Expected Value

The expected value or EV implies an anticipated average value for investment at some time in the future. EV is used by investors to estimate how worthy a financial instrument is in comparison to the risk it bears when invested in.

One of the theories, that is, the Modern portfolio theory (MPT) considers maintaining the optimal portfolio allocation by finding if the investments' expected values are above the standard deviations (i.e., risk).

The Formula for Expected Value (EV) Is:

Where,

X is a random variable

P(X) is the probability of the random variable

The above formula implies that 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.

To calculate the expected value for a single random variable, you must multiply the value of the variable by the probability of that value occurring. 

For instance, a dice has 6 sides. Once you roll the dice, it has an equal one-sixth chance of one, two, three, four, five, or six occurring.

Then, the calculation will be as follows:

If you were to roll a six-sided dice an infinite amount of times, you see the average value equals 3.5.