Expected Value (EV)

What Is Generally anticipated Value (EV)?

The expected value (EV) is an anticipated average value for an investment at some point from now on. Investors use EV to estimate the worthiness of investments, often in relation to their relative riskiness. Modern portfolio theory (MPT), for instance, attempts to solve for the optimal portfolio allocation based on investments' expected values and standard deviations (i.e., risk).

In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will happen and afterward adding those values. By working out expected values, investors can choose the scenario probably going to give the desired outcome.

The Formula for Expected Value (EV) Is:

$\begin EV=\sum P(X_i)\times X_i\end$
where:

• X is a random variable
• P(X) is the probability of the random variable

Hence, 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.

Understanding the Expected Value

Scenario analysis is one technique for ascertaining the expected value (EV) of an investment opportunity. It uses estimated probabilities with multivariate models to examine possible outcomes for a proposed investment. Scenario analysis likewise helps investors determine whether they are taking on an appropriate level of risk given the likely outcome of the investment.

The EV of a random variable gives a measure of the center of the distribution of the variable. Essentially, the EV is the long-term average value of the variable. Because of the law of large numbers, the average value of the variable converges to the EV as the number of repetitions approaches limitlessness. The EV is otherwise called expectation, the mean or the primary moment. EV can be calculated for single discrete variables, single continuous variables, multiple discrete variables, and multiple continuous variables. For continuous variable circumstances, integrals must be used.

Example of Expected Value

To calculate the EV for a single discrete random variable, you must multiply the value of the variable by the probability of that value happening. Take, for example, a normal six-sided die. Once you roll the die, it has an equal one-6th chance of landing on one, two, three, four, five, or six. Given this data, the calculation is direct:
$\begin\left(\frac{1}{6}\times1\right)&+\left(\frac{1}{6}\times2\right)+\left(\frac{1}{6}\times3\right)\&+\left(\frac{1}{6}\times4\right)+\left(\frac{1}{6}\times5\right)+\left(\frac{1}{6}\times6\right)=3.5\end$
If you somehow managed to roll a six-sided die an infinite amount of times, you see the average value equals 3.5.

Features

• In investing, the expected value of a stock or other investment is an important consideration and is used in scenario analyses.
• Expected value (EV) describes the long-term average level of a random variable based on its probability distribution.
• Modern portfolio theory uses expected value related to an investment's risk (standard deviation) to come up with optimized portfolios.

FAQ

How Is the Expected Value of a Stock Used in Portfolio Theory?

Modern portfolio theory (MPT) and related models use mean-variance optimization to come up with the best portfolio allocation on a risk-adjusted basis. Risk is measured as the portfolio's standard deviation, and the mean is the expected value (expected return) of the portfolio.

How Do I Find the Expected Value of a Stock that Doesn't Pay Dividends?

For non-dividend stocks, analysts often use a multiples approach to come up with expected value. For example. the price-to-earnings (P/E) ratio is often used and compared to industry peers. In this way, on the off chance that the tech industry has an average P/E of 25x, a tech stock's EV would be 25 times its earnings per share.

What Is a Dividend Stock's Expected Value?

The expected value of a stock is estimated as the net present value (NPV) of all future dividends that the stock pays. On the off chance that you can estimate the growth rate of the dividends, you can predict how much investors ought to enthusiastically pay for the stock utilizing a dividend discount model, for example, the Gordon growth model (GGM).