TK All-Star posted on 08/12/09 at 09:39 AM

Doc Maher continues his advanced series on ICs.

Welcome back to my series on iron condors. We’ve covered lots of ground already. In part 1, Credit Spreads on the Russell 2000 index (RUT), we explained how credit spreads and iron condors are interrelated trades and both good tools for steady income in sideways markets. In part 2 we set up a theoretical RUT iron condor trade; we then followed up on that trade in Part 3 to see how it fared.

I got two excellent comments from readers, giving me a chance to explore a related strategy, iron butterflies. as well as real-world pointers on managing iron condors successfully once you’ve put the trade on.

Let’s quickly recap what an iron condor is. This trade has four legs, set up like so:

•    Buy a put, Strike A

•    Sell a put, Strike B

•    Sell a call, Strike C

•    Buy a call, Strike D

Usually the underlying will be trading between strikes B and C when you tee up the trade. Its max potential profit is limited to the net credit received when you put the play on. The max potential risk is limited to Strike B minus Strike A, minus the net credit received.

(Credit spreads, iron condors and iron butterflies are all multiple-leg options strategies involving additional risks and multiple commissions and may result in complex tax treatments. keep the risk of early assignment in mind when constructing your own trades. Consult with your tax advisor as to how taxes may affect the outcome of these strategies.)

How wide do your iron condor’s wings stretch?

The Iron Condor strategy utilizes two credit spreads to create a range of profitability – but how wide should that range be? How wide is “wide”, anyway? Today we’ll lay some groundwork necessary to answer that question in a fuller way in the next post.

Answering that involves us in some comparisons. What are the odds of the underlying moving beyond my IC’s range, and how would I calculate them?

Let me underline that we’re dealing in “odds”, not certainties. No tool can give you rock-solid odds on future events. However we can get some hints from the underlying’s past movement and the prevailing outlook among market makers.

Implied volatility and our friends Black & Scholes

To do this we must first understand what Historical Volatility means and how it’s calculated. (TK’s own Options Guy Brian Overby has just kicked off a blog series on options and volatility – should be worth following along on that.) The Black-Scholes options pricing model zeroes in on the various factors impacting options prices. These include:

1. Price of the underlying

2. Strike price of the option

3. Amount of time until expiration

4. Dividends to be paid

5. interest rates

6. Volatility of the underlying

The first two are fairly obvious. The price of the underlying versus the strike price of the option should have an effect on the option price. The next one, time to expiration, is also familiar. More time to expiration usually means the more the option is worth.

The next two are not quite so obvious. Dividends paid out change the price of the stock, so it makes sense that they’d have an impact on option prices. Interest rates are related to the cost of holding an asset. For today’s discussion we will be ignoring these two.

That brings us to volatility. What exactly is volatility, and why does it impact option prices? Well, I think of it like this: if a stock has a chart that looks like this, what are the at-the-money options worth?

You might say we can’t answer that because I haven’t said how much time is left until expiration, or what the price of the underlying is, or much of anything. However it IS possible to answer this question.

That’s right, someone in that back has it. Those options are not worth anything. If the underlying never moves, then you would not be willing to pay anything for a call or a put on that underlying. There is no sense to it because if the underlying doesn’t move you can’t make anything buying options on it.

So, Black and Scholes figured that the amount that the underlying moved would have to be included in the pricing model. So they measured it over a period of time (we usually see the 30-day historical volatility quoted) and put that motion into their model.

Normal distribution and standard deviation

It’s not important that you understand exactly how they did this, but it is helpful to understand what it means. The Black-Scholes model is based on a number of assumptions and we may argue with any one of them. The first assumption is that the underlying is going to act randomly and that its prices are going to fall into what is called a “normal distribution” over time. Sometimes this is called a random walk. It means that the stock moves randomly according to the assumed “normal distribution”. This sort of assumption is not unusual and is the basis of most statistics. More complex models may use other distributions.

To determine what this normal distribution looks like, you need to determine what the “standard deviation” is. What they did was look at the movement over the last 30 days and calculated what the “standard deviation” was based on the prices over that time. The standard deviation is a range that the underlying has a 67 percent chance of staying within, based on the random / normal distribution assumption.

Below I have the normal distribution of expected prices for GE for on 5/16/08 (last year), which I used in an earlier post. What it shows is the probability that GE’s price will be at a certain level on 5/16, 7 days from 5/09 based on the preceding 30 days. GE closed at $32.20 on that 5/09.

Don’t worry about the underlying math here. Just notice that the closer a potential 5/16 closing price is to the starting price of $32.20, the more likely that price will finish at expiration at that level; the farther away from $32.20, the less likely. The most likely price is $32.20. There is almost no chance that the price could get down to $30 or above $34 for this distribution in this 7-day period.

So what has all this got to do with anything? If you know the chances that your underlying will reach a certain price, then you know what the chances of your strategy working are. (TradeKing’s Probability Calculator makes it super-easy to check these chances. View this video tutorial to learn more.)

As it turns out, you can relate volatility to the expected range of prices, measured in standard deviations, going forward. Here’s the formula:

1 standard deviation = (Current price) (Volatility)/square root(number of periods in a year).

Looks confusing, but it’s not. The last term is just how many parts of a year our time interval is. Since we’re looking at one week, we have 52 of those in a year. If we were interested in a month, it would be 12, etc.

Black and Scholes calculated the volatility based on the prices over the last 30 days; we usually see this value referred to as “historical volatility” because it’s based on the history of the stock.

Historical versus implied volatility

If we use the Historical Volatility, we’re expecting GE to continue to act as it did in the past. However there’s also a value called Implied Volatility, based on market makers’ projection of how much movement is expected in the future. If we use the Implied Volatility we are using the “projected movement”. (While implied volatility represents the consensus of the marketplace as to the future level of stock price volatility or probability of reaching a specific price point, keep in mind there’s no guarantee this forecast will be correct.)

Armed with this concept and the above formula, we can determine how many standard deviations wide our Iron Condor is.

I’ll do an example of this in the next post, and you’ll be able to see how we estimate the odds of success for a particular Iron Condor. Stay tuned!

Income Trader

All-Star Commentator

www.tradeking.com/ODD .

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Any strategies discussed and examples using actual securities and price data are for educational and illustrative purposes only and do not imply a recommendation or solicitation to buy or sell a particular security or to engage in any particular investment strategy. In reading content in the Trader Network, you may gain ideas about when, where, and how to invest your money. Although you may discover new ideas or rationale that may be compelling, you must ultimately decide whether or not to put your own money at risk. Consider the following when making an investment decision: your financial and tax situation, your risk profile, and transaction costs.

Jonathan F. Maher, PhD has a professional business relationship with TradeKing.

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