Conversion Strategy

Arbitrage for Risk-Free Profit

Definition

A conversion is a market-neutral arbitrage strategy in options trading designed to capture a risk-free profit when option prices are overvalued relative to the underlying asset.

The strategy exploits temporary pricing inefficiencies between the underlying stock and its synthetic equivalent (a combination of a call and a put).

In essence, the trader buys the stock and simultaneously creates a synthetic short position using options to lock in a small, guaranteed gain.

Conversion Construction

A standard conversion is structured as follows:

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✅ The put–call combination forms a synthetic short stock position, which offsets the long stock.

The net difference between the synthetic and actual stock values determines the locked-in profit.

Profit Formula

Once executed, the profit is fixed and independent of market movement.

It can be calculated as:

Profit= (K – S0) + (C – P)

Or equivalently:

Profit = Strike Price – Purchase Price of Stock + Call Premium – Put Premium

Where:

• K = strike price of both call and put
• S0 = current stock price
• C = premium received from short call
• P = premium paid for long put

📊 Example

Let’s take a concrete example.

Suppose ABC Corp. is trading at $50 in March.

The APR 50 call is quoted at $2.30, and the APR 50 put at $1.70.

A trader performs a conversion as follows:

At expiration:

• If ABC rises to $55 → the short call is exercised. The trader sells his 100 shares at $50, collecting $5,000.
• If ABC falls to $45 → the long put is exercised. The trader again sells at $50, collecting $5,000.

✅ In both cases, proceeds = $5,000 for a cost of $4,940 →

Guaranteed profit = $60 (before commissions).

📈 Payoff Diagram

The payoff of a conversion is flat — the position behaves like a risk-free bond until expiration.

            Profit
              │─────────────
              │
──────────────┼──────────────────────►  Stock Price
              │
              │

There is no directional exposure, and profit remains constant regardless of the underlying’s final price.

🧠 Why It Works

A conversion exploits put–call parity deviations:

C – P = S_0 – K e^{-rT}

When the actual market prices violate this equilibrium, a trader can lock in arbitrage profit by buying or selling the synthetic and real positions until parity is restored.

Such inefficiencies are rare and often corrected within seconds by professional market makers, but small windows still occur during dividend events, volatility spikes, or interest rate changes.

💵 Commissions & Practical Notes

In real trading, the theoretical $60 gain might shrink once you include:

• Option and stock commissions
• Bid–ask spreads
• Financing or margin costs

While commissions are small (often $0.50–$1 per contract), high-frequency arbitrageurs executing dozens of conversions per day must minimize costs through low-fee brokers or direct market access (DMA) platforms.

🔁 Reverse Conversion (Reversal)

When options are underpriced relative to the underlying, traders can execute the reverse conversion, also known as a reversal.

This is essentially the mirror image of a conversion, achieving the same risk-free arbitrage but in the opposite direction.

Key Takeaways

✅ Purpose: Arbitrage strategy capturing risk-free profit

✅ Structure: Long stock + Long put + Short call

✅ Payoff: Flat (market-neutral)

✅ When to use: When options are overpriced

✅ Risk: Negligible (execution or transaction cost risk only)

Example Recap