**Example: 75% payout**

This hypothetical binary option is struck at the current level of the underlying asset and has a potential payout of 75% of the initial investment. The payout is the same whether we are interested in a call or a put. This means that if we are able to accurately predict the closing level of the asset at expiration of the option we will earn back our initial investment plus an additional 75% profit. As an example, if we think the asset is going higher we should buy the call option. For the example we will use a $100 investment. If we are correct and the underlying goes higher we will earn our initial $100 back plus an additional $75.

**How do we decide if this is a good investment**?

In a binary option, only two outcomes are possible. The first possible outcome is that the asset finishes below the strike price, in which case we lose our $100 investment. The second possible outcome is that the asset finishes above the strike price, in which case we make a profit of $75. We want to know the probability that we are correct and the asset finishes above the strike price. We will call that “x”. The probability that we are wrong and the asset finishes below the strike price is then 1-x, since those are the only two possibilities and they must sum to 1. The expected value of this trade is represented by the formula: $75x-100(1-x). For our trade to be profitable, it must have positive expected value so we set this expression greater than 0. Solving for x we get a probability of at least 57%. If we buy the call option we are saying that we think there is a greater than 57% probability that the asset will be higher than the strike price at expiration. If we think there is a 75% chance that the asset is going higher then we should of course do this trade. If we think there is only a 51% chance that the asset is going higher than we should not do this trade.

**Using probability to analyze a trading strategy:**

We can also evaluate our overall trading strategy using this metric. If we invest in a portfolio of binary options each day, we cannot possibly make money on every trade. In order to make money, we need our success rate (the percentage of profitable trades) to exceed 57% assuming they all have the same 75% payout potential. If we are not able to meet this hurdle, we need to re-evaluate our trading strategy.

**Broker’s Spread**

When it comes to a long-term successful trading strategy, there is another numerical analysis we need to discuss. That is, the broker’s spread for the options. Think of the broker as the casino for a blackjack bet or a bookie for a sports bet. The broker’s goal is to make opposing trades and lock in the spread. In a simple example, the broker has one underlying and one strike price, and builds a book of puts and calls in exactly equal amounts. When the option expires, only one of the options will pay out the 75% profit. If it is the calls that expire in-the money, the broker must pay out the 75% payout on his call positions. The put options will expire worthless and the broker will collect 100% for all the puts. The broker’s net profit is the 75% payout to the call buyers minus the 100% profit from the put buyers, or a net of 25%. That 25% is called the spread. In theory, if our trading strategy was not advantaged at all, which means we are equally likely to be right or wrong on each trade, then we would lose the 25% spread over time. In order to make money, we need to be right more often than we are wrong to pay the broker’s spread. This is why it is so important to develop a smart trading strategy.