# CVaR Value at Risk – an Introduction

Xavier Bellouard |
October 8, 2011

Value at Risk (VaR) is a general tool for assessing market risk; it measures the worst expected loss over a given horizon under normal market conditions at a given level of confidence. CVaR value at risk is the most common VaR model used. To properly understand where your risk resides, you need to know what CVaR model, or algorithm, would serve you best in digging deeper into the VaR. We have put together this post to help you better understand some of the common VaR algorithms used in the market.

CVaR – Conditional VaR

CVaR is the basic risk assessment algorithm used to reduce the probability of incurring large losses, and it focuses on the less profitable outcomes. To reach the CVaR rate, the weighted average between the value at risk and losses exceeding that value at risk are calculated.

TVaR – Tail VaR

TVaR is similar to conditional VaR, the difference being that the underlying distribution of the value at risk. TVaR will assess the severity of losses, and not only the chance of losses. This measure is applied for assessing the tail of the distribution.

HVaR – Historical VaR

Historical VaR is used to examine past portfolio performances, or actual historical returns, arranging them from worst to best scenarios, and then calculating the portfolio’s value at risk following the assumptions that historical risk will repeat itself.

IVaR – Incremental VaR

Incremental VaR is used to measure the change in portfolio value at risk that is implied by a change in a position (i.e. shares added or diversified). This type of implementation requires reassessing the entire portfolio value at risk before and after a given change is made, and the difference provides us with the incremental VaR.
MVaR – Marginal VaR

Marginal VaR is used to measure the change that is made in a portfolio’s value at risk when an additional dollar is added to the portfolio. The marginal VaR measured for each change provides us with the amount of risk added to the entire portfolio by the given change.

Component VaR

Component VaR is the contribution of a specific position to the entire portfolio’s value at risk. If this position were removed, then the portfolio value at risk would drop by the component VaR. Thus, portfolio VaR is the sum of all component VaRs. Component VaR actually considers marginal VaR and incremental VaR in its calculation.

Stress VaR

Stress VaR is a forward-looking algorithm that aims to identify extreme events that could result in catastrophic losses in a portfolio. A stress VaR algorithm is based on real adverse and unexpected historical scenarios to recreate and analyze changes in position, up to the worst-case point.

In our ActivePivot real time OLAP system, we have developed a Value at Risk component that simplifies handling VaR complexities with an actionable metric. The ActivePivot analytics tools can calculate all types of VaR within seconds, which eliminates the need to run an overnight OLAP batch for VaR related queries. Beyond the different VaR calculations, the component can also provide marginal VaR, tail analysis, stress scenarios and ‘what if‘ simulations.

The ability of the ActivePivot solution to manipulate VaR distribution as simple objects dramatically reduces storage, access speed, and calculations requirements, thus providing real time complex analysis to assist risk management. For a more extensive explanation on our VaR tool, see our post on the different measures implemented.

To try out ActivePivot’s Value at Risk analytics solution, see our live demo.

#### Xavier Bellouard Deliver innovative data analytics solutions to empower confident decision making for finance.

Company

Products