If an equity fund exhibits a weekly return standard deviation of 0.80%, how is its annualized standard deviation calculated, and what is the resulting annualized figure?

[ A ]Multiply the weekly standard deviation by 52 directly; resulting in 41.60% per annum.

[ B ]Divide the weekly standard deviation by 12; resulting in 0.067% per annum.

[ C ]Multiply the weekly standard deviation by the square root of 52 (sqrt(52)); resulting in approximately 5.77% per annum.[ CORRECT ]

[ D ]Square the weekly standard deviation and add 100; resulting in 100.64% per annum.

Takeaway

Option C is correct: Multiply the weekly standard deviation by the square root of 52 (sqrt(52)); resulting in approximately 5.77% per annum.

Derivation

In statistical finance, standard deviation scales with the square root of time. Since there are 52 weeks in a year, the annualized standard deviation is computed by multiplying the weekly standard deviation by the square root of 52: Annualized Std Dev = Weekly Std Dev * sqrt(52) = 0.80% * 7.2111 = 5.7689% (approx 5.77% p.a.). (For monthly returns, multiply by sqrt(12); for daily trading returns, multiply by sqrt(252)). This question tests the mathematical conversion of periodic volatility to annual metrics. The primary trap is multiplying linearly by 52.

Why the others fail

A — Multiply the weekly standard deviation by 52 directly; resulting in 41.60% per annum.

41.60% incorrectly multiplies standard deviation linearly by 52, violating the square-root-of-time scaling rule of variance.

B — Divide the weekly standard deviation by 12; resulting in 0.067% per annum.

Dividing by 12 is mathematically erroneous and confuses monthly de-annualization with weekly annualization scaling.

D — Square the weekly standard deviation and add 100; resulting in 100.64% per annum.

Squaring standard deviation yields variance, but adding 100 is an arbitrary and meaningless calculation.