I respectfully disagree. Having worked at two bulge bracket IBs,...

I respectfully disagree. Having worked at two bulge bracket IBs, my understanding is that it's all in the hands of the traders. If they have a client who wants to accumulate, the traders' jobs are to pick up the stock and quantity at the best price possible (e.g. below the 50 day MA). If the firm has a prop-trading division then any number of traders could be playing this stock along with others. The relatively small size of the investments would be because the traders individually don't have a huge balance sheet.

I did mention mandates above (e.g. investing in companies over a certain market cap size) but those are more for funds and don't apply to client portfolios and prop-trading (with the exception of restricted stock).