Spotting an Arb Across Two Quoted Markets

The scenario: you're shown two quoted markets for the same asset — say Exchange X shows $100.00 / $100.05 and Exchange Y shows $100.08 / $100.12 — and asked whether there's an arbitrage. The instinct to compare the two "middle" prices ($100.025 vs $100.10) and call it an obvious $0.075 arb is the classic mistake: a genuine riskless arb requires buying at one venue's ask and selling at the other venue's bid, not comparing midpoints, and it has to survive transaction costs on both legs.

The correct check: cross the actual tradeable prices

To lock in a riskless profit you must simultaneously buy where it's cheapest to buy (the lower ask) and sell where it's most valuable to sell (the higher bid). With Exchange X at $100.00 bid / $100.05 ask and Exchange Y at $100.08 bid / $100.12 ask: you can buy on X at $100.05 (X's ask) and sell on Y at $100.08 (Y's bid). That nets 100.08 - 100.05 = \0.03$ per share before costs — smaller than the naive midpoint comparison suggested, because the naive comparison ignored that you have to pay the ask, not the mid, on the side you're buying, and receive the bid, not the mid, on the side you're selling.

Worked example: does the arb survive costs?

Suppose trading 1,000 shares, and each leg costs $0.01 per share in fees and estimated slippage (a total of $0.02 per share round-trip across both legs). Gross profit per share is $0.03 (as computed above). Net profit per share: 0.03 - 0.02 = \0.01$. Total on 1,000 shares:$1{,}000 \times $0.01 = $10 — a real but thin edge, and one that would vanish entirely if per-leg costs were \0.015 rather than $0.01, or if the two legs can't be executed close enough in time that the prices move before both fills complete.

Now check the other direction to make sure there isn't a bigger, opposite arb being missed: buy on Y at $100.12 (Y's ask) and sell on X at $100.00 (X's bid) gives 100.00 - 100.12 = -\0.12 — a clear loss, so that direction is not an arb. Only the buy-X/sell-Y direction is potentially profitable, and only by \0.03 gross, $0.01 net of the assumed costs — a much smaller and more fragile opportunity than the $0.075 the naive midpoint comparison implied.

What this means in practice

The naive-midpoint mistake is exactly the trap interviewers set with this question, and the fix generalizes beyond two venues: in any cross-market or cross-instrument arb question, always identify the specific buy leg (an ask you can hit) and sell leg (a bid you can lift), verify the direction is actually profitable, and subtract realistic transaction costs and execution risk before calling it a genuine opportunity. In live markets, arbs this size are also usually gone within milliseconds, so the mental-math version of the question is really testing the reasoning process, not the expectation that such an arb persists.