## Value at Risk (VaR) ###### Updated on Oct 07, 2020 | By Author Sakshi Shekhawat

Value at Risk (VaR) a statistical tool to measure and quantify financial risk within a firm or portfolio over a specific time frame. This metric is often used by Banks to determine the extent and probability of occurrence of a potential loss on the advances. It is also widely used by risk managers to measure and control the level of risk exposure. It can be applied to a specific position or the whole portfolio. It is quite commonly used as a tool for Risk Management.

VaR modeling is used to determine:

1. Amount of potential loss
2. Probability of occurrence of such loss
3. In a specific time frame

For example, a financial firm may use VaR and determines that one of its assets has a 6% one-month VaR of 1%, representing a 6% chance of the asset declining in value by 1% during the one-month time frame. The conversion of the 6% chance of occurrence to a daily ratio places the odds of a 1% loss at one day per month.

#### Features of Value at Risk (VaR)

• VaR is probability-based. This allows users to interpret possible losses for various confidence levels by calculating or estimating the probability of that scenario occurring.
• It is a consistent measurement of financial risk as it uses the possible dollar loss metric enabling the analysts to make direct comparisons across different portfolios, assets, or even business lines.
• VaR is calculated based on a common time horizon, and thus, allows for possible losses to be quantified for a particular period.

#### Calculation of VaR

The formula to calculate Historic VaR is-

[Expected weighted return of the portfolio − (z-score of the confidence interval × standard deviation of the portfolio)] × portfolio value

Z score    = (return of an instrument - mean return) / Standard deviation​

#### The 4 main reasons why VaR is used

• Risk Management
• Financial Control
• Financial Reporting
• Computing Regulatory Capital

#### Limitations of VaR

• VaR does not quantify the worst-case loss of one-day 1% VaR. Referring to a "maximum tolerable" loss. In fact, two or three such losses can be expected in normal circumstances in any given year.
• VaR is also criticized for being misleading and suggesting a false sense of security.
• Making VaR reduction the central focus of the risk management process/strategy. It is important to plan for what happens when losses exceed VaR.
• VaR gets difficult to calculate with large portfolios.
• VaR is not additive. The VAR of a portfolio containing assets A, B, and C does not equal the sum of VAR of asset A, VAR of asset B, and VAR of asset C.
• Reporting a VaR that has not passed backtesting or sampling.
• VaR output is only as reliable as the inputs and the assumptions. Different VaR models with the same set of data can give differential results.

#### VaR in Investment banks

Investment banks, Hedge funds, and other AMCs commonly apply this technique of VaR modeling to assess the firm-wide risk due to the potential for independent trading desks to unintentionally expose the firm to highly correlated assets.

Using VaR assessment at such a firm-wide level allows them to determine the cumulative risks from aggregated positions held by different trading desks and departments within the investment bank. By using the data provided by such VaR modeling, Investment Banks can check, at any point, whether they have sufficient capital reserves in place to cover losses or whether higher-than-acceptable risks require them to reduce concentrated holdings.

In short, be it an individual or a fund house, a retail banking institution, or an investment bank, VaR is a tool that equips them all to quantify the active risk exposures of their singular asset/positions or across a portfolio. It is also the most common tool after standard deviation for measurement and management of risk for investors worldwide.