Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 22: Value at Risk Multiple Choice Test ank: !uestions "ith #ns"ers 1. Which Which of the follow following ing is true true of the the 99.9% value value at at risk? A. There is 1 chance in in 10 that that the loss will be greater than the value value of risk B. There is 1 chance in in 100 that that the loss loss will be be greater greater than the value of risk C. There is 1 chance in in 1000 that that the loss loss will be be greater greater than the the value of risk D. one one of of the the above above Answer! C A 99.9% "a# $eans that there is a 0.1% chance of the loss ecee&ing the "a# level. This is 1 chance in 1000.
'. The gain fro$ a (ro)ect is e*uall+ e*uall+ likel+ likel+ to have an+ value between between ,-0.1 $illion an& /-0. $illion. What is the 99% value at risk? A. -0 -0.1 .1 $ill $illio ion n B. -0 -0.1 .1 $ill $illio ion n C. -0 -0.1 .12 2 $ill $illio ion n D. -0 -0.1 .10 0 $il $illi lion on Answer! B The gain is unifor$l+ unifor$l+ &istribute& between between 30.1 an& /0. $illion &ollars. The (robabilit+ (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+ e*uall+ likel+ likel+ to have an+ value between between 3-0.1 $illion an& /-0. $illion. What is the 99% e(ecte& shortfall? A. -0 -0.1 .1 $ill $illio ion n B. -0 -0.1 .1 $ill $illio ion n C. -0 -0.1 .12 2 $ill $illio ion n D. -0 -0.1 .10 0 $il $illi lion on Answer! A As 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& e(ecte& loss con&itional con&itional that it is is greater than -0.1 $illion $illion is therefore -0.1 $illion. This is the e(ecte& shortfall. . Which of of the following is true of the historical historical si$ulation si$ulation $etho& for calculating "a#?
A. 4t 5ts historical &ata on the behavior of variables to a nor$al &istribution B. 4t 5ts historical &ata on the behavior of variables to a lognor$al &istribution C. 4t assu$es that what will ha((en in the future is a ran&o$ sa$(le fro$ what has ha((ene& in the (ast D. 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 in all $arket variables &uring the net &a+ is a ran&o$ 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 following A. The 1,&a+ "a# $ulti(lie& b+ 10 B. The 1,&a+ "a# $ulti(lie& b+ the s*uare root of10 C. The 1,&a+ "a# &ivi&e& b+ 10 D. The 1,&a+ "a# &ivi&e& b+ the s*uare root of 10 Answer! B The Basel co$$ittee rules allow the 10,"a# to be calculate& as the one, &a+ "a# $ulti(lie& b+ the s*uare root of 10. This is eactl+ true when losses on successive &a+s have in&e(en&ent nor$al &istributions with $ean 7ero. 8. Which was the $ini$u$ ca(ital re*uire$ent for $arket risk in the 1998 B4 A$en&$ent? A. At least 2 ti$es the 10,&a+ "a# with a 99% con5&ence level B. At least 2 ti$es :,&a+ "a# with a 9:% con5&ence level C. At least ' ti$es ,&a+ "a# with a 9% con5&ence level D. 1,&a+ "a# with a 99% con5&ence level Answer! A The 1998 a$en&$ent calculate& ca(ital as k ti$es the 10,&a+ 99% "a# where k was at least 2. :. An investor has -';000 investe& in stock A an& -;000 in stock B. The &ail+ volatilities of A an& B are 1.% an& 1% res(ectivel+ an& the coe
0.01> A. -1:: B. -12 C. -'1 D. -221
Answer! A The stan&ar& &eviation of the change in the stock A (osition in one &a+ is ';[email protected] -20. The stan&ar& &eviation of the change in the value of the stock B (osition in one &a+ is ;[email protected] -0. The variance of the co$bine& (osition is 20 '/0'/'@0.@20@0 ;00. The stan&ar& &eviation is the s*uare root of this or :8.18 an& the 99% "a# is therefore '.22 ti$es :8.1: this or about -1::. . What is the $etho& of testing how often a "a# with a certain con5&ence level was ecee&e& in the (ast calle&? A. tress testing B. Back testing C. W6A D. The $o&el,buil&ing a((roach Answer! B Back testing involves ea$ining how well a (articular "a# $etho&olog+ woul& have worke& in the (ast. 4t counts ece(tions; which are situations where the "a# level that woul& have been calculate&; was ecee&e&. 9. Which of the following is true when &elta; but not ga$$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 low B. "a# for a long call is too low an& "a# for a long (ut is too high C. "a# for a long call is too high an& "a# for a long (ut is too low D. "a# for a long call is too high an& "a# for a long (ut is too high Answer! D When ga$$a is ignore&; "a# for long o(tion (ositions is too high an& "a# for short o(tion (ositions is too low. This is &e$onstrate& for calls in igures ''. an& ''.8. The sa$e can easil+ be seen to be true for (uts. 10.Which of the following is true? A. The *ua&ratic $o&el a((roi$ates &ail+ changes in using &elta an& ga$$a B. The *ua&ratic $o&el a((roi$ates &ail+ changes using &elta; but not ga$$a C. The *ua&ratic $o&el a((roi$ates &ail+ changes using ga$$a; but not &elta D. one of the above Answer! A The *ua&ratic $o&el uses &elta an& ga$$a to a((roi$ate &ail+ changes as &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 ows B. Cash ow $a((ing is use& to han&le interest rate e(osures in the $o&el buil&ing a((roach C. Cash ow $a((ing is use& to han&le interest rate e(osures in the historical si$ulation a((roach D. one of the above Answer! B Cash 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&itions B. 4t is "a# with a ver+ high con5&ence level C. 4t is "a# $ulti(lie& b+ a factor of 2 D. 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 EF00. Which of the following is true A. 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 &one D. The EF 00 in&e shoul& be $easure& in euros onl+ if the bank has not got a G.. subsi&iar+. Answer! B All 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 variances B. The nu$bers on the &iagonal are stan&ar& &eviations C. 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.
1.Consi&er a (osition in o(tions on a (articular stock. The (osition has a &elta of 1' an& the stock (rice is 10. Which of the following is the a((roi$ate relation between the change in the (ortfolio value in one &a+; &F; an& the return on the stock &uring the &a+; & A. &F1'& B. &F1.'& C. &F1'0& D. &F''& Answer! C 4f is the stock (rice an& the change in the stock (rice is &; fro$ the &e5nition of &elta we know that &F1'&. This $eans that &F1'=&I>. &I is &. 4n this case 10 so that C is correct. 18.A (osition in o(tions on a (articular stock has a &elta of 7ero an& a ga$$a of . The stock (rice is 10. Which of the following is the a((roi$ate relation between the change in the (ortfolio value in one &a+; &F; an& the return on the stock; & A. &F ti$es the s*uare of & B. &F ' ti$es the s*uare of & C. &F '0 ti$es the s*uare of & D. &F '00 ti$es the s*uare of & Answer! D 4f is the stock (rice an& the change in the stock (rice is &; the change in the (ortfolio value is 0.@@=&> '. This is ' '=&I>'. &I is &. 4n this case 10 so that D is correct. 1:.4n a (rinci(al co$(onents anal+sis which of the following is the *uantit+ of a (articular factor in an observation A. actor loa&ing B. actor score C. actor si7e D. actor rating Answer! B The *uantit+ of a (articular factor in the observation of changes on a (articular &a+ is known as the factor score. 1. 4n the case of interest rate $ove$ents the $ost i$(ortant factor corres(on&s to A. A (arallel shift B. A slo(e change C. A bowing D. An increase in short rates Answer! A
The $ost i$(ortant factor is the one corres(on&ing to a (arallel shift. This accounte& for over 90% of the variance for the &ata in ection ''.9. 19.4n the case of interest rate $ove$ents the secon& $ost i$(ortant factor corres(on&s to A. A (arallel shift B. A slo(e change C. A bowing D. An increase in short rates Answer! B The secon& $ost i$(ortant factor is a slo(e change =or twist>. 4n the ea$(le in ection ''.9 this accounte& for about :% of the variance in the &ata. '0.Which of the following is true A. (ecte& shortfall is alwa+s less than "a# B. (ecte& shortfall is alwa+s greater than "a# C. (ecte& shortfall is so$eti$es greater than "a# an& so$eti$es less than "a# D. (ecte& shortfall is a $easure of li*ui&it+ risk wheras "a# is a $easure of $arket risk Answer! B (ecte& shortfall an& "a# can both $easure $arket risk. (ecte& shortfall is the e(ecte& loss level con&itional on the loss level being greater than "a#. B+ &e5nition e(ecte& shortfall $ust be greater than "a#.
