Long Call versus Married Put

Two Rhinos

I’ve noticed a pundit or two saying that a Married Put is not the equivalent position as a Long Call. This drives me up the wall.  The two positions are synthetically identical.  I finally couldn’t take it.  I was reading this article by Kurt Frankenburg on Long Calls vs. Married Puts and decided I had to say something.   Investors and traders should know these two positions are identical.

Let’s begin with the trade Kurt Frankenburg put on.  He quotes these prices on April 27, 2011  (633 days to expiration):

Stock: CTSH at $81.40

Jan 2013 85 Calls at $12.60

Jan 2013 85 Puts at $15.00

I used OptionVue’s back trader at the closest I could get was at 13:00 Central with the following stock and option prices:

Stock: CTSH at $81.42

Jan 2013 85 Calls at $11.80 (bid 11.00 ask 12.60)

Jan 2013 85 Puts at $14.65  (bid 14.30 ask 15.00)

From the start, Frankenburg is stacking the deck in his favor since he’s buying the call at the ask (correct) and selling the put at the ask(incorrect).  He should be selling the put at the bid of 14.30.

You should NEVER pay the ask or sell at the bid unless you have to close a position NOW.  This is rare.  Since we are entering the trade, we can be picky.  I would offer the mid-price of the option.  In Frankenburg’s example, he gives up 0.80 for the call but only 0.35 for the put.

The other factor is the interest in the option pricing model.  This is a 633 day trade.  If you tied up over $8,000 for 633 days, what would the cost of carry be?  This is interest minus dividends.  I don’t think CTSH pays a dividend, so let’s consider dividends to be zero.

The option mid-prices were

Call 11.80

Put 14.65

We can use the Put/Call Parity equation to calculate the interest.

Call – Put = Underlying – Strike + (Interest – Dividend)

Let’s plug in the numbers…

Call – Put = 81.40 − 85.00 + Interest

Call – Put = −3.60 + Interest

11.80 − 14.65 = −3.60 + interest

-2.85 = −3.60 + Interest

Interest = 0.75 per contract or $75

$75 of interest on $8,425 of cash for 633 days is a 0.51% annual rate of return. So the math seems to be correct if you use the option mid-prices. Let’s re-examine the trades with option mid-prices and use the same capital for both trades:

Stock: CTSH at $81.40

Jan 2013 85 Calls at $11.80

Jan 2013 85 Puts at $14.65

Married Put = $8140 stock + $1465 put = $9605 capital

Long Call  = $1180 call + $8425 cash = $9605 capital

What’s the maximum risk for each trade if the stock drops to $50 per share?

Married Put

$81.40 stock purchase price – $85 strike price – $14.65 paid for the put = $1105 Maximum risk

Long Call

$1180 call – $75 of interest received on the initial $8425 cash = $1105 maximum risk

 

What is the profit for each trade if CTSH closes at $100 on Jan 2013 option expiration day?

Married Put

$100.00 stock price – $81.40 stock purchase price – $14.65 paid for the put = $395 Profit

Long Call

$100.00 stock price – $85 strike price  – $1180 call + $75 of interest received on the initial $8425 cash = $395 Profit

 

The risks and profits are identical using the same capital!  The two positions are equivalent.

Which trade is easier to execute? 

The Long Call is one trade with lower option prices because it it out-of-the-money.  This will have less slippage than the Married put.  The Married Put has slippage with the stock and the put.  Clearly it’s easier to keep track of a single Long Call and slippage is less.

Why would you want to do a Married Put?

There are two reasons I can think of:

– You don’t want to be tempted to over-leverage yourself.  Buying a call for $1180 requires you to put the remaining $8425 in a cash for the duration of the trade.  Many people can’t do that.  This is the big point Frankenburg makes, and it is a valid concern.

– You already own the stock AND YOU DON’T WANT TO SELL THE STOCK YET.  Buying the Married Put could be to protect gains in the stock and collect any dividends while protecting you from a decline in the stock price.  This is a different situation than putting the Married Put on together with a stock purchase at the start of the trade that we’ve been discussing above.

What is the danger of a Long Call?

Over leveraging yourself.  It’s easy to do.  You have $8425 of cash for 633 days in this example.  Can you trust yourself to leave it alone and not use it for margin with another trade?  If you have the discipline to not use your cash for margin for other trades, then a Long Call is good substitute for a Married Put

In Summary

The Married Put and the Long Call have IDENTICAL risk charts if you don’t forget to consider interest and dividends.  If you decide to trade with Long Calls, DO NOT over leverage yourself.  All trades have good and bad.  There’s no trade that is better than another trade.  If you think that, you’re missing something.  Look for the risk you aren’t seeing and make sure you really compare apples to apples and not apples to applesauce.

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