2x Trading

A quoting engine is a pipeline with a budget. The market data packet hits the NIC, the book updates, a signal fires, risk allows or blocks it, and an order goes back out. Tick-to-trade here means the time from the packet timestamp at our NIC to the first byte of the outbound order on the wire. The illustrative host budget is 2.40 µs. The cross-connect after that is another 4.1 µs, and it is a different number.

Microprice, the fair value you actually quote around

The mid is the average of bid and ask. The microprice leans toward the thinner side, because the heavy side is the one more likely to pick the next tick off. With a bid of 99.99 for 800 and an ask of 100.01 for 200:

m = (bid · Qask + ask · Qbid) / (Qbid + Qask)
  = (99.99 · 200 + 100.01 · 800) / 1,000
  = 100.006

mid = 100.00
lean = 0.006  (0.6 cents above the mid, toward the ask)

A symmetric quote around 100.00 is a quote around the wrong number. The bid wants to be tighter, or smaller, because the book is already saying the next print is more likely up.

A market maker posts a bid and an ask around fair value and is paid when both sides, or one side plus a hedge, fill. The unit of account is the spread. Everything else — rebate, queue position, inventory skew, the hedge — decides whether that spread survives contact with the tape.

Illustrative quote in hypothetical XYZ, fair value 100.00: bid 99.98, ask 100.02, 400 shares a side, post-only. The quoted spread is 4 cents.

What a round trip is worth

If both passive orders fill and the mid does not move against the inventory, the spread is $16.00 and the maker rebate at 0.20¢ per share on both legs is $1.60. Clearing and regulatory fees of about 0.10¢ per share on the round trip take $0.40. That clean case is $17.20.

Fills are not a coin flip around an unchanged mid. The fills you actually receive are richer in informed flow than the fills you hoped for. Put an expected adverse-selection haircut of 1.5¢ per share on the same 400 shares and the expectation falls to $11.20, or 2.8¢ a share. The haircut that sets the clean case to zero is 4.3¢ per share. Past that, the same quote loses money.

Hedges: futures, and the ETF against the basket

Single-name inventory that shares a factor is not eight separate risks. Illustrative book: $1,200,000 of long single-name exposure with β = 1.1 to the index, so $1,320,000 of beta. The futures example is ES at 5,000 with a $50 multiplier, $250,000 per contract.

contracts = beta dollars / contract notional
          = $1,320,000 / $250,000
          = 5.28

Sell 5 contracts.
Residual = $70,000 of index exposure.
Top up with 140 shares of a $500 ETF.

An ETF-versus-basket trade is the same idea with a creation unit on the other side. If the ETF is rich to the calculated basket by more than creation cost, impact, and borrow, sell the ETF and buy the basket, or sell the ETF and hold the futures until the basket can be printed. What you have locked is the basis only to the extent the basket is complete and the financing is known. Until then it is a relative-value position with a limit, not a risk-free print.

Rebates sit underneath all of this as a tie-break. A 0.20¢ maker rebate is a fifth of a one-cent tick. It is why a marginal quote is posted on a maker-taker venue and why a post-only flag is the default. It is not the strategy. The toxic-fill arithmetic above is the strategy.

A scalp holds for seconds, sometimes a couple of minutes. The target is one to a few ticks. That is the entire gross. Fees, the spread you cross, and slippage are the same order of magnitude, so a win rate that looks healthy in a backtest can still lose money. The gate is expectancy after cost, not the count of green trades.

Win rate times payoff, minus cost

Symmetric case, so the arithmetic is visible. Target and stop are both L = 2 ticks. Round-trip cost is c ticks. Win rate is p.

E[ticks] = (2p − 1) · L − c

c = taker fee − entry rebate + slippage
  = 0.30 − 0.20 + 0.40
  = 0.50 ticks

p* = 1/2 + c / (2L)
   = 0.5 + 0.50 / 4
   = 62.5%

At p = 55%:
E = −0.30 ticks per round trip

A 55% win rate on a 2-tick symmetric scalp has expectancy −0.30 ticks a trade after this cost. You need 62.5% just to be flat. The entry in the formula is posted, so it earns the 0.20¢ rebate. The exit crosses, so it pays the 0.30¢ take fee. Slippage of 0.40 tick is the queue you miss and the partial fill. Change any of those three and the breakeven moves the same day a venue changes its schedule.

Real losers are larger than real winners, because the fills you get are the ones where someone wanted the other side. Use an average win of 1.6 ticks and an average loss of 2.2 ticks, same c:

E = p · 1.6 − (1 − p) · 2.2 − 0.50

p* = (2.2 + 0.50) / (1.6 + 2.2)
   = 71.1%

The breakeven win rate is now 71.1%. That is the honest bar for a directional scalp that pays the spread on the way out. A market-making round trip, both sides posted, is a different formula: the spread is the win, and the loss is the toxic fill in the previous section.

TWAP, VWAP, and the participation cap

Two hundred shares can be one post. Eight thousand shares cannot lift the touch without becoming the footprint. A 10-minute TWAP of 8,000 shares is 40 children, 200 shares every 15 seconds, each child a post-only limit at the bid for a buy. VWAP uses the same children and weights them by the volume curve: more size near the ends of the window, less in the dead minute.

The cap binds before the clock does. If the participation limit is 8% of printed volume and the last 15 seconds printed 1,500 shares, the child is 120 shares, not 200. You fall behind the TWAP schedule. Catching up by crossing spends the edge the breakeven table just priced. Urgency stays off unless a separate risk limit, a hedge that must be on, says otherwise. The schedule is a participation cap with a clock, not a deadline that forces you to pay the spread.

Statistical arbitrage at this horizon is a residual with a half-life. Two prices that should agree — an ETF and the futures, a name and the names that lead it, the same symbol on two venues — pull apart by less than the cost of forcing them back together, or they do not. The trade is the difference. The clock is how fast the difference dies.

Two venues, one public price

The same symbol on two venues, both on direct feeds. A sell prints on venue A and the mid drops from 50.00 to 49.97. Venue B is still bidding 50.00 for size. If an IOC sell reaches B before the market makers there cancel, the stale bid is the trade.

Illustrative timing, same building, two matching engines. The event is t = 0. The order is on the wire toward B at 0.18 ms, at B's gateway at 0.42 ms, and B's quote steps down at 1.05 ms. The open window is 0.63 ms. Five hundred shares times 3 cents is $15.00 gross, and only if the bid had the size and was still live when the order landed. A path that arrives at 1.1 ms is the liquidity the faster cancel trades against.

The trading P&L of a book like this is a short list. Spread capture, maker rebates, and basis or other relative-value capture, minus taker fees, borrow, and adverse selection. Technology, co-location, and market data are a cost underneath that, allocated by the desk rather than by the fill. The shape of the list matters more than any one total: adverse selection is often the same size as a large fraction of the spread. A week where toxic flow rises and the quoted spread does not, the sign flips.

The stack below is a hypothetical single-name session. It is not a day this firm had, and it is not a forecast.

Limits, the kill switch, and fat fingers

The numbers below are illustrative firm limits for the examples on this page. They are not a disclosure of live limits.

Backtests that are allowed to go live

Lookahead.A feature at time t uses messages with exchange timestamp at or before t, and only after the receive delay you actually have. Joining on a bar close to trade that bar's open is lookahead. Using the corrected print, rather than the print that was on the wire, is lookahead. The residual's β is fit on a window that does not include the trade.

Survivorship.The universe is the names listed on that date, including the ones that later delist or halt. A universe of today's index, run backward, flatters the book.

Overfitting. Every added threshold is a degree of freedom. A rule kept because it maximized in-sample Sharpe will not have that Sharpe live. One contiguous period, and one set of names, stay untouched until the end. A parameter added so the edge survives a fee change is a new test.

Paper versus live.A paper fill at the touch assumes you were first in queue. Live, you are behind, and the conditional move after a fill is the adverse-selection column. If paper P&L is the spread and live P&L is the haircut, the simulator is marking the wrong event. The fill model has to include the probability of a fill given that the price traded to your level, and the expected move after that fill. Missing size can be retried on purpose. A duplicate fill from a retried order cannot be un-printed.