[ravibala1]

Not sure I understand why we can assume that its all trades are entirely "independent" here.

Agree with you that HFT performance is not correlated with market direction. But given the volume of trades it would imply that many of the trades are occurring on a smaller pool of equity instruments. I'd think that given liquidity constraints and competition that there's a sweet spot in terms of number of stocks that a given strategy is actually efficient on.

So not entirely sure why we consider every trade to be iid - rapid shocks (flash crash), equity specific news etc would affect a number of trades at once changing the 51% probability?

Also does anyone know if the profitability numbers include payments to be a market-maker?

[tcbawo]

Market makers typically have a requirement to be in the market a certain (high) percentage of the time. In return, they get rebates (which can be a significant source of revenue) and protections from the exchange against overfilling. This can help them for certain shock events.

Most likely, though, their profitability % is tuned by edge and risk parameters. They can adjust size, widen out, or tighten up the spread to tune trade frequency and profitability. They are finding a sweet spot between # of trades and profitability.

[consz]

Those number absolutely include payments. It's rare (in my experience) for an equity market making strategy to be positive in gross terms (prior to the maker-taker rebate). These numbers you hear from Virtu/KCG should be net of exchange trading costs/rebates.