Editing Value at risk (section)

== Varieties ==

The definition of VaR is [[Constructive proof|nonconstructive]]; it specifies a [[Property (philosophy)|property]] VaR must have, but not how to compute VaR. Moreover, there is wide scope for interpretation in the definition.<ref name="Roundtable I">{{cite conference|first1=Joe|last1=Kolman|first2=Michael|last2=Onak|first3=Philippe|last3=Jorion|first4=Nassim|last4=Taleb|first5=Emanuel|last5=Derman|first6=Blu|last6=Putnam|first7=Richard|last7=Sandor|first8=Stan|last8=Jonas|first9=Ron|last9=Dembo|first10=George|last10=Holt|first11=Richard|last11=Tanenbaum|first12=William|last12=Margrabe|first13=Dan|last13=Mudge|first14=James|last14=Lam|first15=Jim|last15=Rozsypal|title=Roundtable: The Limits of VaR|publisher=Derivatives Strategy|date=April 1998}}</ref> This has led to two broad types of VaR, one used primarily in [[risk management]] and the other primarily for risk measurement. The distinction is not sharp, however, and hybrid versions are typically used in financial [[Comptroller|control]], [[Financial statements|financial reporting]] and computing [[capital requirement|regulatory capital]].<ref name="Brown">{{Citation|author=Aaron Brown|title=The Next Ten VaR Disasters|publisher=Derivatives Strategy|date=March 1997|author-link=Aaron Brown (financial author)}}</ref>

To a [[Risk management|risk manager]], VaR is a system, not a number. The system is run periodically (usually daily) and the published number is compared to the computed price movement in opening positions over the time horizon. There is never any subsequent adjustment to the published VaR, and there is no distinction between VaR breaks caused by input errors (including [[information technology|IT]] breakdowns, [[fraud]] and [[rogue trader|rogue trading]]), computation errors (including failure to produce a VaR on time) and market movements.<ref name="Wilmott">{{cite book|first1=Paul|last1=Wilmott|author1-link=Paul Wilmott|title=Paul Wilmott Introduces Quantitative Finance|publisher=Wiley|year=2007|isbn=978-0-470-31958-1}}</ref>

A [[Frequency probability|frequentist]] claim is made that the long-term frequency of VaR breaks will equal the specified probability, within the limits of sampling error, and that the VaR breaks will be [[Statistical independence|independent]] in time and independent of the level of VaR. This claim is validated by a [[backtesting|backtest]], a comparison of published VaRs to actual price movements. In this interpretation, many different systems could produce VaRs with equally good backtests, but wide disagreements on daily VaR values.<ref name="Jorion" />

For risk measurement a number is needed, not a system. A [[Bayesian probability]] claim is made that given the information and beliefs at the time, the [[Bayesian probability|subjective probability]] of a VaR break was the specified level. VaR is adjusted after the fact to correct errors in inputs and computation, but not to incorporate information unavailable at the time of computation.<ref name="Crouhy" /> In this context, "backtest" has a different meaning. Rather than comparing published VaRs to actual market movements over the period of time the system has been in operation, VaR is retroactively computed on scrubbed data over as long a period as data are available and deemed relevant. The same position data and pricing models are used for computing the VaR as determining the price movements.<ref name="Holton" />

Although some of the sources listed here treat only one kind of VaR as legitimate, most of the recent ones seem to agree that risk management VaR is superior for making short-term and tactical decisions in the present, while risk measurement VaR should be used for understanding the past, and making medium term and strategic decisions for the future. When VaR is used for [[Comptroller|financial control]] or [[Financial statements|financial reporting]] it should incorporate elements of both. For example, if a [[trader (finance)|trading desk]] is held to a VaR limit, that is both a risk-management rule for deciding what risks to allow today, and an input into the risk measurement computation of the desk's risk-adjusted [[Return (finance)|return]] at the end of the reporting period.<ref name="Dowd" />

=== In governance ===
VaR can also be applied to [[financial governance|governance]] of endowments, trusts, and pension plans. Essentially, trustees adopt portfolio Values-at-Risk metrics for the entire pooled account and the diversified parts individually managed. Instead of probability estimates they simply define maximum levels of acceptable loss for each. Doing so provides an easy metric for oversight and adds accountability as managers are then directed to manage, but with the additional constraint to avoid losses within a defined risk parameter. VaR utilized in this manner adds relevance as well as an easy way to monitor risk measurement control far more intuitive than Standard Deviation of Return. Use of VaR in this context, as well as a worthwhile critique on board governance practices as it relates to investment management oversight in general can be found in ''Best Practices in Governance.''<ref>{{Citation|title=Best Practices in Governance|author=Lawrence York|year=2009}}</ref>