# 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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- Probability - Basic Terminology
- Two Defining Properties of Probability
- Empirical, Subjective and Priori Probability
- State the Probability of an Event as Odds
- Unconditional and Conditional Probabilities
- Multiplication, Addition and Total Probability Rules
- Joint Probability of Two Events
- Probability of Atleast One of the Events Occuring
- Dependent Vs. Independent Events in Probability
- Joint Probability of a Number of Independent Events
- Unconditional Probability Using Total Probability Rule
- Expected Value of Investments
- Calculating Variance and Standard Deviation of Stock Returns
- Conditional Expected Values
- Calculating Covariance and Correlation
- Expected Value of a Portfolio
- Variance and Standard Deviation of a Portfolio
- Bayes’ Theorem
- Multiplication Rule of Counting
- Permutation and Combination Formula

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