Long Calls vs. Married Puts – Risk Free Interest Rate

Q: During the course of your seminars you talk about the “risk free rate of return” and its impact on options when comparing them to stock, long calls and married puts…could you help me understand how the “risk free rate of return impacts the comparison?

A: Let’s take a look at a comparison between the Jan 2012 $60 call, and the Jan 2012 $60 married put.

The $60 call is trading at $6.00 X $6.50. You could probably get ‘in the spread’ with a limit order, but you probably won’t get it low as $6.00… maybe more like $6.20 or $6.30. With me so far?

The risk, then, will be that you could lose as much as $6.20ish.

Now let’s look at the married put. ESRX is trading at $53.15, and the Jan 2012 $60 puts are $12.20 X $12.60. Again, if you get in the spread, you may be able to pick up the put for $12.40 or so.

Now let’s do a little math:

ESRX shares trading at $53.15
Plus Jan 2010 $60 puts +$12.40
Total Investment $65.55
Minus Strike price -$60.00
Total amount AT RISK $ 5.55

See that? You’ll pay more for the married put than for the call, but the AT RISK amount is different. $5.55 versus $6.20 or so.

Here’s why that is significant: there are many, many self-proclaimed options gurus out there that say that a trading a long call is IDENTICAL to trading a married put… but the call is cheaper and therefore ‘more efficient’.

Hmmm… strange to say that two ‘identical’ things are the same but different… but I digress from correcting their math to correcting their English. Ahem.

The reason that there is a different dollar amount AT RISK is that the options’ pricing reflects what the rest of one’s capital is doing. The Black-Scholes equation ASSUMES that someone trading a long call HAS the capital to buy the stock; he just declines to do so. Instead, he buys a call AND..! This is important! He takes his remaining capital that WOULD be used to buy that stock and instead deposits it at interest.

Enter the risk free interest rate. The difference between the AT RISK amounts in the married put and the long call is what the same money could earn at risk free interest.

Here is where understanding the impact makes a difference: Position Sizing. If one has, say, about $10,000 of capital to trade and has a bullish expectation on a $45 stock, he may get 200 shares of XYZ plus 2 $50 put options and now his capital is spent. Of course, he can only lose the time value portion of the puts, which make his AT RISK picture pretty conservative, while retaining unlimited upside potential.

On the other hand, the temptation is to take that same bullish expectation, look at the pricing and leverage of long calls, and pick up twenty contracts because, after all.. that’s what we have the money to buy. It’s this human nature problem that gets folks into trouble: using the highly leveraged instrument that a long call is, without respect to the fact that it’s intended to be accompanied by a corresponding amount of capital that we DON’T put AT RISK.

Got it? The risk free interest rate affects pricing of these two instruments. Some will argue “but that can’t be… because in an efficient market, you can’t have that kind of disparity in pricing.” Yes you can. You COULD buy a married put, short the same month and strike calls, and make an ‘arbitrage’ profit… but in the end all you have done is solve Black-Scholes for the risk-free interest rate. The same result is attainable by buying T-bills.

Why do I advocate using married puts over long calls? Because position sizing is figured out FOR you… plus you have the opportunity to sell calls and spreads against that arrangement with a lower trading clearance.

About Kurt Frankenberg

Kurt Frankenberg is an author and speaker about entrepreneurship, martial arts, and trading the stock and options markets. One of several "Biznesses" he founded as a teen, The Freedom School of Martial Arts, has been in continuous operation since 1986. Kurt lives in Colorado Springs with his wife Sabrina, German Shepherd Jovi, and his ninja cat Tabi.