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Call-Put Parity Reprise

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Last week, I discussed the reasons why call-selling strategies generally don't (or shouldn't) make use of in-the-money calls.

A few readers asked for another explanation of the concept of call-put parity. Here's an update of a previous article that explains it.

In the original trade, we ended up with a long call option that was deeply in the money and had to decide how to close it. We decided that selling stock was preferable to selling the call. Part of the decision was based on the fact that the bid/ask spread in the stock was tighter than in the call – so we locked in some extra profits on the trade.

The other reason was that selling stock allowed us to decide later whether to exercise the call or not, preserving what’s known as the optionality of the position.

Let’s explain why.

If we purchase a call because we think the stock is going to rise and we are correct, the call increases in value according to its delta until it becomes so deeply in the money that it has a 100 delta and moves exactly as much as the stock in either direction. The profit/loss profile for a long 350 strike call that we paid $4 for looks like:

If we sell 100 shares of stock, we make $100 for every dollar the stock falls and lose $1 for every dollar the stock gains.  The profit/loss profile is linear and looks like this:

If we were to combine the two positions – buying a call and selling 100 shares of stock, the profit and loss profile looks like this:

You’ll notice that when a long call is combined with shorting 100 shares of stock, we profit when the stock price falls below the strike price and lose the premium paid if the price rises above the stock price.

The p/l profile of buying a put at the same strike looks like this:

They’re identical!

(I’ve done the work here, but when I used to train professional options traders, I used to require them to make these p/l diagrams on paper by hand, to drive home the concept. I highly recommend that you do the same – take a pencil and paper and make your own p/l diagrams. It will reinforce the concepts. Simply pick an assortment of possible stock prices, sum up the net profit and loss for each instrument at each price, plot the points and connect them with a line.)

Because of the mathematical relationship between calls and puts - known as “call-put parity”- there is no difference between a position in which we own a call and are short 100 shares of stock and a position in which we own a put on the same strike.

A call is a put and a put is a call - assuming they’re hedged delta neutral with shares or stock.

Read the previous “Know Your Options” article about call put parity here>>>

Our Trade

We owned a call that was in-the-money (the call had a strike of 330 and the stock was trading 350) and we wanted to close it and preserve as much of our profit as possible. We had two choices:

Sell the call for $19.60 or sell the stock at $350.

If we sell the call, we lock in $19.60 minus the premium we originally paid for the call. Our position is closed and we have no further interest in the direction of the stock.

If we instead sell the stock at $350, we lock in at least $20.00 minus the original cost (if the stock is above $350 at expiration, we’ll buy it for $330 when we exercise the call and sold it for $350) but it could be even more because we won’t exercise the call if it’s out-of-the-money, but we’ll still be profiting from the short stock as it declines, potentially all the way to zero in an extreme circumstance – it’s just as if we owned the put for free.

Options that are not In-The-Money

These same concepts are true of all options, not just those that are deeply in the money. Consider the following three p/l diagrams:

Buying 2 350 calls for $5 and selling 100 shares at $350

Buying 2 350 puts for $5 and buying 100 shares of stock for $350

Buying one call and one put for $4 each (owning the straddle at $8)

Once again, they’re all the same – as long as the options are hedged delta-neutral with an offsetting position in the stock.  It doesn’t matter if we’re long calls, puts, or any combination. All positions in options on a given strike act like a straddle if they’re hedged with stock.

Practical Application

Understanding Call-Put Parity will allow you to enter options trades at the most advantageous prices and close trades in a way that maximizes profits and/or minimizes losses while preserving the optionality of any residual long option positions.

Before you execute a trade, use these principles to think about whether there might be a cheaper and better way to do the same thing.


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