Financial Risk Manager Part 1
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If the daily volatility of the price of gold is 0.3% in a given year. What is the annualized volatility of the gold price?
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NNikitesh
A
4.67%
B
3.56%
C
2.56%
D
4.76%
Explanation:
To annualize daily volatility, we use the square root of time rule. Since there are typically 252 trading days in a year, the annualized volatility is calculated as:
σ_annual = √(252 × σ²_daily)
Given daily volatility = 0.3% = 0.003
σ_annual = √(252 × 0.003²) = √(252 × 0.000009) = √0.002268 = 0.047623 = 4.7623%
This matches option D (4.76%).
Key Concept: The square root of time rule assumes returns are independent and identically distributed (i.i.d.), which allows volatility to scale with the square root of time.
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