BROWSE

Variance

What is 'Variance'

Variance is a measurement of the spread between numbers in a data set. The variance measures how far each number in the set is from the mean. Variance is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the squares by the number of values in the set.

Explaining 'Variance'

Variance is used in statistics for probability distribution. Since variance measures the variability (volatility) from an average or mean and volatility is a measure of risk, the variance statistic can help determine the risk an investor might take on when purchasing a specific security. A variance value of zero indicates that all values within a set of numbers are identical; all variances that are non-zero will be positive numbers. A large variance indicates that numbers in the set are far from the mean and each other, while a small variance indicates the opposite.

Variance in Investing

Variance is one of the key parameters in asset allocation. Along with correlation, variance of asset returns helps investors to develop optimal portfolios by optimizing the return-volatility trade-off in investment portfolios. Risk or volatility is often expressed as a standard deviation rather than variance because the former is more easily interpreted.

Example of Variance

Returns for a stock are 10% in year 1, 20% in year 2 and -15% in year 3. The average of these three returns is 5%. The differences between each return and the average are 5%, 15%, and -20% for each consecutive year. Squaring these deviations yields 25%, 225% and 400%, respectively; summing these squared deviations gives 650%. Dividing the sum of 650% by the number of returns in the data set (3 in this case) yields the variance of 216.67%. Taking the square root of the variance yields the standard deviation of 14.72% for the returns.


Further Reading


Finiteness of variance is irrelevant in the practice of quantitative finance
onlinelibrary.wiley.com [PDF]
… in paradigm between the one presented by Bachelier [36] and the modern finance one known … 2.2.3. The actual replication process According to standard financial economics [20(b)], the payoff … on variance, but on mean average deviation, but it is expressed in terms of variance …

In search of the exchange risk premium: A six-currency test assuming mean-variance optimizationIn search of the exchange risk premium: A six-currency test assuming mean-variance optimization
www.sciencedirect.com [PDF]
… in paradigm between the one presented by Bachelier [36] and the modern finance one known … 2.2.3. The actual replication process According to standard financial economics [20(b)], the payoff … on variance, but on mean average deviation, but it is expressed in terms of variance …

Prices and asymptotics for discrete variance swapsPrices and asymptotics for discrete variance swaps
www.tandfonline.com [PDF]
… in paradigm between the one presented by Bachelier [36] and the modern finance one known … 2.2.3. The actual replication process According to standard financial economics [20(b)], the payoff … on variance, but on mean average deviation, but it is expressed in terms of variance …

Markowitz's mean-variance asset–liability management with regime switching: A multi-period modelMarkowitz's mean-variance asset–liability management with regime switching: A multi-period model
www.tandfonline.com [PDF]
… in paradigm between the one presented by Bachelier [36] and the modern finance one known … 2.2.3. The actual replication process According to standard financial economics [20(b)], the payoff … on variance, but on mean average deviation, but it is expressed in terms of variance …

The effect of jumps and discrete sampling on volatility and variance swapsThe effect of jumps and discrete sampling on volatility and variance swaps
www.worldscientific.com [PDF]
… in paradigm between the one presented by Bachelier [36] and the modern finance one known … 2.2.3. The actual replication process According to standard financial economics [20(b)], the payoff … on variance, but on mean average deviation, but it is expressed in terms of variance …

Testing and locating variance changepoints with application to stock pricesTesting and locating variance changepoints with application to stock prices
www.tandfonline.com [PDF]
… in paradigm between the one presented by Bachelier [36] and the modern finance one known … 2.2.3. The actual replication process According to standard financial economics [20(b)], the payoff … on variance, but on mean average deviation, but it is expressed in terms of variance …

The origins of the mean-variance approach in finance: revisiting de Finetti 65 years laterThe origins of the mean-variance approach in finance: revisiting de Finetti 65 years later
link.springer.com [PDF]
… in paradigm between the one presented by Bachelier [36] and the modern finance one known … 2.2.3. The actual replication process According to standard financial economics [20(b)], the payoff … on variance, but on mean average deviation, but it is expressed in terms of variance …

Are Asian stock markets efficient? Evidence from new multiple variance ratio testsAre Asian stock markets efficient? Evidence from new multiple variance ratio tests
www.sciencedirect.com [PDF]
… in paradigm between the one presented by Bachelier [36] and the modern finance one known … 2.2.3. The actual replication process According to standard financial economics [20(b)], the payoff … on variance, but on mean average deviation, but it is expressed in terms of variance …

Valuing Volatility and Variance Swaps for a Non‐Gaussian Ornstein–Uhlenbeck Stochastic Volatility ModelValuing Volatility and Variance Swaps for a Non‐Gaussian Ornstein–Uhlenbeck Stochastic Volatility Model
www.tandfonline.com [PDF]
… in paradigm between the one presented by Bachelier [36] and the modern finance one known … 2.2.3. The actual replication process According to standard financial economics [20(b)], the payoff … on variance, but on mean average deviation, but it is expressed in terms of variance …

Variance-optimal hedging for time-changed Lévy processesVariance-optimal hedging for time-changed Lévy processes
www.tandfonline.com [PDF]
… in paradigm between the one presented by Bachelier [36] and the modern finance one known … 2.2.3. The actual replication process According to standard financial economics [20(b)], the payoff … on variance, but on mean average deviation, but it is expressed in terms of variance …



Q&A About Variance


What is a nature variance?

A nature variance is the difference between actual costs and budgeted costs that results in either over-production or under-production.

What are two types of variances?

There are two types of variances; effect and nature.

What does it mean to have an over production/under production situation with regard to manufacturing operations?

Over production means that more units were produced than needed by customers while under production means that fewer units were produced than needed by customers.

What is an effect variance?

An effect variance is the difference between actual costs and budgeted costs that results in either over-budgeting or under-budgeting.

If you find out that there has been an overproduction/underproduction situation , how do you correct it ?

You will need to look at your sales records as well as your inventory records .

What is variance?

Variance is a measurement of the spread between numbers in a data set. The variance measures how far each number in the set is from the mean.

What do returns for stocks have to do with asset allocation?

Asset allocation uses volatility as one factor when determining an optimal portfolio for investors. Volatility is often expressed as standard deviation rather than variance because it's easier to interpret.

How can you calculate variance?

Calculate by taking differences between each number and the mean, squaring those differences (to make them positive) and dividing the sum of squares by the number of values in a set.

What does a variance represent?

A variance represents the difference between a budgeted, planned, or standard cost and the actual amount incurredsold.

Why would this happen with regard to manufacturing operations ?

This happens because there was not enough time for planning due to unforeseen circumstances .

How can variances be divided?

Variances can be divided according to their effect on the performance of an entity or company.

How does variance differ from correlation?

Correlation measures how two or more variables are related to one another, while variance measures how much each value differs from the mean.

How do you determine if there has been an overproduction/underproduction situation with regard to manufacturing operations ?

You will need to look at your sales records as well as your inventory records .