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.

Mon, 04 May 2026 20:02:20 +0000

**Tracking Losses That Still Turn Positive Over Time: The Hidden Power of Cumulative Log Returns** In today’s fast-moving financial climate, a curious paradox is sparking quiet conversations: Fund A delivers higher cumulative log-return immediately after investment than Fund B—yet Fund B offers a higher absolute rate. On the surface, this challenges conventional wisdom. Why would immediate gains matter if growth is inherently sublinear? The answer lies in how investor psychology, market rhythms, and compounding dynamics shape long-term trust and momentum. Understanding this requires a nuanced look at the fundamental concept of cumulative log returns—an analytical tool that matters more than headline rates when evaluating early performance. ## Why So $ f(t) > 0 $ for $ t > 0 $, meaning Fund A has stronger immediate cumulative log-return than Fund B—contrary to high absolute numbers—but does not guarantee sustained dominance.