Understanding the synthetic long put option

Question

I am having trouble understanding the following synthetic relationship:
Synthetic long put option = Short underlying + long call

Now, if XYZ is at 40, and I short XYZ at 40 and also purchase the 40 call, then:

Short position benefits if underlying goes down, but the long call loses value at the same time. So do I really want the underlying to go down? What exactly should the underlying do for this position to work in my favor? In a long put, I want the underlying to go down, but here I am not able to come to a conclusion.

Answer 1

A long put - you have a small initial cost (the option premium) but profit as the stock goes down. You have no additional risk if the shock rises, even a lot.

Short a stock - you gain if the stock drops, but have unlimited risk if it rises, the call mitigates this, by capping that rising stock risk. The profit/loss graph looks similar to the long put when you hold both the short position and the long call.

You might consider producing a graph or spreadsheet to compare positions. You can easily sketch put, call, long stock, short stock, and study how combinations of positions can synthetically look like other positions. Often, when a stock has no shares to short, the synthetic short can help you put your stock position in place.