# The “Expected Probability Paradox” for Options Traders

I'm going to go out on a limb and publicly declare that this podcast will be one of our top 3 to 5 shows we ever record. Aggressive and overly confident, maybe. But, I have absolutely no doubt this podcast episode will be a game-changer for hundreds of thousands of options traders. I have coined this problem the "expected probability paradox" for options traders, and it is one of the most misunderstood aspects of option selling and premium strategies. The root of this problem starts with the misunderstanding of initial strike price probabilities, perfect pricing of option spreads, and the impact of implied volatility on win rates and drawdowns. On today's show, we are going to dive into the expected probability paradox to help you understand why selling options can outperform the market. We'll also discuss why laddering in some additional active management strategies, such as profit-taking and making adjustments or rolling trades, helps stabilize portfolios and increase returns. Put simply: skip this show at your own risk.

## Introduction:

- Perfect pricing, in any market environment, is always the goal you're reaching for.
- In reality, perfect pricing is not found that often, especially when markets have really low implied volatility.
- Traders end up not making trades because they think they have to hit this magical target of perfect pricing.
- If the market were to play out exactly as the initial probabilities suggest, you might have to get the perfect pricing to make money.
- Traders fear that the few losing trades will be so big that they outweigh all of the small winning trades.
- However, in reality, this is not the case.

## The Expected Probability Paradox

- A lot can happen between when you enter a trade and expiration.
- There is a big difference between probabilities on trade entry and reality at expiration.
- There are intangibles that you don't see in the pricing or the probabilities when you initially make a trade.

## Three Key Elements of the Expected Probability Parad**ox**

### 1. IV's Over Expectation

- Implied volatility is always suggesting the stock will have a huge move one way or another.
- More often than not, stocks do not make those huge moves consistently.
- Of course, there will be times that the stock has huge moves.

### 2. Managing Winners/Profit Taking

- Taking money off the table early can lead to increased profits and decreased drawdowns.
- When to take a trade-off early is dependent on the market scenario.

### 3. Adjustments and Rolling

- You do not have to be great at adjusting and rolling positions.
- If you have the ability to adjust trades and reduce risk by rolling trades and extending duration, you will take your trading to a much higher level.
- With adjustments and rolling, you start to fight the drawdowns, chipping away at losing trades to reduce their impact on the portfolio or completely turn them around.
- When you roll trades, you extend the timeline, giving yourself an extra 30 or 40 days to see if the trade works out.

### Scenario 1: DIA Credit Spread

We back-tested a DIA put credit spread. We set it up to enter at least one trade every week, targeting 40 days to expiration, with no IV filter, allocating 30% of the portfolio to this strategy with 70% sitting in cash. There was no profit exit and no stop-loss. We sold options with the short strike at the 30 Delta — 30% probability of losing on the trade, and a 70% probability of winning. We set up all the put credit spreads to have a $10-wide spread.

#### Results:

- The strategy returned 193% over the testing period.
- The strategy won 83% of the time.
- That 13% differential compared to the 70% probability of winning at trade entry is the over-expectation found in IV.
- The same thing happens if you test call spreads.
- The average premium was $121.70, which is less than half of what traders think they should be taking in with perfect pricing.
- The maximum drawdown was 52%.

### Scenario 2: DIA Credit Spread

We back-tested the exact same strategy — a weekly put credit spread, 40 days to expiration, no IV rank, 30% of your portfolio, short strike at a 30 Delta, spread width of $10. The only change was we added a profit target of 50%. We took money off the table whenever the position reached a 50% profit target.

#### Results:

- The win rate was 89%.
- The maximum drawdown was 50%
- The strategy generated a more stable portfolio than in Scenario 1.

### Scenario 3: IWM Short Strangle

We back-tested an IWM short strangle. We kept the same weekly frequency, the same 40 days until expiration, no minimum IV rank, the same 30% portfolio allocation, no profit-taking, and no stop-loss. We sold the short strike Delta's of 20 on either side - 20% probability of being in the money on either side. The initial probability of success should be around 60%.

#### Results:

- This strategy returned 175% over the same testing period.
- It was 100% neutral, always selling premium on a never-ending basis, letting everything go to expiration, no profit taking, no stop-loss. We should have won 60% of the time.
- This strategy outperformed the market even during the crash.
- The strategy had a 78% win rate, which is the IV over-expectation revealing itself in the form of higher win rates than the initial 60% probability of success at trade entry.
- The maximum drawdown was 45%, resulting in a much more stable portfolio.

### Scenario 4: IWM Short Strangle

We back-tested IWM with the same setup — 40 days till expiration, no IV rank, and no stop loss. The only difference was profit taking at 75%. Instead of letting the trade go all the way to expiration, we held until 75% of the potential profit was captured.

#### Results:

- We saw a total return of 140%. By taking trades off a little early, we slightly sacrificed our total expected gain. We did not make as many total dollars as in the other scenarios.
- However, we did smooth out our portfolio even more than the other scenarios tested due to increased consistency.
- We had better risk-adjusted returns by taking trades off early than by letting them go to expiration.
- The win rate was 81%, and the maximum drawdown was reduced to 41%.
- The average time in trade was 32 days.

### Scenario 5: IWM Short Strangle

We ran the same strategy setup but used a 50% profit target instead of 75%.

#### Results:

- The total return increased to 146%
- The win rate increased to 88%, and the maximum drawdown was 42%.
- The lower profit target Increased the drawdown by 1%. But in exchange, you increased your return by 6% and increased your win rate by almost 7% compared to taking profits at 75%.
- This shows that there is no linear answer to early profit target levels in many respects.
- The average time in trade was 24 days.

## Conclusion

- There is a relationship between taking money off the table early and increasing your win rate, reducing drawdowns, and, in many cases, increasing your potential return.
- This is not to say that this will always be the rule.
- There might be certain scenarios or setups where not taking money off the table is better.
- No "unicorn" strategy works across the board; it is really dependent on the market scenario that you are in.
- If you want to take your trading to the next level and reduce your drawdowns even more, then you've got to get good at adjustments and understand how to roll positions.