This post will show you how profitable traders think about the trades and strategies they are looking at.

Have you ever been having a bad day and someone tries to cheer you up by saying something like "it's all about perspective?"
Most times this does nothing but annoy us. But today, we are going to have a conversation similar to this as we discuss the perspective that professional traders view markets through.
This part is important because it will frame the lessons and discussions that will come in the following parts. So if you have questions about it, please leave them in the comment section and we can discuss them in more detail.
Note: This part is filled with analogies and theoretical ideas. As you go, always ask yourself how this relates back to trading. At the end, I bring it all back to options trading, so stick with me and let’s level up our trading together!

Intro: A challenge with trading

One of the characteristics of trading that makes it challenging is that in every strategy (profitable ones and unprofitable ones) there is a lot of variance.
Over the long run, it’s not reasonable for us to expect our PnL graphs to be a beautiful straight line from the bottom left of the screen all the way to the top right. It’d be nice… but it’s not going to happen unfortunately.
Instead, our PnL is filled with periods of making money, losing money, and not much happening at all.
This trading characteristic comes with a pro and a con.

• Pro: Losing money today doesn’t mean you have a bad strategy
• Con: Making money today doesn’t mean you have a good strategy.

Take this chart for example:
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https://preview.redd.it/xaz74zvu7k2a1.png?width=672&format=png&auto=webp&s=d9843ace8ad15d08d8cd63cc63b29ea6e2febdd9
If this were your strategy, it looks awful, right? In just one month there is almost a 10% drawdown!
But if we zoom out and look at a long time frame..
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https://preview.redd.it/fg2tqvcw7k2a1.png?width=667&format=png&auto=webp&s=91d10fc1e4588f1086612786ed6d4fcf2cb12dab
What this illustrates for us is that today's outcome does not inform us enough about our strategy to know if we are making profitable decisions. At any given point we are just one dot on our PnL graph, and every strategy has variance (winning trades and losing trades). So we need to find a way to think beyond today's trade if we want to actually build a sustainable business out of our trading.

Thinking strategically about strategy.

“Not every good trade is profitable. Not every profitable trade is good.”
Even when you put in a lot of work and have the utmost confidence in an idea, you can still lose money on it. But that doesn’t mean it was a bad idea, or that you shouldn’t take similar trades in the future.
If your analysis was as good as you believe it to be, taking those trades over and over again into the future could be extremely lucrative, even though there are some losers.
In order to see beyond our one trade, we need to be thinking in terms of the expected value of our strategy.

What is expected value?

Expected value is a betting concept that helps us answer this question:
“If I were to take this bet/trade over and over again into the future, how much money will I make or lose?”
It is how professional traders look at their trades because it allows them to quickly and easily assess whether the trade they are looking at is worth taking.
There is actually a formula for calculating the expected value of a strategy. This is what it is.
Your expected value of a bet is equal to:
The probability of you winning multiplied by how much you make if you win. Then you subtract the probability of you losing multiplied by how much you are risking on the bet.
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The Expected Value Formula
We always want to be taking trades that have a positive expected value. A positive expected value tells us that a trade, on average, has a profitable return. And if we keep taking that bet again and again into the future, the average return per trade (total return divided by total bets placed) should be our expected value.

How does having a positive expected value impact our trading?

Think of it like having a weighted coin, where there is a 51% chance of landing on heads. If you only flip the coin once, it is basically 50/50. But the more you flip the coin, the more you will start to see a bias towards heads. To the point where if you flip the coin thousands of times there will be a huge bias towards the number of times the coin lands on heads.
Example 1: Casino expected value
Here is an example of what expected value looks like if you owned a casino.
Let’s set a scenario. Imagine you are the dealer at a blackjack table. Every time someone plays, they bet $10. If the house wins, they take the $10, and if the gambler wins, they make $10 profit. In blackjack, the casino has a 1% edge over the gambler, or a 51% chance of winning. So what’s the expected value? Let’s plug the numbers in and find out.
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The casino on average makes $0.20 per bet placed at the table!
As you can see, the casino’s expected value per bet, is $0.20 cents.
But if any of you have spent time at a casino you know the following: On any given bet, winning or losing is pretty much 50/50. But in the long run, it seems like everyone is down money… except for the casino.
This is the expected value at work. And to help realize their expected value, the casino controls the size of the bet (doesn’t let you bet big enough to take them out), and they have many games going on at the same time to increase the frequency of betting.

How does EV actually play out?

Let's do another example to see how expected value plays out in the real world.
Example 2: The Coin Toss
In this example we are going to do a simulation of people tossing a weighted coin. This means that the coin has a 51% chance of landing on heads, 49% chance of lading on tail. The participants will bet $10 per coin toss, and the R:R is 1:1. ( risk 10 to make 10).
Note: I simulated this data using the r statistical programming language.
Let’s see what happens.
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First person tosses the coin 10 times! Their PnL over each throw is the blue line. Not a bad PnL graph!
The first person tosses the coin 10 times. Check this out! He made some money.
So do we run this strategy now? Is this proof of our expected value?
Maybe not quite yet.. Because check out what happens when 10 people toss the coin 10 times.
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Each player has a different coloured line. Some people make money, some lose money over 10 throws.
Some people make money.. Some people lose money. It looks pretty random. Maybe the expected value is a load of BS! To find out.. Let’s increase the number of times these 10 people toss the coin.
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https://preview.redd.it/x5trpm539k2a1.png?width=675&format=png&auto=webp&s=1eeaf86dc29213334c5427608b35d9f2f986e520
WOW! At 10,000 coin tosses, 9/10 people a pretty crazy return! One person lost a bit of money.
Let's see what happens if we up it to 100,000 tosses.
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https://preview.redd.it/2za72lc59k2a1.png?width=674&format=png&auto=webp&s=a509a9104463cadeae4a2c4f4ae94f952f43523c
My god, at 100,000 tosses EVERYONE who played this game got rich.
So as you can see.. A small edge. JUST ONE PERCENT! Was enough to get rich.
We don’t need to hit home runs every day to make money as traders. We just need a little advantage that gives us that positive expected value.
Now obviously, knowing that you have an edge and being able to really quantify it is trickier than this post makes it seem. But what’s important right now is to at least start thinking this way.

Tying expected value back to some basic options trading strategies

When we look at the market, what do you think the expected value of a trade should be if we are blindly trading?
If the market were perfectly efficient, the EV should be 0!
The market isn’t on your team or my team. It doesn’t inherently try to give anyone an advantage. If the market were perfectly efficient, you shouldn’t really be making money buying OR selling!
Why is this important?
Remember this: The expected value of your strategy takes into consideration the probability of winning/losing and the risk reward of the trade.
So.. when we look at a random trade that has a high “probability of profit”.. What should that tell us about the risk ? if we have a 90% chance of winning, and the market tries to give a 0 EV bet.. That means our risk needs to be much greater than our reward! Check this out:
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https://preview.redd.it/42zvo8z89k2a1.png?width=672&format=png&auto=webp&s=4645a64a34fc2e080239a9c47581a4a8ce4addde
The same goes for strategies with low probabilities of profit, if you have a low chance of winning, the payoff should be bigger than the risk to make the EV 0.
Keep this in mind when looking for trades.
So with this understanding, think about this:
Is selling 0dte delta 20 strangles on SPY really free/easy money? Who is buying those things? What happens if the stock actually does move big?
According to the EV formula… The risk should really outweigh the reward here. Leading to sayings like “picking up pennies in front of a steamroller”.

Is the EV really 0 as a baseline in options?

The short answer is no.
The reason is because options are convex products (If you buy an option and the stock moves like crazy, the payoff is huge), and sellers take on very large exposure. If the EV were 0 , no one would want to sell, and the option buyer could get a free hedge on their portfolio. SO! There is a slightly positive EV for the seller to incentivize them to be there.

How much is the EV for option sellers?

On average, it is 11% / year! This is the Variance Risk Premium, which is the premium paid to option sellers for providing access to big move payoffs.

How else can we increase our expected value?

There’s a couple ways, but the one that has the biggest impact is finding an edge (topic for next post?)
By being more thorough with our analysis, and really digging deep to get an advantage over other market participants, we can increase our returns significantly.

Conclusion

By having the expected value on your side, you are expected to win overall. And this is how we should look at trading. Any individual trade has a big luck component, but as long as we have an advantage in every trade we place, we end up making huge returns as we place more and more trades.
This is so important to understand because in the short term, it can be very hard to know if you are supposed to keep winning if you don’t know your expected value. It is extremely dangerous to play without thinking about the expected value, because if you don’t have it on your side, nothing else matters.
You could be amazing at managing risk, but you will still bleed out slowly over time. That’s what keeps losing traders coming back, because you don’t lose every time. You just so happen to lose more than you win.
But when you do have it on your side, you are setting yourself up for a lifetime of success. A casino wins games, loses games, but they don’t stress. The blackjack deal could be drunk for all we know, and it doesn’t matter. They still make their dollars and know exactly how that system’s expected value works.
If we can do that in our trading, we can build profitable strategies and find profitable trade ideas.
Happy Trading,
~ AG