Arbitrage

An arbitrage position must satisfy two tests at once: it requires no net outlay of the trader's own capital, because the proceeds of the short leg fund the long leg, and it carries no exposure to future price movements, because the legs offset one another state by state. If both hold and the position still generates a positive cash flow today or at settlement, the market has priced two claims on the same payoff differently.

This is why arbitrage functions as a pricing tool rather than merely a trading style. If a portfolio of traded instruments can be built to replicate a derivative's payoff in every future state, then the derivative and the replicating portfolio must trade at the same price. Any deviation invites the offsetting trade, and the act of putting it on pushes prices back together. Derivative valuation therefore proceeds by construction: build the replication, price it, and assign that value to the derivative.

The clearest mechanical illustration is the carry trade on a forward contract. A dealer who buys the spot asset today, finances the purchase at the risk-free rate, holds the asset to the contract's expiry, and simultaneously sells a forward on it has locked in a known outcome: pay the financing cost plus any storage or insurance, receive any income or benefit the asset yields, and deliver against the forward at the agreed price. Because every element is known at inception, the forward price cannot differ from the spot price grossed up by financing and carrying costs and reduced by income received.

If the quoted forward exceeds that level, the trade above earns a riskless margin and dealers execute it until the gap closes. If the forward is too cheap, the reverse applies: sell or borrow the asset short, invest the proceeds, and buy the forward. Compensation for waiting is embedded in the carry terms, not in a risk premium.

Several familiar market structures exist mainly to keep this relationship tight. Authorised participants in exchange-traded funds trade the fund against its basket and use creation and redemption to convert one into the other, which is why an ETF's price tracks net asset value closely. Index futures are disciplined by programme traders arbitraging the basis against the cash basket. In currency markets, covered interest parity ties forward points to the interest differential between the two currencies, and triangular arbitrage keeps cross rates consistent with the two pairs that imply them.

Option markets are policed by put-call parity: a call, a put, the underlying and a risk-free bond form four instruments with only three degrees of freedom, so a synthetic long position built from options and borrowing must cost the same as the outright. Convertible bonds, dual-listed shares and cash-versus-swap spreads are governed by variants of the same logic.

Candidates should be able to move in both directions. Given spot price, financing rate, carrying costs and any yield, compute the no-arbitrage forward or futures price and state whether a quoted contract is rich or cheap. Given a mispricing, specify the trade precisely: which leg is bought, which is sold, how the position is financed, and what the locked-in profit equals at expiry, typically the present value of the difference between the quoted and theoretical price.

Equally important is recognising what happens when frictions bite. Short-sale restrictions, collateral demands, bid-ask spreads and limits on borrowing can leave a visible gap unexploited. Questions often turn on identifying which assumption of the frictionless model has been relaxed, and on distinguishing genuine riskless replication from strategies that merely hedge part of an exposure.