Value at risk (VaR) is one of the most widely known measurements in the process of risk management.  Risk management's aim is to identify and understand exposures to risk, to measure that risk, and then use those measurements to decide how to address those risks. Topically, VaR accomplishes all three; it shows a normal distribution of past losses – of, say, an investment portfolio – and it calculates a confidence interval about the likelihood of exceeding a certain loss threshold; the resulting info can then be used to make decisions and set strategy.

Stated simply, the VaR is a probability-based estimate of the minimum loss in dollar terms we can expect over some period of time.

Pros and Cons to Value at Risk

There are a few pros and some significant cons to using VaR in risk measurement.  On the plus side, the measurement is widely understood by financial-industry professionals and as a measure, it's easy to understand. Communication and clarity are important, and if a VaR assessment led us to say "We are 99% confident our losses won't exceed $5 million in a trading day," we have set a clear boundary that most folks could comprehend. 

There are several drawbacks to VaR, however.  The most critical is that the "99% confidence" in this example is the minimum dollar figure. In the 1% of occasions where our minimum loss does exceed that figure, there's zero indication of by how much. That 1% could be a $100 million loss, or many orders of magnitude greater than the VaR threshold.  Surprisingly, the model is designed to work this way because the probabilities in VaR are based on a normal distribution of returns.  But financial markets are known to have non-normal distributions, meaning they have extreme outlier events on a regular basis – far more than normal distribution would predict.  Finally, the VaR calculation requires several statistical measurements like variance, covariance, and standard deviation. With a two-asset portfolio, this is not too hard, but becomes extremely complex for a highly diversified portfolio. More on that below.

What is the Formula for VaR?

VaR is defined as: 

VaR = [Expected Weighted Return of the Portfolio - (z-score of the confidence interval * standard deviation of the portfolio)] * portfolio value

Usually, a timeframe is expressed in years. But if it's being measured otherwise (i.e., by weeks or days), then we divide the expected return by the interval and the standard deviation by the square root of the interval.  For example, if the timeframe is weekly, the respective inputs would be adjusted to (expected return ÷ 52) and (portfolio standard deviation ÷ √52). If daily, use 252 and √252, respectively. 

Like many financial applications, the formula sounds easy – it has only a few inputs – but calculating the inputs for a large portfolio are computationally intense,  You have to estimate the expected return for the portfolio, which can be error-prone; you have to calculate the portfolio correlations and variance; and then you have to plug it all in. In other words, it's not as easy as it looks. 

Finding VaR in Excel

Outlined below is the variance-covariance method of finding VaR  [please right-click and select open image in new tab to get full resolution of table]:

  1. What does Value at Risk (VaR) say about the "tail" of the loss distribution?

    Learn about value at risk and conditional value at risk and how both models interpret the tail ends of an investment portfolio's ... Read Answer >>
  2. What is a "linear" exposure in Value at Risk (VaR) calculation?

    Learn how the value-at-risk (VaR) calculation is used for portfolios with linear risk as opposed to nonlinear risk, and understand ... Read Answer >>
  3. What's the difference between a confidence level and a confidence interval in Value ...

    Learn about the value at risk, how confidence intervals and confidence levels are used to interpret the value at risk and ... Read Answer >>
  4. Should you calculate Value at Risk (VaR) for counterparty credit risk?

    Learn how value at risk (VaR) may be used to determine the risk of counterparty default for credit default swaps and other ... Read Answer >>
  5. What is the minimum number of simulations that should be run in Monte Carlo Value ...

    Find out how many simulations should be run at minimum for an accurate value at risk when using the Monte Carlo method of ... Read Answer >>
  6. What is stress testing in Value at Risk (VaR)?

    Discover the difference between Value at Risk, or VaR, and stress testing, and learn how the two concepts might be used together ... Read Answer >>
Related Articles
  1. Investing

    Value at Risk (VaR)

    Value at risk, often referred to as VaR, measures the amount of potential loss that could happen in an investment or a portfolio of investments over a given time period.
  2. Investing

    An Introduction to Value at Risk (VAR)

    Volatility is not the only way to measure risk. Learn about the "new science of risk management".
  3. Managing Wealth

    JP Morgan: The Other Side Of The Hedge

    A hedge is supposed to decrease overall risk, but when it's instead used to increase profits, the risk can be multiplied.
  4. Investing

    Understanding Liquidity Risk

    Make sure that your trades are safe by learning how to measure the liquidity risk.
  5. Investing

    Why Standard Deviation Should Matter to Investors

    Think of standard deviation as a thermometer for risk, or better yet, anxiety.
  6. Investing

    Quantitative Analysis Of Hedge Funds

    Hedge fund analysis requires more than just the metrics used to analyze mutual funds.
  7. Investing

    Understanding The Sharpe Ratio

    The Sharpe ratio describes how much excess return you are receiving for the extra volatility that you endure for holding a riskier asset.
  8. Investing

    Using Historical Volatility To Gauge Future Risk

    Use these calculations to uncover the risk involved in your investments.
  9. Personal Finance

    Risk Management Framework (RMF): An Overview

    A company must identify the type of risks it is taking, as well as measure, report on, and set systems in place to manage and limit, those risks.
  10. Investing

    A Simplified Approach To Calculating Volatility

    Though most investors use standard deviation to determine volatility, there's an easier and more accurate way of doing it.
  1. Marginal VaR

    Marginal VaR includes the change in portfolio VaR resulting from ...
  2. Incremental Value At Risk

    The amount of uncertainty added to or subtracted from a portfolio ...
  3. Value At Risk - VaR

    A statistical technique used to measure and quantify the level ...
  4. Conditional Value At Risk - CVaR

    A risk assessment technique often used to reduce the probability ...
  5. Probability Distribution

    A statistical function that describes all the possible values ...
  6. Risk Management

    Risk management occurs anytime an investor or fund manager analyzes ...
Hot Definitions
  1. Yield Curve

    A yield curve is a line that plots the interest rates, at a set point in time, of bonds having equal credit quality, but ...
  2. Gross Profit

    Gross profit is the profit a company makes after deducting the costs of making and selling its products, or the costs of ...
  3. Risk Tolerance

    The degree of variability in investment returns that an individual is willing to withstand. Risk tolerance is an important ...
  4. Donchian Channels

    A moving average indicator developed by Richard Donchian. It plots the highest high and lowest low over the last period time ...
  5. Consumer Price Index - CPI

    A measure that examines the weighted average of prices of a basket of consumer goods and services, such as transportation, ...
  6. Moving Average - MA

    A moving average (MA) is a widely used indicator in technical analysis that helps smooth out price action by filtering out ...
Trading Center