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Problem 3: Logarithmic Return vs. Arithmetic Return
Reframe: Find $ t $ such that average log-return of A > average log-return of B. But better: when does cumulative log-return of A exceed that of B?
So $ f(t) > 0 $ for $ t > 0 $, meaning Fund A has higher cumulative log-return immediately after investment. But this contradicts investment theory—Fund B has higher absolute rate. However, due to compounding, eventually A dominates? No—log-return growth is sublinear.

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