# Expected Value of Investments

Expected value is an important concept in investments. An investor will make use of expected value to estimate the expected returns from their portfolio or to assess other factors such as financial ratios.

We can use a random variable to describe asset returns. The expected value of a random variable is defined as the weighted average of all possible outcomes of the random variable. The weights are the probabilities of each outcome.

Let’s say we have a random variable X. Its expected value can be represented as follows:

E(X) = P(x1) x1 + P(x2) x2 + ...+ P(xn) xn

Where,

• E(X) is the expected value of the random variable
• P(xi) is the probability of each observation
• Xi represents an observed value of a random variable.

In terms of investments, expected returns from an asset can be represented as E(R).

Let’s say an investor is analysing the performance of a stock under different states of economy and comes up with the following:

 State of Economy Probability Return on Stock 1 0.20 15% 2 0.20 -5% 3 0.20 5% 4 0.20 35% 5 0.20 25%

The expected returns from this stock can be calculated as follows:

E(R) = 0.20*15%+0.20*(-5%)+0.20*5%+0.20*35%+0.20*25% = 15%

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