Last updated:

# Value at Risk Calculator (VaR)

Applied approachValue at risk definitionHow to calculate VaR? VaR formulaAdvantages and disadvantage of VaRFAQs

This value at risk calculator (VaR calculator), by employing one of the simplest ways of estimation, is designed to:

• Calculate the potential loss in value of a financial portfolio.

• Quantify financial risk within a firm or portfolio over a specific time frame, incorporating factors like market volatility and price uncertainties.

• Provide a basic background for value at risk estimation.

For a better insight, you may have a look at our risk calculator and investment calculator.

Value at risk is a fundamental tool in financial risk management, offering key insights into:

• The extent of potential losses in investment portfolios; and
• Risk assessment to aid in making informed investment decisions.

• Understanding value at risk: Value at risk definition and its significance in risk management.

• Calculating investment risks using VaR: How to use the VaR formula and value at risk calculation to evaluate potential losses in your investments.

• Practical VaR examples: Real-world applications to help you understand the methodology better.

## Applied approach

This calculator applies the RiskMetrics™ approach, one of the simplest methods to estimate VaR. The model behind RiskMetrics™ was first employed by J.P. Morgan in 1989 for using it to expose trading losses and explain their company's risks.

Shortly after, by releasing the technical document freely available to all marketplaces, J.P. Morgan endeavored to establish a market standard through its RiskMetrics™ system in 1994. Since then, the applied methodologies have flourished, providing ground for extensive academic research and business risk management, including regulatory advancements.

## Value at risk definition

First, let's talk about value at risk definition. Value at Risk (VaR) is a statistical measure used to assess the level of financial risk within a portfolio or a firm over a specific time frame. Essentially, VaR estimates the maximum potential loss that a portfolio could suffer in a given period, typically under normal market conditions, expressed with a certain confidence level.

The key components of VaR are:

• Time period: VaR calculations are based on a set time frame, such as a day, a week, or a month.

• Confidence level: This indicates the probability that the estimated loss will not be exceeded. Common confidence levels used are 95% or 99%.

• Loss amount: VaR provides an estimate of the maximum potential loss in monetary terms.

VaR has become a standard tool in the realm of financial risk management used by banks, investment firms, and corporations to manage and mitigate financial risk. It helps in making informed decisions about portfolio composition, risk tolerance, and capital allocation.

## How to calculate VaR? VaR formula

Let's examine the 5% value at risk (VaR) for a half-year period using Fund Alpha's investment portfolio as our example. The portfolio has the following characteristics:

• Portfolio value: $1,000,000 • Expected half-year return: 10% • Standard deviation: 0.6% 1. Enter the portfolio data. Input the portfolio value and the expected return and standard deviation into the VaR calculator. For Fund Alpha, we have a portfolio value (PV) of$1,000,000, an expected return (ER) of 10%, and a standard deviation (SD) of 0.6%.

You can use our standard deviation calculator to speed up this process.

2. Specify the timeframe in days.

To find VaR for 6 months, you need to express them in days:

6 months ≈ 182.5 days

The Z-score correlates with the confidence level for the VaR. As we are calculating the 5% VaR, we'll use the calculator's Z-score of 1.645.

You can use our Z-score calculator for this calculation.

4. Compute the half-year value at risk (VaR).

Now, you can calculate the value at risk using the VaR formula:

VaR = [ER − (Z-score × √days × SD)] × PV

Applying the value at risk formula to Fund Alpha's portfolio:

VaR = [10% − (1.645 × √182.5 × 0.6%)] × $1,000,000 ≈$33,380

The calculator indicates a half-year VaR of $33,380, meaning there is a 5% confidence level that Fund Alpha's portfolio will lose more than$33,380 over the next year under normal market conditions, given the current risk parameters and historical volatility.

This VaR value is pivotal for long-term risk assessment, allowing Fund Alpha to gauge potential losses and adapt investment strategies accordingly.

By utilizing our value at risk calculator, you can avoid complex manual computation and swiftly understand the risk involved in your investment portfolio over a specified horizon.

• Universality: VaR offers a standardized, universally recognized measure for comparing risk across different assets or portfolios.

• Risk management: It aids in setting risk limits and meeting regulatory capital requirements, helping firms manage potential losses.

• Flexibility: VaR is adaptable to various asset classes and suitable for different time horizons and confidence levels.

• Tail risk: VaR does not account for losses beyond the calculated threshold, missing the potential for extreme events.

• Assumptions: It often assumes a normal distribution of returns, which may not hold true for all asset types, leading to inaccuracies.

• Simplicity: VaR can oversimplify risk, providing a single figure that may not capture the complexity of actual risk profiles.

In essence, while VaR is a useful risk quantification tool, its limitations necessitate the use of complementary risk assessment methods to provide a full picture.

FAQs

### How do I calculate value at risk?

You can calculate value at risk in three steps:

1. Determine the portfolio value, expected return and standard deviation.

2. Specify the time horizon in days.

3. Calculate the z-score.

4. Apply the value at risk formula:

VaR = [expected return − (z-score × √days × standard deviation)] × portfolio value

### What is the portfolio return with $100,000 value and 15% return? The portfolio return will be $15,000. You can calculate it using this formula:

portfolio return = portfolio value × expected return

Note that you need to convert percentages to decimals before you apply the above formula.

### Is VaR applicable to long-term investments?

While VaR is commonly used for short-term risk assessment, it can be adjusted for long-term investments, although the predictive accuracy may diminish over longer time horizons.

### Why is VaR an important metric?

VaR provides a clear and concise measure of risk that can be easily understood and is widely used for regulatory capital requirements and internal risk management.