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Normal random variable

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Definition of Normal random variable

Normal Random Variable Image 1

Normal random variable

A random variable that has a normal probability distribution.



Related Terms:

CARs (cumulative abnormal returns)

a measure used in academic finance articles to measure the excess returns an investor would have received over a particular time period if he or she were invested in a particular stock.
This is typically used in control and takeover studies, where stockholders are paid a premium for being taken over. Starting some time period before the takeover (often five days before the first announced bid, but sometimes a longer period), the researchers calculate the actual daily stock returns for the target firm and subtract out the expected market returns (usually calculated using the firm’s beta and applying it to overall market movements during the time period under observation).
The excess actual return over the capital asset pricing model-determined expected return market is called an ‘‘abnormal return.’’ The cumulation of the daily abnormal returns over the time period under observation is the CAR. The term CAR(-5, 0) means the CAR calculated from five days before the
announcement to the day of announcement. The CAR(-1, 0) is a control premium, although Mergerstat generally uses the stock price five days before announcement rather than one day before announcement as the denominator in its control premium calculation. However, the CAR for any period other than (-1, 0) is not mathematically equivalent to a control premium.


Abnormal returns

Part of the return that is not due to systematic influences (market wide influences). In
other words, abnormal returns are above those predicted by the market movement alone. Related: excess
returns.


Continuous random variable

A random value that can take any fractional value within specified ranges, as
contrasted with a discrete variable.


Cumulative abnormal return (CAR)

Sum of the differences between the expected return on a stock and the
actual return that comes from the release of news to the market.


Discrete random variable

A random variable that can take only a certain specified set of discrete possible
values - for example, the positive integers 1, 2, 3, . . .



Endogenous variable

A value determined within the context of a model.


Exogenous variable

A variable whose value is determined outside the model in which it is used. Also called
a parameter.


Normal Random Variable Image 2

Lognormal distribution

A distribution where the logarithm of the variable follows a normal distribution.
Lognormal distributions are used to describe returns calculated over periods of a year or more.


Normal annuity form

The manner in which retirement benefits are paid out.


Normal backwardation theory

Holds that the futures price will be bid down to a level below the expected
spot price.


Normal deviate

Related: standardized value


Normal probability distribution

A probability distribution for a continuous random variable that is forms a
symmetrical bell-shaped curve around the mean.


Normal portfolio

A customized benchmark that includes all the securities from which a manager normally
chooses, weighted as the manager would weight them in a portfolio.


Normalizing method

The practice of making a charge in the income account equivalent to the tax savings
realized through the use of different depreciation methods for shareholder and income tax purposes, thus
washing out the benefits of the tax savings reported as final net income to shareholders.


Random variable

A function that assigns a real number to each and every possible outcome of a random experiment.


Random walk

Theory that stock price changes from day to day are at random; the changes are independent
of each other and have the same probability distribution. Many believers of the random walk theory believe
that it is impossible to outperform the market consistently without taking additional risk.


Randomized strategy

A strategy of introducing into the decision-making process a random element that is
designed to reduce the information content of the decision-maker's observed choices.


Standardized normal distribution

A normal distribution with a mean of 0 and a standard deviation of 1.



Variable

A value determined within the context of a model. Also called endogenous variable.


Variable annuities

Annuity contracts in which the issuer pays a periodic amount linked to the investment
performance of an underlying portfolio.


Variable cost

A cost that is directly proportional to the volume of output produced. When production is zero,
the variable cost is equal to zero.


Variable life insurance policy

A whole life insurance policy that provides a death benefit dependent on the
insured's portfolio market value at the time of death. Typically the company invests premiums in common
stocks, and hence variable life policies are referred to as equity-linked policies.


Variable price security

A security, such as stocks or bonds, that sells at a fluctuating, market-determined price.


Variable rate CDs

Short-term certificate of deposits that pay interest periodically on roll dates. On each roll
date, the coupon on the CD is adjusted to reflect current market rates.


Variable rated demand bond (VRDB)

Floating rate bond that can be sold back periodically to the issuer.


Variable rate loan

Loan made at an interest rate that fluctuates based on a base interest rate such as the
Prime Rate or LIBOR.


VARIABLE EXPENSES

Those that vary with the amount of goods you produce or sell. These may include utility bills, labor, etc.


Semi-variable costs

Costs that have both fixed and variable components.



Variable cost

A cost that increases or decreases in proportion with increases or decreases in the volume of production of goods or services.


Variable costing

A method of costing in which only variable production costs are treated as product costs and in which all fixed (production and non-production) costs are treated as period costs.


variable expenses

Expenses that change with changes in either sales volume
or sales revenue, in contrast to fixed expenses that remain the same
over the short run and do not fluctuate in response to changes in sales
volume or sales revenue. See also revenue-driven expenses and unitdriven
expenses.


decision variable

an unknown item for which a linear programming
problem is being solved


dependent variable

an unknown variable that is to be predicted
using one or more independent variables


independent variable

a variable that, when changed, will
cause consistent, observable changes in another variable;
a variable used as the basis of predicting the value of a
dependent variable


key variable

a critical factor that management believes will
be a direct cause of the achievement or nonachievement
of the organizational goals and objectives


net cost of normal spoilage

the cost of spoiled work less the estimated disposal value of that work


normal capacity

the long-run (5–10 years) average production
or service volume of a firm; it takes into consideration
cyclical and seasonal fluctuations


normal cost system

a valuation method that uses actual
costs of direct material and direct labor in conjunction with
a predetermined overhead rate or rates in determining the
cost of Work in Process Inventory


normal loss

an expected decline in units during the production process


normal spoilage

spoilage that has been planned or foreseen; is a product cost


slack variable

a variable used in a linear programming problem
that represents the unused amount of a resource at
any level of operation; it is associated with less-than-orequal-
to constraints


surplus variable

a variable used in a linear programming problem that represents overachievement of a minimum requirement; it is associated with greater-than-or-equal-to constraints


variable cost

a cost that varies in total in direct proportion
to changes in activity; it is constant on a per unit basis


variable costing

a cost accumulation and reporting method
that includes only variable production costs (direct material,
direct labor, and variable overhead) as inventoriable
or product costs; it treats fixed overhead as a period cost;
is not acceptable for external reporting and tax returns


variable cost ratio

the proportion of each revenue dollar
represented by variable costs; computed as variable costs
divided by sales or as (1 - contribution margin ratio)


variable overhead efficiency variance

the difference between budgeted variable overhead based on actual input activity and variable overhead applied to production


variable overhead spending variance

the difference between total actual variable overhead and the budgeted amount of variable overhead based on actual input activity


Normal (bell-shaped) distribution

In statistics, a theoretical frequency
distribution for a set of variable data, usually represented by a bell-shaped
curve symmetrical about the mean.


Spoilage, abnormal

Spoilage arising from the production process that exceeds the normal
or expected rate of spoilage. Since it is not a recurring or expected cost of ongoing
production, it is expensed to the current period.


Spoilage, normal

The amount of spoilage that naturally arises as part of a production
process, no matter how efficient that process may be.


Variable cost

A cost that changes in amount in relation to changes in a related activity.
Variance
The difference between an actual measured result and a basis, such as a budgeted amount.


random walk theory

Security prices change randomly, with no predictable trends or patterns.


variable costs

Costs that change as the level of output changes.


Random-location storage

The technique of storing incoming inventory in any
available location, which is then tracked in a locator file.


Variable Annuity

A form of annuity policy under which the amount of each benefit is not guaranteed or specified. The amounts fluctuate according to the earnings of a separate investment account.



 

 

 

 

 

 

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