# VaR – Value at Risk: Risk Exposure Explained

## What Is Value at Risk (VaR)? Risk Exposure Explained Value at Risk (VaR) is a statistical measure of the level of financial risk within a firm, portfolio, or trading position over a specific time frame. This measure is most commonly used by investment and commercial banks.  It helps them to quantify the extent and occurrence of potential losses in their institutions and portfolios.

Risk managers use VaR modeling to measure and control the level of risk exposure. VaR calculations can be applied to specific positions or whole portfolios to measure firm-wide risk exposure.

### Key Points

• Value at Risk (VaR) is a statistical measure of financial risk within a firm, portfolio, or position over a specific time frame.
• This measure is commonly used by investment and commercial banks to determine the extent and occurrence ratio of potential losses in their institutional portfolios.
• Investment banks apply VaR modeling to firm-wide risk due to combat the potential for independent trading desks to unintentionally expose the firm to unacceptable risk levels.

VaR modeling determines the potential for loss and the probability of occurrence for the defined loss. VaR is used to assess the amount of potential loss for an asset or an organization.  There are three key elements – a specified level of loss in value, a fixed time period over which risk is assessed, and a confidence interval. The VaR can be specified for an individual asset, a portfolio of assets, or for an entire firm.

• The confidence level of occurrence
• Amount of loss
• Specified timeframe.

### Individual VaR

When there are multiple positions in a portfolio, you can compute VaR of many individual positions. The VaR of an individual position in a portfolio is known as the individual VaR.  For a given confidence level and a time period, VaR is the largest possible loss. VaR indicates the probability of the losses which will be more than a pre-specified threshold dependent on the confidence level over a holding period. VaR is a numerical figure that is calculated for a given confidence level.  This is essentially the point that separates the tail (losses) from the rest of the distribution. VaR focuses on the lower limit of the tail loss.  In short, VaR is the maximum loss for a given confidence level.

## VaR Examples

For example, a financial firm may determine an asset that has a 5% one-month VaR of 3%.  This represents a 5% chance of the asset declining in value by 3% during the one-month time frame.  Converting the 5% chance of occurrence to a daily ratio places the odds of a 3% loss at one day per month.

• Risk as a percentage – The risk is normally presented as a percentage within a given timeframe. For example, it could be said that an asset has a 5% one-week VaR of 3%. This means that there is a 5% chance that the asset will decline by 3% within a single week.
• Risk as a numerical value – However, it could also be presented as a numerical value. For example, if a portfolio has a 5% one-day VaR of \$1000, it means there is a 5% chance that the portfolio will decline by \$1000 during a day.

Investment banks commonly apply VaR modeling to firm-wide risk.  This is due to the potential for independent trading desks to unintentionally expose the firm to cumulative risks. Using a firm-wide VaR assessment allows for the determination of the cumulative risks.  It measures the collective positions held by different trading desks and departments within the institution. Using the data, financial institutions can determine whether they have sufficient capital reserves in place to cover losses.  Or, higher-than-acceptable risks might require them to reduce concentrated holdings.

• Easy to understand – Value at Risk is a single number that indicates the extent of risk in a given portfolio. Value at Risk is measured in either price units or as a percentage. This makes the interpretation and understanding of VaR relatively simple.
• Applicability – Value at Risk is applicable to all types of assets – bonds, shares, derivatives, currencies, etc. Thus, VaR can be easily used by different banks and financial institutions to assess the profitability and risk of different investments, and allocate risk based on VaR.
• Universal – The Value at Risk figure is widely used, so it is an accepted standard in buying, selling, or recommending assets.

## Limitations

• Large portfolios – Calculation of Value at Risk for a portfolio not only requires one to calculate the risk and return of each asset but also the correlations between them. Thus, the greater the number or diversity of assets in a portfolio, the more difficult it is to calculate VaR.
• Different methods – Different approaches to calculating VaR can lead to different results for the same portfolio.
• Assumptions – Calculation of VaR requires one to make some assumptions and use them as inputs. If the assumptions are not valid, then neither is the VaR figure. (Source: corporatefinancialinstitute.com)

## Problems with Risk Calculations

There is no standard protocol for the statistics used to determine asset, portfolio, or firm-wide risk. For example, statistics applied from a period of low volatility may understate the potential for risk events to occur.  It could also understate the magnitude of those events. The risk may be further undervalued using normal distribution probabilities.  Normal distributions rarely account for extreme or black-swan events.

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 financial crisis of 2008 that exposed these problems as relatively benign VaR calculations understated the potential occurrence of risk events posed by portfolios of subprime mortgages. 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. (Source: investopedia.com)

## VaR Value at Risk – Final Words

### Pros

• Easy to Understand – One of the main advantages of the metric is that it is easy to understand and use in the analysis. This is why it is often used by investors or firms to look at their potential losses.
• Useful to Traders – The metric can also be used by traders to control their market exposure. Normally, a traditional measure of risk is market volatility.  But this might not be useful for traders as volatility can create a range of opportunities to go long and short. Instead, VaR looks at the odds of losing money and can act as a guide to creating a risk management strategy.

### Cons

• No Standardized Method for applying Data – There isn’t a standardized process for gathering the data needed to determine and quantify risk.  This means that different values at risk methods can lead to different results.
• Does not Measure Maximum Loss Potential – VaR does not show a trader the maximum possible loss.  It is simply the probability that a loss will occur. The actual risk to a portfolio could be higher than the calculated figure.  This is why value at risk should be used as just one small part of a risk management strategy.
•  Not Additive – Figures of components of a portfolio do not add to the VaR of the overall portfolio.  The measure does not take correlations into account and a simple addition could lead to double counting.
• Results Differ – Different calculation methods give different results.

## Up Next:  Understanding & Calculating Market Premiums

The market risk premium is the difference between the expected return on a market portfolio as compared to a risk-free rate of return.  This premium is the additional return an investor should receive, or expect to receive for holding a market portfolio with higher risk compared to risk-free assets.

The market premium is part of the Capital Asset Pricing Model (CAPM).  Many analysts and investors use CAPM to calculate the acceptable rate of return for an investment.  At its core is the concept of risk, as measured by volatility, and reward, as measured by the rate of returns.  Investors invariably prefer to have the highest possible rate of return combined with the lowest possible volatility and risk.