where 
thus the ev of a random variable x is taken as each value of the random variable multiplied by its probability and each of those products is summed expected value in portfolio constructioninvestors need to understand several key factors when they want to construct their investment or financial portfolios these include how assets work and their associated risks investors should also have a firm grasp on their financial situation investment goals and investment time horizon once they thoroughly understand these factors investors and their financial advisors can employ ev to build a portfolio that maximizes their returns while minimizing their risks you can use ev to determine the potential return of an investment and therefore which assets to add to your portfolio based on your preference for return so to calculate expected value first multiply the probability of a positive outcome by the potential return say an investment has a 60 chance of increasing in value by 10 000 the calculation would be 0 6 x 10 000 6 000 then multiply the probability of a negative outcome by the potential loss for instance the investment also has a 40 chance of decreasing in value by 5 000 the calculation would be 0 4 x 5 000 2 000 finally subtract the second result from the first 6 000 2 000 4 000 that s the ev for this investment next you may wish to compare two or more investments in which you re interested follow the same steps and compare the expected returns this can help you make selections as you build your portfolio also bear in mind that different assets have different evs that is a stock comes with a different expected value and risk profile than a bond or an exchange traded fund etf it s useful to calculate evs for the various assets that you re interested in and compare those results you can also use ev to adjust your portfolio once it s built for instance compare evs to determine whether selling an underperforming asset with no expectation of a rise in value and replacing it with another with a higher ev makes sense example of expected valueto calculate the ev for a single discrete random variable you must multiply each value of the variable by the probability of that value occurring take for example a normal six sided die once you roll the die it has an equal one sixth probability of landing on the values of either one two three four five or six given this information the calculation is 1 6 1 1 6 2 1 6 3 1 6 4 1 6 5 1 6 6 3 5 begin aligned left frac 1 6 times1 right left frac 1 6 times2 right left frac 1 6 times3 right left frac 1 6 times4 right left frac 1 6 times5 right left frac 1 6 times6 right 3 5 end aligned 61 1 61 2 61 3 61 4 61 5 61 6 3 5 if you were to roll a six sided die an infinite amount of times you would find that the average value equals 3 5 