# Expected Value

Every investor has a similar set of goals when they start trading. Some dream of monthly income, others of earning millions. Setting a realistic goal (or dream) makes it easier to attain but also possibly makes it less attractive. Will our trading system allow us to reach our goals?

Check it with a relatively simple statistical equation of expected value. Not only will you how much each dollar spent should return longer term it will avoid disappointment when we set our sights to high. Thirty trades are necessary to verify such a calculation.

## Expected value formula

#### EV = PW*AP – PL*AL EV – expected value PW – probability of winning AP – average profit PL – probability of loss AL – average loss

Although this formula is mathematically correct, it does not work on investments. Imagine that we have investment system that works on 40% of transactions and on average we earn 300 USD. The average loss Is 100 USD and it happens in 60% of cases. If we use the formula above we will get the result:

#### EV = 0.4*300 – 0.6*100 = 120 – 60 = 60 USD

Every transaction should earn \$60. Perform 100 trades and you will earn \$60k. Not quite a million but a useful step.It looks tough considering how long it would take to do 1000 trades. Maybe the goal is a little too high. So, consider this; again a 40/60 win/loss ratio. Now the average profit is \$600 and the loss \$200. The equation looks like this:

#### EV = 0.4*600 USD – 0.6*200 USD = 240 USD – 120 USD = 120 USD

While this looks much better, how is it achieved? What has changed. Well, primarily, we have doubled the position size. It follows that, mathematically, our formula should work no matter what position size we enter. The formula needs to be amended as follows.

#### EV = PW*(AP/AL) – PL

The aarlier formula just divided the average profit by the average loss. So check the new formula on the examples:

#### EV = 0.4*(600/200) – 0.6 = 1.2 – 0.6 = 0.6

Instead of a value, the result is a fraction. So to interpret the result, we can say that every one dollar invested should return sixty cents. This can now be used to interpret the value of our trading system and verify our goal. We have to consider how many trading opportunities will present themselves, so this can also be used to verify how we calibrate our trading system.

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This is the clue of this article. No matter what kind of investment system we will use, we only want to earn money. Calculating expected value and number of transaction opportunities let us estimate how much we can earn using this system. Thanks to that we will know whether our dreams and plans are possible to realize. We will know whether our investments will be only additional income or they will let us become independent financially.

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