Tales of a Technician: The Math of Making Money
January 3, 2022
I’m prepping for this Wednesday’s Team Phoenix trading lab and thought it would be nice to share my notes and process for piecing together a presentation. The topic is: The Math of Making Money, and will focus on how it pertains to the Tackle Trading Trade Journal and the strategies we use in my lab. Namely: scaling credit spreads, naked puts, covered calls and boomerangs.
Let’s start with the formula that governs profitability:
Sum of winners > sum of losers = profitable
The “No-Duh” Formula
Simply put, the sum of your winners must exceed the sum of your losers. Otherwise, you won’t make money. This applies to the most sophisticated systems as well as the most elementary. It is inescapable.
There are four metrics that are relevant to the formula:
- average gain
- average loss
- win rate (aka % profitable)
- loss rate
High probability systems like those we employ in my lab usually have a high win rate but a smaller average gain. By comparison, directional systems boast a lower win rate but a larger average gain.
Suppose I’m selling $5-wide bull put spreads for 50 cent credit. Further, I stop out and lose $1.25 when prices reach the short strike. Finally, my win rate is 82%. Now, will I make money over time with this system?
To answer that question, we turn to a second formula which calculates the average result of this approach. If the average is positive, then the system should make money over time. If the average is negative, then it would be expected to lose money.
(average gain x probability of winning) – (average loss x probability of losing)
The Expectancy Formula
Plugging the numbers in yields this:
(0.50 x 0.82) – (1.25 x 0.18) = (0.41 – 0.225) = 0.185
The average result is 18.5 cents per share, or approximately $18.5 per contract. Despite the average loss being over two times greater than the average win ($1.25 vs. 50 cents), this system would still print profits. Why? Because of the sky-high win rate. So what could screw up the system?
- A drop in the win rate (e.g., below 60%)
- A drop in the average gain (e.g., we’re only making 30 cents per spread)
- A rise in the average loss (e.g., it jumps from $1.25 to $1.60)
- Or some combination thereof
For high probability systems, it’s difficult to get your average loss below your average gain. Let’s look at some of the numbers for our Practice Journal from Team Phoenix.
Let’s take these numbers at face value. First, the win rate is 74%. What can you infer about such a high number? We must be doing high probability trades (we are). Knowing that, you would expect the average winning trade to be lower than the average losing trade because, again, we usually lose more when high odds trades go against us. And yet, our average winning trade is $48.35, and our average loser is only $30.46.
A high win rate with a higher average gain than loss!?!? What gives?
As I survey our losing 24 trades, 9 of them were actually breakeven. And three more lost less than $10. The spreadsheet counts trades with a “$0” outcome as losers, so it really skews the numbers. To try to overcome this, what if I make each one of those breakeven trades profitable by $1. My guess would be that the average loss rises (fewer low numbers weighing on the average), and the average gain shrinks (I’ll now have nine $1 gain trades).
Sure enough, here’s what happens after adjusting all breakeven trades to $1 profit:
First, the percent profitable (aka win rate) jumps to 84%.
Second, the average losing trade is now higher than the average winner ($42.88 vs. $48.73).
Now, it’s still fair to say that our average loss isn’t near as high as you’d expect. After all, on a typical $5-wide credit spread where you’re getting 50 cents and stopping out at your short strike, you would lose upwards of $1.25 per spread. Which effectively means your average loss should be over $100 per trade. Yet ours is only $48. Why?
Out of our 15 losing trades, only two have losses mirroring what you’d expect (-$150 and -$212). The other 13 losers were much smaller. There are a few reasons.
- One: Some of the losses were taken off well before reaching the short strike because broad market conditions were souring and I decided to close down some positions to get smaller. When doing this, I usually prioritize those that have gains, breakevens, or small losses.
- Two: Because I’m assuming we have a larger account and are able to handle assignment, I give our trades a loose leash. That means I don’t automatically exit at the short strike. Instead, I give time and room for the stock to come back prior to expiration. And with very few exceptions, they all have. In fact, of the 93 trades there’s only one short put that I’ve allowed get assigned.
If you like this type of discussion and want to see what we’re doing in Team Phoenix, you can get a free trial here.
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Great explanation. I appreciate you demonstrating the numbers for expectancy and yields formulas.