Explanation

Correct Answer: C

This question involves converting monthly volatility to annual volatility using the square root of time rule.

Calculation:

• Monthly volatility (σ_monthly) = 4.5% = 0.045
• Number of months in a year = 12
• Annual volatility (σ_annual) = σ_monthly × √12
• σ_annual = 0.045 × √12 = 0.045 × 3.464 = 0.1559 ≈ 15.6%

Why other options are incorrect:

A and B are incorrect: These refer to "implied volatility," which is derived from option prices and market expectations, not from historical return data. Implied volatility is forward-looking, while the question provides historical data.

D is incorrect: This option incorrectly scales volatility linearly by multiplying 4.5% by 12 (0.045 × 12 = 0.54 = 54%), rather than using the square root of time rule. Volatility scales with the square root of time, not linearly.

Key Concept:

The square root of time rule states that volatility scales with the square root of the time period when returns are independent and identically distributed (i.i.d.). This is a fundamental principle in quantitative finance for converting volatility across different time horizons.