BONUS – Step 1: Value
After completing the “7 Must Know Concepts Before Learning Options”, you’ve exercised your mind to take in new concepts. Those concepts start here. This class is about keeping it simple, which means we’ll avoid some of the smaller details in order to focus on the bigger picture. Getting lost in the details at this stage will just lead us to trouble. We’re going to define and establish a fundamental understanding of the following:
Throughout this process, I’ll be asking you questions. It’s important that you answer each, and push yourself to think. Push yourself to understand the “Why?” Why is that the answer?
We’ll finish this class with a game. The game will ask you to rearrange a series of options into their appropriate order based on what you’ve learned. Step 1 is designed to accomplish 4 things:
- Challenge you;
- Lead you to ask better questions;
- Give you confidence; and,
- Encourage you to learn more.
I’ll leave you as always with Q&A to work through for review. Let’s begin.
The game of Plinko comes in many variations and is often called by different names. Regardless, the game is generally played the same way.
As a kid, Plinko was always enticing. All you had to do was place a quarter in the opening slot and watch it fall down several levels. If it fell in one of the end slots, then you would win a huge prize - A large stuffed animal. What a great PAYOUT!
Even if it fell in the few slots next to it you could win a smaller stuffed animal. In this area, you would get a pencil for trying. And here – well, you’d get a smile and a: “Want to try again?”
Now, here’s a question: Do you think it’s easier to have the coin land here or here?
Of course, in the middle section. That was an easy question. But why and how did you get that answer?
Some may know the mathematical answer. However, most will assume that if there’s a bigger prize at the end slots over the middle slots, then it must be harder to land on the end slots. That’s good logic – your process went backwards from the PAYOUTS to get the answer.
You most likely did it as well when I asked you this question: Who’s considered the worst team?
You were able to see the large payout for every $1 bet Philadelphia offered. $650 to 1!
And you could assume that Las Vegas would only pay that much because the Philadelphia 76ers had little chance of winning. Now think about answering this question without seeingthe payouts – that would be a lot more difficult.
Our minds have been programmed to think this way - judging circumstance by payout. One thing that makes options confusing is that this type of thought process doesn’t necessarily present itself so clearly. For this reason, I want you to look at the Plinko question forward– essentially without making assumptions from the resulting payout.
When you place the quarter in the opening slot, at the first peg it will go 1 of two ways: left or right.
At the next peg, again left or right. And at the next peg, left or right. All the way until it reaches its final position.
While the quarter can take many different paths, here are a few:
These are the only 2 paths that get the quarter to the end slots. To find out the chance of a quarter landing on this end slot needs the following understanding:
At each level, there is one positive outcome out of two total possible outcomes – or ½.
In order to reach the end peg, you would need to multiply ½ by itself for each level. In this case, there are 13 levels:
½ x ½ x ½ x ½ x ½ x ½ x ½ x ½ x ½ x ½ x ½ x ½ x ½ = 1 / 8,192
That’s 1 time in 8,192 total times, or 0.01%. You aren’t going to win that stuffed animal often!
For the other bins you can add all the different ways to reach the bin to find its probability. We won’t be doing that. What you’ll find is that the results of playing a lot will look something like this:
Most of the quarters will be in these middle bins. Only very few will be in these end bins. So, to answer our question, it is easier to have the quarter land here because of the math embedded in the game.
We’re not done.
The piles of coins eventually produce a result that can be graphed like this. Not like this. No! There is some curvature.
This is called a Normal Distribution Curve.
Remember this concept I gave you regarding a Market Stock Price?
You can see the % probabilities here multiplied by some gain or loss. Also notice that it looks like a triangle distribution up and down. Well that wasn’t exactly correct. It’s more like a Normal Distribution Curve!
This means that it’s more likely for the stock to land somewhere in here, rather than out here. Let’s move on.
Options are essentially a contract between two parties where each side agrees to the terms. There are two types of options. Calls and Puts. We’ll start with Call Options.
When you hear “Call option,” I want you to immediately think about the upside– risk to the upside.
With Calls, one party has the right (but not the obligation) to buy the stock at a specific level until a specified date. The other party agrees to sell the stock if the first party exercises his right to buy it. That specific level is called the Strike Price. And the date is called the Expiration Date.
Assuming that we own a Call option with a $105 Strike Price on XYZ stock ($100), this means that we have the right to buy the stock for $105 until the expiration date no matter where the stock is at that time! Even if the stock goes to $150, we can exercise our right to buy the stock for $105.
Now, how much would the option be worth at expiration with the stock at $150?
Let’s think about it.
I want you to get a post-it and write down the following: “I have the right to BUY XYZ stock for $105.”
Now assume that the stock is trading in the market for $150, meaning you can buy or sell it there. With the stock at $150, would you buy the stock at $105?
Of course, you would. You’re able to buy it at a discount. Note that when the stock price is above the Call Option’s Strike price, the option is said to be In-the-Money (ITM).
Now imagine I was your counterparty for this option written down on that post it. You would come to my office hand me the post-it and pay me $105 for the stock. I would give you 1 share of XYZ stock. You could hold the stock, or you could immediately sell it in the market place at $150.
What would your profit be? $45.
This is also the value of the $105 call option.
The Call Value at Expiration = Stock price - Strike Price (Only if the value is positive)
Also note, when the stock is ITM (above the strike price with a Call Option), the difference between the market stock price and the Strike price is called PARITY. At expiration, Parity equals the value of the Call option.
So, if the stock price is at $135 (with a $105 Call Strike), then what is parity? $30.
How about $125? $20. Good.
How about $100? $0.
Remember, Parity for a Call option exists only if the stock price is above the strike price.
Which leads us to a good point. If at expiration, the stock price is anywhere below $105, then the $105 Call option is worth $0. Why?
Well, if you have the right to buy XYZ at $105 and it’s trading at $90 in the market, then would you call me up and exercise your right to buy stock from me?
If on expiration you want to own the stock then you would buy XYZ stock in the market for $90 and rip up our contract because it would serve you no purpose. In this example, the stock is below the Call Option’s strike price. The option is “Out of the money” (OTM). Note that, If the stock price was equal to or very near the strike price, then we call that “at-the-money” (ATM).
Ok, now let’s look at another Strike – the $115 Call option.
What is the value of the $115 Call option at expiration if the stock goes to:
Now, holding that post it in your hand. Can you see that it has value?
If you and I were in that contract that piece of paper places me at risk of losing a lot of money in the event XYZ stock price went much higher?
Even though I know you’d be very happy to have that post-it for free, I wouldn’t sign that contract unless you paid me some upfront amount for the risk I was taking. How much?
Frankly I’m not sure but definitely some amount. In order to have the ability to buy XYZ stock at a certain price (Strike Price) by a predetermined date (Expiration), you will need to pay me a fee, the Option Premium.
Now, here’s a question.
Which option has a greater value – The XYZ $105 Call Option or the $XYZ $120 Call Option?
Whatever your answer is, make sure you have a reason “why” that’s your answer.
Let’s look at what the two options are worth at expiration with different stock prices:
With the stock at $150 the 105 Calls are worth $45 ($150-105) and the $120 Calls are worth $30 ($150-120).
With the stock at $130, the 105 Calls are worth $25 (130 – 105) and the $120 Calls are worth $10 (130-120).
At $100, both options are worth 0 because the option is OTM.
We can actually think about these values as payouts at expiration.
Now, if I was offering you one of these options for free, which option would you rather have?
Clearly the $105 Call. Right?
At each level it outperforms the $120 strike option.
So yes, the XYZ $105 Call has a greater value. In other words, you’ll need to pay me a higher upfront options premium in order for me to sell you the option.
If we added another strike, we can do the exercise again. Let’s add the $110 Calls:
These are the values for the $110 with the corresponding stock prices.
$40 at 150.
$30 at 140.
$20 at 130.
$10 at 120, and 0 with the stock at $100.
If I offered these options for FREE, which one would you rather own? Still the $105 C.
How about the choice between the $110 C or the $120 C? The $110 C.
You’ll find that the lower strike Call always has a greater value and a higher options premium.
XYZ $105 C > XYZ $110 C > XYZ $120 C
Notice I didn’t use the words “Expensive” or “Cheap.” XYZ $105 C has a higher premium than the other options, but we don’t know yet if it’s “more expensive.” We’ll get to that at a later time.
Here’s one question many people have:
“If I own this option, can I sell it at any time or do I have to wait until expiration?”
That post-it is a contract between you and I while it’s in your hands. You’re able to sell the contract in the market at any time from the moment we agree on it until expiration. At what price?
Keep that thought but we’re getting ahead of ourselves. Right now, we are focusing on the value of the options at Expiration.
We’ve been talking about Call Options. Now let’s look at Put Options.
With Puts, the buyer has the right (but not the obligation) to sell the stock at a specific level, (the strike price), until a specified date (the Expiration date). The seller of the Put agrees to buy the stock at the Strike Price if the buyer exercises his right.
This means that instead of having the “right to buy” that call options provide, you’re gaining the benefit of being able to sell the stock at a certain level in the event it declines. Even to $0!
You can buy a Put even if you don’t own the stock. Remember, you don’t have to exercise your right to sell the stock, you can just sell the Put back out into the market to someone else. Your decision to exercise or not doesn’t affect the value of the Put.
Puts are about the downside– risk to the downside!
Assume that you own the $95 Put and XYZ stock declines to $70 at expiration. Let’s talk about how much that Put Option is worth.
With the stock trading at $70, you can buy the stock in the market and then exercise the option to sell it (in this case) to me at $95. What would your profit be?
Yes. $25. ($95 you receive from exercising the put contract less the $70 you paid in the market.)
The Put Value at Expiration= Strike price - Stock Price (Only if the value is positive) otherwise it’s worth 0.
Let’s go through a few more examples…
What is the value of the $95 Put Option at expiration if the stock goes to:
$50? $45. (95-50)
$70? The Put is worth $25.
$80? It’s worth $15.
$90? Then the Put is worth $5. (95-90)
Similar to Call options, Parity is equal to the value of the Put at expiration.
What’s the value of these Put Options with the following stock prices:
With the stock at $80, the $70 and $80 Puts are worth $0, but the 90 Puts are worth $10.
At $60, the puts are worth $10, $20, and $30, respectively.
If offered any of these for FREE, which would you choose? The $90 Puts. Why?
Because at any stock price below $90 the $90 Put will outperform the other 2 puts.
You’ll find that the higher strike Put options always have greater value and higher option premiums.
XYZ $90 P > XYZ $80 P > XYZ $70 P
When looking at puts and calls we can gauge which has a greater value by comparing payouts at different levels. But conceptually, we can look at our normal distribution curve around a market price to better understand why certain options have a greater value than others.
Remember, the curve tells us where the stock will land most of the time and where it has the least chances of going. The way OTM Calls and Puts have a much less likelihood of being reached than the options closer to the stock price; therefore, they are worth less.
The $105 Call is worth more than the $115 Call today because it’s more likely that the $105 Call is worth more in the future due to the probabilities of where the stock will land. Notice that the $105 Calls has this much more shaded area than the $115 Calls.
Same goes for the Puts.
The Lower the Put, the less its worth because the probability of the stock being ITM at expiration declines. This can be seen by comparing the shaded part of the Curve between the two strikes – here is the difference. The $95 Put has more.
Now here’s a question for you. What’s the probability of the stock going higher? Or Lower?
For now, let’s just say approximately equal probability. 50% up or 50% down. Keep this in mind when you are comparing calls and puts above and below the stock price. Let’s move on to time…
Options and Time
Let’s think about insurance, specifically about the cost of insurance.
Assume that you’re looking to buy home insurance. The insurance company offers you 3 quotes:
- Home insurance plan for 1 year, Total Cost: $2,000
- Home insurance plan for 2 years, Total Cost: $2,000 (same policy)
- Home insurance plan for 3 years, Total Cost: $2,000 (same policy)
Which one would you choose?
3 should be obvious. You’re receiving the same policy in all three choices but 3 gives you coverage for a longer period of time AT THE SAME PRICE! That’s a no brainer, right?
Time is valuable when you’re looking at buying insurance policies. And time is valuable when you’re looking at options.
We saw how an option’s value can change with different Strike Prices. The value of options also increases or decreases with changes in time.
Let’s take a look…
Assume that we’re looking at two Call options both with a $105 Strike. The only difference is that one option expires in 1 month and the other option expires in 2 months.
Similar to the house insurance example, the option with more time has a greater value.
Let’s dig a little further and solidify our understanding of “Why?”
We’ll start by looking at the normal distribution curve for both time periods. For the 1 month option, the normal distribution curve will look something like this. The stock will most likely end up between here.
And for the 2-month option, the normal distribution curve looks something like this.
Notice that when compared to the 1-month option there are greater probabilities of the stock moving further away from where it starts. It’s this larger distribution of possible prices over time that give the 2-month option a higher probability of a greater future value.
Put Options work in the same way.
Let’s play a game!
Using the concepts learned in this class and the following assumptions,
Today is January 1st
STOCK = $100
The stock has NO dividends and interest rates are 0%.
Do your best to place these nine options in order from least value to highest value.
Use real post-its so you can move the options around.
Try to have a reason why each post-it is in its box.
You will likely have questions.
Write them down.
And don’t get frustrated with unanswered questions, or if you’re having trouble getting the post-its in order.
Questions are good!
It means that you’re thinking.
As far as answers to your questions, I’m sure that I’ve heard most (if not all) of them and I’m positive that they’ll be answered in future lessons.
This game is designed to have you make some assumptions to complete the task.
Write them down.
And just go with it.
The game will force you to try to connect the dots.
Good luck. I’ll see you in Step 2!