Volatility measures the variability of an asset’s or portfolio’s returns. Portfolio construction uses it alongside expected return to compare risk–reward trade-offs, plot efficient frontiers, and evaluate allocations. section 2.0 section 3.0
For historical returns, calculate daily standard deviation and annualize it by multiplying by the square root of 252. Covariance matrices instead annualize daily variances and covariances by multiplying by 252. These estimates are straightforward but can become impractical for thousands of securities and may miss volatility that changes over time. section 3.2.1
Two ways volatility changes
Historical daily returns produce annualized volatilities of approximately 39.3% for AAPL, 25.9% for FE, and 23.5% for WMT. Separately, a 60/40 stocks-and-bonds portfolio with constant annual returns drifts toward about 83% stocks over 30 years; its volatility rises from about 10% to 14%, motivating periodic rebalancing. section 3.2.1 section 13.1.1
stock_returns.std() * (252**0.5)
Inspect the compact Python expression for converting a return series’ daily standard deviation into annualized volatility. section 3.2.1
