Returns at Fund with Subscale vs Scaled AUM

Let's consider a scenario between funds with $500M AUM and $500B AUM with the same strategy. My understanding is that the returns from the $500M should be higher than that of the $500B fund.

I guess what I'm trying to understand, without going into specific numbers, is how much higher would the returns have to be in the $500M firm to provide confidence that it would be able to match the returns the returns of the $500B fund at that same scale?

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