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Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 22: Value at Risk Multiple Choice Test Bank: Questions with Answers 1. Which of the following is true of the 99.9% value at risk? A. There is 1 chance in 10 that the loss will be greater than the value of risk B. There is 1 chance in 100 that the loss will be greater than the value of risk C. There is 1 chance in 1000 that the loss will be greater than the value of risk D. None of the above Answer: C A 99.9% VaR means that ther
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  Hull: Options, Futures, and Other Derivatives, Ninth EditionChapter 22: Value at Risk Multiple Choice Test ank: !uestions ith #ns ers 1.Which of the following is true of the 99.9% value at risk?A.There is 1 chance in 10 that the loss will be greater than the value of riskB.There is 1 chance in 100 that the loss will be greater than the value of riskC.There is 1 chance in 1000 that the loss will be greater than the value of riskD.one of the above Answer! CA 99.9% a# $eans that there is a 0.1% chance of the loss ecee&ing the a# level. This is 1 chance in 1000.'.The gain fro$ a (ro)ect is e*uall+ likel+ to have an+ value between ,-0.1 $illion an& /-0. $illion. What is the 99% value at risk?A.-0.1 $illionB.-0.1 $illionC.-0.12 $illionD.-0.10 $illion Answer! B The gain is unifor$l+ &istribute& between 30.1 an& /0. $illion &ollars. The (robabilit+ that it will be between 30.1 an& 30.1 $illion &ollars is therefore 1%. This $eans that there is a 99% chance that the loss will not be greater than -0.1 $illion. This is the 99% a#. 2.The gain fro$ a (ro)ect is e*uall+ likel+ to have an+ value between 3-0.1 $illion an& /-0. $illion. What is the 99% e(ecte& shortfall?A.-0.1 $illionB.-0.1 $illionC.-0.12 $illionD.-0.10 $illion Answer! AAs e(laine& in the answer to the (revious *uestion the a# level is -0.1$illion. Con&itional on the loss being greater than -0.1 $illion it is e*uall+ likel+ to have an+ value between -0.1 $illion an& -0.1 $illion.  The e(ecte& loss con&itional that it is greater than -0.1 $illion is therefore -0.1 $illion. This is the e(ecte& shortfall..Which of the following is true of the historical si$ulation $etho& for calculating a#?  A.4t 5ts historical &ata on the behavior of variables to a nor$al &istributionB.4t 5ts historical &ata on the behavior of variables to a lognor$al &istributionC.4t assu$es that what will ha((en in the future is a ran&o$ sa$(le fro$what has ha((ene& in the (astD.4t uses 6onte Carlo si$ulation to create ran&o$ future scenarios Answer! C The historical si$ulation $etho& assu$es that the (ercentage changes inall $arket variables &uring the net &a+ is a ran&o$ sa$(le fro$ the (ercentage changes in a certain nu$ber of (ast &a+s..The 10,&a+ a# is often assu$e& to be which of the followingA.The 1,&a+ a# $ulti(lie& b+ 10B.The 1,&a+ a# $ulti(lie& b+ the s*uare root of10 C.The 1,&a+ a# &ivi&e& b+ 10D.The 1,&a+ a# &ivi&e& b+ the s*uare root of 10 Answer! B The Basel co$$ittee rules allow the 10, a# to be calculate& as the one,&a+ a# $ulti(lie& b+ the s*uare root of 10. This is eactl+ true when losses on successive &a+s have in&e(en&ent nor$al &istributions with $ean 7ero.8.Which was the $ini$u$ ca(ital re*uire$ent for $arket risk in the 1998 B4 A$en&$ent? A.At least 2 ti$es the 10,&a+ a# with a 99% con5&ence levelB.At least 2 ti$es :,&a+ a# with a 9:% con5&ence levelC.At least ' ti$es ,&a+ a# with a 9% con5&ence levelD.1,&a+ a# with a 99% con5&ence levelAnswer! A The 1998 a$en&$ent calculate& ca(ital as k ti$es the 10,&a+ 99% a# where k was at least 2.:.An investor has -';000 investe& in stock A an& -;000 in stock B. The &ail+ volatilities of A an& B are 1.% an& 1% res(ectivel+ an& the coe<cient of correlation is 0.. What is the one &a+ 99% a#? Assu$e that returns are $ultivariate nor$al =ote that =,'.2'8>0.01> A.-1::B.-12C.-'1D.-221   Answer! A The stan&ar& &eviation of the change in the stock A (osition in one &a+ is ';000@0.01 -20. The stan&ar& &eviation of the change in the value of the stock B (osition in one &a+ is ;000@0.01  -0. The variance of the co$bine& (osition is 20 ' /0 ' /'@0.@20@0  ;00. The stan&ar& &eviation is the s*uare root of this or :8.18 an& the 99% a# is therefore '.22 ti$es :8.1: this or about -1::..What is the $etho& of testing how often a a# with a certain con5&ence levelwas ecee&e& in the (ast calle&?A.tress testingB.Back testingC.W6AD.The $o&el,buil&ing a((roachAnswer! BBack testing involves ea$ining how well a (articular a# $etho&olog+ woul& have worke& in the (ast. 4t counts ece(tions; which are situations where the a# level that woul& have been calculate&; was ecee&e&.9.Which of the following is true when &elta; but not ga$$a; is use& in calculating a# for o(tion (ositions?A. a# for a long call is too low an& a# for a long (ut is too lowB. a# for a long call is too low an& a# for a long (ut is too highC. a# for a long call is too high an& a# for a long (ut is too lowD. a# for a long call is too high an& a# for a long (ut is too highAnswer! DWhen ga$$a is ignore&; a# for long o(tion (ositions is too high an& a# for short o(tion (ositions is too low. This is &e$onstrate& for calls in igures ''. an& ''.8. The sa$e can easil+ be seen to be true for (uts.10.Which of the following is true?A.The *ua&ratic $o&el a((roi$ates &ail+ changes in using &elta an& ga$$a B.The *ua&ratic $o&el a((roi$ates &ail+ changes using &elta; but not ga$$aC.The *ua&ratic $o&el a((roi$ates &ail+ changes using ga$$a; but not &eltaD.one of the above Answer! A The *ua&ratic $o&el uses &elta an& ga$$a to a((roi$ate &ail+ changesas &escribe& in ection ''.  11.Which of the following is true?A.Cash ow $a((ing is a wa+ of calculating the (resent value of cash owsB.Cash ow $a((ing is use& to han&le interest rate e(osures in the $o&el buil&ing a((roachC.Cash ow $a((ing is use& to han&le interest rate e(osures in the historical si$ulation a((roachD.one of the above Answer! BCash ow $a((ing is a wa+ to han&le interest rates when the $o&el buil&ing a((roach is use&. =ee (age 08,0:>1'.Which of the following &escribes stresse& a#?A.4t is base& on $ove$ents in $arket variables in stresse& $arket con&itionsB.4t is a# with a ver+ high con5&ence levelC.4t is a# $ulti(lie& b+ a factor of 2D.one of the above Answer! Atresse& a# was intro&uce& in Basel 44.. 4t calculates a# base& on $ove$ents in $arket variables in stresse& $arket con&itions.12.A er$an bank has e(osure to the EF00. Which of the following is trueA.The EF 00 in&e shoul& be alwa+s be $easure& in G.. &ollars when a# is calculate&B.The EF 00 in&e shoul& be alwa+s be $easure& in euros when a# is calculate&C.ither A or B can be &oneD.The EF 00 in&e shoul& be $easure& in euros onl+ if the bank has not got a G.. subsi&iar+.Answer! BAll foreign assets shoul& be $easure& in the &o$estic currenc+.1.Which of the following is true of a covariance $atri?A.The nu$bers on the &iagonal are variancesB.The nu$bers on the &iagonal are stan&ar& &eviationsC.The nu$bers on the &iagonal are all one. D.The nu$bers on the &iagonal are all 7ero Answer! A The &iagonal nu$bers are variances. The oH,&iagonal nu$bers show the covariance between two variables.
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