I want to examine how the Law of Large Numbers relates to the Options Chain’s Probability of OTM.

You must be imaginative, strong-hearted.
You must try things that may not work,
and you must not let anyone define your limits…
Your only limit – is your soul.

– Auguste Gusteau (Movie: Ratatouille)


Probability of OTM - flip a coin

Flip a Coin

If I flip a coin, I have a 50% probability that it will land as heads. If I only flip the coin one time and it lands heads, and I stop flipping forever, then I can say, “if I flip a coin, it will land 100% of the time as heads.” That is what I saw.

Consider then if I flip the coin 100 times. Even if the first flip lands heads and the second flip also lands heads, after the 100th flip, the resulting ratio of heads to tails will be reasonably close to 50/50. Should I continue flipping the coin 1,000 times, the results will be much closer to 50/50 than by flipping just 100 times.

The more I flip the coin, the closer to an exact 50/50 ratio. So after a million flips, the fractional difference will be minuscule. That’s the Law of Large Numbers at work.

Can I rely on the Probability of OTM

Probably – to my ruin.

The probability theory of the Law of Large Numbers roughly says that if I perform the same probability test a large number of times, the results will be reasonably close to the probability chosen. So in this journal entry, I want to examine how the Law of Large Numbers relates to the Options Chain’s Probability of OTM.

To make this relevant, say I constructed a Vertical Bull Put Credit Spread where the short leg will have the Probability of OTM at 80% (80% chance of expiring worthless). If I open this spread one time, the position will have a high probability of success. Even entering into the same position 2 or 3 times, I may feel confident I will win each. But after executing 100 Vertical Bull Put Credit Spreads with an 80% probability of OTM, the Law of Large Numbers tells me I will end up reasonably close to winning 80% of the time, and losing 20%.

At first shrug, this seems fair. But keep reading below – because there is a gotcha.

Observed Market Behavior

The Stock Market consists of a bunch of people’s money, all of whom desire to make even more money. With the advent of IRAs, 401Ks, and online trading, a significant percentage of the market’s equity base is from investors following the ‘buy and hold’ strategy. Thus if the market has an intrinsic force-of-nature, then the force of that nature would be to slog its way higher.

Law of Large Numbers
Dow Jones – DJIA – 30 Year Historical Chart

In the past 5-years, the DOW has had sudden drops of multiple-hundreds points (mini-corrections) many times. When these markets’ pull-backs occur, stock prices fall fast and then take their sweet time to slog their way back. From my historical log, they seldom recover in time to save my Options Spread. Without a Conditional Trailing Stop Limit exit strategy, I tended to hit Max Loss most of these times.

So I need to construct my spread configurations to slow down the rate of max loss.

Critical Revelation

Consider this pretend Vertical Bull Put Credit Spread:

DIA: 260p/250p  – Open 09/08/20 – Expires 10/02/20 – Premium=$1.35

  • Short-Strike price of 260 has a Probability of OTM = 73%
  • Long-Strike price of 250 has a Probability of OTM = 82%
  • Max Gain = $135, Max loss = $865, ROR = 15.6%

Suppose I entered this pretend position once a month for twelve months. Based upon the Law of Large Numbers, this position should expire worthlessly 8 times for a profit of (8 * $135 = $1,080). It should also suffer max loss 2 times for a loss of (2 * -$865 = -$1,730). The other two will also be a loss but less than -$865.

For the year, this strategy will have a net loss of somewhere between -$650 and -$2,595.

Combining the Law of Large Numbers and the Probability of OTM, this strategy alone is foredoomed to lose from the get-go. NOT GOOD!

Manage the Rate of Max Loss

Having 8 of these trades expire worthlessly is good, but I cannot have 2 or more hit max loss. Hitting max loss twice will make my effort negative for the year. So my income for my Options training requires a way to exit losing positions before it hits max loss.

Managing max loss requires having an exit strategy. And I am chagrined that I did not have one until last month, and I still feel my exit strategy is lacking. I need to systematically exit any losing positions before it gets halfway to max loss while keeping max gain for those I win.

If I can exit a losing position before it gets halfway to max loss, I can turn around a -$650 losing process to a consistent profit. It’s not a loser, but neither a golden egg-laying goose either.

Lessons Learned

When considering the Law of Large Numbers in conjunction with the Probability of OTM, I must reason that the strategy of only trading Vertical Bull Put Credit Spreads for income is, at best, like a trip to a casino. When depending on this strategy alone during a year like 2020 (politicized pandemic plus an election year crisis-mongering), I can’t imagine any more losing scenario.

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This Week’s Market Sentiment

(As of 09/07/2020)

This Market Sentiment is as of the start of my trading week. This analysis is typically completed by midday Monday morning, and I will use it to help guide my trading decisions for this week. By the time this journal is published, it will be a week old.

VIX – Broad Market Volatility:

VIX = 9-Day SMA Jumped to 26.2 from 23.5 last week.

The VIX is an emotion-gauge for the general investing population. It is thought to be driven by the Marketeers’ current level of greed or fear. As a one-month forward-looking volatility matrix, it is not designed to tell us which direction the market will be going, but more of how fast it can get there.

A VIX of 15% is assumed to be a market at rest. But since the intrinsic nature of the Stock Market is to move up, a VIX closer to 15% or below will have an innate tendency to rise.

CBOE Market Volatility Index - Law of Large Numbers
CBOE Market Volatility Index

Last Thursday and Friday, the sharp sell-off shot the VIX to a high of 38% on Thursday morning. And what is even scarier is the current VIX flew above the 200-Day SMA. There was a slight recovery on Friday, but not enough to declare if this a new trend or a blip.

I did not change the trend channel to adjust to last week’s trajectory change because I wanted to see what happens Tuesday and Wednesday. But this cliff-hanger may be enough to hold back entering into new positions until the trajectory can be identified.

Put/Call Ratio:

9-day SMA (all OCC options): continued mostly flat at 0.57 from 0.60 last week.

Put Options are frequently used as protection against existing investments falling. When the ratio between Put Options bought versus Call Options bought is above 1, then this is an indicator that the Marketeers are buying insurance to what they may see as declining Markets. Conversely, when the Put/Call Ratio falls below 1, then there is a general sense that the broader Markets will increase, and more investors are buying more than selling.

Daily Put/Call Ratio for all OCC Options - Law of Large Numbers
Daily Put/Call Ratio for all OCC Options

Following suit of the selloff last week, the Put/Call Ratio shot up over the 9-Day, 50-Day, and even the 200-Day SMA. This clammer for protection may be the first step in a significant market pullback.

But to keep a perspective on last week’s shakedown, it should be noted that the Marketeers continue to be buying more Call Options than Puts by keeping the ratio well below 1.0. So, through this snapshot in time, investors still see the Bull continuing.

The trend of buying protection may just now be starting, or it may just be a knee-jerk reaction to a tech sector adjustment. I will wait until after the first trading day (or two), to see if the trajectory continues.

Consumer Sentiment Index (CSI):

The Consumer Sentiment index hopes to take a broad snapshot of what we all feel to be the direction of the U.S. economy. It measures how consumers feel about their personal financial situation and compares that to what they believe is happening to others throughout the country. The survey contains 50 questions and is conducted to more than 500 people each month.

A low rating is a general dissatisfaction with our current management of U.S. economic policies. This dissatisfaction will imply that something has to change.

A high satisfaction rating suggests approval of the current policy management and implies market stability.

United States Consumer Sentiment - Law of Large Numbers

The U-M’s Consumer Sentiment Index remains unchanged as of this writing.

National economic numbers continue to be positive as they are released. Unemployment dropped four months in a row to 8.6, the US added 1.4 million jobs in August, and retail spending increased significantly.

But on the negative side, the national debt will be higher than the US GDP for the first time since WWII.

I still believe that this indicator will continue to inch up through September and October, but will remain relatively low until after the election. The future mechanics of our economic engine is very much in question. So I would expect most those who participate in this survey to continue to feel unsure about the future.

Market Indexes:

DOW = 28,133 – Down 1.8% from 28,654 last week.
S&P 500 = 3,427 – Down 2.3% from 3,508 last week.

The S&P 500 is a stock market index that tracks the 500 largest companies in the U.S. This index represents about 80% of all the capitalization for the country. The S&P is widely considered the best indicator of how all the U.S. markets are performing.

Daily S&P 500 Index - Four-Months
Law of Large Numbers
Daily S&P 500 Index – Four-Months

This chart seems to show the selloff last week to be a reaction to the general market exuberance that preceded it. There appears to be a similar pattern back in June.

The telling story will be this coming week if the selloff continues or resumes its 4-month trend. It is conceivable that a short-term correction (profit taking) may happen over the next week or two, sending the S&P 500 value towards the bottom or below the trend channel.

Geopolitical Tree-Shakers (GTS):

  • Election year politics exacerbating the economy and COVID fears
  • US national debt at $27 trillion – will be bigger than GDP next FY
  • Are we in a Tech-Bubble
  • Continued sham unrest across the country
  • Stalled negotiations over a Stimulus Package
  • Agreement on a continuing resolution for the Federal budget
  • Better-than-expected economical news
  • Narrowing polls for the president election

Riot-fatigue is rising across the country and is starting to backfire on the Democratic strategy to send Trump packing. Suburbanites realize that the city and government leaderships are deliberately giving oxygen to this unrest effort, mainly via a Blame-The-Police movement. All of this is pushing the momentum for this November election towards the GOP.

My sentiment for this coming week:

The past two months’ stock market rally abruptly shifted into reverse as of Thursday of last week and sold off sharply through last Friday. The question to ask is, does the end-of-week shakedown signal the start of a new 10% correction? Is the Tech-Bubble bursting?

Of my five indicators above, the VIX, P/C Ratio, and CSI are screaming a trajectory change. But the S&P 500 depicted more of a mini-corrective movement due to the index adjustments made after Apple and Tesla’s stock splits.

GTS is mainly old news, but the national debt projection for the next fiscal year may be what threw the Marketeers into a defensive tizzy.

These five indicators show that there is no consensus over the short-term market projection. A continuing selloff is highly likely when the markets open on Tuesday, but that could be mostly the queued up orders set during the weekend.

For this week I will observe more than participate. If the longer-term trend does not resume, I may just sit this week out.

This week, I will focus on:

  1. Limit the max risk per trade to < $1,000.00
  2. Short Stike Price to be 4% – 5% below the current underlining’s price
  3. Keep the week’s total dollar risk < $1,000.00
  4. Keep the overall dollar risk to be below $3,000
  5. Will focus on mid-term trades: 4-5 weeks
  6. Credit spreads only (need positive cash flow for psychological reasons)
  7. Will consider only Bull Spreads
  8. Set Conditional-Trailing-Stop-Limits

Profit and Loss Statement

(As of 09/11/2020)

YearMonthWeek #
Beginning Account Balance$9,000.00$3,283.24$3,181.11
Deposits (Div. & Int.)$38.52$0.02$0.00
Withdraws (paycheck)-$2,125.24$0.00$0.00
Premiums on Open$5,277.00$248.00$0.00
Premiums on Close-$8,850.00-$347.00-$0.00
Fees Paid (total)-$158.12-$2.10-$0.00
Ending Account Balance$3,181.10$3,181.10$3,181.10
Total Gain/Loss-$5,470.84-$102.13-$0.00

Realized Profit by Strategy

YearMonthWeek #
Vertical Bull Put Credit Spread-$3,713.45-$172.15$0.00
Vertical Bear Call Credit Spread-$182.79$0.00$0.00
Vertical Bull Put Debit Spread$0.$0.00$0.00
Vertical Bull Call Debit Spread-$66.83$0.00$0.00
Icon Condors$0.$0.00$0.00
Cover Calls

Schedule for this Week

Goals for this week: (09/08/20 – 09/11/20) (Week 37)

  • Max dollars at risk (for the week) < $1,000.00
  • Max dollar risk per trade (new trades) = $1,000.00
  • Update Trading Log as trades occurs

Entry Rules for Vertical Bull Put Credit Spreads:

  • Expiration date set at <= 4 weeks?:
  • Probability of OTM > 60%?:
  • Short-Strike price (Head Room) >= 4.0% below the current price?:
  • Dollar risk per trade <= $1,000.00?:
  • Total dollar risk <= $3,000:
  • Put/Call ratio below 1.5, or flat, or falling over that last 2-3 weeks?:
  • The Trend-Channel is Bullish?:
  • Short-Strike price below the trend channel at expiration?:
  • The current price within the bottom 1/2 of Bull Trend Channel?:
  • The current 1-week or 2-week trajectory bullish?:
  • 9-Day SMA above 50-Day SMA?:
  • The current price above 9-Day SMA?:
  • Set a GTC Conditional Trailing Stop Limit (CTSL): (see screenshot below)


  • Determine/update this week’s market sentiment section
  • Calculate/record Put/Call Ratios for all stocks on the watch list
  • Review/tweak Trend-Channels for all stocks in the watch list
  • Set target expiration dates for all options as follows:
    • Bull Credit Spreads: Oct 02 (<4 weeks)
  • Look up Ex-Dividend dates for positions in/approaching ITM (MarketWatch/Calendar)
  • Stage possible trades for all watch list stocks by 10:00 AM
  • NO TRADING BEFORE 10 AM. (Let the Market find its direction after the weekend.)
  • Watch one Webcast or take one online mini-course to be completed by Friday.

Tuesday – Thursday:

  • Review how yesterday’s staged trades moved. Adjust premiums to take advantage of movements.
  • Submit a couple of Spreads, but keep a close watch. If one is accepted, cancel the others (we want only one new active trade per day).
  • Be mindful of Entry Rules.


  • Review the total technical dollars at risk for this week. If significantly below $500, then submit additional spreads if prudent.
  • Update and post weekly journal (this blog) with any lessons learned or strategy changes.


This Week’s Trade Activity

(As of 09/11/2020)

Spread Count Summary:

YearMonthWeek #
Vertical Bull Put Credit Spread6520
Vertical Bear Call Credit Spread1200
Vertical Bull Put Debit Spread000
Vertical Bull Call Debit Spread700
Iron Condor000

Current Dollars at Risk:

YearMonthWeek #
Vertical Bull Put Credit Spread$1,767.00$872.00$0.00
Vertical Bear Call Credit Spread$0.00$0.00$0.00
Vertical Bull Put Debit Spread$0.00$0.00$0.00
Vertical Bull Call Debit Spread$0.00$0.00$0.00
Iron Condor$0.00$0.00$0.00
Total Dollar Risk$1,767.00$872.00$0.00
Max Risk Allowed$3.000.00$1,000.00

New Trades Opened This Week

(09/08/2020 – 09/11/2020)

No new positions this week.

Trades Currently Cooking

(As of 09/04/2020)

See Conclusion for Exit Strategy tweak.

SPY: 333p/323p  – Open 08/26/20 – Expires 09/18/20 – Max Gain = $105.00
(Vertical Bull Put Credit Spread)
At Open: Prob. OTM=75.5%, Head Room=-4.1%, Max Loss=$894.00, IV%=19%
Now: Prob. OTM=80.3%, Head Room=-5.0%, IV%=22%

Conditional Trailing Stop Limit order

DIA: 273p/263p  – Open 09/01/20 – Expires 09/25/20 – Max Gain = $128.00
(Vertical Bull Put Credit Spread)
At Open: Prob. OTM=72.1%, Head Room=-4.3%, Max Loss=$871.00, IV%=21%

Conditional Trailing Stop Limit order

Trades Closed This Week

(As of 09/04/2020)


The NASDAQ went through a +10% correction via the abrupt decline of those tech stocks that enjoyed an exuberant run-up over the past few months. Not wanting another premature exiting of another position, I canceled both of the Conditional Trailing Stop Limit orders for those positions still cooking.

For an Exit Strategy tweak, I reentered those CTSL with the Conditional activation price 2 strikes below the Short-Strike, instead of activating at the Short-Strike.

The reasoning is to give time for the position to recover from a temporary price adjustment. But if the price of the underlying has fallen more than 2 strikes below the Short-Strike, then deem it too far gone and exit before one half of max loss (hopefully).

It is continuing to be apparent that I still need a better strategy of managing open positions. I’ll spend the next couple of weeks on the thought.


Even though I have tried to make it clear that this blog is my journal, documenting my trek into Options Trading, it has been suggested by others that I, nevertheless, include a general disclaimer. So here goes…

“This blog and the information contained herein is not intended to be a source of advice or analysis concerning the material presented. The information and/or documents contained in the blog do not constitute investment advice.”

Contact Me

To contact me or ask me a non-post related question, please use this form. If you want to comment on this post’s topic, please use the “Leave a Reply” box below so it can be attached to the post for future reference. – Thanks

Options Trades by Damocles
Options Trades by Damocles