Conversion
Arbitrage

What is a conversion?

A conversion is an arbitrage that combines three legs at one strike price: you go long the underlying, buy a put option and sell a call option. The long put and short call together form a synthetic short that exactly offsets the long stock, so the position's value at expiry no longer depends on where the underlying settles. What is left is a fixed, locked outcome — the very definition of an arbitrage.

The trade exists because of put-call parity, the relationship that ties a call, a put, the strike and the underlying together. When the market briefly prices the call too richly relative to the put plus the cost of carrying the stock, a conversion captures that gap as a small, near-certain profit. It is a market-maker and professional-desk tool rather than a directional bet.

Key takeaways

• A conversion is an arbitrage, not a directional view — the payoff is flat across all prices.
• Construction is long underlying + long put + short call, all at the same strike and expiry.
• The put and call form a synthetic short that cancels the long stock, locking the result.
• Profit comes from put-call-parity mispricing when the call is relatively overpriced.
• The real risks are dividends, financing cost, early assignment and costs — not the market.

How a conversion works

Set up all three legs at the same strike, say strike K. Being long the stock means you gain point-for-point as price rises; the short call caps that gain above K, while the long put protects you below K. Above K the call you sold is exercised against you and you deliver the stock at K; below K you exercise your put and sell at K. Either way you end up selling at K, so your terminal value is fixed and the only thing that matters is the net cost you paid to assemble the package versus the strike.

In India this is harder than the textbook suggests. Selling the call blocks SPAN + exposure margin, the long stock ties up capital or carries a financing cost, and STT, brokerage and the bid-ask spread all nibble at the edge. Theta and implied volatility are irrelevant to the locked payoff because the option legs hedge each other — but they do drive the entry mispricing you are trying to capture. Index options like NIFTY are cash settled, while many single stocks settle by physical delivery, which changes how the legs unwind.

The numbers that matter

Worked NIFTY example

Suppose NIFTY is near 22,500 and you spot a small dislocation at the 22,500 strike. You buy NIFTY exposure at 22,500, buy the 22,500 put for ₹150 and sell the 22,500 call for ₹190. Your net cost is 22,500 + 150 − 190 = 22,460 per unit, while every leg resolves at the 22,500 strike. With a lot size of 75, the locked profit is about (22,500 − 22,460) × 75 = ₹3,000 before costs (illustrative figures):

NIFTY at expiry	Outcome	P&L (1 lot)
21,500	Put exercised, sell at 22,500	+₹3,000
22,500 (strike)	Both options expire near zero	+₹3,000
23,000	Call assigned, deliver at 22,500	+₹3,000
24,000	Call assigned, deliver at 22,500	+₹3,000

Notice the P&L column never changes. The flat row is the whole point — the conversion turns a directional instrument into a fixed return, with the only variable being whether that ₹3,000 survives transaction costs, financing and any dividend adjustment.

When to use a conversion

• You see a call trading rich relative to the put plus carrying cost at the same strike.
• You have low-cost financing and margin so the small edge is not eaten by carry.
• You can execute all three legs together to avoid leg-in slippage.
• You are running a professional or market-making book that monetises tiny, repeatable edges.

Risks to respect

• Dividends: an unexpected or larger dividend on a stock conversion can flip the locked profit into a loss.
• Early assignment: an in-the-money short call can be assigned before expiry, breaking the hedge.
• Financing & margin cost: the carry on long stock and the blocked SPAN margin can exceed the tiny edge.
• Execution slippage: the gap is so small that a poor fill on any leg can erase the whole trade.

Conversion vs reversal

The reversal is the exact mirror of the conversion: short the underlying, sell a put and buy a call at one strike. A conversion is the play when the call is relatively expensive; a reversal is the play when the put is relatively expensive. Both lock a flat payoff from the same put-call-parity relationship, just from opposite sides. Desks switch between them depending on which option in the pair the market has temporarily mispriced.

Conversion vs box spread

A box spread reaches the same locked, near risk-free outcome but uses four option legs across two strikes instead of holding the underlying. The conversion needs you to actually carry the stock — with its financing and dividend exposure — whereas the box is purely option-based and so sidesteps stock carry. Both are interest-rate-style arbitrages rather than market bets, and both depend entirely on costs staying below the captured edge.

Common adjustments

If the short call drifts deep in the money on a dividend-paying stock, traders often roll or close it early to dodge assignment around the ex-date. Many desks also unwind the whole package before expiry the moment the parity gap closes, rather than carrying it to settlement — taking the edge as soon as it appears and freeing the margin for the next dislocation.

Frequently asked questions

Is a conversion risk-free?

It is near risk-free at expiry — the long put and short call fully hedge the long stock, so direction does not matter. The residual risks are dividends, financing cost, early assignment and execution slippage, not market moves.

How does a conversion make money?

It captures put-call-parity mispricing. When the call is rich relative to the put plus carry, locking long stock against a long put and short call yields a small fixed profit regardless of the settlement price.

What is the difference between a conversion and a reversal?

A conversion is long stock plus a long put and short call; a reversal is short stock plus a short put and long call. A conversion exploits a relatively rich call, a reversal a relatively rich put.

Why are conversions hard to find in India?

Liquid NSE markets price options close to parity, so any edge is tiny and usually eaten by STT, brokerage, the spread and margin cost. They surface mostly in illiquid strikes or around dividend and expiry dislocations.

The bottom line

The conversion is the cleanest example of options arbitrage: long stock locked against a synthetic short, leaving a flat payoff whose only variable is whether the captured put-call-parity edge survives costs. It is not a way to trade a view — it is a way to monetise a pricing error. For Indian retail traders the edges are usually too thin to be worth the margin and carry, which is why conversions live mostly on professional desks; but understanding them is the key to understanding how every synthetic position is built.

Related strategies & terms

• Reversal — the mirror image that exploits a relatively rich put.
• Synthetic Short — the long-put-plus-short-call core that hedges the stock.
• Box Spread — the same locked return using four option legs, no stock.
• Assignment · SPAN Margin · Expiry