True arbitrage
A trade that makes money with certainty and no capital at risk. If gold trades at 2,000 in London and 2,010 in New York and you can transact both instantly, you buy one and sell the other.
In practice these are competed away in microseconds by firms with faster infrastructure. If you can see one, you are almost certainly missing a cost, a constraint, or a risk.
The costs that eat it
The interview version of this question always hides at least one:
- Transaction costs and the spread on both legs.
- Execution risk - you fill one leg and not the other.
- Funding and carry - the position must be financed until it converges.
- Settlement and delivery - the two assets may not be fungible in the timeframe you assumed.
- Counterparty and regulatory constraints - short-selling may be unavailable or expensive.
A strong answer names these unprompted.
Relative value
What most quant strategies actually do. Two related instruments diverge from their usual relationship, you bet on convergence, and you carry residual risk because the relationship is statistical rather than mechanical.
The failure mode is that the relationship changes rather than reverting. Convergence trades that were "sure things" have caused several well-known blow-ups, and the mechanism is always the same: the position is sized as if it were arbitrage when it is not.
Statistical arbitrage
A large number of small, weakly predictive relative-value bets, diversified so that idiosyncratic risk cancels and the aggregate edge survives. Related to edge and expected value: small edge, high repetition, controlled variance.
The classic interview question
"Instrument A and instrument B are economically identical but trade at different prices. What do you do?"
The naive answer is "buy the cheap one, sell the expensive one". The good answer starts with "why are they different?" - and then enumerates the frictions above before deciding whether the residual is worth trading.
Interviewers are testing scepticism. A candidate who takes a free-money setup at face value is telling them something.
Related: put-call parity, which is the closest thing to a genuine no-arbitrage relationship you will be asked about.