Inquiring Minds Want to Know
As you can imagine, I get lots of questions and comments about my articles. Last month I shared some of the questions I received with you and since it was so well received, I decided to answer questions on a monthly basis, so keep them coming. Also, next week I won't be writing; I’ll be on a Caribbean cruise instead. Finally I'll have some free time to reread some of my favorite options books. Wow, aren't vacations great?!
The questions this month cover a wide range of topics, but what amazes me the most, is that I'm still getting questions on the probability questions that I asked in the February 14, 2008 article, "Probability, Expectation and Options." Some of the email was actually quite hostile! I was told that I didn't understand the math and that my credibility on other topics would be compromised, if I didn't admit that I was wrong. Since I was taught from a young age that the customer is always right, I will try one final time to convince you that my answer is correct as written, so I can continue to live by this adage. (Hope you followed that logic.)
Q) Here is the exact question restated:
"A man states that he has 2 children at least one of which is a boy. What is the probability that he has a girl?"
A) The correct answer is still 66 2/3%. This actually is a basic problem dealing with conditional probability, and problems like this arise in high school and undergraduate college texts. Here's another way to look at it that may be more intuitive. Assume a town has 1000 families that have 2 children. You would expect the gender breakdown of the children to be close to: 250
families with 2 boys, 250 families with 2 girls, and 500 families having a boy and girl. Now if we eliminate those families that have 2 girls, we are then left with 750 families. Of those, 500 have a boy and a girl, and 250 have 2 boys. Therefore, the probability that a family has a girl is: 500/750 or 2/3. Anyway, I promise not to mention this probability question again.
Q) Can you provide the Black-Scholes formula that you referred to in your article on options pricing? I would like to put it in an Excel worksheet and see the effect of varying the variables.
A) There is commercial software available on the internet that already has the Black-Scholes formula programmed, but if you are talented enough to do the programming, more power to you. I'm certainly impressed by your motivation!
First, we define the variables,
C = theoretical value of the Call
P = theoretical value of the Put
S = Stock price
X = eXercise price
T = Time to expiration (expressed as a fraction of a year)
V = annual Volatility
R = annual Risk-free rate of return
N(x) = the cumulative normal distribution, i.e., the area under the normal distribution curve
SQRT(x) = the square root of x
Next, we calculate an intermediate value:
H = LN(S/X) + (R + (V^2)/2)*T |
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V * SQRT(T) |
And Finally,
C = S * N(H) – X * e^(-R*T) * N(H-V*SQRT(T))
and
P = -S * N(-H) + X * e^(-R*T) * N(V*SQRT(T)-H)
This is the original formula and applies to European options on stocks that don't pay dividends. If dividends are payable, you can modify the formula by subtracting out the present value of dividends expected to be paid out over the life of the option from the stock price. There's still some controversy as to how to adjust the formula to account for the early exercise provision in American options.
I know to non-mathematicians this may seem daunting, but not to worry. First of all, if it looks complicated, that's because it is complicated! That's why Messrs. Black and Scholes won a Noble prize in economics. More importantly though, it's nice to know it's there, but just like you don't need to be an engineer to drive a car, you don't need to know the formula to trade options.
Q) I am selling Puts and Calls on the same stock every month. At expiration, either the Put or Call will expire worthless and I buy back the other option which is ITM but doesn't have any time value. I've been taking in a lot of premium, i.e. gains. Is this a decent strategy?
A) I haven't discussed it in my articles yet, but what you've described is either a short Straddle or Strangle. If the Put and Call are at the same strike price, it's a Straddle, if they're at different strikes it's a Strangle. (Just for completeness, if both of the options in a Strangle are ITM, it's called a Guts.) The real issue isn't what it's called, but rather the fact that there is huge exposure on the downside as well as the upside. Sure, if the stock doesn't move very much you'll capture the premium as the options decay, but if the stock makes a large move in either direction the losses can be very significant. Furthermore, if the move is sudden the volatility of the options will increase, making them even more expensive to buy back. We'll look at these positions in a few weeks and see what the graphs and Greeks look like. Overall, unless they're done in a very small size, these positions tend to lead to sleepless nights. They're not for the faint of heart.
Q) I have been trading options and I am challenged with the fact that I keep breaking even! Here's an extrapolation from my trading plan of my basic setup. Please help.
Setup Criteria for Bull Call and Bear Put spreads:
- Stock will have a completion of an Elliot wave 4 (bull or bear), using 150 Elliot wave bars on a daily chart. The wave 4 subdivides into a full ABC correction.
- Price at the wave 4 must end at one of the three Fibonacci retracements 23.6, 38.2, 50
- Direction of the stock must match the direction of the price oscillation - no divergence
- Implied volatility must be less than or equal to statistical volatility at entry.
A) I'm sorry to hear that you're not making money with your trading, but the first step is to not lose money and it sounds like you're there. Also, I commend you on having a written plan, as it's more important than most people think because it takes the emotion out of trading and helps you to analyze why a particular trade worked or didn't work.
My methods of trading are apparently different from yours. I don't try to predict the
direction of particular stocks. I don't use Fibonacci or Elliot Waves at all. The technical indicators that I use most often are basic support and resistance, moving averages, and
volume data, sometimes a trend line or two. To me, options trading is all about redicting changes in volatility. Here's my basic concept: to make money trading anything, you have to predict something. Generally, options traders believe that predicting volatility is more reliable than predicting the price movement of stocks. Of course, if you feel comfortable predicting volatility and price changes, the potential gains could be much greater.
Q) Peabody coal (BTU) lists options with 2 different symbols for the same expiration date and strike price, (PWU & BTU). PWU root options are trading at a higher price than the BTU root options. If I buy BTU and sell PWU at a higher price, will they cancel at expiration leaving me with a profit?
A) Sorry, it's not that easy. In Oct 2007, Peabody Energy (BTU) spun off Patriot Coal (PCX) to existing shareholders with one share of PCX for every 10 of BTU owned. The deliverable shares for options trading with root symbol BTU are 100 shares of BTU stock. The deliverable for shares trading with the PWU root is 100 shares of BTU stock plus 10 shares of PCX stock. That's why the equivalent options with the PWU root are trading at a higher price than the BTU root options. They are not equivalent and will not cancel at expiration.
I'll be back in 2 weeks, hope you enjoy my vacation!
As always, if you have any questions about my articles, have suggestions for future topics, or want more information about our options mentoring program, feel free to email me at: sfreifeld@tradingacademy.com or call me at: (888) OTA-2580 ext. 2010.
11. Know Thy Options!
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Stan Freifeld comes to us from the Floor of the American Stock Exchange where he traded options for his own account from 1994-2001. He was a Market Maker for the options on several popular equities including Dupont, Schering Plough, Walgreen's, CBS, U.S. Surgical and Biovail.When he is not trading or thinking about trading, Stan relieves his stress by playing competitive squash, competing in local road rallies with his Ferrari Cabriolet and tutoring local high school students for the SAT's. The bottom line is that Stan, a long time MENSA member, is an engaging teacher with an extraordinary background in options trading and risk management. He is helpful and patient by nature and equally at ease with all levels of traders, from complete novices to advanced pros and academics. He'll be happy to teach you to trade!