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The Law of Large Numbers: A Statistical Advantage to Trading Options

The foundation of statistically-based options trades looks to one statistical law – The Law of Large Numbers.


The Law of Large Numbers states that as you increase your sample size (e.g. number of trades), our expected value or probability of success will come to fruition.


This is because the Central Limit Theorem shows us that actual values will converge on expected values.


Trade often applies the Law of Large Numbers/Central Limit Theorem. Because of the Central Limit Theorem, we know how much variability we can expect between our average P&L and the long-term average based on the number of trades we made. The more trades we make, the more likely our average P&L is to be closer to the long-term historical average of all trades.


KEY: More trades = less uncertainty.


If held to 21 days to expiration, the key takeaway is that the volatility of total Profit & Loss goes down significantly meaning you take less risk and are more profitable.


Avoid the gambler’s fallacy that says the past will continue in the future. If the last 9 out of 10 trades are winners, the 10th trade is not guaranteed to be a winner. Trade based on mechanics discussed in this paper. The key point is to trade smaller rather than bigger as you can get overly confident. This is one of the hardest things to master as a trader.


For the Central Limit Theorem to work, we need a large enough sample size or a number of observations – in our case, trades. This is where the Law of Large Numbers comes in.