back

intro to spreads

Introducing Defined-Risk Strategies

Learning to establish limits using vertical spreads

Calculating a Fair Bet

Risk and Probability of Profit

When trading vertical spreads, it's a good idea to make sure you're setting yourself up for a fair opportunity. Your probability of profit should be proportional to the risk you are taking. To calculate a fair POP you simply divide your maximum risk by the sum of the risk AND the reward, which in this case is simply the width of the spread, and multiply by 100%:
POP = [Max Risk ÷ (Max Risk + Max Reward)] × 100%
Making this calculation can help you determine if the trade you are making is balanced and logical. If your break-even does not line up with a delta that is equal to, or greater than, your calculation then you may want to adjust your strikes or reconsider placing the trade. For example:
Imagine XYZ is trading at $34. You're looking to buy a 31 delta call, and sell a 37 delta call for a $3.05 total debit. This creates an $6-wide vertical spread in which you are risking $3.05 to make $2.95. Using the equation mentioned above, let's calculate what a fair POP should be given the risk...
POP = [$3.05 ÷ ($3.05 + $2.95)] × 100%
= [$3.05 ÷ $6] × 100%
= 0.51 × 100%
= 51%
A fair probability of profit in this scenario would be about 51%. Let's make sure the b/e lines up with the 51 delta...
Figure 2
It appears our b/e (XX) lands just above the 50Δ. This seems like a pretty fair bet. Keep in mind that numbers don't always have to line up to the penny. The difference between theoretical delta and the calculated odds just need to be close enough to make the trade a reasonable prospect.
What if this spread had been trading for a $4.00 debit instead? In this case, you would be risking $4.00 on a $6-wide spread. Let's check it out:
POP = [$4 ÷ $6] × 100%
= 0.67 × 100%
= 67%
A fair probability of profit for this scenario would be around 67%. Which delta does the break-even land on?
Figure 1
As you can see our b/e sits on the 40Δ, not the 67. This means we only have a 40% POP rather than the 67% we determined would be fair. This would NOT be a good trade, based on our calculations. In this case, maybe we should try different strikes or consider taking the opposite side. This is the beauty of two-sided markets! If we don't like something, we can simply do the opposite. Instead of buying the 31 strike and selling the 37, let's instead sell the 31 and buy the 37:
Figure 4
The result is an exact reciprocal of our original trade. Now, we have a $6-wide spread with $2 in risk. Using our calculation, the fair odds would be around a 33% POP, but our risk profile shows we actually have 60% odds (100 - 40Δ; I'll explain this subtraction method in the next example).
Note: I am showing you exaggerated examples so you can plainly visualize my point. Also keep in mind that this technique is specifically for defined risk strategies. While probability analysis can be done for
it is not quite as clean and simple. Understand that the market does not make mistakes so if you find discrepancies as drastic as this, there is probably good reason for it. Proceed with caution in those circumstances.

Translating Delta to Match The Assumption

One last example. Imagine you sell a $6-wide put spread for $2. Since we are collecting money up front, $2 is our max profit. Our max loss would be $6 - $2 = $4:
POP = [$4 ÷ ($2 + $4)] × 100%
= [$4 ÷ $6] × 100%
= 0.67 × 100%
= 67%
The fair probability of profit in this scenario would be around 67%. Let's see how it lines up with the risk profile:
Figure 3
Our break even appears to line up with the -31Δ. 31% is the probability of our break-even expiring in the money. Since our spread is short, we want to know the probability of it expiring out of the money, because that's how we would profit. Another way to think about this is that these are negative deltas, but our position is bullish. That means we want to find the positive delta reciprocal. In this case, all we have to do is subtract 31 from 100...

100 - 31 = 69Δ

It looks like our b/e has a 69% probability of expiring out of the money. In other words, we have a 69% POP. That's even better than what we deemed to be fair, so in this case our risk looks very reasonable relative to our probability of profit.

The Probabilities Are Endless!

Calculating probabilities this way can be an extremely enlightening tool. Remember these relationships so they might help you recognize good opportunities, and avoid bad ones. This is not just true of trading, but for any risk management scenario you might find yourself in.

BONUS: Calculating Probability of Loss

Just for your information, your probability of loss (POL) is also easily calculated. All you have to do is subtract your probability of profit from 100%:
POL = 100% - POP
Alternatively, you could divide the width of your spread by your max potential profit. It's sort of the opposite of calculating POP.

back

intro to spreads
Open a Tastyworks Brokerage Account