Synthetic positions

Conversion and Reversal

Construct conversions and reversals using stock, calls and puts. Compare equivalent cash flows while accounting for financing, dividends and stock borrow.

Mechanics & mathematicsHypothetical examples

What Is It?

A conversion combines long stock, long put and short call at the same strike and expiry. A reversal combines short stock, long call and short put. With matched European contracts and no dividends, their terminal values are respectively +K and −K per underlying unit.

These trades implement put–call parity through synthetic forward exposure. Their economics resemble lending or borrowing against a fixed cash flow. Actual financing, dividends, short availability and settlement determine whether a quoted gap produces a realizable surplus.

How It Works

A long call and short put pay Sₜ − K, the payoff of a long forward struck at K. Adding a short share cancels Sₜ and leaves −K: a reversal. Conversely, stock plus put minus call leaves +K: a conversion. These are payoff equivalences, not a claim that long call minus put is free spot ownership.

With known cash dividends, a conversion also receives the dividends while the stock is held; a reversal must compensate the stock lender for them. Compare all dated cash flows, using the appropriate borrowing rate for a financed conversion and the achievable lending rate for reversal proceeds. Borrow fees and short-sale collateral restrictions can make the two sides asymmetric.

Mathematical Formula

C_T-P_T=S_T-K

Matched European call-minus-put is a synthetic forward payoff, before the initial option premiums and funding.

V_{\mathrm{conv}}=S_0+P-C=Ke^{-rT}+\operatorname{PV}(\mathrm{dividends})

The equality assumes known cash dividends, feasible stock trading and common frictionless financing. With no dividends, the conversion is a synthetic zero-coupon claim paying K.

\mathrm{Credit}_{\mathrm{rev}}=S_{\mathrm{bid}}+P_{\mathrm{bid}}-C_{\mathrm{ask}}

A reversal shorts stock and the put while buying the call. The credit must fund the future K payment, dividend compensation, borrow costs and other implementation costs.

Worked Example

Illustrative prices · not market data

Assume no dividends, European options, K = 100 and an available discount factor of 0.98 to expiry. The executable stock ask is 100, put ask 4 and call bid 6.30.

Buy the conversion for 100 + 4 − 6.30 = 97.70. It pays 100 at expiry whether the stock ends above or below the strike.
Borrow 98 today with an agreed 100 repayment. After paying for the conversion, the initial gross surplus is 0.30.
If total costs measured today are 0.12, the modeled net initial surplus is 0.18 per underlying unit.
If the conversion instead costs more than the discounted fixed payment, examine a reversal using the reverse executable sides; the long conversion's prices cannot simply be negated.

The example assumes the borrowing facility is actually available and collateral can be met. Otherwise the conversion is an investment with an implied yield, not an immediately financeable arbitrage.

Execution Considerations

Match share quantity to option multiplier and ensure all legs represent the same deliverable after corporate actions. Obtain stock borrow before entering a reversal and check recall, substitution and dividend-compensation terms.

Account for loan interest, any rebate on short proceeds, expiry cash flows and possible early assignment separately. A broker may hold the reversal's credit as collateral, preventing the assumed cash investment. Reconcile contract settlement and share delivery dates.

Risks & Limitations

American exercise changes cash-flow timing and can unwind only part of the structure. Dividend surprises and adjustments can make a spot-equity hedge incomplete.

Borrow recalls, wide spreads, partial fills, corporate actions and financing changes can make small parity discrepancies uneconomic. Margin and counterparty exposure remain even when the terminal payoff is fixed.

Frequently Asked Questions

Is a conversion a bullish stock position?

Its stock exposure is offset by the matched put and short call at European expiry. The intended result is a fixed payment plus any stock dividends, subject to the construction's assumptions.

How does a reversal differ from a conversion?

It reverses every leg: short stock, long call, short put. Borrow constraints and financing mean its executable economics need not mirror the conversion.

Can dividends be ignored for short maturities?

Only if none occur within the holding period or the amounts are genuinely immaterial to the calculation. One ex-dividend date can dominate a small parity gap.

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References & Further Reading

Background sources for the concepts above. Apply the assumptions stated in this guide to each formula.

Options Industry Council: Put/Call Parity

Educational material only; not investment advice or an offer to trade. Examples are hypothetical. Trading involves execution, financing and capital-loss risks; no return is guaranteed.