# Risk and reward of a synthetic option position

For example, if your stock is at \$100 per share and the you sell a 105 Call and buy a 105 Put, you have zero risk (and zero profit potential).

I understand that the sale of the call finances the put. But if underlying goes to 103 at expiration, both the call and the put expire worthless, so profit = 103 - 100 = 3 \$. What is wrong with my assessment?

• Check the formula on how to create a synthetic option. That will clear it up. Mar 5, 2015 at 16:33
• The formula only holds when the call and the put are at the same strike, and which also equals the current underlying price. Correct? Mar 5, 2015 at 16:47

You sold a call, and have a risk if the stock rises. You bought a put and gain when the stock drops. You, sir, have a synthetic short position.

Suppose you own Long Stock and the company is going to report earnings but you’re going on vacation. How can you hedge your position without selling your stock? You can short the stock synthetically with options!

Short Stock = Short Call + Long Put

They conclude with the net zero remark, because the premise was an existing long position. A long plus this synthetic short results in a neutral set of positions (and the author's ability to go on vacation not concerned about any movement in the stock.)

• Thank you. But my confusion is that why the author says the position has zero profit potential. The position profits between 100 and 105. This profit + the premium obtained on the call is greater than the purchase price of the put, correct? So there is a net profit? Mar 6, 2015 at 14:23
• @Victor123 - see my update. Let me know that this settles it for you. Mar 6, 2015 at 18:02

But if underlying goes to 103 at expiration, both the call and the put expire worthless

If the stock closes at 103 on expiration, the 105 put is worth \$2, not worthless.

I understand that the sale of the call finances the put. But if underlying goes to 103 at expiration, both the call and the put expire worthless, so profit = 103 - 100 = 3 \$. What is wrong with my assessment?

For ease of discussion, let's ignore carry cost.

• Buy stock XYZ for \$100
• Sell \$105 call for \$1
• Buy \$105 put for \$6

You have executed a conversion and your total cost is \$105. No matter what the stock does, you'll get \$105 for the position. If it drops, you'll exercise the put and receive \$105 for your stock. If it rises, your short call is assigned and you'll sell your stock for \$105. As stated in the article (dead link), there is zero risk and zero profit.

As noted in the other answer, Short Call + Long Put is equivalent to being short the stock. Since you are long the stock, adding the two option positions negates it. IOW, plus one minus one equals zero.

For future reference:

There are 6 basic synthetic positions relating to combinations of put options, call options and their underlying stock in accordance to the synthetic triangle:

1. Synthetic Long Stock = Long Call + Short Put

2. Synthetic Short Stock = Short Call + Long Put

3. Synthetic Long Call = Long Stock + Long Put

4. Synthetic Short Call = Short Stock + Short Put

5. Synthetic Short Put = Long Stock + Short Call

6. Synthetic Long Put = Short Stock + Long Call

And if you're really understand this, you'll be able to figure out why collared long stock is equivalent to a bullish vertical spread :->)