AIM38.9:Explainthe roleofliquidityin crisis situations anddescribeapproaches
toestimatingcrisis liquidity risk.
Ena crisis,assumptions concerningdielevelofliquidityand other properties thatare reasonableina‘normal* marketmaynothold. Suchcriseshaveoccurredin1987, 1992, 1998, and2007—2008.Someeventusuallyprecipitates diecrisis,such asalargefallinsome assetprices, whichleadstolower demand and wider bid-askspreads.Thetime neededfor sellingorders tobeexecutedincreases.Marketliquidityfallsat thevery time the market needsit.
Manydiingschangeduring thecourseofacrisis,anda researcher needsamodel that takes
intoaccount thedistinctivefeatures ofa crisis (e.g., largelosses,high bid-askspreads).
CrashMetrrcs may be one waytoaddress this.Asanexample, thefollowingis theprofit/loss
onaderivative positionbasedonadelta-gammaapproximation.
n =f>AS+—(AS)2
2 where:
AS = changein diestock price
Takingthe derivativeof thismeasurewithrespect toASand solvingforAS givesthe changethat producesthemaximumloss: AS = and thatmaximumlossinabsolute
valueterms is:
max(loss)= min(II)= — $2
21
Foraderivative position that requires marginandmark-to-market,lettingmequal the margin requirement, theworst-casecash outflow issimplym timesthis amount:
mx This approximationcan bemoreprecisewiththe inclusion of die effects of other Greeks(e.g., thetas),counterpartyrisk,andotherfactors.
Another methodfor examining dieliquidityconsequencesassociatedwith worst-case
scenarios is toapplythe basic procedure abovetoanextreme-value mediod estimated widi expectedshortfall (ELS).The cash flow would dien bein x ES.
These twovariationsofestimatingtheworst-casecash flow donotaddressmany real-world complications.Aresearcher mightalso wishtoaddressthecomplicationswith simulations designedforspecific complications.Thosecomplications include:
• The discretenessof creditevents.
* Theinterdependencyofcreditevents.
• Theinteracdonof credit and marketrisk lactors.
* Complicationsarising from dieuse of credit-enhancementmethods,suchas netting arrangements, periodicsettlement,creditderivatives,creditguarantees,and credit triggers.
Crisis-scenarioanalysis isan alternative to theprobabilistic approachesdescribed
previously.This wouldinvolveanalyzing the potential problemsofaparticularevent(e.g.,
Topic38
CrossReferencetoGARPAssignedReading-Dowd,Chapter14
thefailureofa majorinstitution) and workingthrough thespecificdetailsof howthis might occur.This has dieadvantageofworkingdiroughscenariosatachosen level of detail and accountinglorcomplicationsandinteractions.Theproblemis that there will bealotof subjectivity,and theresultswilldepend heavily ondie assumptions used.
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Topic38 CrossReferencetoCARPAssigned Reading—Dowd,Chapterl4
KEY CONCEPTS
AIM38.1
Liquidityriskis diedegree towhicha tradercannottradeaposition withoutexcesscost, risk,orinconvenience.Liquidity dependsonfactors suchasthe number of tradersinthe market,thefrequencyand sizeoftrades,dietime it takestocarryout a trade, thecost,and the riskof dietransaction notbeingcompleted. ItaJso dependsoil the typeofassetanddie degreetowhich theasset is standardized,
AIM 38.2
Awider (narrower)spreadindicates lower (higher) liquidity. Ifanassetbecomes lessliquid, thespreadincreases,and diecostsof tradingtheassetincrease.
AIM38.3
Exogenousliquidityrefers tothe bid-askspread notbeing affected by the individual trades madebyinvestors. This is morelikelyto be thecasewhen the tiradesarerelativelysmall.
Endogenous liquidityreferstowhenagiventradecan influence theliquidityriskof the trade(i.e.,a trader submittingabuyor sell order that increases thespread),
AIM38.4
Themainchallengeinestimating liquid!tyisfindingthe best method.Oneapproachis Endingadjustmentstoaddon to the basicVaR.The researchermust understand how die inputs affect the'‘add-ons1'and,ifthereare morethanone,how the add-onsinteract, AIM38.5
Theconstantspread approach assumes diebid-askspreadisCOILScantandtheliquiditycost
issimply, LC= 0.5x spread xV,whichcan headdedinto theVaR formula.
VaR = [1—exp(p—oxzÿ)]x V
LVaR VaR + LC-[1-exp(p-ITHza) +0.5 xspread] xV
AIM38.6
Toaccountforendogeneity,a tradermayestimate theelasticityof the price to the
proportion of themarket inagiven large trade,denoted E, theproportion itself,denoted AN/N,andadjust dieVaR formula,
AP AN
LVaR =VaR x 1- ---- =VaRx 1~Ex
P N
CrossReferencetoGARPAssignedReading-Dowd,Chapter14
AIM38.7
Attemptingtosell quicklywill usuallyincrease the transactionscostsand may havean
unfavorableimpacton thesellingprice.Takingmore time tosellcanincreasetheexposure
toexogenousandunfavorablepricechanges.
AIM 38.8
Liquidityat risk (LaR)isalso known ascash flowat risk (CFaR) and is themaximumlikely cash outflowover the horizon periodataspecifiedconfidencelevel.
LaRcan be verydifferent from theVaRof thesameposition.Forexample,abondhedged witha futurescontracthas low VaR buthighLaRfrom thepossiblemargin callon the futurescontract.
Factorsthat affect future cashflowsare:borrowingorlending,margin requirements, collateralobligations,options positions, and changesin riskmanagement policy.
AIM38.9
Manythings changeduring thecourseofacrisis,anda researcherneedsamodel thattakes
intoaccount the distinctivefeatures ofa crisis(e.g.,largelosses,high bid-askspreads).
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Topic3ft CrossReferencetoGARP AssignedReading—Dowd,Chapter14
CONCEPT CHECKERS
Suppose diat portfolioXYZ hasa$1*000,000portfolio investedinastock that has adallystandarddeviationof2%,Thecurrent bid-askspreadof that stockis1%.
Assumingaconstantspread, whatis theliquidity-adjustedVaR (normal VaR)atdie 95% confidence level?
A. $5,000.
B. $38,000.
C. $44,200.
D. $43,000.
I.
Whichof thefollowingactionswould mostlikelyincreaseliquidityrisk?
A. Arapidexecution oforders.
B. Ahigherlevelof standardization of theasset.
C. An increase in the numberof tradersand adecrease in thesizeof those trades.
D. Adecreasein die number of traders andanincreasein thesizeof those trades.
2.
Whenagiventradecaninfluence theliquidityriskofa trade, this typeofliquidityis known as:
A. exogenous liquidity B. undefined liquidity.
C. endogenous liquidity.
D. operational liquidity.
Assuming thefollowing parameters: C, u=0.006, spread= 0.01,anda95%
confidencelevel, the ratioof LVaR toVaR isclosestto:
A. I.OS.
B. 1.51.
C. 1.66.
D. 2.04.
3.
4.
A trader hasa position worth5% of diesizeof the market(i.e.,AN/N -0.05) and
estimatesthat dieelasticityof pricetosizeof tradeis:E=-0.2.TheratioofLVaR to
VaR basedonlyonendogenousfactorsisclosestto:
A. 0.99.
B. 1.01.
C. 1.05.
D. 1.40.
Foradditional Book3, Topic38practicequestion*sec:
5.
Self-Test Questions:$4(page273)
PostFRM Exam Questions:95—9 (p&ge279)
CrossReferencetoGASP Assigned Reading—Dowd,Chapter 14
CONCEPT CHECKER ANSWERS
1. B LVaR= (1,000,000x1.65x0-02)+ (0.5 x1,000,000 *0.01)-,$38,000
2. D Larger and fewertraderswillultimatelylowerliquidity1-andincreaseliquidity'risk,
3, C Itis‘ÿendogenous"' becauseit isdeterminedbythetrading activityitself.
I,VaR 0.01
4. B VaR— =14-2x[l —ecp(—0.006x1.65)] =1.508
5. B APfl?=ExAN/N =-0,2x0.05=-0.01
LVaRVaR LTKHit-'”III =1—<—0.01)=1.01
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TheTallowingisireviewof (heOperilinjujHidIllLegfuLeclRiskManagementprinciplesdesignedLuaddress
theAIMstatements setforth hyGART®.This topicisaisocovered in:
MODEL RISK
Topic39
EXAM FOCUS
Modelrisk isthe risk associated with usingfinancial models diat areinherentlyflawed. Errors canarisefrom dataerrors, model misapplication, and inappropriate underlyingassumptions.
Properriskmanagementnecessitatesknowledgeablemanagersand processesfordocumenting, testing,and updating models. For die exam,be able to identifysources of model risk, and understandhow model riskcan he managed.