Understanding synthetic long stock positions

You can create a synthetic stock position using options. This should be setup with an at-the-money (ATM) call and an ATM put. In this article, we discuss the characteristics of such a strategy.

Strike matters

A synthetic long stock position involves going long on an ATM call and short on an ATM put. The ATM call will become ITM when the stock moves above the strike price. The intrinsic value of the call will move one-to-one with the stock. But the option price cannot move by the same magnitude as the stock price because the option will lose value due to time decay. The short ATM put should, however, gain from time decay. So, the value lost due to time decay on the long call can be recovered through the short put.

What if the underlying declines? Holding the stock would mean that your losses will be equal to the magnitude of the price change; if the stock declines by 10 points, your loss will be 10 points times the number of the shares you hold. For the synthetic stock, the position will accumulate loses because of the short ATM put. This put will become ITM and will, therefore, gather intrinsic value. In addition, the position will lose because of time decay from the long ATM call.

Suppose you buy the 17600 call and short the same strike put with the underlying at 17562. Note that we chose the 17600 instead of 17550 because the 50 strikes on the Nifty index are not liquid. This position can be set up for a net credit of 36 points because the 17600 put is ITM (even though we consider it as a tradable ATM strike).

If the underlying moves to 17700 two days later, the synthetic stock position would have gained 136 points, most of which would come from the decline in the value of the put option. In comparison, the September futures contract would have gained 138 points. What if the underlying declines to 17500 during the same period? The synthetic stock would have lost 64 points (attributed to large time decay of the long call) whereas the September futures position would have lost 62 points.

What if the underlying were to sit exactly at a tradable ATM strike? Suppose the Nifty Index were at 17600 when you setup the synthetic long stock position. Assuming the same implied volatility as above, you could have setup the synthetic long stock position with the 17600 call/put for a net debit of two points. If the Nifty index moves up 100 points, this position could generate 98-point profit. And if the index declines 100 points, the position could generate 102-point loss.

Optional reading

Depending on the position of the underlying relative to the strike, either the put or the call may carry some intrinsic value at the time you set up the position. As you are setting up a synthetic long stock, the position will profit if the short put has intrinsic value at the time of contract initiation. If both the call and the put carry only time value, then the gain due to time decay in the short put could be offset by the loss in time decay from the long call.

The loss on this position is equal to the (short) put strike minus the underlying price plus net debit (or minus net credit). The breakeven is (long) call strike plus net debit (or minus net credit). The position would be optimal to setup for a net credit, especially, when the implied volatility on the put is greater than that of the call option.

There is a caveat. While the synthetic stock position can be set up for a small outlay compared to buying an equivalent position of the underlying or its futures contract, you must post margins for the short put.

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