Whether a professional trades options, stocks, or pokemon cards, the way they think about their strategy doesn’t really change. The core trait that makes them a professional is the lens through which they view the world and their strategy.
We call this lens see the world in terms of Expected Value.
In this article we are going to explain what expected value is and why thinking about decision making in this way is paramount when it comes to running a profitable option selling strategy.
Key Takeaways:
- Expected Value (EV):
- EV helps determine if a trade will be profitable on average, ensuring that every trade has a positive EV for long-term success. There’s a formula for it.
- Finding an Edge:
- Achieving a positive expected value requires finding an edge—a statistical advantage over the market or the person on the other side of the trade. This edge ensures consistent profitability.
- Long-Term Profitability:
- Most edges that are available to us are small, but persistent. Which means tat the real difficulty in monetizing our edge comes down to execution, cost and risk management, and portfolio management.
Understanding Expected Value in Option Selling Strategies
Expected value (EV) is a statistical concept that helps traders determine if, on average, they should make money by taking a particular trade.
“If I make this decision over and over again into the future, do I make money on average?”
This concept is not exclusively a trading idea. It’s a fundamental decision making framework taught to everyone who studies decision making and statistics. A common example of a business that directly implements the idea of expected value is casino. Every single game that you can play when you walk into a casino is designed such that each time a game is played, the casino has a slight statistical advantage which positions them to slowly extract earnings from gamblers over time. This is expected value at work.
To calculate the expected value, we use the following equation:
EV = (Probability of Winning × Amount Won) – (Probability of Losing × Amount Lost)
If this calculation yields a positive number, it indicates that, on average, engaging in that trade or game will result in a profit.
Casino Roulette Example
To show you what expected value looks like in practice, let’s look at a simple and common example: the casino game called Roulette. Imagine a casino has a roulette table where in each round players place a $10 bet. If the player wins, they gain $10, and if they lose, the casino keeps the $10.
When you analyze the set up of a roulette table, you’ll realize that on each round, the house (casino) has a 52% chance of winning, while the player has a 48% chance.
We now have all the numbers we need to replace the variables in our Expected Value equation and get the output.
EV = (0.52 × $10) – (0.48 × $10) = $5.20 – $4.80 = $0.40
This positive expected value of $0.40 means that for every $10 bet placed on roulette, the casino makes an average profit of 40 cents.
Now obviously this doesn’t mean that they make $0.40 on each round. They either make $10 or lose $10. But what you will see if after thousands of rounds being played, if you take the total profit generated by the casino and divide it by the number of games played, it will average out to roughly $0.40 in profit per game.
What would the casino do if the output of the expected value equation was negative?
The answer is simple. They would stop hosting the game. Why? The casino is only running games because they want to make money. If you weren’t immediately sure of the answer to this question read this article here.
Long-Term Profitability with Positive Expected Value
In practice, this means that although a gambler might get lucky in the short term and win several bets in a row, over a large number of bets (e.g., 1,000), the casino’s consistent edge ensures that it will come out ahead. This is why casinos don’t kick you out when you start to win. Rather, they do everything they can to keep you playing. Whether it buying you drinks, giving you a free room if you agree to play for a while, they will do everything they can to keep you at the table. They know that the more you play, the better the odds that they come out the winner.
The crudely drawn graph below shows you what the PnL of different roulette tables may look like over a large number of games being played. As you can see, none of them are constant winners. But all tables become extremely profitable over a long enough period of time.
As traders, this is really the best that we can hope for. It’s pretty much not going to happen that we find a strategy that makes us money 100% of the time. Which means that we are going to inevitably experience a drawdown at some point in time. And when we do, we need something to keep us confident that we are supposed to make money. This is why we need to have an idea of the expected value of decisions that we make.
Casino style games are the best ones to run, and the worst ones to try and beat.
The reason is because of this expected value. It is baked into the way the game works. What this means is that as a gambler playing roulette at a casino, you cannot win. No amount of risk management, strategy, or psychological “will power” can change the tides in your favor.
On the flip side, this is why a casino would be an epic business to own (from a financial perspective). If you run enough tables and play enough games, you win.
Applying Expected Value to Option Selling Strategies
This casino example directly translates to trading. A profitable trader continually asks, “Do I have a positive expected value with every trade I place?” By ensuring each trade has a positive EV, we can manage risk and spread bets across multiple trades to secure long-term profitability.
Developing an Edge in Trading with Expected Value
Just like how the casino did, we need to find “games” in the market that people are willing to play with us in which we are able to secure a positive expected value.
Since we need to assume that other market participants are making rational decisions, this means that we need to find areas where the other persons motivations for “playing” with us are not directly monetary.
To find these situations in the options space, we typically just need to look for areas where someone is looking to offload risk. The two most common areas, and the ones that we focus on in our private community for Predicting Alpha are selling volatility on ETFs and around Earnings Events.
The Path to Success in Option Selling
Understanding and applying the concept of expected value transforms trading from a gamble into a strategic, disciplined practice. The goal is to ensure that every trade has a positive EV, creating a path to long-term profitability.
Other Articles You May Like
- What Profitable Traders Have In Common: Here’s a hint, it’s not about having good “emotional control”.
- 6 Characteristics of Options: Let’s get clear on what exactly an option is.
- Trading Implied VS Realized Volatility: Most of the time this is what option sellers are trading.
Conclusion
One of the assumptions that goes into the expected value equation is that the outcome of your “bet” is binary. You either win, or you lose. It also assumes that you know the exact probabilities of each scenario.
Obviously in trading and especially in options in which the payoff is a distribution of returns, we do not have such finite answers. So rather than trying to be super mathematical with this formula, just ask yourself if the decision you are making is actually supposed to make money on average.
If you can answer yes (usually a combination of data and logic goes into this) then you should feel confident that you are making decisions that should get you paid. Of course you will have the opportunity to compare your assumptions against what happens in reality as you run your strategies, and win or lose on any given day, if what you are seeing matches what you know could potentially happen, then you can feel confident in continuing to run your strategy, that over time your expected value will show through and you will make some cash.
