What is a Synthetic Covered Call? Definition, Formula, and Example
A synthetic covered call replicates the payoff of owning stock and selling a call option using a long call and a short put at the same strike.
What is a Synthetic Covered Call?
A synthetic covered call is an options strategy that replicates the exact risk/reward profile of owning 100 shares of stock and selling one call option against them. The position combines a long call option and a short put option at the same strike price and expiration date. The long call provides unlimited upside above the strike, while the short put obligates you to buy the stock if it falls below the strike, mirroring the downside exposure of stock ownership.
This strategy exists because of put-call parity, which mathematically links the price of a call, a put, and the underlying stock. When you buy a call and sell a put at the same strike, the combination behaves identically to owning the stock itself, minus the cash outlay for the shares. The synthetic position costs less upfront than buying 100 shares, but it carries the same margin and assignment risks.
How the Synthetic Covered Call is Constructed
The strategy uses two legs:
- Long call at strike price K, expiration date T
- Short put at the same strike K, expiration T
The net debit or credit depends on the relative premiums. If the call costs more than the put, the position debits cash. If the put premium exceeds the call premium, the position credits cash. The formula for the position value at expiration is:
Payoff = max(S_T - K, 0) - max(K - S_T, 0)
Where S_T is the stock price at expiration. This simplifies to:
Payoff = S_T - K
This is the same payoff as owning the stock at price K, which is the definition of a covered call with a short call at strike K.
Worked Example: Synthetic Covered Call on AAPL
Assume AAPL trades at $210. You want a covered call at the $220 strike expiring in 45 days.
- Buy the $220 call for $3.50
- Sell the $220 put for $5.20
Net credit: $1.70 per share, or $170 per contract. Your maximum profit occurs if AAPL closes above $220 at expiration. The long call is worth S_T - $220, and the short put expires worthless. Your profit is:
Profit = (S_T - $220) + $1.70
At S_T = $240, profit is $21.70 per share. At S_T = $221, profit is $2.70. At S_T = $220, profit is $1.70.
If AAPL falls to $190, the call expires worthless and the short put obligates you to buy shares at $220, incurring a loss of $30 per share, minus the $1.70 credit, for a net loss of $28.30. This loss profile matches owning AAPL at $220 minus the $1.70 premium received from the short call in a standard covered call.
When Traders Use a Synthetic Covered Call
Traders use this strategy when they want covered-call exposure but prefer not to deploy the full capital required to buy 100 shares. The synthetic version ties up less cash because the net debit or credit is small relative to the stock price. It also allows the trader to control a position in a high-priced stock like BRK.B without paying for the shares.
The strategy also appeals to traders who want to avoid the stock-borrow costs associated with short selling, since the short put creates a synthetic short-stock position when combined with the long call. The position benefits from theta decay when the stock stays near the strike, similar to a standard covered call.
Limitations and Common Misconceptions
The synthetic covered call does not pay dividends. If the underlying stock pays a dividend, the synthetic position underperforms actual stock ownership by the dividend amount. The short put also carries assignment risk at any time before expiration if it goes deep in-the-money, unlike the stock position which has no assignment risk.
Another misconception is that the synthetic covered call is cheaper in terms of risk. It is not. The margin requirement for the short put equals roughly the strike price minus the credit received, which can be substantial. The position also loses the ability to sell the stock at a loss for tax purposes, since the short put is a separate instrument.