Variance Formula

Difference between actual and predicted results.

The difference between actual and predicted results is measured by variance. It's used in personal budgeting and management accounting to assess if an individual or organization's income and spending have surpassed or fallen short of their planned amounts.

In other words, we can say that it represents the average squared deviation from the mean used to calculate the spread of a group of integers.

An individual or organization can compute the difference between actual and planned revenue and spending after the budgeting or accounting period to see if they went over or under budget. 

By analyzing variation, an entity can take the necessary measures to align actual and planned amounts during the following accounting period, allowing them to deploy funds and negotiate better financial agreements more efficiently.

Your objective isn't to eliminate variance-that's nearly impossible, given that you'll almost certainly have fixed and variable expenditures. Instead, your goal should be to reduce variation. 

The precise reason for the variance in your budget will determine how you go about lowering friction. Therefore, you'll need to examine that problem first.

We will now define what risk in an investment is, which is the primary definition of the variance.

Risk overview 

The risk may be the possibility of an unexpected or negative consequence. Risk is defined as any action or behavior that may result in any loss. There are several sorts of dangers that a company may encounter and must overcome. 

Business risk, non-business risk, and financial risk are the three sorts of hazards that may be identified.

Risk management is known as analyzing the risk exposure and choosing the best action to handle it. 

The fundamental objectives of risk management strategy are to comprehend the significant risks and manage them within reasonable limits. 

Plans for risk response are created collaboratively with the stakeholders who are most knowledgeable about the risks and capable of managing them.

When performing risk analysis, it's essential to consider the probability of unfavorable outcomes brought on by evil or unintentional human activity or by natural phenomena such as intense storms, earthquakes, or floods. 

Finding the potential for harm from these events and their likelihood of occurring is a crucial component of risk analysis.

Types of risks

Systematic risk is the market unpredictability of investment, representing outside factors that impact all (or many) businesses in a given sector or group. 

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Asset-specific risks that can impact an investment's performance are referred to as unsystematic risks.

1. Financial Risk

As the name implies, financial risk refers to businesses' chance of financial loss. Financial risk comes primarily from financial market volatility and losses caused by changes in stock prices, currencies, interest rates, and other factors.

2. Business Risk 

These are risks that businesses face to maximize shareholder value and profits. Companies, for example, incur high-risk marketing costs to introduce a new product to, hopefully, increase sales.

3. Non-business risk

These hazards are outside the control of businesses. Non-business risks are those that develop as a result of political and economic imbalances.

Through progressive risk management, risks with a high priority are handled more aggressively and vice versa. Additionally, the regime will be armed with the data they need to decide wisely and maintain the company's profitability.

Types of financial risk 

Financial risks are shared, appear in various forms, and influence almost everyone. Therefore, everyone should at least be aware of the most common financial dangers.

  1. Market Risk: This risk emerges due to price fluctuations in financial instruments. Directional risk and non-directional risk are two types of market risk. Stock price, interest rate, and other factors contribute to directional risk. Volatility hazards, on the other hand, are non-directional risks. 

  2. Credit Risk: This sort of risk occurs when one fails to meet one's commitments to counterparties.

  3. Liquidity Risk: This risk emerges when transactions cannot be completed. Asset liquidity risk and funding liquidity risk are two types of liquidity risk.

  4. Operational Risk: This risk is caused by operational failures, like mismanagement or technology faults. Fraud risk and model risk are two types of operational risk. 

  5. Legal Risk: This financial risk is caused by legal restrictions, such as litigation. A legal risk exists whenever a corporation must incur financial losses due to legal procedures.

Risk management

Risk management identifies, evaluates, and contains threats to an organization's resources and earnings.

The risk may arise from various factors, including financial uncertainty, contractual commitments, technological difficulties, strategic management errors, accidents, and natural disasters.

Two people working together

A corporation may examine all the risks it faces using an effective risk management program. The relationship between risks and the possibility that they may influence an organization's strategic goals is another component of risk management.

Risk management has never been more critical than it is right now. Because of the increasing speed of globalization, the risks that modern firms confront have become more complicated. New hazards regularly emerge, many of which are tied to and caused by the now-ubiquitous usage of digital technology. 

Risk specialists have labeled climate change a "threat multiplier."

Supporting sustainability, resiliency, and corporate agility is gaining popularity. Companies are also looking at how artificial intelligence and advanced governance, risk, and compliance (GRC) solutions might help them manage risk better.

Variance formula  

Standard deviation is generated from variance and indicates how much each number deviates from the mean on average. It is the square root of the conflict of a dataset. 

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  1. Standard deviation:  Expressed in the same units as the original values (e.g., meters).
  2. Variance: expressed in the unit squared (e.g., meters squared)

Since the units of variation are significantly larger than the units of an average value in a data collection, the variance number is more challenging to understand intuitively. Standard deviation is, therefore, usually employed as the leading indicator of variability.

The variance, as opposed to the standard deviation, offers additional details about variability and is used for statistical analysis.

Several formulas are used to determine variance, depending on whether you have data from the entire population or just a sample.

Population variance: you can acquire a precise figure for population variance once you've collected data from every member of the population you're interested in.

Population variance

Because the population variance measures dispersion, the conflict for a collection of identical points is zero. 

The population standard deviation is the square root of the population variance, which reflects the average departure from the mean.

Sample variance

To determine how diverse a sample is, one uses sample variance or s2. An example is a small subset of a population aiming to emulate the larger population. 

For instance, it would not be possible (from a time or financial perspective) to measure the weights of every member of the population if you were measuring the consequences on Americans.

When you collect data from a sample, the sample variance is used to make estimates or inferences about the population variance.

The average squared deviations from the mean are how variance is technically defined. What does that signify in English, though? Let's divide the calculations into steps so that everyone can understand what one does to calculate variance: 

  1. Determine the mean (the average weight). 
  2. Square the outcome of each data point after subtracting the mean. 
  3. Calculate the average of those differences.

Sample variance

Xi: The value of an observation

X̅: The average of all observations

N: The number of observations 

Because using n would give us a biased estimate that regularly underestimates variability, we use n – 1 in the formula with samples. As a result, the sample variance is likely smaller than the population's genuine variance.

Now, we'll introduce portfolio variance...

Portfolio variance

Portfolio variance is a measure of a portfolio's return dispersion. It refers to the portfolio's overall returns over a specific period. In current portfolio theory, the portfolio variance formula is widely used. 

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Portfolio variance is calculated by squaring the weights of the various stocks in the portfolio, multiplying it by the standard deviation of the portfolio's assets, and then squaring it again. 

The numbers are then multiplied by the covariance of the individual assets multiplied by two, the weights of each stock multiplied by two, and the correlation between the different stores in the portfolio multiplied by two.

The formula may be summarized as follows:

 W(1) * O(1) ^2 + W(2) * O(2) ^2 + 2 * P(1,2) * W(1) * W(2) * O(1) * O(2) 

  • W (1): Weight of the first stock in the portfolio squared
  • O (1): The standard deviation of the first asset in the portfolio squared.
  • W (2): The squared weight of the second stock in the portfolio.
  • O (2): The squared standard deviation of the portfolio's second asset
  • P(1,2): The correlation between the two assets in the portfolio (between the first and second asset)

Example of 2- to 3-asset variance

We use this formula when we have more than one asset and a maximum of 3 purchases.


We use this formula once we have a portfolio containing more than three assets to simplify the work.

This is known as the VAR-COVAR Matrix on Excel


The variances of the variables are contained in the matrix's diagonal elements, while the covariances of every possible pair of variables are included in the off-diagonal members.

Minimum variance portfolio: A group of assets forming a minimum variance portfolio work together to reduce the entire portfolio's price volatility. Volatility is a gauge of how much a security's price fluctuates (ups and downs).

A minimal variance portfolio could have several high-risk equities, for example, but each from distinct sectors, or various sized firms, so they do not correlate with one another.

How does a minimum variance portfolio work?

Assets in a minimum variance portfolio work together to reduce the total portfolio's price volatility. Volatility is a gauge of how much a security's price fluctuates (ups and downs).

There are two ways to create a portfolio with low volatility. Choose a few volatile investments that have almost no connection with one another, or stick to low-volatility investments.

As an illustration, you might invest in the tech and fashion industries, which is a typical scenario for creating this portfolio.


Using mutual fund categories with a reasonably low connection with one another is a popular strategy for creating a portfolio with minimum volatility. This adheres to a core-satellite portfolio structure, with a possible allocation like this:

Although the first three fund types can be somewhat volatile, there is little link between any of the four. The combination of all four has lower volatility than any of them alone, except for the bond index fund.

What are the advantages and disadvantages of variance?

Variance benefits by treating all departures from the mean equally, regardless of their direction. However, one disadvantage of conflict is that it gives outliers more weight.

The analysis examines the differences between a company's actual and budgeted financial performance. Understanding why variations occur and what can or should be done to lessen unfavorable variance is helpful. This ultimately leads to better budgeting. 

What are the limitations of variance analysis?

  • Long procedure
  • Expensive process
  • Interpretative judgment
  • Reactive strategy
  • Data manipulation
  • Short-term strategy

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One drawback of utilizing variance is that more significant outliers in the dataset might lead to some data skewing. Thus, it isn't always an accurate calculation.

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Researched and authored by Charbel Yammine | LinkedIn

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