What is a Synthetic Put? Definition, Formula, and Example
A synthetic put is an options strategy that replicates the payoff of a long put option by combining a long call option with a short position in the underlying stock.
What is a Synthetic Put?
A synthetic put is an options strategy that creates the same risk/reward profile as a long put option using a different combination of instruments. The standard construction is buying a call option and simultaneously shorting the underlying stock. This combination produces a payoff that mirrors a long put: limited risk to the downside (the premium paid for the call) and unlimited profit potential to the upside (as the stock price falls). The strategy is used when a trader wants put-like protection but finds the direct put option overpriced or illiquid, or when the trader already holds a short stock position and wants to cap the upside risk.
How a Synthetic Put is Constructed / Identified
The synthetic put is constructed with two legs:
1. Long Call: Buy a call option with a specific strike price and expiration date.
2. Short Stock: Sell short the underlying stock at the current market price.
The payoff at expiration, excluding the premium paid for the call, is:
Payoff = Max(Stock Price at Expiration - Strike Price, 0) + (Initial Stock Price - Stock Price at Expiration)
This simplifies to a constant profit of Initial Stock Price - Strike Price when the stock is below the strike, and a loss that increases linearly with the stock price above the strike. The net payoff, after subtracting the call premium, mirrors a long put with the same strike and expiration. The breakeven price is the initial stock price plus the call premium.
Worked Example
A trader wants downside protection on TSLA at a strike of $250 but finds the $250 put expensive at $12.00. Instead, the trader buys a $250 call for $10.00 and shorts 100 shares of TSLA at $260.
If TSLA falls to $220 at expiration, the call expires worthless (loss of $1,000 in premium), but the short stock gains $4,000 ($40 per share × 100 shares). The net profit is $3,000, minus the $1,000 premium, for a total of $2,000. The direct put would have yielded the same $2,000 profit.
If TSLA rises to $300, the call is exercised, forcing the trader to buy the stock at $250, covering the short position. The loss on the short stock is $4,000, and the gain on the call is $5,000, for a gross profit of $1,000. After the $1,000 premium, the net loss is $0. The direct put would also have a net loss of $0 at $300.
When Traders Use a Synthetic Put
Traders use synthetic puts when the direct put option is overpriced relative to the call, often due to high implied volatility skew. The strategy is also used when the trader already has a short stock position and wants to hedge against a rally without buying a put, which would be redundant. Institutional traders use synthetic puts to exploit arbitrage opportunities when put-call parity is violated. The strategy is also a building block for more complex positions, such as synthetic straddles or conversion arbitrage.
Limitations / Common Misconceptions
A synthetic put is not identical to a long put. The short stock leg requires a margin account and is subject to buy-in risk if the stock is hard to borrow. The short stock leg also exposes the trader to dividend risk: if the stock pays a dividend, the trader must pay the dividend to the lender of the shares. The synthetic put has unlimited risk if the stock price rises dramatically and the call is not exercised in time, although the long call caps the risk at expiration. A common misconception is that a synthetic put is free; it requires capital for the call premium and margin for the short stock. The strategy also has different margin requirements than a long put, which can tie up more capital.