Does a dynamic trade size result in what is effectively compound interest? And the relevant calculation

Assuming monthly return stays constant and trade size is 100% (dynamic), am I correct in saying that to calculate monthly return for a strategy that has 50% return in 3 months for example, you would do
1.5^(1/3)=1.145
So an average 14.5% return per month?

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Yes, you are correct. 1.145^3 = 1.5.