How could you mitigate the negative size bias induced by, Portfolio Management

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How could you mitigate the negative size bias induced by

1. How could you mitigate the negative size bias induced by the long-only constraint?

2. Imagine that you are a stock trader, and that a portfolio manager plans to measure your trading prowess by comparing your execution prices with volume-weighted average prices. How would you attempt to look as good as possible by this measure? Would this always coincide with the best interests of the manager?

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