What is the 'Expected Value'
The expected value (EV) is an anticipated value for a given investment. In statistics and probability analysis, the EV is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur, and summing all of those values. By calculating expected values, investors can choose the scenario most likely to give them their desired outcome.
BREAKING DOWN 'Expected Value'
Scenario analysis is one technique for calculating the EV of an investment opportunity. It uses estimated probabilities with multivariate models, to examine possible outcomes for a proposed investment. Scenario analysis also 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 longterm 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 infinity. The EV is also known as expectation, the mean or the first moment. EV can be calculated for single discreet variables, single continuous variables, multiple discreet variables and multiple continuous variables. For continuous variable situations, integrals must be used.
Basic Expected Value Example
To calculate the EV for a single discreet random variable, you must multiply the value of the variable by the probability of that value occurring. Take, for example, a normal sixsided die. Once you roll the die, it has an equal onesixth chance of landing on one, two, three, four, five or six. Given this information, the calculation is straightforward:
(1/6 * 1) + (1/6 * 2) + (1/6 * 3) + (1/6 * 4) + (1/6 * 5) + (1/6 * 6) = 3.5
If you were to roll a sixsided die an infinite amount of times, you see the average value equals 3.5.
A More Complicated Expected Value Example
The logic of EV can be used to find solutions to more complicated problems. Assume the following situation: you have a sixsided die and want to roll the highest number possible. You can roll the die once and if you dislike the result, roll the die one more time. But if you roll the die a second time, you must accept the value of the second roll.
Half of the time, the value of the first roll will be below the EV of 3.5, or a one, two or three, and half the time, it will be above 3.5, or a four, five or six. When the first roll is below 3.5, you should roll again, otherwise you should stick with the first roll.
Thus, half the time you keep a four, five or six, the first roll, and half the time you have an EV of 3.5, the second roll. The expected value of this scenario is:
(50% * ((4 + 5+ 6) / 3)) + (50% * 3.5) = 2.5 + 1.75 = 4.25

Random Variable
A variable whose value is unknown or a function that assigns ... 
Sensitivity Analysis
Sensitivity analysis is a technique used to determine how different ... 
Shadowing
The process of creating values for variables that don't rely ... 
Rolling Returns
The annualized average return for a period ending with the listed ... 
Multivariate Model
A popular statistical tool that uses multiple variables to forecast ... 
Variability
The extent to which data points in a statistical distribution ...

Investing
Scenario Analysis Provides Glimpse Of Portfolio Potential
This statistical method estimates how far a stock might fall in a worstcase scenario. 
Investing
Find The Right Fit With Probability Distributions
Discover a few of the most popular probability distributions and how to calculate them. 
Markets
Understanding Regression
Regression is a statistical analysis that attempts to predict the effect of one or more variables on another variable. 
Investing
Understanding The Time Value Of Money
Find out why time really is money by learning to calculate present and future value. 
Trading
What's a Sensitivity Analysis?
Sensitivity analysis is used in financial modeling to determine how one variable (the target variable) may be affected by changes in another variable (the input variable). 
Retirement
401(k) Rollovers: Which Option Makes You the Most?
Know the choices that net you the most on a 401(k) rollover â€“ including big tax benefits (capital gains, not income tax) when company stock is involved. 
Trading
Time Value Of Money: Determining Your Future Worth
Determining monthly contributions to college funds, retirement plans or savings is easy with this calculation. 
Markets
Stock and Flow Variables Explained: A Closer Look at Apple
The difference between stock and flow variables is an essential concept in finance and economics. We illustrate with financial statements from Apple Inc. 
Trading
Multivariate Models: The Monte Carlo Analysis
This decisionmaking tool integrates the idea that every decision has an impact on overall risk. 
Retirement
Tips For Moving Retirement Plan Assets
Moving assets is common when changing jobs or retiring, but you have to do this carefully to avoid penalties.

What variables are most important when making a prediction through sensitivity analysis?
Explore sensitivity analysis and how this method considers different variables to determine a course of action based on statistical ... Read Answer >> 
Which is wiser, rolling over my traditional IRA to variable annuity or vice versa? ...
I am 46 years old. I have a traditional IRA and Variable Annuity. What will it cost me to roll either way? ... Read Answer >> 
Should I get a variable rate student loan?
I'm cosigning a loan for my daughter for college. With a variable rate, what is the max interest rate they can charge? Is ... Read Answer >> 
I want to roll over a portion of my retirement plan with my employer and I have been ...
This is based on the rules that an individual can roll over a portion of his or her retirement plan balance, rather than ... Read Answer >> 
Can a variable annuity be rolled into an IRA?
Learn how to roll over your variable annuity to an IRA when you retire or change jobs. Here's how to do it without triggering ... Read Answer >> 
How do you use a financial calculator to determine present value?
Learn how to utilize a financial calculator to calculate present value. Understand the necessary data, why it is important ... Read Answer >>