Editing Value at risk (section)

== Backtesting ==
Backtesting is the process to determine the accuracy of VaR forecasts vs. actual portfolio profit and losses.
A key advantage to VaR over most other measures of risk such as [[expected shortfall]] is the availability of several [[backtesting]] procedures for validating a set of VaR forecasts. Early examples of backtests can be found in Christoffersen (1998),<ref>{{Cite journal|last=Christoffersen|first=Peter|date=1998|title=Evaluating interval forecasts|journal=International Economic Review|volume=39|issue=4|pages=841–62|doi=10.2307/2527341|jstor=2527341|citeseerx=10.1.1.41.8009}}</ref> later generalized by Pajhede (2017),<ref name="Pajhede 2017 597–613">{{Cite journal|last=Pajhede|first=Thor|date=2017|title=Backtesting Value-at-Risk: A Generalized Markov Framework|url=https://poseidon01.ssrn.com/delivery.php?ID=743026093126097113080092123125124066037017048084024017014107075023102020031076102024041053042031049004119124091109095066083031111041044041067010097001066114108022002006052110086104075075017104068112081094116072094091102090000094072124002013089021065&EXT=pdf|journal=Journal of Forecasting|volume= 36|issue=5|pages=597–613|doi=10.1002/for.2456}}</ref> which models a "hit-sequence" of losses greater than the VaR and proceed to tests for these "hits" to be independent from one another and with a correct probability of occurring. E.g. a 5% probability of a loss greater than VaR should be observed over time when using a 95% VaR, these hits should occur independently.

A number of other backtests are available which model the time between hits in the hit-sequence, see Christoffersen and Pelletier (2004),<ref>{{Cite journal|last1=Christoffersen|first1=Peter|last2=Pelletier|first2=Denis|date=2004|title=Backtesting Value-at-Risk: A Duration-Based Approach|journal=Journal of Financial Econometrics|volume=2|pages=84–108|doi=10.1093/jjfinec/nbh004 }}</ref> Haas (2006),<ref>{{Cite journal|last=Haas|first=M.|date=2006|title=Improved duration-based backtesting of value-at-risk|journal=Journal of Risk|volume=8|issue=2|pages=17–38|doi=10.21314/JOR.2006.128}}</ref> Tokpavi et al. (2014).<ref>{{Cite journal|last=Tokpavi|first=S.|title=Backtesting Value-at-Risk: A GMM Duration-Based Test|journal=Journal of Financial Econometrics}}</ref> and Pajhede (2017)<ref name="Pajhede 2017 597–613"/> As pointed out in several of the papers, the asymptotic distribution is often poor when considering high levels of coverage, e.g. a 99% VaR, therefore the parametric bootstrap method of Dufour (2006)<ref>{{Cite journal|last=Dufour|first=J-M|date=2006|title=Monte carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics|url=https://depot.erudit.org/id/002897dd|journal=Journal of Econometrics|volume=133|issue=2|pages=443–477|doi=10.1016/j.jeconom.2005.06.007|hdl=1866/532|hdl-access=free}}</ref> is often used to obtain correct size properties for the tests. Backtest toolboxes are available in Matlab,<ref>{{Cite web |url=http://www.econ.ku.dk/pajhede/BackTestToolbox%20v1.0.zip |title=Archived copy |access-date=2017-07-12 |archive-date=2017-10-02 |archive-url=https://web.archive.org/web/20171002165607/http://www.econ.ku.dk/pajhede/BackTestToolbox%20v1.0.zip |url-status=dead }}</ref> or [https://cran.r-project.org/web/packages/backtest/backtest.pdf R]—though only the first implements the parametric bootstrap method.

The second pillar of [[Basel II]] includes a [[backtesting]] step to validate the VaR figures.