theta is the measure of how much an option’s price decays for each day of time that passes.
That means if the S&P index is at 1300, our theta is +80, and the market traded flat and closed at 1300, we would have made $80 for the day.
delta is the amount by which an option’s price will change for a corresponding one point change in price by the underlying entity…. (I don’t want to get too technical).
Basically delta will help us know if we want our underlying, the S&P index, to go up or down. If our delta is +30, then it’s as if we owned 30 shares of the S&P so we would want the S&P to move up. Conversely, if our delta is negative, then we would profit from the index moving downwards.
Back to the example where our delta is at +30, we know we want the S&P index to move up. But what happens when it does move up? Well, our delta will decrease. Eventually it will reach an optimal point where our delta will be 0.
Ideally we want our delta to be zero, delta neutral. At this point our unrealized profit is at its maximum and our risk is at a minimum.
Mathematics and statistics are important to Texas Holdem poker and online option and stock trading because they help you better understand the risk and reward of the situation. Knowing the risk and reward in turn will help you gain realistic and Healthy Expectations. This way when things are going well, you will not go crazy and expose yourself to too much risk. Conversely if things are not going well, you will not give up.
Here’s is a Texas Holdem poker example.
My worst string of losing AA was 7 in a row.
We will assume that there was only a 20% chance of losing each of the 7 pocket aces. This means statistically the chance of losing seven AAs in a row is (20%*20%*20%*20%*20%*20%*20%) = .00128% or 1 out of 78,125. Does this mean it’s wrong to play AA? Of course not, you still welcome those situations because you know that your Expected Value is positive and that you will win in the long run.
Some people would call this bad luck. But it’s just statistics. If you play 10 tables at a time at 50 hands per hour for 4 hours a day, that equals 2000 hands a day. You do this for 2 years (we’ll use estimate 300 days/year) then you would have played 600*2000 = 1,200,000. With that knowledge, it is no longer surprising that a situation that happens only 1 out of 78,125 occurred. (I’m just surprised I’ve never lost eight AAs in a row! j/k. Knock on wood.)
Our Texas Holdem poker-like option positions are the same. Even though the winning percentage is currently 100%, 3 for 3, we know that there will come a day when we will take a loss. In fact, we can expect a losing month for every four winning money if our winning percentage is 80%. But that’s okay as long as the money we gain from the four winning month is greater than the loss we take on the losing month.
Looking at the math and stats will give a lot of people headaches. But knowing the mathematics and statistics when so much money is on the line will help you sleep better at night.
An option is the right to buy or sell an underlying for a limited period of time.
- a stock option is the right to buy or sell a stock for a limited period of time.
- an index option is the right to buy or sell an index (like the S&P500) for a limited period of time
There are thousands of stocks and indexes to pick from and they all exhibit their own unique characteristic, such as risk, reward, volatility, etc….
Since this site aims to educate and show results, we will keep things simple our two option variables constant. Our first variable, the underlying, will be the S&P 500 Index Option. The second variable, time period, will be approximately 2 month out (So in June we are considering the different option contracts of August).
The other two other option specifications, type and striking price, were covered in a previous post.
If you want to make a fortune trading stocks and options online, you will need to have a good understanding of volatility.
volatility - measures the amount the underlying is expected to flectuate in a given period of time.
So, high volatility means the price of the underlying stock or option can change dramatically in either direction in a short amount of time. Low volatility means the change in price is not dramatic in a short amount of time.
If you are buying options, you usually want to buy when the volatility is low. This is because the option is cheaper when the volatility is low. Even if the price of the underlying doesn’t move and the volatility suddenly increases, the price of the option will go up. In fact you can even trade volatility by trading the symbol VIX.
If you are selling options, the opposite is true. You want to sell the option when volatility is high so you can sell a higher price.
options usually come with four specifications:
- underlying stock name
- expiration date
- striking price
- call or put
Here is an option position I recently sold and blogged:
Option Trading Mathematics
We entered an Index Option position today.
1175/1200 - 1375/1400 x2
Max option trading reward : $456 if 1200 - 1375 (83.41%)
- underlying stock/index name
- not included because we only trade one underlying (S&P 500)
- expiration date
- This is the October option which expire on Oct 20th
- striking price
- 1175/1200 - 1375/1400 x2. There are 4 striking prices and the x2 means 2 contracts of each.
- call or put
- the lower two numbers are put options and the two higher numbers are call options. In this case 1175/1200 are puts options and 1375/1400 are call options.
- additionally 1200 and 1375 were sold. 1200 sold for $4 and 1375 sold for $1.6. What this means is if the S&P 500 index stays between 1200 and 1375 by Oct 20th, we would make $5.6×100 sharesx2 contracts = $1120.
- 1175 and 1400 were bought for protection. This helps limit the maximum option trading risk . We paid $2.6 for the 1175 and $.7 for the 1400 for a total of $3.3×100 shares x2 contracts = $660.
- $1120 - $660 = $460
We are looking to establish positions with an 70 - 80% winning percentage. 80% is similar to holding AA in Texas Hold’em Poker while your opponent is holding a lower pair. Being in this position makes Texas Hold’em players very happy as this is considered a dominating position.
When we set up an option position, we can adjust how much risk and reward we want in our position. We want our winning percentage very high because of the length of time involved, 30 - 80 days.
In Texas Hold’em poker we welcome any situation as long as the Expected Value is positive because we play lots of hands in a short amount of time. In the world of option trading we want to make sure we have a position Expected Value AND a high winning percentage.
Risk: How much of our portfolio do we want to put at risk? We need to consider what happens when we have a losing position. If we had $1000 and we risked $500 (50%) and lost it, we would have $500 left. In order for us to get back to break even our $500 would have to make another $500 (100%), very difficult. But if we limit each of our position to 1%, a loss can be recovered with only a 1.01% gain.
- If you lose x%, you will need to gain y% to recover from your lost
- -1%, +1.01%
- -2%, +2.04%
- -9%, +9.89%
- up to here the two percentages seem pretty even with a ratio that’s close to 1:1.
- -10%, +11.11%
- -11%, +12.36%
- -12%, +13.64%
- in this zone the gap between the two percentages is more than 1% and growing.
- -13%, +14.94%
- -15%, +17.75%
- -20%, +25%
- -30%, +42.86%
- -50%, +100%
- as the risk amount continue to increase, it becomes increasingly impossible to recover the loss.
We will consider 1 - 9% as safe, 10 - 12% as acceptable, and anything above 13% as dangerous.
Reward: Next we need to consider how much reward we seek to gain. If we wanted to be super safe and risk only 1% of our portfolio on any given position, we would divide our portfolio into 100 seperate lots. With 100 lots we are only risking 1% of our portfolio. With this low risk comes, unfortunantly, low rewards. If we had $100,000, only $1,000 would be put to work while $999,000 would be collecting dust. Even if the $1,000 appreciated 10% that would only increase our total portfolio by $100. On the other extreme if we risk 50% of the portfolio, we would divide our portfolio into 2 lots. This means $50,000 would be going to work for us and a 10% gain would equal a $5,000 gain. The less lots we break our portfolio into, the more effecient and rewarding it becomes. (Unfortunantly, we previously demonstrated why 50% is too much risk).
- If you risk x%, you would have to break your portfolio into y lots
- 1%, 100
- 2%, 50
- 3%, 33
- 4%, 25
- 5%, 20
- 6%, 17
- as we increase our risk by 1%, the number of lots drop at a quick rate. This also means the effeciency increases at a quick rate. We only need to increase our risk by a little and our reward climbs by a lot.
- 7%, 14
- 8%, 13
- 9%, 11
- 10%, 10
- 11%, 9
- 12 - 13%, 8
- 14 - 15%, 7
- 16 - 18%, 6
- 19 - 22%, 5
- in this group we have to increase our risk in order for our lot number to decrease. This means our efficiency is increasing at a slower rate. The correlation between the risk and reward are fair. A little more risk equals a little more reward.
- 23 - 28%, 4
- 29 - 40%, 3
- 41 - 50%, 2
- in this group we need to increase our risk by a lot just to decrease our lot by 1. This means we need to take on a lot more risk for a little reward.
Since this is speculation money (money one can afford to lose), one can afford to be more aggressive. We will consider the first group 100 - 17 lots as too conservative, the second group of 14 - 5 lots as acceptable, and the last group of 4 - 2 as unacceptable because it would give us great rewards but way too much risk.
Balance: So from the risk point of view we want to have 10 - 12% of risk and from the reward point of view we want 14 - 5 lots. 8 - 10 lots satisfy these two conditions. So our initial capital will be divided into 8 lots and gradually increased to 10, and up to a max of 14.
Expected Value (EV) - Texas Hold’em Poker Expected Value - n. The sum of all possible values for a random variable, each value multiplied by its probability of occurrence.Let us first apply this to Texas Hold’em Poker. The game starts with each player being dealt TWO cards.
- We will pretend that we have the strongest starting Texas Hold’em Poker starting hand, AA.
- We will also assume that our opponent was dealt the second strangest Texas Hold’em Poker starting hand, KK.
Because these hands are the two best starting hands, players often end up betting all their chips against each other (a.k.a. All-In). When this happens the KK opponent will only have a 18.55% chance to win, at best, while the player holding AA, will win 81.06% of the time. If we bet $1000 against each other our Expected Value formula will look like:
EV = (Winning Amount x Winning %) + (Losing Amount x Losing %)
EV = ($1000 x 81.06%) + (-$1000 x 18.55%)
EV = $810.6 - $185.5
EV = $775.1
This means that in the long run you will gain an average of $775.1 every time this situation happens.
In Texas Hold’em poker, you can sit in with $5, $10, $25, $50….even $2000, but
- There is a limit to the availability of high limit games
- Playing at higher limits equals harder competition (less positive EV situations)
- Time consuming - you only get dealt AA once every 225 hands
Expected Value (EV) - Stock or Index Option Trading Strategy
Stock or Index options allow us to create positions that are similar to having AA in a Texas Hold’em poker game but
- Allow us to trade at a much higher limit. In fact the minimum to establish a S&P Index Option position is approximately $2000.
- Increased limit does not decrease positive EV situations because of the size of the stock and option market. A $20,000 position will have the same risk/reward ratio as a $2000 position.
- Not time consuming. You can trade options on your own schedule.
