Management Project FINC 556 DERIVATIVES AND FINANCIAL MARKETS PROF. BODURTHA 2/26/2009

Transcription

1 Derivative-Based i Risk Management Project FINC 556 DERIVATIVES AND FINANCIAL MARKETS PROF. BODURTHA 2/26/2009

2 Project Group Members 2

3 Definition of Business Problem 3 Our team is taking the position of the long/short portion Georgetown University Endowment. After a suboptimal 2008 combined with dampened optimism for 2009, we have reduced our equity index-based position to 20% (roughly $200,000,000) of total assets on book. These funds are 100% allocated to an S&P 500 Index Fund. Therefore, Georgetown University is long the S&P 500, as an increase in the value of the S&P 500 fund is favorable for our investment. Exposure: +F SP $200,000, Loss Limit: We want only an 5/100 (5%) chance of losing more than 10% of our exposure ($20,000,000).

4 Futures Market Situation and Evolution Each contract constitutes 250 units of S&P 500 futures. At the current price of (on 2/9/09), each contract represents 250 x = $215, Therefore our total long exposure is: SP -- $200,000,000 / (250 * 861.9) = +929 Contracts (Actual number ) Underlying S&P 500 (June) Mar Jun Sep Dec Current date (2/9/09) / Settle (Close) Price Actual Maturity date (Check web, & may need to discuss) 3/20 6/19 9/18 12/18 Symbol SPH9 SPM9 SPU9 SPZ9 Subsequent date (2/13/09) Settle (Close) Price Subsequent (next maturity) date mark to market market

5 Brief Overview Market Outlook The markets in aggregate have demonstrated unparalleled high volatility since late summer 2007 with the implosion of the United States subprime mortgage sector and its epidemic spread across the entire economy. In the past four months alone, the Volatility Index (VIX) has peaked at over 80 with the S&P 500 Index itself hemorrhaging from roughly 1000 to the mid 750s over the same period. However, despite the index avalanche, recent metrics have indicated that S&P 500 volatility as measured by VIX has tempered, with values plateauing in the mid to high 40s. 5 A fundamental perspective of the S&P 500 with current PE ratio of (ten-year cyclically adjusted PE ratio of 14) may indicate the index is presently undervalued. However, we anticipate that further depressed first quarter 2009 earnings will temporarily bolster the PE ratio to approximately 25 closer to recent high levels and supportive of our ultimate forecast that the market has further room to fall.

6 Brief Overview Market Outlook (cont d) 6 The forecast.org view from February to June 2009 also suggests a bearsish S&P 500 outlook but with diminishing changes month to month arriving at an approximate floor in low 700s. (Please see table on slide 8) Given the above, our forecast through h June 2009 is consequently that the price of the S&P 500 Index will continue to decline to 700 vs the 714 implied forecast (or for the June 2009 futures contract), and with volatility consistent at current market levels (i.e., we do not expect volatility to either increase or decrease). We believe this view is corroborated by market fundamentals and moreover by the forecast.org figures.

7 Plot of VIX Index Oct 08 Feb 09 7 Plot indicates relatively stable volatility in January and February of 2009

8 SPX Recent Performance / Future Forecast 8 S&P 500 Stock Index Forecast 1 Forecast 50% 80% Month Date Value Correct +/ Correct +/ 0 Jan Feb Mar Apr May Jun Jul Aug Sep Updated Sunday, February 08, As previously stated our view As previously stated, our view is down & stable

9 Risk / Exposure Stance Total exposure value: $200,000,000. Our desired dollar loss limit for our exposure is 10% ($20,000,000) Our desired loss probability is 5% (5/100) Thus, our critical probability level and the loss limit level yields the following statement: We want only a 5% chance of losing $20,000,000 (10% of exposure) or more 9

10 Scenario Detail Underlying Exposure 0F T = (SPM9 on Bloomberg) R = 1.28%; RP = 5% T = 130/365 =.356; Annualized σ = 48.07% Expected Future Spot Price = (861.9*(1+(1.28%+5%)*.356))/(1+(5%*.356))) LOWER Critical Price = (865.76*e^-(1.645*48.07%*sqrt.356)) HIGH Critical Price = (865.76*e^+(1.645*48.07%*sqrt.356)) 27% of our long exposure may be retained (so must decrease position by ~ 73%) We must sell 676 futures contracts to meet risk targets

11 Portfolio VaR Price Value at Risk Underlying SP Today 2/9/2009 Futures price Monthly price volatility (stan. dev.) Risk Limit -20,000,000 # of contract underlying 250 For Volatility - standard deviation information, #sd s.d. V@R( (e.g. 1.00) 164E 1.64 Exposure (+/-Contracts) i / /d / d /i d i Exposure (maturity) Date 6/19/2009 $ underlying $200,176,275 user is guriskmetrics For risk premium-adjusted V@R Adjustment (+/-Contracts) -676 OK@ 253 password is riskmetrics Funding Rate 1.28% Monthly Estimates T>30 days= 130 Risk Premium Estimate 5.00% Riskmetrics (optional) Riskmetrics inferred (optional) weight last 150 obs. Own estimate monthly vol*sqrt(130/30) Own estimate Standard deviations (s.d. E.g. 1% as 1.0) Long price*exp(-#*sd) $ V@R -10,918,191-10,918,191-19,969,262-19,969,262 Long price*exp(+#*sd) $ profit 14,213,326 14,213,326 34,589,664 34,589,664 Probability of doing worse V@R Center and Confidence Interval 45% than standard deviation 40% 35% (or ) is 5.05% 30% 25% 20% 15% 10% 5% 0% Notes Quick & Dirty Check Target Loss -9.99% Simple Log Loss % % % Keep 27.3% 21.9% 11 Set no hedge & To Match "Keep" 27.2% Probability 1 out of with for 1.00 s.d 15.87% 6 6.5% loss for 1.28 s.d 10.03% 03% % 1%loss for 1.44 s.d 7.49% % loss for 1.65 s.d 4.95% % loss for 2.00 s.d 2.28% % loss for 2.33 s.d 1.00% % loss for 3.09 s.d 0.100% % loss Hedge -72.7% -78.1% Check # s.d. 1.6

12 Team View Direction & Volatility 12 Level of Confidence Vol vs. market Unsure-Vol =Market Sure-Stable Vol vs. market Direction vs. market view View = Vol up View = Vol stable View = Vol down Direction vs. market view Up-Unsure forward & options forward cheap forward cheap Up-Sure cheap & options fair & options expensive No direction -? options forward & options options No direction - Sure cheap fair expensive Down-Unsure forward expensive forward expensive forward & options Down-Sure & options cheap & options fair expensive

13 Hedging Possibilities Explored 13 Based on our market view (down) and volatility remaining at current levels we looked at the following strategies: Level of Confidence Vol vs. market Unsure Vol =Market Sure Stable Vol vs. market Direction vs. market view View = Vol up View = Vol stable View = Vol down Direction vs. market view (options cheap) (option prices fair) (options expensive) Up Unsure Up Sure (forward cheap) (forward cheap) No direction? (forward price fair) +F+2P +F 2C No direction Sure (forward price fair) Down Unsure (forward expensive) F+C F+C/2 %F Down Sure (forward expensive)

14 Related ATM & OTM Options 14 Closest to maturity futures price & maturity date (June 2009 CME Calls & Puts): Calls Puts ATM / OTM Strike Price Price Quote Strike Price Price Quote ITM 700 $ $ ITM 750 $ $ ATM* 860 $ $ OTM 900 $ $ OTM 1000 $ $ ( /spm9_ ; *ATM in reference to SPM9 = $861.9)

15 Hedging Strategy 15 We are naturally LONG the S&P 500 (+F SP ) Due to our view that the S&P will go down in price until the June maturity date and that volatility will remain at current levels, we would ultimately like to be SHORT the S&P (- F SP ) in some of our positions There are several scenarios by which we could achieve this short position, and they are explored in the following slides. Note that in several of the following scenarios we take derivative positions greater than the number of futures contracts equivalent to our underlying exposure. Accordingly, we would report such nonhedging g derivative positions as per FAS 133/ IAS 39.

16 Scenario #1 : -F +C/2 16 L or S (Long/Short) S L F, C, or P (Forward, Call, Put) F C Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts Calculated Profit of a Combined -258F+129C Position Prices at -258F +129C 258F+129C Profit Maturity ,257, ,807,276 Step size ,357, ,907, ,457, Input ,007,276, Futures=> ,381, Price ,606, ,831, ,056, Strike F ,281,449 to update ,506, Critical ,855,367 Prices ,933,618 Max Loss ,731,449 Combined -258F+129C Position ,062 1,262 1,462 Price at Contract Maturity Down, Stable (Trade, Insure) Since we are +F 929 Contracts to begin with, by shorting 1187 Futures contracts, and buying 129 Calls, our overall position would yield: -258F + 129C

17 Scenario #2 : -%F 17 L or S (Long/Short) L S F, C, or P (Forward, Call, Put) F F Forward/Strike Price Price (C or P), 0.0 (F) - FV Net Number of Contracts Calculated Profit of a Combined +929F-1075F Position Prices at +929F -1075F +929F-1075F Profit Maturity ,900, ,250,000 Step size ,600, ,950, ,300,000 Input ,650,000 Futures=> Price ,650, ,300, ,950,000 Strike F ,600,000 to update ,250, ,900,000 Critical ,486,517 Prices ,865,246 Max Loss ,900,000 Combined +929F-1075F Position ,062 1,262 1,462 Price at Contract Maturity Down, sure (Trade) Since we are +F 929 Contracts to begin with, by shorting 1075 Futures contracts, our overall position would yield: -146F

18 Scenario #3: +F -2C 18 L or S (Long/Short) L S F, C, or P (Forward, Call, Put) F C Forward/Strike Price Price (C or P), 0.0 (F) - FV Number of Contracts Calculated Profit of a Combined +201F-402C Position Prices at +201F -402C +201F-402C Profit Maturity ,537, ,512,789 Step size ,487, ,462, ,437, Input ,587,211, Futures=> ,421, Price ,396, ,628, ,653, Strike F ,678,739 to update ,703, Critical ,201,419 Prices ,927,468 Combined +201F-402C Position ,062 1,262 1,462 Price at Contract Maturity No direction, sure (Trade, Income): Synthetic Short Straddle Since we are +F 929 Contracts to begin with, by shorting 728 Futures contracts, and buying 402 Calls, our overall position would yield: +201F -402C

19 Scenario #4: -F +C 19 L or S (Long/Short) S L F, C, or P (Forward, Call, Put) F C Combined -1083F+1083C Position Forward/Strike Price Price (C or P), 0.0 (F) - FV Lower +929F Number of Contracts Calculated Profit of a Combined -1083F+1083C Position Pi Prices at -1083F +1083C 083F+1083 Profit Maturity ,942, Input ,567,477 Futures=> ,993, ,867,477 60,717,477 Step size ,792,477 33,642, Price ,993, ,993, ,993,098 Strike F ,993, ,062 1,262 1,462 to update ,993,098, Price at Contract Maturity Critical ,697,257 Prices ,993,098 Max Loss ,993,098 Down, Vol (Trade, Insure): Synthetic Long Put Since we are +F 929 Contracts to begin with, by shorting 2012 Futures contracts, and buying 1083 Calls, our overall position would yield: -1083F C

20 Scenario #5: +F +2P 20 L or S (Long/Short) L L F, C, or P (Forward, Call, Put) F P Forward/Strike Price Price (C or P), 0.0 (F) - FV Lower +929F Number of Contracts Calculated Profit of a Combined +548F+1096P Position Prices at +548F +1096P 548F+1096 Profit Maturity ,682, ,982, Step size ,282, ,582, ,882,643 Input ,817,357, Futures=> ,996, Price ,296, ,403, ,103,243 Strike F ,803,243 to update ,503, Critical ,596,419 Prices ,565,945 Max Loss ,996,757 Combined +548F+1096P Position ,062 1,262 1,462 Price at Contract Maturity No direction, Vol (Trade, Insure): Synthetic Long Straddle Since we are +929F Contracts to begin with, by shorting 381 Futures contracts, and buying 1096 Puts our overall position would yield: +548F C

21 Recommendation & Conclusion 21 We believe that the S&P500 underlying will continue to fall and volatility will remain stable until our June exposure. Based on our exposure (+929F), market views and loss limits, our strategy is to sell 1187 Futures contracts, buy 129 Calls, for an overall position that would yield: -258F + 129C