# Value at Risk (VaR)

Whilst the most popular method of calculating risk is volatility, it has a number of limitations. A stock can be more volatile because of sudden gains as well as losses. Most investors are not averse to sudden gains. Investors are often not really afraid of risk, they’re afraid of loss.

Value at Risk (VaR) addresses the question of “How much could I potentially lose?” or more precisely, “With 95% (or 99%) confidence – what’s the most I can expect to lose over the next day (or month)?”

It’s important to note this isn’t the maximum possible loss; it’s the maximum probable loss. There is still a 5% (or 1%) chance of losing more than the VaR amount.

Value at Risk (VaR) therefore, is a statistical technique used to measure and quantify the level of financial risk within a firm or investment portfolio over a specific time frame. Value at risk is used by risk managers in order to measure and control the level of risk which the firm undertakes. The risk manager’s job is to ensure that risks are not taken beyond the level at which the firm can absorb the losses of a probable worst outcome.

Value at Risk is measured in three variables:

• the amount of potential loss
• the probability of that amount of loss
• the time frame

For example, a financial firm may determine that it has a 5% one month value at risk of \$100 million. This means that there is a 5% chance that the firm could lose more than \$100 million in any given month. Therefore, a \$100 million loss should be expected to occur once every 20 months.

### Marginal VaR

Marginal VaR (value at risk) is the additional amount of risk that a new investment position adds to a portfolio. Marginal VaR allows risk managers to study the effects of adding or subtracting positions from an investment portfolio. Since value at risk is affected by the correlation of investment positions, it is not enough to consider an individual investment’s VaR level in isolation. It must be compared with the total portfolio to determine what contribution it makes to the portfolio’s VaR amount.

An investment may have a high VaR individually, but if it is negatively correlated to the portfolio, it may contribute a much lower amount of VaR to the portfolio than its individual VaR. For example, take a portfolio with only two investments: investment X has a value at risk of \$500 and investment Y has a value at risk of \$500. Depending on the correlation of investments X and Y, putting both investments together as a portfolio might result in a portfolio value at risk of only \$750. This means that the marginal value at risk of adding either investment to the portfolio was \$250.

### Incremental Value at Risk

Incremental Value at Risk is the amount of uncertainty added to or subtracted from a portfolio by purchasing a new investment or selling an existing investment. Investors use incremental VaR to determine whether a particular investment should be undertaken, given its likely impact on potential portfolio losses.

Incremental VaR is based on VaR, which attempts to calculate the likely worst-case scenario for a portfolio as a whole in a given time frame. To calculate incremental VaR, an investor needs to know the portfolio’s standard deviation, the portfolio’s rate of return and the asset in question’s rate of return and portfolio share.

### Measuring risk at StatPro

We understand a certain level of risk is essential to any investment strategy but equally essential is managing this risk. With StatPro’s risk management solutions, an investment manager will have a transparent view of risk for portfolio construction, regulatory requirements, and investor relations.

We not only provide standard measures of risk and volatility, but we have also pioneered many enhancements that will help managers isolate critical drivers of risk. We employ advanced models yet present the results in a highly transparent and intuitive interface and visual dashboards that can easily be digested by both sophisticated practitioners and concerned investors.

### Hosted risk management at StatPro

Our hosted risk management software enables you to manage risk with a number of ex-ante risk measures including Value-at-Risk and CVaR (expected shortfall) at a variety of confidence levels, potential gain, volatility, tracking error and diversification grade. These measures are available in both absolute and relative basis.

Key features also include a stable and reliable assessment of tail risk called Hybrid VaR that counters the pro-cyclicality of other measures in the market. Along with conditional VaR, Hybrid VaR provides a clear indication of tail risk that traditional measures don’t capture.

### StatPro Revolution: measuring your Value at Risk

StatPro Revolution is the culmination of the breadth and depth of StatPro’s incredible expertise in portfolio analytics, including risk measurement and reporting. StatPro Revolution provides this powerful analysis in a beautiful and simple way so you get the most value from your portfolio data.

Use our risk management tools to visually display your control of portfolio risk by highlighting the portfolio, sector- or security-level Value at Risk (VaR). You can even highlight areas in the portfolio susceptible to various risk scenarios such as interest rate movements or market shocks.

Building upon expertise and methodologies developed during years of creating sophisticated risk measurement products, StatPro Revolution offers a multi-asset risk tool. It offers historical simulation-based VaR (Value at Risk) estimates at custom timeframes and confidence intervals with detailed segment- and stock-level breakdown. The estimated dispersion of ex-ante returns is also shown visually, giving instant overview of distribution, including fat tails. In addition to VaR, the engine calculates Expected Shortfall (CVaR), Expected Upside and Diversification Grade for all portfolio sectors and constituents.

StatPro Revolution can also store the history of your portfolio’s ex-ante VaR, generating a trend line of Value at Risk at selected confidence intervals.

The Risk Limits Monitoring module within StatPro Revolution enables users to oversee the risk and exposure of selected portfolios. The main dashboard provides an overview of each portfolio’s Value at Risk (VaR) and liquidity risk together with stress tests and back testing. From the dashboard users can drill down into individual portfolios and produce risk reports.

Using the VaR methodology, this daily tool enables users to complete the following, as requested by the European Union on collective investments (UCITS) without the hassle of further implementation:

• establish, implement and maintain a documented system of internal limits concerning the measures used to manage and control the relevant risks
• conduct a rigorous, comprehensive and risk-adequate stress testing program
• monitor the accuracy and performance of its VaR model, by conducting a back testing program
• comment on and export daily risk reports, breaches and warnings
• compute the leverage
• monitor the liquidity risk of the assets included in the portfolio
In addition to portfolio Value at Risk (VaR), StatPro Revolution can also compute benchmark VaR. At present benchmark VaR is computed at 95%, 97.5% and 99% confidence intervals, at a one day holding period only, presented as a single % number which appears in the main analysis dashboard.

Benchmark VaR is being calculated for:

• All system indices (both total and constituent level)
• Custom indices (containing up-to-date holdings and constituent level)
• Portfolio-as-index (except NAV-only)