What is Expected Value and 3 ways to use it

This article is the first in a series of educational articles that will describe some of the advanced concepts implemented in Option Samurai option scanner.  In this article we will focus on Expected Value.

What is Expected Value

Expected value is a statistic measure that tries to predict the value of the strategy, assuming you could have executed it many times at different dates but with the same prices/distances etc. It is calculated by summing the payout at expiration multiplied by the probability of that payout. The expected value is derived from: Stock price, option prices, Implied volatility, time to expiration, distance of strikes from last price, dividends and risk-free rate. Usually you are aiming to have the highest expected value possible, as it indicates a statistical edge.

Example: Expected Value of put spread

In this example we will see how the Expected value is calculated on a bull put spread. This spread is built with a short put (strike A) and a protective long put (strike B) where both options have the same expiration and A>B.

We can divide the spread to 3 ranges:

1. Maximum profit range (where the price is greater than A) – Range 1 in the example
2. Maximum loss range (where the price is lower than B) – Range 2 in the example
3. Between A and B the spread will show profit or loss that is linear changing depends on the stock price – Range 3 in the example

To calculate the expected value we add:

• The probability of being above A * max profit (positive)
• The probability of being below B * max loss (negative)
• For the area between A and B we use log-normal distribution and multiply it by the payout.

The sum of the 3 components is the Expected value.

How to use Expected value:

After explaining what is expected value we get to the most important part: How can we use it to find better trades.

1. Filter according to Expected value

This is the most obvious and powerful way to use this value. With our option scanner you can instantly find only the profitable trades according to the expected value, in real time. This means that you only analyse trades where you have a statistical edge. This saves you time and in the long run helps your edge compound.

You can also set the expected value filter to be more than \$100 or any other value to account for commissions and unexpected scenarios and even increase your edge.

2. Sort from max to min

After getting your results, you can sort by expected value to compare different strikes, expiration and tickers to find the optimal trade when taking into considerations all the different variables (profit, loss, liquidity, growth, trend, sentiment, IV etc).

The sorting helps you manage your time more efficient by looking at the trades with the highest edge first (Important note – The fact that the EV is positive, doesn’t mean you will necessarily make profit, it is just indicating there is an edge in this trade in your favor).

3. Create a ratio using expected value

A more advance way to use expected value would be to create a custom ratio unique to your trading style. The best way to do it is to export the results to excel using our export feature.

After you have all the data in excel you can start playing with it. Some ratios for example:

1. Expected value / Max loss – This ratio combines EV (higher is better) and Max loss (lower is better). sorting the trades according to this ratio takes into account the worse case scenario when you analyse a trade
2. Expected value * IV rank (if credit strategy) or Expected value / IV rank (for debit strategy) – This ratio combines the EV with the Implied Volatility rank. It means that trades with high IV will get precedence if it is a credit strategy and Low IV trades will get precedence if it is a debit strategy.
3. Expected value * Growth rate – This ratio combines the EV (higher is better) with the fundamental  measure of the company expected EPS growth (higher is better). This combines 2 measures from different ‘domains’ and gives precedence to higher growth

You can of course create more ratios that fits your style: Divide by days to expiration (EV per day), use PE (see how expensive the stock), div yield and much more.

Conclusion

Expected value is a statistical measure that tries to predict how profitable a strategy will be. It uses the market conditions, such as: option prices, implied volatility, stock price, dividends and more to give a dollar amount of the expected profit (or loss) of the strategy.

Though expected value gives a dollar value, it does not mean that this will be the profit from the trade. It is better to think of the EV as the integrated edge in the trade. Over many similar trades you are expected to collect this edge and increase your profits.

You can use the Expected value to:

• Filter trades that have positive EV and have edge.
• Sort by EV to save time and compare trades
• Create your own custom ratios that will help you to uncover the trades that best fit you.