarios
• Normal Distribution: Predict return ranges

Limitations:

• Assumes normal distribution (fat tails exist)
• Treats upside and downside equally
• Historical SD may not predict future
• Doesn't capture all types of risk

Typical SD Ranges:

• Money Market: 0-1%
• Bonds: 5-10%
• Stocks: 15-25%
• Emerging Markets: 25-35%