Sticking to the Numbers: Navigating the Options Market with Statistical Precision

I'm a quant, through and through.

Almost every decision I make as a trader/investor relies on a strict adherence to mathematical and statistical methods. And it's the main reason I've successfully navigated the markets over the past 20+ years: simply sticking to the probabilities.

Quantitative or statistically-based options trading stands on a fundamental statistical principle – The Law of Large Numbers.

This law dictates that as the sample size increases, or in our context, the number of trades, the expected value, otherwise known as the probability of success will align closely with our predictions. The Central Limit Theorem further reinforces this concept by demonstrating that actual values will converge towards expected values.

However, to apply the Central Limit Theorem, we require a sufficiently large sample size or number of observations, which is where the Law of Large Numbers becomes essential.

You might recall encountering a similar mathematical exercise during your middle school years; the classic coin toss. This example was how most of us were first exposed to the theory of probability.

Consider the Coin Toss Example:

In a series of coin flips, with a coin having a 50% chance of landing on heads or tails, the Law of Large Numbers suggests that over a large number of flips, the proportion of heads or tails should approach 50%, which serves as our expected value. As the number of trades increases, our win ratio should converge towards our expected value of 50%.

However, it's crucial to acknowledge the presence of variance when adopting a quantitative or statistical approach to trading.

Variance Plays a Role:

For instance, when flipping a coin ten times, the variance in the number of heads can range from three to seven. With more observations (coin flips), this range narrows until the overall probability of success stabilizes at approximately 50%. Yet, early on, we may encounter fluctuations known as sequencing risk due to variance.

Sequencing risk implies that despite the expected value being 50%, the actual outcomes may deviate from this, with statistical outliers occurring occasionally. Nevertheless, as the number of observations (trades) increases, the Law of Large Numbers consistently aligns outcomes with the expected value.

Understanding this concept is crucial because, unlike a simple coin flip with a 50% success probability, high-probability trading offers a significantly higher probability of success, typically between 70% and 85%.

When using a high-probability approach to trading through the use of a variety of different options selling strategies, I know that my expected outcome or win ratio will fall within this range (70% to 85%) before entering each trade.

The high-probability approach underscores why many professional options traders often continue trading long after retirement, whereas stock traders, with at best a 50% probability of success, call it quits much earlier. The difference lies in the options strategies ability to create a high probability approach, and when your probabilities are considerably higher, the Law of Large Numbers becomes a favorable force.

We want this law to validate our strategies, translating our expected success rates of 70% to 85% into tangible outcomes over the long term. This foresight enables us to proactively manage risk, which is paramount in investing and trading and a topic I'll discuss on numerous occasions in future posts.

Here's a snapshot of how I use probabilities to implement a high-probability trading strategy during bearish market environments using probabilities.

Bearish Trade

For this example, the SPDR S&P 500 ETF (SPY) is trading at 589.49, and I have a short-term (30-60 days) bearish to neutral outlook on the S&P 500. Based on my outlook over the next 30 to 60 days, I opt for what's known in the options world as a bear call spread strategy.

A bear call spread involves selling a call at a higher strike price than the current price of the stock and simultaneously buying a call at an even higher strike price within the same expiration cycle, thereby defining the risk of the trade.

So again, with SPY trading at 589.49, I decide to sell a call at the 612 strike and buy a call at the 617 strike, thereby establishing a bear call spread.

Executing the February 21, 2025, 612/617 bear call spread, I could earn around $1.08, representing a return of 27.6% over the next 43 days. As seen in the image above, the probability of success in this trade is approximately 80.10%.

As long as SPY remains below our short call strike at expiration, 612, we stand to collect the entire 27.6%. Our margin of error on the trade is just under $23, calculated as the difference between the short strike of 612 and the current price of SPY, 589.49.

📈 Key Trade Details:

• Premium Collected: $1.08

• Potential Return: 27.6% (over 43 days)

• Probability of Success: 80.10%

• Margin of Error: $23 (The margin of error is calculated as the difference between the short strike price (612) and the current SPY price (589.49), which equals $22.51.)

💡 Why It Works:

• Break-Even Point: SPY must remain below 612 (short call strike) at expiration to capture the full profit. The breakeven is the short call strike (612) plus the credit received (1.08), which equals 613.08.

• Risk-Defined: Maximum loss is limited by the width of the spread, ensuring controlled risk. (5 - 1.08 = 3.92)

• High Probability: With SPY trading at 589.49, there’s a significant buffer before reaching the short strike of 612. The probability of success for the trade is 80.10%.

In summary, with a probability of success exceeding 80%, our win ratio should gravitate around 80% as we accumulate more trades with approximately the same probability of success. However, and this is a significant caveat, consistent success hinges on disciplined risk management, which involves adhering to strict position-size guidelines. Again, I will talk about this in upcoming articles, videos, posts, etc., many times in the future, as risk management truly allows you to be successful over the long term.

You need it to stand a chance.

May your deltas always be in your favor,

Andy Crowder

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