Arbitrage in the strict academic sense is a riskless profit from a price discrepancy between two markets — buy in the cheap venue, sell in the expensive one, pocket the difference. In practice, true riskless arbitrage barely exists outside of high-frequency market makers and dedicated arbitrage desks.
The retail-accessible variants are all 'statistical arbitrage' — trades that *should* converge on average but carry real risk on any given day. Pairs trading (long one stock, short a correlated one, bet on the spread reverting), index arbitrage (mispricings between an ETF and its underlying basket), futures-cash basis trades, and crypto cross-exchange spreads are all examples.
The math is the math: any edge that's truly riskless will be arbitraged away by participants with cheaper capital and faster execution than you. What remains for retail traders is statistical relationships that *usually* hold and pay a small premium for taking the convergence risk. These trades carry tail-event ruin risk — see LTCM 1998, when 'riskless' arbitrage spreads blew out far enough to bankrupt a fund staffed with Nobel laureates.
If you're considering an arbitrage strategy, the honest framing is: you're not collecting riskless profit, you're getting paid a small premium to absorb dislocations that occasionally do not converge. Size accordingly. The position-sizing math for arb trades is fundamentally different from directional trading — leverage tolerances of 5-10× are common because the per-trade volatility is small, which is exactly the trap that has historically blown up the most arbitrage funds.