A simple argument suggests that an investor concerned with maximizing their influence ought to maximize the expected fraction of world wealth they control. This means that the value of an extra dollar of investment returns should vary inversely with the total wealth of the world. This means that the investor should act as if they were maximizing the expected log-wealth of the world.
Could someone explain how the final sentence follows from the others?
If I understand correctly, the first sentence says an investor should maximize E(wealth-of-the-investor / wealth-of-the-world), while the final sentence says they should maximize E(log(wealth-of-the-world)). Is that right? How does that follow?
This depends a lot on how many stocks you’re buying, right? Or would you still make this claim if someone were buying < 10 stocks? < 5?