# How to Calculate Value at Risk (VaR) for Financial Portfolios

## What Is Value at Risk (VaR)?

Value at Risk (VaR) is an essential tool for [investment](https://www.investopedia.com/terms/i/investmentbank.asp) and [commercial banks](https://www.investopedia.com/terms/c/commercialbank.asp) to measure potential financial losses over a set time period. VaR calculations help risk managers understand the probabilities and extents of potential losses in portfolios, specific positions, or an entire firm. This insight allows institutions to assess their [risk exposure](https://www.investopedia.com/terms/f/financial-exposure.asp) and determine the adequacy of their capital reserves, ultimately guiding strategic decisions and mitigating excessive risks.

### Key Takeaways

*   Value at Risk (VaR) quantifies potential financial losses within a firm or portfolio over a specified timeframe, helping risk managers control exposure.
*   There are three main methods to compute VaR: the historical method, the variance-covariance method, and the Monte Carlo simulation, each with unique assumptions and applications.
*   VaR faces criticism for potentially understating risks by not accounting for extreme events and only measuring the minimum expected loss.
*   The historical method is the simplest way to manually calculate VaR by analyzing past returns to anticipate future losses.

![Value at Risk](https://www.investopedia.com/thmb/FzdkwMMQbtOxD4okOc2EQP5NuWM=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Value_At_Risk-41be4adde1ef4915a1ca7f85407d77c6.jpg)

*— Lara Antal / Investopedia*

## The Basics of VaR: Quantifying Financial Risk

VaR modeling assesses potential losses and the probability they will occur over a specified time frame

For example, a financial firm may determine an asset has a 3% one-month VaR of 2%, representing a 3% chance of the asset declining in value by 2% during the one-month time frame. The conversion of the 3% chance of occurrence to a daily ratio places the odds of a 2% loss at one day per month.

A firm-wide VaR assessment helps identify cumulative risks from all trading positions within the institution. Using the data provided by VaR modeling, financial institutions can determine whether they have sufficient capital reserves in place to cover losses or whether higher-than-acceptable risks require them to reduce concentrated holdings.

## Exploring VaR Methodologies: Historical, Variance-Covariance, and Monte Carlo

There are three main ways of computing VaR: the historical method, the variance-covariance method, and the Monte Carlo method.

### Historical Method

The [historical method](https://www.investopedia.com/terms/h/historical-returns.asp) looks at one’s prior returns history and orders them from worst losses to greatest gains—following from the premise that past returns experience will inform future outcomes. See “Value at Risk (VaR) Example” below for the formula and how it’s calculated.

### Variance-Covariance Method

Rather than assuming that the past will inform the future, the variance-covariance method, also called the [parametric method](https://www.investopedia.com/ask/answers/041715/what-variancecovariance-matrix-or-parametric-method-value-risk-var.asp), instead assumes that gains and losses are [normally distributed](https://www.investopedia.com/terms/n/normaldistribution.asp). This method frames potential losses as [standard deviation](https://www.investopedia.com/terms/s/standarddeviation.asp) events from the mean.

The variance-covariance method works best for risk measurement in which the distributions are known and reliably estimated. It is less reliable if the sample size is very small.

### Monte Carlo Method

A third approach to VaR is to conduct a [Monte Carlo simulation](https://www.investopedia.com/terms/m/montecarlosimulation.asp). This technique uses computational models to simulate projected returns over hundreds or thousands of possible iterations. Then, it takes the chances that a loss will occur—say, 5% of the time—and reveals the impact.

TThe Monte Carlo method applies to various risk measurement problems, assuming the probability distribution for risk factors is known.  

![Distribution of Daily Returns](https://www.investopedia.com/thmb/SRlVuwK046h_HutpaR0Pbqxs-Ys=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Variance-CovarianceMethod5-5bde86ce7819405ca63f26aa275a4bd2.png)

*VaR. — Image by Julie Bang © Investopedia 2020*

## Benefits of Using Value at Risk (VaR) for Risk Management

There are several advantages to using VaR in risk measurement:

1.  It is a single number, expressed as a percentage or in price units, and is easily interpreted and widely used by financial industry professionals.
2.  VaR computations can be compared across different types of assets—shares, bonds, derivatives, currencies, and more—or portfolios.
3.  Thanks to its popularity, VaR is often included and calculated for you in various financial software tools, such as a [Bloomberg terminal](https://www.investopedia.com/articles/professionaleducation/11/bloomberg-terminal.asp).  
    

## Limitations and Criticisms of Value at Risk (VaR)

One problem is that there is no standard protocol for the statistics used to determine asset, portfolio, or firm-wide risk. Statistics from low-[volatility](https://www.investopedia.com/terms/v/volatility.asp) periods may underestimate the likelihood and magnitude of risk events. Using normal distribution probabilities can further downplay the occurrence of rare, extreme events.

Statistics pulled arbitrarily from a period of low [volatility](https://www.investopedia.com/terms/v/volatility.asp), for example, may understate the potential for risk events to occur and the magnitude of those events. Risk may be further understated using normal distribution probabilities, which rarely account for extreme or [black swan events](https://www.investopedia.com/terms/b/blackswan.asp).

Another disadvantage is that the assessment of potential loss represents the lowest amount of risk in a range of outcomes. For example, a VaR determination of 95% with 20% asset risk represents an expectation of losing at least 20% one of every 20 days on average. In this calculation, a loss of 50% still validates the risk assessment.

The [2008 financial crisis](https://www.investopedia.com/articles/economics/09/financial-crisis-review.asp) revealed that VaR calculations often underestimated the risk of [subprime mortgage](https://www.investopedia.com/terms/s/subprime_mortgage.asp) portfolios. Risk magnitude was also underestimated, which resulted in extreme leverage ratios within subprime portfolios. As a result, the underestimations of occurrence and risk magnitude left institutions unable to cover billions of dollars in losses as subprime mortgage values collapsed.

## Value at Risk (VaR) Example

The formula sounds easy, as it only has a few inputs. However, manually calculating the VaR for a large [portfolio](https://www.investopedia.com/terms/p/portfolio.asp) is computationally laborious.

The historical method is the simplest way to calculate VaR among various approaches:

**Value at Risk = vm (vi / v(i - 1))**

M is the number of days from which historical data is taken, and vi is the number of variables on day i. The purpose of the formula is to calculate the percent change of each risk factor for the past 252 trading days (the total number in a year). Each percent change is then applied to current market values to determine 252 scenarios for the security’s future value.  

## What Is the Value at Risk (VaR) Formula?

You can use [several different methods](https://www.investopedia.com/ask/answers/041615/what-riskmetrics-value-risk-var.asp), with different formulas, to calculate VaR, but the simplest method to manually calculate VaR is the historical method. In this case, m is the number of days from which historical data is taken and vi is the number of variables on day i.

**Value at risk formula** (using the historical method):  
**vm (vi / v(i - 1))**

## What Is the Difference Between Value at Risk (VaR) and Standard Deviation?

Value at risk (VaR) is a measure of the potential loss that an asset, portfolio, or firm might experience over a given period of time. [Standard deviation](https://www.investopedia.com/ask/answers/021915/how-standard-deviation-used-determine-risk.asp), on the other hand, measures how much returns vary over time. It is a measure of volatility in the market: The smaller the standard deviation, the lower an investment’s risk, and the larger the standard deviation, the more volatile it is.

## What Is Marginal Value at Risk (VaR)?

[Marginal VaR](https://www.investopedia.com/terms/m/marginal-var.asp) is a calculation of the additional risk that a new investment position will add to a portfolio or a firm. It is simply an estimate of the change in the total amount of risk, not the precise amount of risk that a position is adding to or subtracting from the whole portfolio. That more precise measurement is known as [incremental VaR](https://www.investopedia.com/terms/i/incremental-value-at-risk.asp).

## The Bottom Line

Value at risk (VaR) is a well-known, commonly used risk assessment technique. The VaR calculation is a probability-based estimate of the minimum loss in dollar terms expected over a period. The data produced is [used by investors to strategically make investment decisions](https://www.investopedia.com/ask/answers/041715/what-backtesting-value-risk-var.asp).

VaR is often criticized for offering a false sense of security, as VaR does not report the maximum potential loss. One of its limitations is that the statistically most likely outcome isn’t always the actual outcome.

> **Article Sources**
>
> 1.  Financial Crisis Inquiry Commission, via GovInfo. “[The Financial Crisis Inquiry Report](https://www.govinfo.gov/content/pkg/GPO-FCIC/pdf/GPO-FCIC.pdf),” Page 44 (Page 73 of PDF).