Chap 4 Practice - For the: problems of Chapter-43.,...

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Unformatted text preview: For the: problems of Chapter-43., consider the following two 13th 3.0. extracts Oil-g, with fixed Costs of $20! barrel and variable costs 0f $3fbarr l. I! The one-year forward price of oil is $42fha1‘1'el, The levee-year can 4%. Che year oil Option prices are shown in the table helew: Stuke Call Price Put Page 35 ' $8.085 $1.359 40 $5.106 $3 185 42 $4.174 $4 174 45 $303: $5 915 50 $1 71 1 $9 397 2. - Compute the estimated profit in one year if 30.. buys a put Option wit. a strike of $40(_$_50). Draw 1 pro-fit diagrams for both options, and include- the unhedged prefit. Des ribe the difference in the pt‘Ofit diagrams of the $40~strike hedged and the $50-Jst1‘ike hedged peitieh. 3. If Plastics Corp. dees scathing to manage all price risk, what is its pro. ehe year fmm new? per barrel 01“ oil? If it wants to hedge the price of oil, should Plastics Corp buy or sell oil forward-s? e their oil price exposure with future so'that they are completely ' 7 e, how manyeil futures shehld they'uy per unit of resin pI-‘educed? w"? Construct graphs illu tratihg both unhedged and _ '. ' - 4. If Plastics Corp. chooses te‘hedg immune to changes in the oil prie- What is its estimated profit one yew; from he hedged pesitions. ' 7. Seppos Find the strike price for an oil _ put that wouid generate a zero-ms cdntinuouely compouflded interest mike 0f 4%, one year. The oil forward prim is $42. Use the fellowng Table far Questiems 4.9 and 4.10: Extratfien Schedule (Millions of Barreie) Scenarm A Scenarm B (b) What is the eerreletion coefficient between eil price and the ex -What about the correlanen coefficiem between 0i ' difference. if any. W-.- Compute me variance—miniming hedge mtie for 8.0.? s revenues fer Seenarie C. What is the reducuon m the standard deviatien BEE 3.033 revenge? " A 1'1 Swer 50m 911' 7 7 _ . Chapter 4' Introduction to Risk Maeagement 1. The following tame summarizes the unhedged "and hedged prefit calenhtiene: Hal-f'FHII‘“ fl Unhedged Profit on 1/2 She 1 Net Income on {Oil Price per Barrel _ Forward Centrfet fledged Pmfit ' in One Year Tetal Cast Profit $25 $20 ' —-—$3 ' . $8.50 $5.50 $30 ‘ * $2.8 +$2 $6 ' ' $8 $35 _ $28 ' +557 - $3.50 - P $10.50 $40 $28 +$12 $1 $13.00 " $45 $28 ' +$17 451.50 $1550 550 $28 +$22 —$4 $13.00 r T_ . m_._-.—- _.__... #HLM-H_J_-HMF_—u—g—Iflu—_A_Fu_nl—I —-_-.._._- '-—'—I-I-I——I——I-'I-rl- u-ru—-a--—a,—In_n_--—-_-_ -|--—--u—-.—.—.— 3' '1' '3 i1 EDI CE ri. .—-|..—_-'F‘ ‘‘‘ _I_-I-I. m .—-.l----n- nay—Hm .- fl-u—u—u—I-a-I_- #WWH -I-.—- Wlmmmqum I F f I _M_'_'_ ________ ____m I___';l1—“_m._u _ _ .-\-.-\.!r 21—“! ——-r-I- wwwww a-I.-u—Ia—u.-.-n—u——_-\.—u.— _u_-u-n--— aaaaa flmHII-u—l—l-L-flri—I—I-J—w-n-n—J fl'umJflmufipi-MII—n-i’I—fl-lmrl 78 2. McDonald Please note that the continuously compounded effective annual interest rate is esp(0.04) -— .._ $3.315. The following tab for the other put is similar hedging strategies. ' Derivatives Markets, Second Edition rate of interest is given: it is 4%. Therefore. the "- 0.0408. Ia this exercise, to calcul te overall profit-s. Onstrike put. it is: 3.185 >4 1.0408. 2 he $40.00—strike n at. The calculation 1e shows the profit calculations for t rams for both . The figure on the next page compares the profit dia Profit on Long Oil Price Unhedged $40.00—Strike Put Net Income on in One Year Total Cost Profit Option Pot Pie mm fledged Profit $25 $28 —-$3 $15 $33 5 $8.685 $30 $28 +$2 $10 $33 - 5 $8.685 $35 $28 +$7 $5 $33 5 $8.685 $40 $28 +$12 0 $33 5 $8,685 $45 $28 +9517 0 $3.3 5 $13685 $50 $28 +3322 0 $3.3 5 $18.685 Profit diagram $4t3-etrike put 60 5E! 30- 40 higher oil prices than the difference for the $40 + unhedged profit- %2 hedged prefit 40 Oil price fl p59. 35 40 Cat price 50' D 20 lease, the unhedged positin yields less profit than . - he protection on the downide. Also note that the he unhedged position and the 50-strike hedged position is larger for strike. We receive in return a higher profit in the low oil price region with the $50 oil price. - . m..."— - - —--. . ._"“_-.--. r a _ l i . _ . 1"- —.- fiwHI—hrmjr—pp- -'I.-J-||-r—\.- 9999 III-I—I-I-I-Ihl'I-r-II—I-fi—u—ni—I'I—h“ —..-J Iona—mi- r 'r'il‘rl-fihmm ”-'_"'— ‘ ' ' 1 1 '- LJ-J Answer Sectioa ' _ 7‘) he variablr oil costs per onii of resin - produce two units of resin. T c sis. minus oil-variable coSts. Plastics uses one barrel of oii to minus fixed are thus 0.5 x pun. We can write out the profits as revenue and minus non-oil variable cost: = 04:410..“ $15 #957 ~— $3.30 W 0.5m“i :2 $4.70 ~— 0.1m“ ' 1" unit of l‘esio of Plastics l orp. depends on the oil price. PE. iasties The following graph shows how the profit pe Profit diagram of unheaged pflfiiiififi ._n-.-.-.- “lap—l—I-I-I'I '——I——I' —I—_-——- —l--l'-'I'-—I—l—-'-I'I-I—I--\. 5 r—w— H—MflT—flc—Wtfi—"w'“*‘THW.--.--__. .. f _ ' H- uohedged profit ‘ E T t ._ _ - .. __ __ 4 i_. ‘7— . _: l l w + i 3i” + -i i + l "i . 1 i '-“' 2 i- - i: i' I ':. i. ii— i 1 l' ‘ i- E ‘l g EL l -l {3 §~ “ I l i - I —+ l l f l i .3- ‘1 a 1 l i ~1- 1 + _ ‘El' i + i l * l i + l L 'i -3 i + i i -4 ..__._.. ..-___-__ -.1_-.._.._._-...- a- .... ._i . ____. . _ E- .1 _ __- E. - 3 D 18 2D“ SCI 45} Si} ED fl! ' *fl The higher the oil price. the lowet the profits of Plastics Corp. Therei re. Plastics Corp. needs to buy futut'es to hedge their esposure. that the profit of Plastics Corp. can be esci‘ibed as: i 3 $4.70 -— (ll >< p“ii ' iiiiisiiss 0 of a futures contract to completey remove the oil pr- 4. We have seen in question 4.3 Therefore. we will need to buy 1/ 1 ice risk from Plastics Corpfs profits. ' Profit on 1/10 'Uhhedged Profit Long Forward fledged ’mfit s25 . $2.20 is} .70 - s0. 0 $30 $1.70 - ds120 — $0-0 $35 $1.20 saw s0. -. $40 $0.70 —s0.20 - s0. 0 $45 $0.20 ' $0.30 s0. 0 s50 _ _ I $0.30 $0.80 __ s0. 80 McDDnald ' Derivaz‘iws Markets, Sacend Edition M We: abtain the following profit diagrams: Pmfit diagram {if unhedged Wait-inn and hedged Wait-1cm 5 1 . : + unhedged pmfii ' + J“ I 9% hedged pmfit 4 ++ T+ %. 3 +4 .1... + + 2 ++ + + .1..— 1 ++ E _+ E'ifit+++:&+-fivi++vr+fl€$7h~llfiv$fii$$iifi§c$1¢7§+++++$i~¥+$+fi¥ u. .—}-_ ed ' Profit on 1/10 0113 Oil Price Unhedg in One year Profit $35.00-Strike Call $25 $.20 0 ' 30.8415 $30 $1.70 " 0 $08415 $35 $1.20 0 $08415 $40 $0.70 $0.50 $03415 $45 $0.20 $1 #00 $03415 $50 —$O.30 $ 1. .50 _ $03415 WWW Anzawur Scam-n ' '3! We obtain the following pmfit diagrmm: OH price Plastics Corp. will sell a 20113:; which maans that they buy 2 {ion pramium position, and find it; future: value. We haw gative value I am; we haw a cash inflow. to compute for. each case the net Up ($1.71 1 ~— $3.185) >< 1.0408 :2 w$i534¢ Note: that tha FIE: Oil Price in Unhedged Profit on .1116 Pnjfit on 1/10 Short 40 PM Long One Year Profit "$25 $2.20 451.50 $30 $1.70 H$I .00 $35 $1.20 #33050 $40 $0.70 a $0 $45 $0.20 $0 $550 45030 $0 “We”. r—--— J_ -...__.___.,._.-_ _i M 46 {iii {an ca 0 0 0 0 .0 0. 50 Call he can he and gel! the, put leg. WE haw: _ Nt fledged Pren .ium Profit —-$04.!53 $0.853 “$0 153 $0.853 #330 153 $0,853 -—$0 153 330.853 ~—$0 .153 $01,353 #320 153 —$0. 147 8'2 McDeaald ' Derivatives Markets. Second Editicn Profit diagram: Prefitdiagram $40 eat. $5042.31! cotter 4 W—Wwfi—r— A gecd starting point is t chapter. We can see that the $45wsttike call costs $3.032... Since the put prices are decreasing in the strike price. we k strike marginain lower than $40. Ttiai and Bt‘i‘Ot‘ results in the premium on the bought call and sold put cancel each ether cut. (a) The hedged profit can be rewritten. as: P: N P +£H~N6)PG #HXF H“ H" The last term is known and has :10 variance. rule for variance. with b = (H -— N C;) VtIFIZcIX—t bY) = (12 Var (X) + b1 Var (Y) + Zechv (X. Y) (b) If we differentiate equation. 4.4 with respect to H and set it equal to zero. 201 “was: +2N..po‘.fia = 0 N pa 6 N pct T “___ 1,! 1.‘ G __ 'gfr 42> H—NGm— “ 2" #N6— 1 “ 06 0G (C) We need to plug the tiptimal hedge fade, Ha: Simplifying yields; new that we need t a strike price of $3,662. At that strike. r 6: Obtain: If, n. ___ Equation 4.4 is a direct appii aticn (3f the feiicwittg ...
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This note was uploaded on 02/27/2012 for the course FINANCE 101 taught by Professor Yuy during the Spring '12 term at Centenary College New Jersey.

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Chap 4 Practice - For the: problems of Chapter-43.,...

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