Definition of Variance

Variance

A measure of dispersion of a set of data points around their mean value. The mathematical
expectation of the squared deviations from the mean. The square root of the variance is the standard deviation.

Variance

The weighted average of the squared deviations from the
expected value

variance

a difference between an actual and a standard or
budgeted cost; it is favorable if actual is less than standard
and is unfavorable if actual is greater than standard

Variance

The dispersion of a variable. The square of the standard deviation.

variance

Average value of squared deviations from mean. A measure of volatility.

Covariance

A statistical measure of the degree to which random variables move together.

Mean-variance analysis

Evaluation of risky prospects based on the expected value and variance of possible outcomes.

Mean-variance criterion

The selection of portfolios based on the means and variances of their returns. The
choice of the higher expected return portfolio for a given level of variance or the lower variance portfolio for
a given expected return.

Mean-variance efficient portfolio

Related: Markowitz efficient portfolio

Minimum-variance frontier

Graph of the lowest possible portfolio variance that is attainable for a given
portfolio expected return.

Minimum-variance portfolio

The portfolio of risky assets with lowest variance.
Minority interest An outside ownership interest in a subsidiary that is consolidated with the parent for
financial reporting purposes.

Portfolio variance

Weighted sum of the covariance and variances of the assets in a portfolio.

Serial covariance

The covariance between a variable and the lagged value of the variable; the same as
autocovariance.

Variance minimization approach to tracking

An approach to bond indexing that uses historical data to
estimate the variance of the tracking error.

Variance rule

Specifies the permitted minimum or maximum quantity of securities that can be delivered to
satisfy a TBA trade. For Ginnie Mae, Fannie Mae, and Feddie Mac pass-through securities, the accepted
variance is plus or minus 2.499999 percent per million of the par value of the TBA quantity.

Variance analysis

A method of budgetary control that compares actual performance against plan, investigates the causes of the variance and takes corrective action to ensure that targets are achieved.

budget variance

the difference between total actual overhead
and budgeted overhead based on standard hours allowed
for the production achieved during the period; computed
as part of two-variance overhead analysis; also
referred to as the controllable variance

controllable variance

the budget variance of the two variance approach to analyzing overhead variances

fixed overhead spending variance

the difference between the total actual fixed overhead and budgeted fixed overhead;
it is computed as part of the four-variance overhead analysis

fixed overhead volume variance

see volume variance

labor efficiency variance

the number of hours actually worked minus the standard hours allowed for the production
achieved multiplied by the standard rate to establish
a value for efficiency (favorable) or inefficiency (unfavorable)
of the work force

labor mix variance

(actual mix X actual hours X standard rate) - (standard mix X actual hours X standard rate);
it presents the financial effect associated with changing the
proportionate amount of higher or lower paid workers in production

labor rate variance

the actual rate (or actual weighted average rate) paid to labor for the period minus the standard rate multiplied by all hours actually worked during the period;
it is actual labor cost minus (actual hours X standard rate)

labor yield variance

(standard mix X actual hours X standard rate) - (standard mix X standard hours X standard rate);
it shows the monetary impact of using more or fewer total hours than the standard allowed

material price variance

total actual cost of material purchased
minus (actual quantity of material  standard
price); it is the amount of money spent below (favorable)
or in excess (unfavorable) of the standard price for the
quantity of materials purchased; it can be calculated based
on the actual quantity of material purchased or the actual
quantity used

material quantity variance

(actual quantity X standard price) - (standard quantity allowed  standard price);
the standard cost saved (favorable) or expended (unfavorable)
due to the difference between the actual quantity
of material used and the standard quantity of material
allowed for the goods produced during the period

material mix variance

(actual mix X actual quantity X standard price) - (standard mix X actual quantity X standardprice);
it computes the monetary effect of substituting a nonstandard mix of material

material yield variance

(standard mix X actual quantity X standard price) - (standard mix X standard quantity X standard price);
it computes the difference between the
actual total quantity of input and the standard total quantity
allowed based on output and uses standard mix and
standard prices to determine variance

noncontrollable variance

the fixed overhead volume variance;
it is computed as part of the two-variance approach to overhead analysis

overhead efficiency variance

the difference between total budgeted overhead at actual hours and total budgeted
overhead at standard hours allowed for the production
achieved; it is computed as part of a three-variance analysis;
it is the same as variable overhead efficiency variance

overhead spending variance

the difference between total actual overhead and total budgeted overhead at actual
hours; it is computed as part of three-variance analysis; it
is equal to the sum of the variable and fixed overhead
spending variances

total overhead variance

the difference between total actual overhead and total applied overhead; it is the amount of underapplied or overapplied overhead

total variance

the difference between total actual cost incurred
and total standard cost for the output produced during
the period

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

variance analysis

the process of categorizing the nature (favorable or unfavorable) of the differences between standard and actual costs and determining the reasons for those differences

volume variance

a fixed overhead variance that represents
the difference between budgeted fixed overhead and fixed
overhead applied to production of the period; is also referred
to as the noncontrollable variance

Covariance

A measure of the degree to which returns on two assets move in
tandem. A positive covariance means that asset returns move together; a
negative covariance means they vary inversely.

Direct materials mix variance

The variance between the budgeted and actual mixes of
direct materials costs, both using the actual total quantity used. This variance isolates
the unit cost of each item, excluding all other variables.

Labor efficiency variance

The difference between the amount of time that was budgeted
to be used by the direct labor staff and the amount actually used, multiplied
by the standard labor rate per hour.

Labor rate variance

The difference between the actual and standard direct labor rates
actually paid to the direct labor staff, multiplied by the number of actual hours
worked.

Materials price variance

The difference between the actual and budgeted cost to
acquire materials, multiplied by the total number of units purchased.

Materials quantity variance

The difference between the actual and budgeted quantities
of material used in the production process, multiplied by the standard cost per
unit.

Production yield variance

The difference between the actual and budgeted proportions
of product resulting from a production process, multiplied by the standard unit cost.

Selling price variance

The difference between the actual and budgeted selling price for
a product, multiplied by the actual number of units sold.

Correlation coefficient

A standardized statistical measure of the dependence of two random variables,
defined as the covariance divided by the standard deviations of two variables.

Country beta

Covariance of a national economy's rate of return and the rate of return the world economy
divided by the variance of the world economy.

Hedging demands

Demands for securities to hedge particular sources of consumption risk, beyond the usual
mean-variance diversification motivation.

Homogenous expectations assumption

An assumption of Markowitz portfolio construction that investors
have the same expectations with respect to the inputs that are used to derive efficient portfolios: asset returns,
variances, and covariances.

Magic of diversification

The effective reduction of risk (variance) of a portfolio, achieved without reduction
to expected returns through the combination of assets with low or negative correlations (covariances).
Related: Markowitz diversification

Markowitz diversification

A strategy that seeks to combine assets a portfolio with returns that are less than
perfectly positively correlated, in an effort to lower portfolio risk (variance) without sacrificing return.
Related: naive diversification

Markowitz efficient portfolio

Also called a mean-variance efficient portfolio, a portfolio that has the highest
expected return at a given level of risk.

Naive diversification

A strategy whereby an investor simply invests in a number of different assets and
hopes that the variance of the expected return on the portfolio is lowered.
Related: Markowitz diversification.

Standard deviation

The square root of the variance. A measure of dispersion of a set of data from their mean.

Budgetary control

The process of ensuring that actual financial results are in line with targets – see variance
analysis.

backflush costing

a streamlined cost accounting method that speeds up, simplifies, and reduces accounting effort in an environment that minimizes inventory balances, requires
few allocations, uses standard costs, and has minimal variances
from standard

Correlation coefficient

A statistic in which the covariance is scaled to a
value between minus one (perfect negative correlation) and plus one (perfect
positive correlation).

Implied volatility

For an option, the variance that makes a call option price
equal to the market price. Given the option price, strike price, and other
factors, the Black-Scholes model computes implied volatility.

Markowitz model

A model for selecting an optimum investment portfolio,
devised by H. M. Markowitz. It uses a discrete-time, continuous-outcome
approach for modeling investment problems, often called the mean-variance
paradigm. See Efficient frontier.

Standard deviation

A measure of the variation in a distribution, equal to the
square root of the arithmetic mean of the squares of the deviations from the
arithmetic mean; the square root of the variance.

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.

standard deviation

Square root of variance. Another measure of volatility.

Record accuracy

The variance between book and on-hand quantities, expressed
as a percentage.

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