Option Investor
Educational Article

Probability Of Profit, Part II

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By Lee Lowell

In the previous article, we talked about how to use a probability calculator to figure out your chances of success of your desired option position. It was mentioned to me that some people had concerns with the "expected return" of the position at the same time. Let's discuss that issue.

Expected return, or expected profit/loss, is the amount you can expect to receive or lose from a trade if you do it over and over again. If given the chance to repeat that same trade many times, you should be able to hit that expected profit/loss number pretty closely.

Expected return is calculated very easily. All you need to do is take the maximum gain on the trade and multiply it by your probability of success, and then take the maximum loss and multiply it by your probability of loss. Subtract these two numbers and you will have your expected return.

Debit and credit spreads are very easy to use when figuring out an expected profit/loss. If a credit spread has a 70% chance of success with the maximum gain of $3, and a probability of loss of 30% with a maximum loss of $7, your expected return on this trade is $0. If you do this same trade 100 times, you would make $3 on 70 attempts and you would lose $7 on 30 attempts, basically making it a wash trade. For long-term success, you want to find trades that have a positive expected return. Usually, with a positive expected return comes a smaller probability of profit, so you need to find the right balance. Does it mean that you shouldn't do a trade if your expected return is negative? Or should you do a trade with a high expected return but a low probability of profit? It depends.

If you have a trade with a 99% probability of profit, and your maximum gain is $.50, but that probability of loss is unlimited, will you take the trade? Maybe, maybe not. This is the case with many naked selling option positions. Using spreads will always contain that unlimited loss, so your probabilities and expected returns are all known beforehand.

I agree with the theory that you should have a positive expected return for every trade, but that's not always going to happen, especially if your odds of success are getting above 90%. It is my belief that you will never be able to perform the exact same trade twice in the markets. Something is always going to be different about every option trade you make, so it's hard to justify the theory of expected return working out in the long-run (in my opinion). This is why I suggested that any trade with a probability of 80% or higher is worth taking a shot at. Nevertheless, we'll explain some trades with the correct balance. Let's go back to the examples I used last week and I'll show you the numbers and how to get around negative expected return figures.

OEX @ 668, Target Price = 706
Calendar days remaining: 24
Percent Annual Volatility: 25

Probability of stock being above Target Price: 19.4%
Probability of stock being below Target Price: 80.5%

This was our probability estimates for the March OEX 705/710 call credit spread for $1. Our maximum gain is $100 and our maximum loss is $400. What's our expected return? Using the formula I gave above, we get (.805*$100 - .194*$400) = +$2.90. So if we do this same trade many times over, we will make $2.90 over the long run on each trade. I know this seems like such a small number, but that's how expected profit/loss is calculated in the long-run. You have to remember, the OEX can close at any price level on expiration day. In order for us to walk away with the $2.90 profit, the OEX would have to close somewhere around 705.97 on expiration day. On this specific trade though, we are hoping the OEX closes anywhere below 705 for us to receive the full $100. Based on all the parameters we've entered for this trade, in the long-run, we'll be a winner by $2.90.

So what we have here is an all-around good trade. We have an 80% chance of success and we also have a positive expected return of $2.90. That's what you want to see in most of your trades. What do we do if our expected profit/loss is negative and we still have a high probability of success? Let's look at an example.

CSCO @ $24.75, Target Price = $31.0625
Calendar days remaining: 136
Percent Annual Volatility: 74

Probability of stock being above Target Price: 30.7%
Probability of stock being below Target Price: 69.2%

Here's a trade using real numbers for a CSCO July '01 $30/$35 call credit spread with an initial credit of $1 1/16. We have a 69.2% chance of CSCO expiring below our breakeven of $31 1/16 and a 30.7% chance of loss.

Let's do the math: 0.692*$106.25 - 0.307*$393.75 = -$47.38

We have a negative expected return of -$47.38 on this trade even though the probability of success is close to 70%. What should we do? You have a few options.

First, here's a quick test to see what minimum credit you need to bring in on a trade in order to have the profit/loss be positive, or at least a breakeven number. Take the difference between the strike prices (35-30=5) and multiply that by the probability of loss figure (5*.307=1.54). In order for this specific trade to have at least a $0 expected return, you need to take in at least 1.54 points ($154) for the initial credit. Let's see if the $154 floats in our original formula (.692*$154 - .307*$346 =$0). Yes, it works! So what you need to do now if you want to trade this CSCO spread, is to set a limit price of at least 1.54 points for your initial credit. This will ensure a balanced trade between risk/reward and expected return.

The other trick for getting this to a balanced trade is to take the negative expected return figure of -$47, turn it to a positive +$47 and add it to the first initial credit. So we take $47.38 an add that to our initial credit of $106.25 and we get $154. Again, we need to take in at least 1.54 points initial credit for the credit spread to be properly balanced.

You can figure these numbers for any kind of option trade you like. I used the credit spreads because the breakeven points are easy to see. In the case of a long call where your profits are unlimited and the downside is limited, you just need to pick a specific point on the upside to use in your equations. Most people would pick a point that the underlying must reach in order to double your premium. "Percent to double" as it's called.

I hope the math hasn't confused too many people, but it's really not that hard once you get the hang of it. Try it and you'll see.

Good luck.


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