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1 ACT 2020, FINAL EXAMINATION ECONOMIC AND FINANCIAL APPLICATIONS APRIL 16, :00AM - 11:00AM University Centre RM (Seats ) Instructr: Hal W. Pedersen Yu have 120 minutes t cmplete this examinatin. When the invigilatr instructs yu t stp writing yu must d s immediately. If yu d nt abide by this instructin yu will be penalised. Each questin is wrth 10 pints. If the questin has multiple parts, the parts are equally weighted unless indicated t the cntrary. Prvide sufficient reasning t back up yur answer but d nt write mre than necessary. This examinatin cnsists f.12 questins. Answer each questin n a separate page f the exam bk. Write yur. name and student number n each exam bk that yu use t answer the questins. Gd luck! GJ.: [1~l'f QI 7 f,f~j ~ Suppse yu desire t shrt-sell 400 shares f JKI stck, which has a bid price f $25.12 and an ask price f $ Yu cver the shrt psitin 180 days later when the bid price is $22:87 and the ask price is $ a. Taking int accunt nly the bid and ask prices (ignring cmmissins and interest), what prfit did yu earn? b. Suppse that there is a 0.3% cmmissin t engage in the shrt-sale (this is the cmmissin t sell the stck) and a 0.3% cmmissin t clse the shrt-sale (this is the cmmissin t buy the stck back). Hw d these cmmissins change the prfit in the previus answer? c. Suppse the 6-mnth interest,rate is 3% and that yu are paid nthing n the shrt-sale prceeds. Hw much interest d yu lse during the 6 mnths in which yu have the shrt psitin?

2 c ~ rh) c J f~.» C"I(isJ ABC stck has a bid price f $40.95 and an ask price f $ Assume there is a $20 brkerage cmmissin. 3. What amunt will yu pay t buy 100 shares? b. What amunt will yu receive fr selling 100 shares? c. Suppse yu buy 100 shares, then immediately sell 100 shares with the bid and ask prices being the same in bth cases. What is yur rund-trip transactin cst? [ q ~-_.-~._ An ff-market frward cntract is a frward where either yu have t pay a premium r yu receive a premium fr entering int the cntract. (With a standard frward cntract, the premium is zer.) Suppse the effective annual interest rate is 10% and the S&R index is Cnsider I-year frward cntracts. (I) m --- n 'u ' n._un._._ [Suppse yu are ffered a lng frward cntract at a frward price f C; t h) $1200. Hw much wuld yu need t be paid t enter int this cntract? (~J '\ Suppse yu are ffered a lng frward cntract at $1000. What wuld [ 5«0..1 yu be willing t pay t enter int this frward cntract? [ pf,'c.t-.(.i. c~_ L -#- 'f. J C '>,b) t.\tb) [tf{}) Suppse MNO stck pays n dividends and has a current price f $150. The frward price fr delivery in ne year is $ Suppse the ne-year effective annual interest rate is 5%. (a) Graph the payff and prfit diagrams fr a shrt frward cntract n MNO stck with a frward price f $ (b) Is there any advantage t shrt selling th~ stck r selling the frward cntract? (c) Suppse MNO paid a dividend f $3 per year and everything else stayed the same. Is there any advantage t sellii1g the frward cntract? [ r h v. J ~ ) Idt: r. c.." t..v~ f~, Jve- di'-jinl,-c.; - J

3 h,(' Q5 ~ 6l Cc::1 ) assume the effective 6-mnth interest rate is 2%, the S&R 6-mnthfnvard price is $1020. and use these premiumsfr S&R ptins with 6 mnths t expiratin: Strike $ Call $ Put $ Suppse the premium n a 6-mnth S&R call is $ and the premium n a put with the same strike price is $ What is the strike price? ~2~!.tlJ..IJ-----u--u u.. m ' Suppse yu invest in the S&R index fr $1000, buy a 950-strike put, and sell a 1100-strike call. Draw a prfit diagram fr this psitin. / r"f";/;- l~d~.s,] c.-b 5~ """I'.. /011", [ C/c""'/J C-J,..lIr( -/:.0.. L I(\~~! -iltc.. ~.;.A.rVfL [,- e '(.t- '1.ll:~,_ Suppse that firms face a 40% im:me tax rate n all prfits. In particular, lsses receive full credit. Firm A has a 50% prbability f a $1000 prfit and a 50% prbability- f ;-$600 lsseach-year.--pfrmub has a 500/0 prbability f a $300 prfit and a 50% prbability f a $100 prfit each year. a. What is the expected pre-tax prfit next year fr firms A and B? b. What is the expected after-tax prfit next year fr firms A and B? KidC Cereal Cmpany sells "Sugar Crns" fr $2.50 per bx. The cmpany will need t buy 20,000 bushels f crn in 6 mnths t prduce 40,000 bxes f cereal. Nn-crn csts ttal $60,000. What is the cmpany's prfit if they purchase call ptins at $0.12 per bushel with a strike price f $1.60? Assume the 6-mnth interest rate is 4.0% and the spt price in 6 mnths is $1.65 per bushel..---_.---

4 The MNO stck trades at $66, the risk-free rate is 5%, and the MNO stck pays cnstant quarterly dividends f $0.45. Assume that the first dividend is cming three mnths frm tday, and the last ne cming immediately befre the expiratin f the frward cntract. Yu can trade MNO single stck futures with an expiratin f nine mnths. Suppse yu bserve a 9-mnth frward price f $ What arbitrage wuld yu undertake? [ (l. ~I.(:t-lt J<..Jcr", b<- "!'--~'.f 7~'" f.of _k.~ lo"~ Cnj[.. f/,,""j.. :f( 6 I h,-" ~ <. - J ~ ;:; :5-15J Suppse the S&R index is 800, and that the dividend yield is O. Yu are an arbitrageur with a cntinuusly cmpunded brrwing rate f 5.5% and a cntinuusly cmpunded lending rate f 5%. n _ Suppsing that there are n transactin fees a cash-and-carry arbitrage is nt Pr"fitahIe if the frward price is less than A. A reverse cas~_-_<l.nd -carryartiitrage-is" n6tpifi iabie -ifthef'-i-ward pircels greater than 6" Nw suppse that there is a $1 transactin fee, paid at time 0, fr ging either lng r shrt the frward cntract. C~~,-,.ie. the upper and lwer n-arbitrage bunds F - a ~ F -t

5 Suppse that il frward prices fr 1 year, 2 years, and 3 years are $20, $21, and $22. The I-year effective annual interest rate is 6.0%, the 2-year interest rate is 6.5%, and the 3-year interest rate is 7.0%. What is the 3-year swap price? ':;~r I ~./i.j Using the zer-cupn bnd yields in Table 8.9, what is the fixed rate in a 4-quarter interest rate swap?

6 fa) A shrt sale f JKI stck entails brrwing shares f JKI and then selling them, receiving cash, and we learned that we sell assets at the bid price. Therefre, initially, we will receive the prceeds frm the sale f the asset at the bid (ignring the cmmissins and interest). After 180 days, we cver the shrt psitin by buying the JKI stck, and we saw that we will always buy at the ask. Therefre, we earn the fllwing prfit: 400 x ($25.12), x ($23.06) = $ S z..tj. c~ b) We have t pay the cmmissin twice. The cmmissin will reduce ur prfit: 400 x ($25.12) x ($25.12.) x (400 x ($23.06) x ($23.06) (.c3) 4-0 <) [ Z.5., L ( I -.c~) b (I T "".;)J.=: f 7 b6. {'Cif c) The prceeds frm shrt sales, minus the cmmi~sin charge are $10,011#88 (r $1O,Oltt' if yu ignre the cmmissin charge). Since the 6-mnth interest rate is given, and the perid f ur shrt sale is exactly half a year, we can directly calculate the interest we culd earn (and that we nw lse) n a depsit f $10,01;'8: 8 - I 0/ c) I'7. 'tg (. 03) r, withut taking int accunt the cmmissin charge: a) Remember that the terminlgy bid and ask is frmulated frm the market makers perspective. Therefre, the price at which yu can buy is called the ask price. Furthermre, yu will have t pay the cmmissin t yur brker fr the transactin. Yu pay: ($41.05 x 100) + $20 = $4, b) Similarly, yu can sell at the market maker's bid price. Yu will again have t pay a cmmissin, and yur brker will deduct the cmmissin frm the sales price f the shares. Yu receive: ($40.95 x 100) - $20 = $4, c) Yur rund-trip transactin csts amunt t: $4, $4, = $50

7 (jj The frward price f $1,200 is wrse fr us if we want t buy a frward cntract. T understand this, suppse the index after ne year is $1,150. While we have already made mney in part a) with a frward price f $1,100, we are still lsing $50 with the new price f $1,200. As there was n advantage in buying either stck r frward at a price f $1,100, we nw need t be "bribed" t enter int the frward cntract. We smehw need t find an equatin that makes the tw strategies cmparable again. Suppse that we lend sme mney initially tgether with entering int the frward cntract s that we will receive $100 after ne year. Then, the payff frm ur mdified frward strategy is: $ST - $1,200 + $100 = $ST - $1,100, which equals the payff f the "brrw t buy index" strategy. We have fund the future value f the premium smebdy needs us t pay. We still need t find ut what the premium we will receive in ne year is wrth tday. We need t discunt it: $100/ ( ) = $ Similarly, the frward price f $1,000 is advantageus fr us. As there was n advantage in buying either stck r frward at a price f $1,100, we nw need t "bribe" smene t sell this advantageus frward cntract t us. We smehw need t find an equatin that makes the tw strategies cmparable again. Suppse that we brrw sme mney initially tgether with entering int the frward cntract s that we will have t pay back $100 after ne year. Then, the payff frm ur mdified frward strategy is: $ST - $1,000 - $100 = $ST - $1,100, which equals the payff f the "brrw t buy index" strategy. We have fund the future value f the premium we need t pay. We still need t find ut what this premium we have t pay in ne year is wrth tday ) = $ We shuld be willing t pay $90.91 t We simply need t discunt it: $100/0 enter int the ne year frward cntract with a frward price f $1,000. (a) It des nt cst anything t enter int a frward cntract-as a seller, we d nt receive a premium. Therefre, the payff diagram f a frward cntract cincides with the prfit diagram. The graphs have the fllwing shape: 200 Payff ciagram f a shrt psitin in the xyz r""""rd I 1 _ -t- shrt frward cruact ~ 1>7 50 -s ISO s Stck price

8 (b) We can invest the prceeds frm the initial shrt-sale. We d s by lending $150. After ne year we receive: $150 x (I ) = $ Therefre, ur ttal prfit at ex.piratin frm the shrt sale f a stck that was finflnced by a lan was: $ Sf' where Sr is the value f ne share f MNO at expiratin. But this prfit frm selling the stck and lending the prceeds is the same as the prfit frm ur shrt frward cntract, and nne f the psitins requires any initial cash-but then, there is n advantage in investing in either instrument. (c) The wner f the stck is entitled t the dividend. If we brrw an asset frm a lender, we have the bligatin t make any payments t the lender that she is entitled t as a stckhlder. Therefre, as a shrt seller, we have t pay the dividend. As the seller f a frward cntract, we d nt have t pay the dividend t ur cunterparty, because she nly has a claim t buy the stck in the future fr a given price frm us, but she des nt wn it yet. Therefre, it des matter nw whether we shrt-sell the stck r the sell the frward cntract. Because everything else is the same as in part (a) and (b), it is nw beneficial t sell the frward cntract. This questin is a direct applicatin f the Put-Call-Parity. We will use equatin (3.1) in the fllwing, and input the given variables: Call (K, /) - Put (K, t) = PV (F.t - K) } Call (K, /) - Put (K, t) - PV (FOt) = -PV (K) } Call (K, t) - Put (K, t) - S = -PV (K) K, 1.02 } $ $ $1000 = -- } K = $ Our initial cash required t put n the cllar, i.e. the net ptin premium, is as fllws: -$ $ = -$ Therefre, we receive nly 10 cents if we enter int this cllar. The psitin is very clse t a zer-cst cllar. The prfit diagram lks as fllws:

9 100 ~ it a 0,- Prfit lia!tam: lng index. lng 950 P~. shrt 1107.caB -20,- -40" ,- 80,- II' : _/C.,(} -60 H I I I I I I I I gio I Index price 1100 I A It '--0'-" -t. (. 5~1V. t-. "\A :,:: D S [5.,. _ JDOU-"--)Jr Uqs-s. ) (I-L)J +- (. >1. '67"}{L..2.-) - (5. -1I.:.7)-t-J ~h 90 ) -10.':; 5,. ~ Q50 S - 1 t. Q50 L- >,.- = I/7L.5-r (I"'L I\'~ >< L,fl v.i. '-J r "~-h ' IA (! kll r f-. J

10 a) Expected pre-tax prfit Firm A: E[Prfit) = 0.5 x ($1,000) x (-$600) = $200 Firm B: E[Prfit] = 0.5 x ($300) x ($100) = $200 Bth firms have the same pre-tax prfit b) Expected after tax prfit Firm A: (I) Pre-Tax Operating Incme (2) Taxable Incme (3) 40% (3b) Tax Credit After-Tax Incme (including Tax credit) This gives an expected after-tax prfit fr finn A f: bad state -$600 $0 $240 -$360 gd state $1,000 $ 1,000 $400 $600 ELPrfitJ = 0.5 x (-$360) x ($600) = $120 Firm B: (I) Pre-Tax Operating Incme (2) Taxable Incme (3) 40% (3b) Tax Credit After-Tax Incme (including Tax credit) bad state $100 $100 $40 $60 gd state $300 $300 $120 $180 This gives an expected after-tax prfit fr firm B f: ELPrfit] = 0.5 x ($60) x ($180) = $120 If lsses receive full credit fr tax lsses, the tax cde des nt have an effect n the expected after-tax prfits f firms t!1athave the same expected pre-tax prfits, but different cash-flw variability. % Pc~:t -:;:::;-- ~ <."(.~" '-;. Lf,/ c" ( t..5);; /19 /" L' 0 C.5-l-; ~ I? 0 ~." -f r; c ( I. bs) == t{} 0 C.D / / / H dyt. fj d Cf;; 1-~ (HO"" [ (j. b5 - J. b<» + -. j'l (I. ~<I)J ::;: 0<> rr.,.~:f. ; IQ~D-'>V -- 9~cv.;> + (-lif9h) ~ ~5lf (A",-S,vlr :; 11 S;5V CF - J «Iff b 5. II "Ij,(f-'J"': 1.5..( '111., ~) - ~ cuo ()u. II.bl c.,(.tt.){/.clfj / / / ) / ~ f ~5'01 "

11 First, we need t find the fair value f the frward price. We plug the cntinuusly cmpunded interest rate, the dividends and the time t expiratin in years int the valuatin frmula: F;, T = S ert - ~ Derx(T-ti). 0 Li=1 = $66eO.OSXO.75 _ 0.45 x eo.05x(o s,) x eo.05x{o i) x eo.osx(o.7s-0.75,) = $ x ( I) = $ x(3.0379) = $ If we bserve a frward price f $67.50, we \cnw that the frward is t expensive, relative t the fair value we have detennined. Therefre, we will sell the frward at $67.50, and create a synthetic frward fr $67.155, making a sure prfit f $ ~ we sell the real frward, we engage in cash and carry arbitrage: Descriptin Shrt frward Buy stck Brrw Receive 1st dividend, invest dividend Receive 2nd dividend, invest dividend Receive 3rd dividend TOTAL Tday -$66.00 $66.00 in 3 Mnths $66.00 $0.45 -$0.45 in 6 Mnths $0.45 -$0.45 in 9 Mnths $ Sr Sr -$ $ $ $0.45 $0.345 This psitin requires n initial investment, has n MNO price risk, and has a strictly psitive payff. We have explited the mispricing with a pure arbitrage strategy. () 00 F:._;:; b1.155.j' Sh y- i-.+:,y' ~(p.-j {l;~l ("'1C"<-1 E1- ~j (I', r-.f;-r'"\. ht.- in \,.. e-r (.. Lh l. A +ii~k

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13 We first slve fr the present value f the cst per three barrels, based n the frward prices: $20 $21 $ = (1.065)2 (1.07)3 We then btain the swap price per barrel by slving: x x x = (1.065)2 (1.07)3 - } x = c-f(~1'-f).t L P{~'ll-)+ L f(~~'f)tc: d(~,) + (1(,,/1) / - P (.)/,),Olc;'j () 0<:- Frm the given zer-cupn bnd prices, we can calculate the ne-quarter frward interest rates. They are: Quarter Frward interest rate Nw, we can calculate the swap prices fr 4 and 8 quarters accrding t the frmula: X = ~, "'! I P (0, ti )r (ti-i, ti), where n = 4 r 8 I:7=, P (0. ti) This yields the fllwing prices: 4-quarter fixed swap price: % J