There were no brokers either internal or external at HCM. There were a large number of traders. It had been a very successful arbitrage hedge fund (effectively) for many years. But the successful principal wanted more cash and left to form Convexity Capital. They specialized in “Triangle style” trades, but also other arbitrage type trades in fixed income and fx. I am sure they had some equity presence but it must have been quite small and was probably event arbitrage and stuff like that. Most of their trades were in government bonds, swaps, interest rate contacts and fx. And of course options on all of the above.
A large amount of the cash was put out to external management. Some of those managers would have been Algo managers like Ren tech, DE shaw, 2 Sigma etc. However those funds are hardly bargains in terms of the deals offered to external investors. Many algo managers restrict their “best funds” to their principals.
As for setting up their own internal algo, I think it would be a mistake unless HCM had been able to find a manager who had provable results. Indeed there is a case to suggest that many Algos are also breaking the law - although the SEC currently sees it differently. However one can argue that “order sniffing” is a form of front running. Of course, “algo” is not a well defined term. I referred to what are effectively market-makers. However do different things. That said, the funds which are price takers and take longer term positions are generally not as successful as the liquidity providing funds.