Explanation

To annualize daily volatility, we use the square root of time rule:

$\sigma_{\text{annual}} = \sqrt{252 \times \sigma_{\text{daily}}^2}$

Given:

• Daily volatility (σ_daily) = 0.3% = 0.003
• Number of trading days = 252

Calculation: $\sigma_{\text{annual}} = \sqrt{252 \times (0.003)^2} = \sqrt{252 \times 0.000009} = \sqrt{0.002268} = 0.047623 = 4.7623\%$

Therefore, the annualized volatility is approximately 4.76%, which corresponds to option D.

Key Points:

• The square root of time rule assumes returns are independent and identically distributed
• For volatility scaling, we use variance (σ²) which is additive over time
• The square root of 252 is approximately 15.87, but we multiply variance by 252 first, then take the square root