No-Hedge Trading versus Arbitrage

Both strategies can compare related markets, but they sell different products. Arbitrage purchases or sells a complete set of payoffs so the outcome no longer determines whether the package profits. No-hedge owns only one side and remains exposed to settlement.

Locked binary arbitrage #

If exact complementary YES and NO shares can both be bought at $p_Y$ and $p_N$, their combined payoff is always 1. Before costs,

$$Locked\ PnL=1-p_Y-p_N.$$

At $p_Y=0.52$ and $p_N=0.45$, total cost is 0.97 and locked settlement profit is 0.03, provided both trades execute, contracts truly match, and settlement/counterparty risks are honored.

Unhedged expected profit #

Buying only YES at $p$ with estimated probability $q$ gives

$$EV=q-p.$$

but realized PnL is $1-p$ or $-p$. At $q=0.65$, $p=0.60$, expected profit is 0.05—larger than many locked spreads—but the 35% loss branch remains.

Life analogy #

Buying an item after comparing two appraisals is speculation on resale. Simultaneously signing an enforceable purchase and higher resale contract is closer to arbitrage. The appraisal alone is not the second contract.

Risk–return exchange #

No-hedge can show higher expected ROI because it does not spend capital on the offsetting leg and accepts directional probability risk. That potential return is compensation for retained uncertainty, not a free improvement over arbitrage.

Application to no-hedge #

Label reports accurately: reference-derived edge is estimated EV, while a jointly executed complete payoff package may be locked PnL. Never sum the no-hedge discount as if it were realized arbitrage income.