Derivative Based Risk Management Group Project October 17, 2008

Transcription

1 Derivative Based Risk Management Group Project October 17, 28 Team Members Cris Benavides Warren Choi Tatyana Litvak Wei Sun

2 Project Assignment 1 1. Group Members Cris Benavides Warren Choi Tatyana Litvak Wei Sun 2. (From the WSJ) The Hoya Index Fund is a new fund started out of the ashes of the financial crisis. Four MBA classmates banded together (because they couldn t find a job) to start an index fund. Since they had done poorly in finance classes, they figured an index fund was a heck of a lot easier to manage than an actively managed fund where they would actually have to pick stocks. Fortunately for them, so many mutual funds had gone out of business that Hoya quickly became popular with the sovereign funds that now ruled the financial world. Hoya quickly had 1 million in assets, and the founders realized that if they suffered big losses, they would be out of business. So they devised a hedging strategy that would limit the downside risk for the $1M invested in S&P 5 index futures. Long exposure of +F SP $1,, and a loss of 1% or more with only a 1/1 chance. +F SP 3. Futures market situation and evolution: Underlying SS = S&P 5 SP Dec 8 Mar 9 Jun 9 Sep 9 Current date 1/8/8 Settle (Close) Price Actual Maturity date 12/19/28 3/2/29 6/19/29 9/18/29 Symbol SPZ8 SPH9 SPM9 SPU9 Subsequent (next maturity) date 1/1/8 Settle (Close) Price Subsequent (next maturity) date mark to market ($9.) ($9.6) ($9.6) ($9.9) Each contract represents: 25 x 981 = $245,25 for December 28. Last trade as of 1/1/28: $891

3 4. Brief overview of market outlook for the S&P 5: As we know with the recent events in the US economy, the market has become extremely volatile while stock prices have reach historical lows. Looking at the S&P chart 6 month chart, stock prices have decreased almost 2%, with the DOW dropping a whopping 8 points in one day this month. It is obvious to state that the economy, with all of its fluctuations have begun to show some signs of improvement once again, with all of the government aid to banks, and the hype of the new presidential hopeful in the next month. Warren Buffet's recently released statements about his belief that the economy can only rebound and that longing stocks is the wise thing to do. We believe that as the S&P is at historical lows, and the air surrounding the market is so fickle according to its immediate environment, we believe the S&P will go up. So we are bullish on direction. With volatility at historical highs due to uncertain future outlook on the economy, we believe that the volatility will more or less remain where it is without increasing to higher levels. In fact, we would expect in the long run for the volatility to decrease and revert back to pre-september times, but not until well into next year.

4 S&P 5 6-mo

5 A. Price risk management as of 1/8/8. Project Assignment 2 1. We seek to manage the business risk of an S&P 5 Index Portfolio. 2. Our exposure is long, owning a $1,62, portfolio. a. (From the WSJ) The Hoya Follow-The-Herd Index Fund is a new fund started out of the ashes of the financial crisis. Four MBA classmates banded together (because they couldn t find a job) to start an index fund. Since they had done poorly in finance classes, they figured an index fund was a heck of a lot easier to manage than an actively managed fund where they would actually have to pick stocks. Fortunately for them, so many mutual funds had gone out of business that Hoya quickly became popular with the sovereign funds that now ruled the financial world. Hoya quickly had 1 million in assets, and the founders realized that if they suffered big losses, they would be out of business. So they devised a hedging strategy that would limit the downside risk for the $1M invested in S&P 5 index futures. 3. IF OUR EXPOSURE WERE SHORT: a. (From the WSJ) The Hoya Follow-The-Herd Hedge Fund is a new fund started out of the ashes of the financial crisis. Four MBA classmates banded together (because they couldn t find a job) to start this new hedge fund. They had done poorly in finance classes, but they figured shorting the S&P 5 index was a no-brainer since the markets continued to fall. Fortunately for them, so many hedge funds had gone out of business that Hoya quickly became popular with the sovereign funds that now ruled the financial world. Hoya quickly had 1 million in assets with which to short the S&P 5. The founders realized that if the markets moved up, they d suffer big losses, and they would be out of business. So they devised a hedging strategy that would limit the downside risk for the $1M invested in S&P 5 index futures. 4. The risk management problem we will address is a long exposure. 5. To set our business context we must determine our total exposure and a dollar loss limit. The dollar loss limit should be a reasonable fraction of our total exposure. 6. Total exposure value is $1.62M. 7. A dollar and percentage loss limit for our exposure is $1M and 1%. 8. We want only a 1% chance of losing more than $1M and 1%. # of standard deviations from current futures price: 2.33 Associated loss probability: 1% # of times out of n that loss limit is exceeded: 1 out of 1 For the S&P 5 underlying 12/19/28 maturity date and 72 (1/8/28-12/19/28) day futures contract: F t = 981 with R = 2% and RP = 5%

6 Our 1% loss limit critical price level is calculated relative to a measure of a consensus market expectation: Expected future price = and based on an annualized standard deviation estimate of 53.26% (from Riskmetrics 3-day monthly estimate of 15.27% (365/3)) For a long exposure, the lower critical price level = For a short exposure, the upper critical price level = B. If we had a Long Exposure From the calculation above, there is a 1% chance that the underlying price will be at or below in a year. The associated loss relative to selling the underlying at the current futures price of 981 equals the loss at the lower critical price level = % Therefore, we determine how much of our long exposure may be retained: loss limit / loss at lower critical price level = -1%/-41.81% = 23.9% Roughly, we must decrease our exposure by 1 (loss limit/loss at critical price level) = % = 76.1% For the underlying position of $1.62M, we must sell $76.95M or 76.1%. Our underlying exposure equals 48 contracts ($1,,/($25*$981)). We must sell 311 futures contracts to meet our risk targets. C. If we had a Short Exposure From the calculation above, there is a 1% chance that the underlying price will be at or above in a year. The associated loss relative to buying the underlying at the current futures price of 981 equals the loss at the upper critical price level = % Therefore, we determine how much of our long exposure may be retained: loss limit / loss at lower critical price level = -1%/-41.81% = 23.9% Roughly, we must decrease our exposure by 1 (loss limit/loss at critical price level) = % = 86.7% For the underlying position of $1M, we must sell $86.717M or 86.72%. Our underlying exposure equals 48 contracts ($1,,/($25*$981)). We must buy 354 futures contracts to meet our risk targets. D. Spreadsheet analysis Long Position

7 Price Value at Risk Underlying SP5 Today 1/8/28 Futures price 981 Monthly price volatility (stan. dev.) Notes Quick & Dirty Check Risk Limit -1,, # of contract underlying 25 For Volatility - standard deviation information, Target Loss -9.99% # s.d. V@R (e.g. 1.) 2.33 Exposure (+/-s) 48 /riskmetrics.com/clients/data/cde/index.cgi Simple Log Exposure (maturity) Date 12/19/28 $ underlying $1,62, user is guriskmetrics Loss % % % For risk premium-adjusted V@R Adjustment (+/-s) -311 OK@ 97 password is riskmetrics Keep 23.9% 18.5% Funding Rate 2.% Monthly Estimates T>3 days= 72 Hedge -76.1% -81.5% Risk Premium Estimate 5.% Riskmetrics (optional) Riskmetrics inferred (optional) weight last 15 obs. Own estimate monthly vol*sqrt(72/3) Own estimate Set no hedge & To Match "Keep" 23.9% Standard deviations (s.d. E.g. 1% as 1.) Probability 1 out of with Long price*exp(-#*sd) for 1. s.d 15.87% 6 4.9% loss $ V@R -7,53,666-7,53,666-9,945,677-9,945,677 for 1.28 s.d 1.3% 1 6.1% loss Long price*exp(+#*sd) for 1.44 s.d 7.49% % loss $ profit 1,34,676 1,34,676 17,898,16 17,898,16 for 1.65 s.d 4.95% 2 7.6% loss Probability of doing worse for 2. s.d 2.28% % loss V@R Center and Confidence Interval 5% than standard deviation for 2.33 s.d 1.% 1 1.% loss 4% (or ) is.99% for 3.9 s.d.1% % loss 3% 2% 1% % Note: Riskmetrics assumes Check # s.d. 2.3 a zero risk premium. If the graph doesn't plot, click the X-axis and format axis "scale" to bracket price range. Short Position Price Value at Risk (V@R) Underlying SP5 Today 1/8/28 Futures price 981 Monthly price volatility (stan. dev.) Notes Quick & Dirty Check Risk Limit -1,, # of contract underlying 25 For Volatility - standard deviation information, Target Loss -9.99% # s.d. V@R (e.g. 1.) 2.33 Exposure (+/-s) -48 /riskmetrics.com/clients/data/cde/index.cgi Simple Log Exposure (maturity) Date 12/19/28 $ underlying -$1,62, user is guriskmetrics Loss % % -56.1% For risk premium-adjusted V@R Adjustment (+/-s) 354 OK@ -54 password is riskmetrics Keep 13.3% 17.8% Funding Rate 2.% Monthly Estimates T>3 days= 72 Hedge 86.7% 82.2% Risk Premium Estimate 5.% Riskmetrics (optional) Riskmetrics inferred (optional) weight last 15 obs. Own estimate monthly vol*sqrt(72/3) Own estimate Set no hedge & To Match "Keep" 186.7% Standard deviations (s.d. E.g. 1% as 1.) Probability 1 out of with Short price*exp(+#*sd) for 1. s.d 15.87% % loss $ V@R -5,736,624-5,736,624-9,963,924-9,963,924 for 1.28 s.d 1.3% % loss Short price*exp(-#*sd) for 1.44 s.d 7.49% % loss $ profit 3,926,783 3,926,783 5,536,769 5,536,769 for 1.65 s.d 4.95% % loss Probability of doing worse for 2. s.d 2.28% 44 ######### V@R Center and Confidence Interval 5% than standard deviation for 2.33 s.d 1.% 1 ######### 4% (or ) is.99% for 3.9 s.d.1% 1 ######### 3% 2% 1% % Note: Riskmetrics assumes Check # s.d. 5.9 a zero risk premium. If the graph doesn't plot, click the X-axis and format axis "scale" to bracket price range.

8 Project Assignment 3 1. Business problem and risk: The Hoya Index Fund has a portfolio with $1M invested in S&P 5 index futures. This is equivalent to 48 S&P 5 futures contracts. We want only a 1% chance of losing more than $1M. 2. See Project Assignment Market outlook: Our view for December futures is up and stable. We expect the market to move up. Even though volatility is high, we expect it will remain at these levels for the foreseeable future. 4. Closest to maturity futures price and maturity date is December 28 futures price of $981. Strikes Calls Puts 8. ATM 24.1 OTM ATM 91.5 OTM ATM 8.2 ATM OTM 17.6 ATM OTM 5 ATM Direction View Direction Up No Direction Direction Down Volatility View Volatility Up Volatility Stable Volatility Down +48F+48P (S#3) +97F+48P (S#16) +97F (S#1) +48F+48Potm (S#4) +48F-48Cotm+48Potm (S#9) +97F+48P-49C (S#14) +25F+5P (S#5) Preferred Practice for +F: +66F-132C (S#11) -25F+5C (S#6) Bull Spread (S#9) -66F-132P (S#12) -48F+48Cotm (S#8) -48F+48Cotm-48Potm (S#1) -54F-27Potm+27Cotm (S#13) -48F+48C (S#7) -54F+27C (S#15) -54F (S#2) Note: Positions are in black font if we start with long exposure, red font with short exposure. The S# indicates the number of scenario that contains the detail description for the corresponding position in the following section.

9 # 1 Up/Sure Trade +97F Description: Based on our risk control requirement specified in Project Assignment #2, we must sell 311 future contracts. The remaining long exposure is =97 contracts. This position has 1 out of 1 chance of losing more than $1M. L or S (Long/Short) l F, C, or P (Forward, Call, Put) f Forward/Strike Price 981. Price (C or P),. (F) - FV. Number of s 97 Underlying per Long Forward Position f Total Gain(Loss) Prices at 441. (52,38.) (13,95,) Maturity 531. (43,65.) (1,912,5) 621. (34,92.) (8,73,) Step size 711. (26,19.) (6,547,5) (17,46.) (4,365,) 891. (8,73.) (2,182,5) Input futures price ,73. 2,182, ,46. 4,365, ,19. 6,547, ,92. 8,73, ,65. 1,912, ,38. 13,95, 6, +97F V@R up-sure/trade 4, 2, (2,) (4,) (6,)

10 # 2 Down/Sure Trade -54F Description: Based on our risk control requirement specified in Project Assignment #2, we must buy 354 future contracts. The remaining short exposure is =54 contracts. This position has 1 out of 1 chance of losing more than $1M. L or S (Long/Short) S F, C, or P (Forward, Call, Put) F Forward/Strike Price 981. Price (C or P),. (F) - FV. Number of s 54 Underlying per Short Forward Position 25-54F Total Gain (Loss) Prices at ,16. 7,29,. Maturity ,3. 6,75, ,44. 4,86,. Step size ,58. 3,645, ,72. 2,43, ,86. 1,215,. Input futures price (4,86.) (1,215,.) (9,72.) (2,43,.) (14,58.) (3,645,.) (19,44.) (4,86,.) (24,3.) (6,75,.) (29,16.) (7,29,.) 4, 3, 2, 1, (1,) (2,) (3,) (4,) -54F V@R down-sure/trade

11 # 3 Up/Unsure Trade, Insure +48F+48P (Syn +48C) Description: The maximum loss for this position is $8.18M, which meets our risk control requirement. L or S (Long/Short) L L F, C, or P (Forward, Call, Put) F P Forward/Strike Price Price (C or P),. (F) - FV Number of s Underlying per Combined +48F+48P Position 25 Prices at +48F +48P +48F+48P Total Gain(Loss) Maturity 441. (22,32) 187,598 (32,722) (8,18,4) 531. (183,6) 15,878 (32,722) (8,18,4) Step size 621. (146,88) 114,158 (32,722) (8,18,4) (11,16) 77,438 (32,722) (8,18,4) 81. (73,44) 4,718 (32,722) (8,18,4) Input 891. (36,72) 3,998 (32,722) (8,18,4) Futures=> 981. (32,314) (32,314) (8,78,4) Price ,72 (32,314) 4,46 1,11, ,44 (32,314) 41,126 1,281, ,16 (32,314) 77,846 19,461, ,88 (32,314) 114,566 28,641, ,6 (32,314) 151,286 37,821, ,32 (32,314) 188,6 47,1,6 25, +F Insure up-unsure/trade-insure +48F+48P Position 2, 15, 1, 5, (5,) (1,) (15,) (2,) (25,) Scenario View Purpose Position

12 # 4 Up/Unsure Trade, Insure +48F+48Potm Description: The maximum loss for this position is $9.34M, which meets our risk control requirement. When compared with +F+Pitm, this position s maximum loss is bigger and its potential gain on the up side is also bigger. L or S (Long/Short) L L F, C, or P (Forward, Call, Put) F P Forward/Strike Price Price (C or P),. (F) - FV. 7.6 Number of s Underlying per Combined +48F+48Potmotm Position 25 Prices at +48F +48Potm +48F+48Potm Total (Gain/Loss) Maturity 441. (22,32) 182,947 (37,373) (9,343,2) 531. (183,6) 146,227 (37,373) (9,343,2) Step size 621. (146,88) 19,57 (37,373) (9,343,2) (11,16) 72,787 (37,373) (9,343,2) 81. (73,44) 36,67 (37,373) (9,343,2) Input 891. (36,72) (653) (37,373) (9,343,2) Futures=> 981. (28,85) (28,85) (7,21,2) Price ,72 (28,85) 7,915 1,978, ,44 (28,85) 44,635 11,158, ,16 (28,85) 81,355 2,338, ,88 (28,85) 118,75 29,518, ,6 (28,85) 154,795 38,698, ,32 (28,85) 191,515 47,878,8 25, +F Insure OTM up-unsure/trade-insure +48F+48Potm Position 2, 15, 1, 5, (5,) (1,) (15,) (2,) (25,) Scenario View Purpose Position

13 # 5 No Direction/Volatile Trade, Insure +25F+5P (Syn Long Straddle) Description: The maximum loss for this position is $9.9M, which meets our risk control requirement. L or S (Long/Short) L L F, C, or P (Forward, Call, Put) F P Forward/Strike Price Price (C or P),. (F) - FV Number of s 25 5 Underlying per Combined +25F+5P Position 25 Prices at +25F +5P +25F+5P Total Gain(Loss) Maturity 441. (135,) 229,9 94,9 23,725, 531. (112,5) 184,9 72,4 18,1, Step size 621. (9,) 139,9 49,9 12,475, (67,5) 94,9 27,4 6,85, 81. (45,) 49,9 4,9 1,225, Input 891. (22,5) 4,9 (17,6) (4,4,) Futures=> 981. (39,6) (39,6) (9,9,) Price ,5 (39,6) (17,1) (4,275,) , (39,6) 5,4 1,35, ,5 (39,6) 27,9 6,975, , (39,6) 5,4 12,6, ,5 (39,6) 72,9 18,225, , (39,6) 95,4 23,85, 25, 2, 15, 1, 5, (5,) (1,) (15,) (2,) +F Vol volative/trade(vol)-insure +25F+5P Position

14 # 6 No Direction/Volatile Trade, Insure -25F+5C (Syn Long Straddle) Description: The maximum loss for this position is $9.9M, which meets our risk control requirement. L or S (Long/Short) S L F, C, or P (Forward, Call, Put) F C Forward/Strike Price Price (C or P),. (F) - FV. 8.2 Number of s 25 5 Underlying per Combined -25F+5C Position 25 Prices at -25F +5C -25F+5C Total Gain(Loss) Maturity , (4,1) 94,9 23,725, ,5 (4,1) 72,4 18,1, Step size , (4,1) 49,9 12,475, ,5 (4,1) 27,4 6,85, , (4,1) 4,9 1,225, Input ,5 (4,1) (17,6) (4,4,) Futures=> 981. (39,6) (39,6) (9,9,) Price 171. (22,5) 5,4 (17,1) (4,275,) (45,) 5,4 5,4 1,35, (67,5) 95,4 27,9 6,975, (9,) 14,4 5,4 12,6, (112,5) 185,4 72,9 18,225, (135,) 23,4 95,4 23,85, 25, 2, 15, 1, 5, (5,) (1,) (15,) (2,) -F Vol unsure/trade(vol)-insure -25F+5C Position

15 # 7 Down/Unsure Trade, Insure -48F+48C (Syn +48P) Description: The maximum loss for this position is $8.8M, which meets our risk control requirement. L or S (Long/Short) S L F, C, or P (Forward, Call, Put) F C Forward/Strike Price Price (C or P),. (F) - FV. 8.2 Number of s Underlying per Combined -48F+48C Position 25 Prices at -48F +48C -48F+48C Total Gain(Loss) Maturity ,32 (32,722) 187,598 46,899, ,6 (32,722) 15,878 37,719,6 Step size ,88 (32,722) 114,158 28,539, ,16 (32,722) 77,438 19,359, ,44 (32,722) 4,718 1,179,6 Input ,72 (32,722) 3, ,6 Futures=> 981. (32,314) (32,314) (8,78,4) Price 171. (36,72) 4,46 (32,314) (8,78,4) (73,44) 41,126 (32,314) (8,78,4) (11,16) 77,846 (32,314) (8,78,4) (146,88) 114,566 (32,314) (8,78,4) (183,6) 151,286 (32,314) (8,78,4) (22,32) 188,6 (32,314) (8,78,4) 25, 2, 15, 1, 5, (5,) (1,) (15,) (2,) (25,) -F Insure down-unsure/trade-insure -48F+48C

16 # 8 Down/Unsure Trade, Insure -48F+48Cotm Description: The maximum loss for this position is $2.5M, which meets our risk control requirement. When compared with -F+Citm, this position s maximum loss is smaller and its potential gain on the down side is also smaller. L or S (Long/Short) S L F, C, or P (Forward, Call, Put) F C Forward/Strike Price FV days Price (C or P),. (F) - FV <-@.% Number of s Underlying per Combined -48F+48Cotm Position 25 Prices at -48F +48Cotm -48F+48Cotm Total Maturity ,32 (82,49) 138,271 34,567, ,6 (82,49) 11,551 25,387,8 Step size ,88 (82,49) 64,831 16,27, ,16 (82,49) 28,111 7,27, ,44 (81,641) (8,21) (2,5,2) Input ,72 (44,921) (8,21) (2,5,2) Futures=> 981. (8,21) (8,21) (2,5,2) Price 171. (36,72) 28,519 (8,21) (2,5,2) (73,44) 65,239 (8,21) (2,5,2) (11,16) 11,959 (8,21) (2,5,2) (146,88) 138,679 (8,21) (2,5,2) (183,6) 175,399 (8,21) (2,5,2) (22,32) 212,119 (8,21) (2,5,2) 25, 2, 15, 1, 5, (5,) (1,) (15,) (2,) (25,) -F Insure otm down-unsure(<atm)/trade-insure(<atm) -48F+48Co

17 # 9 Limited Up/Volatility Trade, Insure, +48F-48Cotm+48Potm Stable Income (Syn Bull Spread) Description: The maximum loss for this position is $7.55M, which meets our risk control requirement. L or S (Long/Short) L L S F, C, or P F P C Forward/Strike Price Price (C or P),. (F) - FV Number of s Underlying per Combined +48F+48Potm- 48Cotm Position 25 Prices at +48F +48Potm - 48Cotm +48F+48Potm- 48Cotm Total Gain(Loss) Maturity 441. (22,32) 182,947 7,181 (3,192) (7,548,) 531. (183,6) 146,227 7,181 (3,192) (7,548,) Step size 621. (146,88) 19,57 7,181 (3,192) (7,548,) (11,16) 72,787 7,181 (3,192) (7,548,) 81. (73,44) 36,67 7,181 (3,192) (7,548,) Input 891. (36,72) (653) 7,181 (3,192) (7,548,) Futures=> 981. (28,85) 7,181 (21,624) (5,46,) Price ,72 (28,85) 7,181 15,96 3,774, ,44 (28,85) 2,693 47,328 11,832, ,16 (28,85) (34,27) 47,328 11,832, ,88 (28,85) (7,747) 47,328 11,832, ,6 (28,85) (17,467) 47,328 11,832, ,32 (28,85) (144,187) 47,328 11,832, 25, 2, 15, 1, 5, (5,) (1,) (15,) (2,) Syn. Bull Spread limited up-worry big down/t-inc-ins +48F+48Potm-48Cotm (25,) F +48Po tm -48Cotm +48F+48Potm-48Cotm

18 # 1 Limited Down / Trade, Insure, -48F+48Cotm-48Potm Volatility Stable Income (Syn Bear Spread) Description: The maximum loss for this position is $9.45M, which meets our risk control requirement. L or S (Long/Short) S S L F, C, or P F P C Forward/Strike Price Price (C or P),. (F) - FV Number of s Underlying per Combined -48F- 48Potm+48Cotm Position 25 Prices at -48F -48Potm +48Cotm -48F- 48Potm+48Cotm Total Gain(Loss) Maturity ,32 (136,762) (19,339) 64,219 16,54, ,6 (1,42) (19,339) 64,219 16,54,8 Step size ,88 (63,322) (19,339) 64,219 16,54, ,16 (26,62) (19,339) 64,219 16,54, ,44 9,71 (19,339) 63,811 15,952,8 Input ,72 9,71 (19,339) 27,91 6,772,8 Futures=> ,71 (19,339) (9,629) (2,47,2) Price 171. (36,72) 9,71 (1,771) (37,781) (9,445,2) (73,44) 9,71 25,949 (37,781) (9,445,2) (11,16) 9,71 62,669 (37,781) (9,445,2) (146,88) 9,71 99,389 (37,781) (9,445,2) (183,6) 9,71 136,19 (37,781) (9,445,2) (22,32) 9,71 172,829 (37,781) (9,445,2) 25, 2, 15, 1, 5, (5,) (1,) (15,) (2,) (25,) Syn. Bear Spread Limited down-worry big up/t-ins-inc -48F-48Potm+48Cotm F -48Potm +48Cotm -48F-48Potm+48Cotm

19 # 11 No Direction/Sure Trade, Income +66F-132C (Syn Short Straddle) Description: The loss of this position is greater than $1M when future price is below $219 or above $1,743. This price range corresponds to below -6.39*Sigma and above +2.39*Sigma around the expected future price. The probability is.83%, which meets our risk control (less than 1%). L or S (Long/Short) L S F, C, or P (Forward, Call, Put) F C Forward/Strike Price Price (C or P),. (F) - FV. 8.2 Number of s Underlying per Combined +66F-132C Position 25 Prices at +66F -132C +66F-132C Total Gain(Loss) Maturity 219. (5,292) 1,586 (39,76) (9,926,4) 346. (41,91) 1,586 (31,324) (7,83,9) Step size 473. (33,528) 1,586 (22,942) (5,735,4) (25,146) 1,586 (14,56) (3,639,9) 727. (16,764) 1,586 (6,178) (1,544,4) Input 854. (8,382) 1,586 2,24 551,1 Futures=> ,454 1,454 2,613,6 Price ,382 (6,31) 2,72 518, ,764 (23,74) (6,31) (1,577,4) ,146 (39,838) (14,692) (3,672,9) ,528 (56,62) (23,74) (5,768,4) ,91 (73,366) (31,456) (7,863,9) ,292 (9,13) (39,838) (9,959,4) 6, 4, 2, (2,) (4,) (6,) (8,) +F Stable stable/trade(vol)-income +66F-132C Position (1,)

20 # 12 No Direction/Sure Trade, Income -66F-132P (Syn Short Straddle) Description: The loss of this position is greater than $1M when future price is below $219 or above $1,743. This price range corresponds to below -6.39*Sigma and above +2.39*Sigma around the expected future price. The probability is.83%, which meets our risk control (less than 1%). L or S (Long/Short) S S F, C, or P (Forward, Call, Put) F P Forward/Strike Price Price (C or P),. (F) - FV. 8.2 Number of s Underlying per Combined -66F-132P Position 25 Prices at -66F -132P -66F-132P Total Gain(Loss) Maturity ,292 (89,866) (39,574) (9,893,4) ,91 (73,12) (31,192) (7,797,9) Step size ,528 (56,338) (22,81) (5,72,4) ,146 (39,574) (14,428) (3,66,9) ,764 (22,81) (6,46) (1,511,4) Input ,382 (6,46) 2, ,1 Futures=> ,586 1,586 2,646,6 Price 118. (8,382) 1,586 2,24 551, (16,764) 1,586 (6,178) (1,544,4) (25,146) 1,586 (14,56) (3,639,9) (33,528) 1,586 (22,942) (5,735,4) (41,91) 1,586 (31,324) (7,83,9) (5,292) 1,586 (39,76) (9,926,4) 6, -F Stable stable/trade(vol)-income -66F-132P Position 4, 2, (2,) (4,) (6,) (8,) (1,)

21 # 13 Down/Sure Trade, Insure -54F-27Potm+27Cotm Description: This position is benchmarked by the F only position (-54F). The loss will be smaller on the upside, and the gain will be smaller on the downside. L or S (Long/Short) S S L F, C, or P F P C Forward/Strike Price Price (C or P),. (F) - FV Number of s Underlying per Combined -54F- 27Potm+27Cotm Position 25 Prices at -54F -27Potm +27Cotm -54F- 27Potm+27Cotm Total Gain(Loss) Maturity ,852 (14,396) (1,28) 24,176 6,43, ,21 (11,75) (1,28) 2,855 5,213,7 Step size ,568 (7,754) (1,28) 17,534 4,383, ,926 (4,433) (1,28) 14,213 3,553, ,284 (1,112) (1,28) 1,892 2,722,95 Input , (1,28) 6,5 1,51,2 Futures=> (1,28) (637) (159,3) Price 114. (6,642) (5,821) (1,455,3) (13,284) 643 3,499 (9,142) (2,285,55) 135. (19,926) 643 6,82 (12,463) (3,115,8) (26,568) 643 1,141 (15,784) (3,946,5) (33,21) ,462 (19,15) (4,776,3) (39,852) ,783 (22,426) (5,66,55) 5, Down-Sure/T-Ins -54F-27Potm+27Cotm 4, 3, 2, 1, (1,) (2,) (3,) (4,) (5,) F -27Potm +27Cotm -54F-27Potm+27Cotm

22 # 14 Up/Sure Trade, Insure +97F+48Potm-49Cotm Description: This position is benchmarked by the +F only position (+97F). The loss will be smaller on the downside, and the gain will be smaller on the upside. L or S (Long/Short) S S L F, C, or P F P C Forward/Strike Price Price (C or P),. (F) - FV Number of s Underlying per Combined -54F- 27Potm+27Cotm Position 25 Prices at -54F -27Potm +27Cotm -54F- 27Potm+27Cotm Total Gain(Loss) Maturity ,852 (14,396) (1,28) 24,176 6,43, ,21 (11,75) (1,28) 2,855 5,213,7 Step size ,568 (7,754) (1,28) 17,534 4,383, ,926 (4,433) (1,28) 14,213 3,553, ,284 (1,112) (1,28) 1,892 2,722,95 Input , (1,28) 6,5 1,51,2 Futures=> (1,28) (637) (159,3) Price 114. (6,642) (5,821) (1,455,3) (13,284) 643 3,499 (9,142) (2,285,55) 135. (19,926) 643 6,82 (12,463) (3,115,8) (26,568) 643 1,141 (15,784) (3,946,5) (33,21) ,462 (19,15) (4,776,3) (39,852) ,783 (22,426) (5,66,55) 5, Down-Sure/T-Ins -54F-27Potm+27Cotm 4, 3, 2, 1, (1,) (2,) (3,) (4,) (5,) F -27Potm +27Co tm -54F-27Potm+27Cotm

23 # 15 Down/Stable Trade, Insure -54F+27C Description: This position is benchmarked by the -F only position (-54F). The loss will be smaller on the upside, and the gain will be almost the same on the downside. L or S (Long/Short) S L F, C, or P (Forward, Call, Put) F C Forward/Strike Price Price (C or P),. (F) - FV. 8.2 Number of s Underlying per Combined -54F+27C Position 25 Prices at -54F +27C -54F+27C Total Gain(Loss) Maturity ,852 (2,165) 37,687 9,421, ,21 (2,165) 31,45 7,761,15 Step size ,568 (2,165) 24,43 6,1, ,926 (2,165) 17,761 4,44, ,284 (2,165) 11,119 2,779,65 Input ,642 (2,165) 4,477 1,119,15 Futures=> 981. (2,138) (2,138) (534,6) Price 114. (6,642) 1,183 (5,459) (1,364,85) (13,284) 4,54 (8,78) (2,195,1) 135. (19,926) 7,825 (12,11) (3,25,35) (26,568) 11,146 (15,422) (3,855,6) (33,21) 14,467 (18,743) (4,685,85) (39,852) 17,788 (22,64) (5,516,1) 5, down-stable/trade-insure -54F+27C Position 4, 3, 2, 1, (1,) (2,) (3,) (4,) (5,)

24 # 16 Up/Stable Trade, Insure +97F+48P Description: This position is benchmarked by the +F only position (+97F). The loss will be smaller on the downside, and the gain will be almost the same on the upside. L or S (Long/Short) L L F, C, or P (Forward, Call, Put) F P Forward/Strike Price Price (C or P),. (F) - FV Number of s Underlying per Combined +97F+48P Position 25 Prices at +97F +48P +97F+48P Total Gain(Loss) Maturity 441. (52,38) 22,7 (3,31) (7,577,4) 531. (43,65) 17,75 (25,9) (6,474,9) Step size 621. (34,92) 13,43 (21,49) (5,372,4) (26,19) 9,11 (17,8) (4,269,9) 81. (17,46) 4,79 (12,67) (3,167,4) Input 891. (8,73) 47 (8,26) (2,64,9) Futures=> 981. (3,82) (3,82) (95,4) Price ,73 (3,82) 4,928 1,232, ,46 (3,82) 13,658 3,414, ,19 (3,82) 22,388 5,597, ,92 (3,82) 31,118 7,779, ,65 (3,82) 39,848 9,962, ,38 (3,82) 48,578 12,144,6 6, up-stable/trade-insure +97F+48P Position 4, 2, (2,) (4,) (6,)

25 5. We recommend hedging our long position in 48 futures contracts by selling 48 C otm (out of money) call options with a strike price of $115 and a premium of $17.6, and buying 48 P otm (out of money) put options with a strike price of $96 and a premium of $7.6. This limits our loss in case of a market downturn to $7.55M. (This is Scenario #9 in the charts above). Especially with the current volatility of the market, with this bull spread it will greatly reduce our position cost due to the fact that we are selling calls and buying puts out of money.