How to annualize a weekly geometric mean?

Question

I've calculated the geometric mean of 3 years of weekly returns (i.e. 156 returns) to be 0.001954. How do I annualize that return?

Is it ((1 + 0.001954)^52 - 1) = 0.106823?

Or some other method?

Thanks in advance.

Answer 1

You should have taken the geometric mean of (1+weekly return). To annualize that you would take (geometrtic mean(1+weekly return))$^{52}-1$. Suppose you were $+10\%$ one week and $-8\%$ the next. You couldn't take the geometric mean of the returns, but you could take $\sqrt{1.1 \cdot 0.92}\approx 1.00598$ to get the approximate gain per week and say if you did that for $52$ weeks you would end up with about $1.3636$ for a $36.36\%$ annual return.