Step #1: Answers
1. C. 8
The quarter is most likely to go to the center. That’s where, if calculated, the probabilities would show the highest percentage chance. The end bins have the lowest percentage chance of seeing the quarter.
2. A. 1
Plinkois a probability game where the largest prize will be awarded if the quarter lands in the bin with the lowest probability of success.
3. B. A Normal Distribution Curve
Normal Distribution Curves have more outcomes squeezed into the center of the curve. It resembles a triangle with the sides squeezed toward the middle. We’ll dig further into theses curves at a later time. These are all examples of a Normal Distribution Curve:
4. B. 50%
Generally speaking, the probability of going up or down is about 50%. There are a few unique situations that might change that; however, 50% will be your best choice most of the time.
Calls give you the right, but not the obligation, to buy a stock at a certain Strike Price until the Expiration Date.
6. Call Value at Expiration = Stock Price – Strike Price (If greater than 0, otherwise 0)
7. For Call Options:
ITM Stock Price > Strike Price
ATM Stock Price = Strike Price
OTM Stock Price < Strike Price
When you own an option, whether Call or Puts, you can sell it at any time during market hours or hold it until expiration. The price of that option will be determined by the market. You can find those prices on an Options Chain (you will see and get comfortable with an Options Chain in Step 4).
9. B. The Options Premium
The price you pay/receive to buy/sell an option is called the Option Premium. While the Options Value is generally synonymous with the Options Premium, the distinction is that the Option Premium is the actual dollar amount you receive or pay for an option.
On occasion, especially near expiration, you may choose to buy/sell an option slightly higher/lower than the option value. (Further explanation will come in a later chapter on Executing Options)
10. C. $125, $115, $105.
Since they are all Call Options in January, we only need to focus on the Strike Prices. Given the same expiration, the lower the Call Option Strike, then the higher the value. In this case, the $105 Calls have the highest value and the $125 Calls have the lowest value. It may help to make an assumption that the stock is $100. If the stock is $100, then the $125 Calls have the lowest chance of being ITM and so they are valued the least. Or simply, the “Lower Strike” Call Option is worth more because it gives you the right to buy a stock at a cheaper price.
11. Put Value at Expiration = Strike Price – Stock Price (If greater than 0, otherwise 0)
12. For Put Options:
OTM Stock Price > Strike Price
ATM Stock Price = Strike Price
ITM Stock Price < Strike Price
Given the same Expiration Date, a higher strike Put Option is alwaysmore valuable than a lower strike Put Option. The “Higher Strike” Put Option gives you the right to sell the stock at a higher price; therefore, it should be worth more.
14. C. $100, $105, $115
Since they are all Put Options in January, we only need to focus on the Strike Prices. As stated in problem #12, the higher strike Put Options are the most valuable. The lower strike put options are the least valuable, they are furthest OTM with the least chance of becoming ITM.
A Call Option gives you the right, but not the obligation, to buy the stock at a certain Strike Price until the Expiration date. The further OTM that the Strike Price is from the stock price, there is a less likelihood that the stock will reach that Strike Price. If you think about a Normal Distribution Curve around the stock price and where the stock is most likely to end up (black arrow lines), then you can see that the stock is more likely to end up above Call Strike #1 (in the diagram below) than Call Strike #2, given the same Expiration Date.
Given the same type of option (Call or Put) AND Strike Price, longer-dated options on a particular stock are always more expensive than shorter-dated options on that stock. (This assumes “American-style options”, the most common options, which will be explained at a later time.) More time equals greater chance for the stock to end up ITM. This means that the Normal Distribution Curve widens out with an increase in time (See below).
17. B. Feb, Jun, Dec
The three options are all Put Options and have the same Strike Price. They are differentiated only by their Expiration Date, which makes the options with longer time worth more.
18. There are several answers that could be right depending on a few assumptions you might have made. The point of the exercise was to make you think, and to force you to judge whether time or distance from the stock was more important. The best thing to do with this type of example is to start with what you are sure of and build from there.
We can be sure of this order:
And this order:
Leaving us these two:
We can then place the AUG $100C after the AUG $95P. If we assume that the AUG $100C approximately equals the AUG $100P (Not given to us), then the AUG $100P would be greater than AUG $95P.
If AUG $100C = AUG $100P > AUG $95P
Then AUG $100C > AUG $95P
We can make this assumption because stocks conceptually have a 50% probability of going higher and a 50% probability of going lower, making the ATM Put and ATM Call approximately equal. This isn’t always the case and we’ll discuss in further studies, but right now that is a safe assumption. Using the same logic, we can also place the DEC $100 Calls after the DEC $95 Puts.We’re also making an assumption between the AUG $100C, the SEP $95P, and the DEC $95P. You must weigh one month (and 4 month) extra time vs. 5% difference in strike. The answer is “it depends.” Usually, the AUG $100 C will be more valuable than the SEP $95P, but less than the DEC $95P (More in Step 2). Forgetting about where you placed the post-it, your attempt to try to answer this part of the question should cement the fact that there is a give and take between Strike Price and Time.
Leaving us these three:
Next, we can look at the SEP $105C. These Calls are $5 higher than the Stock Price, while we also have the SEP $95P, which are $5 lower than the Stock Price. With the assumption we made above (regarding the probability of the Stock Price going up or down to be approximately equal), then an extension of that assumption would likely make these two options also approximately equal. In reality, they generally are not. The question this brings up is “Why?” Think about what might make one, or the other, more expensive and we’ll discuss the possible answers in Step 2. For now, you get credit for placing the SEP $105C and SEP $95P next to each other.
Leaving us these two:
Frankly, the answer for these last two post-its will be “it depends.”
When we focus on the FEB $100C there are two issues:
- It has less Time than the other options, specifically the nearest option – the JUN $95P.
- It has a closer Strike Price ($100) than the JUN option ($95)
When we focus on the DEC $75P there are two issues:
- It has a lower Strike than the DEC $95P; but,
- It has more time than most of the other options.
For both options, we must again try to weigh how much time means to the value of the option vs. the differences in strikes.
Under most assumptions, these two options belong at the beginning of the sequence. My answer would be as follows:
Step 1 explained the concepts of Strike Price and Time. This exercise is designed to cement the connection between the two and how they affect option values. Step 2 will get you more answers to some of the issues and questions that have surfaced.