Arbitrage Spreads

The last spreads in this unit are not directional bets at all. A conversion and a reversal are professional, market-maker trades that lock in a small, near-riskless profit when the options and the underlying futures drift out of a fixed pricing relationship. The concept is what the exam tests, not any invented price.

Put-Call Parity Is the Anchor

Everything here rests on put-call parity, the fixed relationship between a call, a put, the strike, and the futures.

• For options on futures, buying a call and selling a put at the same strike and expiration replicates a long futures position. That combination is a synthetic long futures.
• Parity ties the four pieces together. When market prices drift out of that relationship, the synthetic and the real futures are momentarily worth different amounts, and that difference is an arbitrage.
• Because a synthetic and the real futures should be worth the same, a trader can hold one and sell the other to pocket the discrepancy with the directional risk hedged away.

Think of it this way: if two things that must end up worth the same are priced differently today, you buy the cheap one, sell the rich one, and collect the gap when they converge. The direction of the market never enters into it.

This is professional territory. The gaps are small, rare, and closed quickly by traders watching for them.

Conversion vs Reversal

Both trades combine a real futures position with a synthetic futures position built from options, so the two cancel and leave a hedged, near-riskless spread.

• Conversion: long the futures + long a put + short a call at the same strike and expiration. The long put plus short call is a synthetic short futures, which offsets the real long futures, so the position's value is effectively independent of the futures price. Used when the call is relatively overpriced (options rich): selling the rich call side while holding the long futures captures the mispricing.
• Reversal (reverse conversion): the mirror. Short the futures + long a call + short a put at the same strike and expiration. The long call plus short put is a synthetic long futures, which offsets the real short futures. Used when the call is relatively underpriced (options cheap): buying the cheap call side while holding the short futures captures the mispricing.

Either way, the trade is built to be hedged and near-riskless, profiting purely from the parity misalignment, not from where the futures settles.

Memory Aid: Always trade against the mispriced call. Call too rich? Sell it: that is the conversion (real long futures, synthetic short overlaid on top). Call too cheap? Buy it: that is the reversal (real short futures, synthetic long). The synthetic leg cancels the real futures either way, so only the option mispricing pays.

Exam Tip: Gotchas

• A conversion and a reversal earn a near-riskless arbitrage from a mispriced put-call parity, not from a market view. Both hedge out direction, so the payoff is effectively independent of where the futures settles. Treating either one as a directional bet misses the entire point.
• Conversion = long futures + long put + short call, used when the call is overpriced. Reversal is its exact mirror: short futures + long call + short put, used when the call is underpriced. Swapping the option legs, or mismatching the trade to the mispricing, turns a hedged position into an unhedged one.
• Match the trade to the call. Rich call → sell the call side → conversion. Cheap call → buy the call side → reversal. The relative price of the call is the tell for which trade to put on.