# What is expected value?

The expected value of your trade plan is how much you will profit or lose based on statistics. The expected value is calculated by multiplying the probability of being right times the reward and subtracting this from the probability of being wrong times the loss.

Expected value = Probability (right) * Reward (right)-Probability (wrong) * Loss (wrong)

# Trading systems with positive expectancy

To calculate the expected value of a trading system, you need to know the probability of profit and the expected reward potential. In addition, you must know the probability of losing and the loss potential.

First, you should set up a risk management system to base your win and loss size. Let’s say you will limit the loss size to \$200, and the win size will be \$60. The breakeven win rate of a strategy with this risk-reward is 76.7%, which means you must win more than 76.7% of your trades to make money.

Now you have to backtest a trading system that wins more than 76.7% of the time. Strategies like this are best used with options since probabilities of profit are given upon trade entry. If you sell puts on a stock index with a .15 delta, you should win about 85% of your trades over time.

However, the option delta is the percent chance an option will be ITM at expiration. If you take profit and manage it before expiration, this number will have less meaning. You must backtest and find out how often you will take profit versus hitting a stop loss. If you are making a profit on at least 77% of your trades, you will at least break even in this example.

# Your PnL is just statistics

The amount of money you make or lose on the stock market is simple statistics. You must create a positive expectancy system based on win rate and risk-reward.

If you skew the statistics in your favor, you are bound to make a profit over many trade occurrences. Options are beneficial to statistical traders since probabilities of profit are generated by the Black-Scholes model.

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