If you’ve looked at my posts here before, you’ll know that I have a win rate on puts of approximately 75%. That means every time I sell a put on Monday morning, there is a 75% chance that it will expire worthless on Friday. This also means that I “lose” 25% of the time (it’s not really losing, since my capital is just transferred into shares, but we can call it “losing” for now).

You can also see that my median weekly ROI for puts & calls that I sell is 2.5%. Using these numbers, I’ll go into some theory about why my strategy should work long-term.

**Expected Value** is a term in probability that essentially translates to “what should happen on average”. If you knew for a __fact__ that something will happen 90% of the time, how much would you be willing to bet on it? Well, you can use Expected Value (EV) to decide. It’s given by this equation:

EV = P_win x profit – P_lose x risk

So in the above scenario, P_win is 90% and P_lose is 10%. How much you are willing to risk depends on what your profit will be. If the profit is $100, then you should risk no more than $900, since your EV would be exactly 0 in this case (0.90 x $100 – 0.10 x $900 = 0).

In my case with selling puts, we can construct the same equation to determine what my EV should be for any given trade, knowing that I “win” 75% of the time. EV = 0.75 x profit – 0.25 x risk. We can put everything into ROI terms and rewrite the equation as EV = 0.75 x ROI – 0.25 x LOI [loss on investment]. I’ve told you that my typical weekly ROI is 2.5%. So now we can compute what my LOI has to be in order to have a net positive EV. From the equation, LOI needs to less than 0.75/0.25 x ROI, which = 3 x ROI, or 7.5%.

That’s a lot of math and a lot of numbers, but it really is simple: if on a given week I can manage to lose no more than 7.5% of my investment, then my strategy will be net positive long-term.

Let’s look at a real-world stock example to see this in detail. If I sell a put on stock “ABC” at a strike price of $10 and I’m paid $25 in premium, then my investment = $1000 (100 shares x $10 strike price) and my ROI = 2.5% ($25 / $1000). From the calculations earlier, for the trade to be profitable I need my LOI to be less than $75 (7.5%). Now, my break-even price for the stock is $9.75 (strike – premium), so in order for me to lose $75, the stock would have to fall to $9 by expiration. This is $1, or 10%, below my chosen strike. If you think about it, that’s a really nice extra cushion on this trade!

But wait, it gets even better! Because a “loss” is not really a loss, but rather a conversion of cash into shares, we can then turn to the latter half of the Wheel strategy and continuously sell covered calls. We’ll get paid every week simply for our willingness to (possibly) sell our shares. This helps to *reduce* any ongoing loss, increasing the likelihood that at the end of the day, we will be net positive.

The stock market is a risky, crazy place. But with a little math and probability, we can at least give ourselves a better chance to come out ahead in the end.