A stale quote can be picked off for 8 cents on 200 lots and the chance arises 40 times a day. Five firms race for each one and the winner takes all of it. A colocation and market data package costs $8,000 a month, about $400 per trading day. What win rate justifies the spend?

A stale quote can be picked off for 8 cents on 200 lots and the chance arises 40 times a day. Five firms race for each one and the winner takes all of it. A colocation and market data package costs $8,000 a month, about $400 per trading day. What win rate justifies the spend?

Approach: Compute the gross value of the daily opportunity set, then solve for the win probability that makes expected revenue equal the fixed daily cost of the infrastructure.

62.5%. Each race is worth 200 * $0.08 = $16, and 40 races a day makes the gross opportunity set 40 * $16 = $640. Setting p * $640 = $400 gives p = 0.625, so the expected value of the spend only turns positive above a win rate of five races in eight. An even split across five firms would give a 20% win rate and $128 a day of revenue, losing $272 a day against the fixed cost. That is the winner-take-all structure of latency arbitrage: being second in a race pays nothing, so the marginal dollar of speed is justified only by the probability of being first, and the same package that is obviously worth buying for the fastest firm destroys money for the third fastest.

Follow-up: If the five firms sit at 1, 2, 3, 4 and 5 microseconds from the event with 2 microseconds of random jitter, what is each firm's win rate?

Key concepts: latency arbitrage, win rate, fixed cost, expected value.