MBA-555 Final Project Written Case Analysis Jason Rouslin Matthew Remington Chris Bumpus Part A: Option-Based Risk Mitigation Strategies II. Micro Hedge: The Equity Portfolio. Apple Inc. We decided to use Apple Inc. as our micro hedge for our equity portfolio. The stock has traded in a 52wk range of 310.50 and 426.70 (numbers obtained from yahoo.com/finance), giving the stock an upside potential from its current price levels, 389.70, of 9.494%, and downside potential of 20.3%. Since the stock is significantly off both its lows and its highs for the year we have decided to implement a user specified strategy with a Long Gut base. Since we are bullish on the stock, and bullish on the market as whole, the strategy has us, the investors, buying 1 375 March Call for 36.12 and buying 1 405 March put for 34.55, and selling 1 390 March Put for 26.65. The total invested is 44.02(36.12-34.55+26.65) or 4,402. This strategy allows us to have a maximum loss of 29.03 or $2903, and an unlimited upside potential. Obviously this hedging strategy is used to increase profitability on the specific stock because we are bullish on the underlying security. Decision Date and Risk Free Rates Apple Inc. Long Gut Bond Yields Decision Date (Today) Spot Instrument 91-Day Newsprint Yahoo! Price Treasury Bill Data Market Yields 03-Dec-11 $389.700 U.S. Markets Div / F-int 91 T-Bill / Bid. 0.00% 91 T-Bill / Ask. Actual
Days to Maturity. T-Bill Avg Bid / Ask. Yield Bill Price. T-bill Yield. 0.000% EUR=1 / AM=0 Risk-Free Estimate 0.000% 1
Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Mar-12 101 1 375.00 36.130 15.470 Call 2 16-Mar-12 101 0 380.00 33.170 10.470 Call 3 16-Mar-12 101 0 385.00 30.380 5.470 Call 4 16-Mar-12 101 0 390.00 27.880 0.470 Put 1 16-Mar-12 101-1 390.00 26.650 0.000 Put 2 16-Mar-12 101 0 395.00 29.100 4.530 Put 3 16-Mar-12 101 0 400.00 31.700 9.530 Put 4 16-Mar-12 101 1 405.00 34.550 14.530
III. Equity Options Assignment: Micro Hedging Basics Option Strategies for Apple Inc. 1. Option Strategy- Bull Call Spread The option strategy Bull Call Spread has the investor buying one December 11 370 call for $20.95 and selling one December 11 375 call for $18.10. The total invested is $2.85 (20.95-18.10) or $285. The maximum lost for the strategy is $285 and the maximum profit is $215.00. Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 1 370.00 20.950 19.700 Call 2 16-Dec-11 13 0 375.00 18.100 14.700 Call 3 16-Dec-11 13 0 380.00 14.200 9.700 Call 4 16-Dec-11 13 0 385.00 10.750 4.700 Put 1 16-Dec-11 13 0 385.00 5.350 0.000
Put 2 16-Dec-11 13 0 390.00 7.380 0.300 Put 3 16-Dec-11 13 0 395.00 9.970 5.300 Put 4 16-Dec-11 13 1 400.00 13.220 10.300 2. Option Strategy- Bull Put Spread The option strategy Bull Put Spread has the investor buying one December 385 Put for $5.35 and selling one December 395 Put for $9.97. The total premium collected is $4.62 (9.97-5.35) or $462.00. The maximum loss for the strategy is $538.00 and the maximum profit for the strategy is the premium collected or $462.00 Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 0 370.00 20.950 19.700 Call 2 16-Dec-11 13 0 375.00 18.100 14.700 Call 3 16-Dec-11 13 0 380.00 14.200 9.700 Call 4 16-Dec-11 13 0 385.00 10.750 4.700 Put 1 16-Dec-11 13 1 385.00 5.350 0.000 Put 2 16-Dec-11 13 0 390.00 7.380 0.300
Put 3 16-Dec-11 13-1 395.00 9.970 5.300 Put 4 16-Dec-11 13 0 400.00 13.220 10.300 3. Option Strategy- Bear Call Spread The option strategy Bear Call Spread has the investor selling one December 370 call for $20.95 and buying one December 375 call for $18.10. The total premium collected is $2.85(20.95-18.10) or $285.00. The maximum loss for the strategy is $215.00 and the maximum gain for the strategy is the premium collected or $285.00. Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13-1 370.00 20.950 19.700 Call 2 16-Dec-11 13 1 375.00 18.100 14.700 Call 3 16-Dec-11 13 0 380.00 14.200 9.700 Call 4 16-Dec-11 13 0 385.00 10.750 4.700 Put 1 16-Dec-11 13 0 385.00 5.350 0.000 Put 2 16-Dec-11 13 0 390.00 7.380 0.300
Put 3 16-Dec-11 13 0 395.00 9.970 5.300 Put 4 16-Dec-11 13 0 400.00 13.220 10.300 4. Option Strategy- Collar The option strategy Collar has the investor buying one December 385 call for $10.75 and selling one December 385 Put for $5.35. The total invested is $5.40(10.75-5.35) or $440.00. The maximum loss and gain for the strategy are unlimited. At a sorted price of $339.103 the loss for the strategy is $5,129.70, and at sorted price $428.179 the profit will be $3,779.10. Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 0 370.00 20.950 19.700 Call 2 16-Dec-11 13 0 375.00 18.100 14.700 Call 3 16-Dec-11 13 0 380.00 14.200 9.700
Call 4 16-Dec-11 13 1 385.00 10.750 4.700 Put 1 16-Dec-11 13-1 385.00 5.350 0.000 Put 2 16-Dec-11 13 0 390.00 7.380 0.300 Put 3 16-Dec-11 13 0 395.00 9.970 5.300 Put 4 16-Dec-11 13 0 400.00 13.220 10.300 5. Option Strategy- Long Call Butterfly The option strategy Long Call Butterfly has the investor buying one December 370 call for $20.95, selling 2 December 375 calls for $18.10 each, and buying one December 380 call for $14.20. The total premium collected for the strategy is $1.05 ((18.10X2)-20.95-14.20) or $105.00. The minimum gain for the strategy is $105 or the premium collected and the maximum gain for the strategy is $2.3679 or $236.79 at a price of $379.682. Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 1 370.00 20.950 19.700 Call 2 16-Dec-11 13-2 375.00 18.100 14.700
Call 3 16-Dec-11 13 1 380.00 14.200 9.700 Call 4 16-Dec-11 13 0 385.00 10.750 4.700 Put 1 16-Dec-11 13 0 385.00 5.350 0.000 Put 2 16-Dec-11 13 0 390.00 7.380 0.300 Put 3 16-Dec-11 13 0 395.00 9.970 5.300 Put 4 16-Dec-11 13 0 400.00 13.220 10.300 6. Option Strategy- Short Put Butterfly The option strategy Short Put Butterfly has the investor selling one December 385 put for $5.35, buying 2 December 390 puts for $7.38 each, and selling one December 395 put for $9.97. The total premium collected is $56(5.35+9.97-(7.38X2)) or $56.00. The Maximum loss for the strategy is $130.51 at a price of $393, and the maximum gain for the strategy is the premium collected or $56.00 Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 0 370.00 20.950 19.700 Call 2 16-Dec-11 13 0 375.00 18.100 14.700
Call 3 16-Dec-11 13 0 380.00 14.200 9.700 Call 4 16-Dec-11 13 0 385.00 10.750 4.700 Put 1 16-Dec-11 13-1 385.00 5.350 0.000 Put 2 16-Dec-11 13 2 390.00 7.380 0.300 Put 3 16-Dec-11 13-1 395.00 9.970 5.300 Put 4 16-Dec-11 13 0 400.00 13.220 10.300 7. Option Strategy- Short Straddle The option strategy Short Straddle has the investor selling one December 370 Call for $20.95 and selling one December 385 put for $5.35. The total premium collected for the strategy is $26.30(20.95+5.35) or $2,630.00. The maximum loss for the strategy is unlimited, both on the upside and the down side. When the price goes above $400 in addition to when the price goes below $355 the losses start to incur, while the maximum gain for the strategy is $1130.00 at a price of $368.812. Option Portfolio
Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13-1 370.00 20.950 19.700 Call 2 16-Dec-11 13 0 375.00 18.100 14.700 Call 3 16-Dec-11 13 0 380.00 14.200 9.700 Call 4 16-Dec-11 13 0 385.00 10.750 4.700 Put 1 16-Dec-11 13-1 385.00 5.350 0.000 Put 2 16-Dec-11 13 0 390.00 7.380 0.300 Put 3 16-Dec-11 13 0 395.00 9.970 5.300 Put 4 16-Dec-11 13 0 400.00 13.220 10.300 8. Option Strategy Long Strap Strategy For the option strategy, Long Strap, profits are unlimited however the losses are also extremely high if the option price goes down. The largest total profit calculated was $7339 at a sorted option trading price of $430.32, however as stated the profits are unlimited if this prices were to increase further. The maximum losses are at sorted option trading price of $366.63, where total losses were $2888. A slight decrease in losses did occur at the next lowest trading level, signifying that the losses are not unlimited.
Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 2 370.00 20.950 19.700 Call 2 16-Dec-11 13 0 375.00 18.100 14.700 Call 3 16-Dec-11 13 0 380.00 14.200 9.700 Call 4 16-Dec-11 13 0 385.00 10.750 4.700 Put 1 16-Dec-11 13 1 385.00 5.350 0.000 Put 2 16-Dec-11 13 0 390.00 7.380 0.300 Put 3 16-Dec-11 13 0 395.00 9.970 5.300 Put 4 16-Dec-11 13 0 400.00 13.220 10.300 9. Option Strategy- Long Strangle For the Long Strangle, the maximum profit as determined by WinORS was found to be $2922 at a sorted option trading price of $430.32. However, in reality the profits can be unlimited if the
stock prices increase to a level higher than this sorted trading price. The maximum loss is found to be at a sorted option price $383.33 where the maximum loss is $1443. Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 0 370.00 20.950 19.700 Call 2 16-Dec-11 13 0 375.00 18.100 14.700 Call 3 16-Dec-11 13 0 380.00 14.200 9.700 Call 4 16-Dec-11 13 1 385.00 10.750 4.700 Put 1 16-Dec-11 13 1 385.00 5.350 0.000 Put 2 16-Dec-11 13 0 390.00 7.380 0.300 Put 3 16-Dec-11 13 0 395.00 9.970 5.300 Put 4 16-Dec-11 13 0 400.00 13.220 10.300 10. Option Strategy- Long Call Condor
For the Long Call Condor, profits are limited however there is very little risk involved with this options strategy. Maximum profits are at a sorted option price of $378.76 where the total profit levels are found to be $560. There would be no profit losses, where the minimum profit levels out to $60 at all trading prices found in WinORS with the exception of the sorted option prices of $378.76, $381.76, and $381.88. In the range of these option prices are where higher profit levels are obtained. Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 1 370.00 20.950 19.700 Call 2 16-Dec-11 13-1 375.00 18.100 14.700 Call 3 16-Dec-11 13-1 380.00 14.200 9.700 Call 4 16-Dec-11 13 1 385.00 10.750 4.700 Put 1 16-Dec-11 13 0 385.00 5.350 0.000 Put 2 16-Dec-11 13 0 390.00 7.380 0.300 Put 3 16-Dec-11 13 0 395.00 9.970 5.300 Put 4 16-Dec-11 13 0 400.00 13.220 10.300
11. Option Strategy- Long Put Condor For the Long Put Condor, profits are limited while the maximum losses are also limited. Maximum profits are at a sorted option price of $391.28, where the total profits would be $378. The maximum losses would be $122 at all levels with the exception of the sorted option prices of $391.28, $395.72, and $397. At all other levels aside from these 3 losses would be incurred. Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 0 370.00 20.950 19.700 Call 2 16-Dec-11 13 0 375.00 18.100 14.700 Call 3 16-Dec-11 13 0 380.00 14.200 9.700 Call 4 16-Dec-11 13 0 385.00 10.750 4.700 Put 1 16-Dec-11 13 1 385.00 5.350 0.000
Put 2 16-Dec-11 13-1 390.00 7.380 0.300 Put 3 16-Dec-11 13-1 395.00 9.970 5.300 Put 4 16-Dec-11 13 1 400.00 13.220 10.300 12. Option Strategy: Long Gut The option strategy Long Gut has the investor buying 1 370 December call for 20.95 and buying 1 400 December Put for 13.22. The total amount invested is 34.17(20.95+13.22) or $3,417.00. The maximum loss for the strategy is 2.48 or $248, and the maximum profit is unlimited. Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 1 370.00 20.950 19.700 Call 2 16-Dec-11 13 0 375.00 18.100 14.700 Call 3 16-Dec-11 13 0 380.00 14.200 9.700 Call 4 16-Dec-11 13 0 385.00 10.750 4.700
Put 1 16-Dec-11 13 0 385.00 5.350 0.000 Put 2 16-Dec-11 13 0 390.00 7.380 0.300 Put 3 16-Dec-11 13 0 395.00 9.970 5.300 Put 4 16-Dec-11 13 1 400.00 13.220 10.300 Written Interpretation for Greek Terms: Option Chosen: December Call-Exercise price of $385.00 Delta: When there is volatility in the price of the underlying, the hedge ratio must be recomputed in order to have a perfectly hedged portfolio. This ratio is delta, which is the degree to which an option price will move given a small change in the underlying stock price. The hedge ratio is simply the derivative of the call price with respect to the stock price: dv/ds=n(d 1 )=dc/ds where N(d 1 ) is the computed delta. There was a Delta value of 0.99972 meaning that the option will move 0.99972 cents for every full cent movement in the underlying stock. This can be computed as if S falls by a small amount (e.g., $0.01) the investor will lose (0.01)(999.72) on the stock or $9.9972. The option price will fall by (0.01)(0.99972) or $0.0099972. This means that the option price will move 99.972 percent of the move in S. Theta: As an option advances through time towards the expiration date, the option s premium shows sensitivity with the change in time. The sensitivity is Theta. Theta is used in computing the expected change in the option price: E( )C=(Original expiration-revised expiration)(theta) There was a Theta value of -0.0196. So if there is 90 days to expiration and the analyst needs to know how much the option price will change with 75 days remaining until expiration, one can compute the expected change in the option price as (0.2466-0.2055)(-0.0196) E( )C=$-0.00061 Gamma: Gamma measures the risk that the stock price will not change by a small amount but a large amount. This means that option hedge is no longer perfect. Gamma is largest when the stock price is near the exercise price. Our Gamma had a value of 0.0008. This is the rate at which delta will change with respect to changes in the underlying price.
Vega: Vega captures the sensitivity of the option s price to a change in the underlying s stock price volatility. There was a Vega value of 0.0762. Expected Change in call price (E( )C)=(change in 2 )(Vega) One then can compute the expected change of price with some sort of change in volatility such as 0.01 as follows: E( )C=0.01*0.0762 E( )C=$0.000762 Rho: Rho is the option s sensitivity to interest rate changes (rate volatility). There was a Rho value of - 0.1692. One can then compute the Expected change in call price as follows: E( )C=(new r-old r)(rho) If the risk free rate were to increase by ½ a percent: E( )C=(0.020-0.015)(-0.1692) E( )C=-0.000846 or (-0.0846%) Implied Volatility: Implied volatility is the market s measurement of volatility. It is the volatility that, when used in a particular pricing model, yields a theoretical value for the option equal to the current market price of that option. Implied Volatility=27.900%
Implied Volatility Implied Volatility Simulation: 1. Call Implied Volatility: Apple Inc. Call Implied Volatility 175 150 125 100 75 50 25 100 150 200 250 300 350 400 Strike Price 450 500 550 600 50 100 150 200 250 300 350 400 Time 450To 500 Maturity 550 600 Time To Maturity 650 700 750
Implied Volatility 2. Put Implied Volatility: Apple Inc. Put Implied Volatility 125 100 75 50 25 100 150 200 250 300 350 400 Strike Price 450 500 550 600 50 350 300 250 200 150 100 750 550 600 650 700 400 Time 450 500 To Maturity Time To Maturity
IV Equity Portfolio: Macro Hedging Basics The DJX option index current price level is 121.75 1. Option Strategy- Bull Call Spread The option strategy Bull Call Spread has the investor buying one December 120 Call for $2.34 and selling one December 121 call for 1.79. The total invested is $.55(2.34-1.79) or $55.00. The maximum loss for the strategy is $55.00 and the maximum gain for the strategy is $45.00. Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 1 120.00 2.340 0.190 Call 2 16-Dec-11 13-1 121.00 1.790 0.000 Call 3 16-Dec-11 13 0 123.00 0.910 0.000 Call 4 16-Dec-11 13 0 124.00 0.590 0.000 Put 1 16-Dec-11 13 0 121.00 2.460 0.810 Put 2 16-Dec-11 13 0 122.00 2.980 1.810 Put 3 16-Dec-11 13 0 123.00 3.550 2.810 Put 4 16-Dec-11 13 0 124.00 4.280 3.810
2. Option Strategy Put Bull Spread The option strategy Put Bull Spread has the investor buying one December 121 Put for 2.46 and selling one December 123 put for $3.55. The total premium collected is $1.09(3.55-2.46) or $109.00. The maximum loss for the strategy is $91.00 and the maximum gain for the strategy is the premium collected or $109.00. Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 0 120.00 2.340 0.190 Call 2 16-Dec-11 13 0 121.00 1.790 0.000 Call 3 16-Dec-11 13 0 123.00 0.910 0.000 Call 4 16-Dec-11 13 0 124.00 0.590 0.000 Put 1 16-Dec-11 13 1 121.00 2.460 0.810 Put 2 16-Dec-11 13 0 122.00 2.980 1.810
Put 3 16-Dec-11 13-1 123.00 3.550 2.810 Put 4 16-Dec-11 13 0 124.00 4.280 3.810 3. Option Strategy- Long Call Butterfly The option strategy Long Call Butterfly has the investor buying one December 120 call for $2.34 selling 2 December 121 calls for $1.79 each, and buying one 123 call for $.91. The total premium collected for the strategy is $.33((1.79X2)-2.34-.91) or $33.00. The maximum loss for the strategy is $67.00 and the maximum gain for the strategy is $111.65 at a price of 121.213. Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 1 120.00 2.340 0.190 Call 2 16-Dec-11 13-2 121.00 1.790 0.000 Call 3 16-Dec-11 13 1 123.00 0.910 0.000 Call 4 16-Dec-11 13 0 124.00 0.590 0.000
Put 1 16-Dec-11 13 0 121.00 2.460 0.810 Put 2 16-Dec-11 13 0 122.00 2.980 1.810 Put 3 16-Dec-11 13 0 123.00 3.550 2.810 Put 4 16-Dec-11 13 0 124.00 4.280 3.810 4. Option Strategy- Long Straddle The option strategy Long Straddle has the investor buying one December 120 call for $2.34 and buying one December 121 put for 2.46. The total amount invested is $4.80(2.34+2.36) or $480.00. The maximum loss for the strategy is $480.00, or the amount invested, and the maximum gain is unlimited, both on the upside and the downside. Option Portfolio Option Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 1 120.00 2.340 0.190 Call 2 16-Dec-11 13 0 121.00 1.790 0.000
Call 3 16-Dec-11 13 0 123.00 0.910 0.000 Call 4 16-Dec-11 13 0 124.00 0.590 0.000 Put 1 16-Dec-11 13 1 121.00 2.460 0.810 Put 2 16-Dec-11 13 0 122.00 2.980 1.810 Put 3 16-Dec-11 13 0 123.00 3.550 2.810 Put 4 16-Dec-11 13 0 124.00 4.280 3.810 5. Option Strategy Long Strangle For the long strangle options strategy on the Dow Jones Index, the risk is very low as losses are minimized while profits are unlimited. The highest calculated profits are at the sorted option price of $76.72, where the total profit levels are $4123. This means that profits are at a maximum when the option price is lower, with profits being even greater if the price decreased even further. Maximum losses were $305 at a sorted option price of $123.19. ption Expire Remaining Contracts Exercise Last Trade Min Value
Call 1 16-Dec-11 13 0 120.00 2.340 0.190 Call 2 16-Dec-11 13 0 121.00 1.790 0.000 Call 3 16-Dec-11 13 0 123.00 0.910 0.000 Call 4 16-Dec-11 13 1 124.00 0.590 0.000 Put 1 16-Dec-11 13 1 121.00 2.460 0.810 Put 2 16-Dec-11 13 0 122.00 2.980 1.810 Put 3 16-Dec-11 13 0 123.00 3.550 2.810 Put 4 16-Dec-11 13 0 124.00 4.280 3.810 6. Long Gut Strategy For the long gut strategy, similar to the long strangle strategy, risk is minimal as losses are minimized while profits are unlimited as the option price decreases. Maximum profits as calculated in the program are $4066 at a sorted option price of $76.72, with profits being even greater as the option price decreases. Largest losses are found at the sorted option price levels of $120.86 and $123.19, where losses are found to be $262. Comparing to the long strange, which is a very similar strategy in terms of risk and profit potential, profit levels are slight lower while the amount of losses associated with are also lower than with the long strange.
ption Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 1 120.00 2.340 0.190 Call 2 16-Dec-11 13 0 121.00 1.790 0.000 Call 3 16-Dec-11 13 0 123.00 0.910 0.000 Call 4 16-Dec-11 13 0 124.00 0.590 0.000 Put 1 16-Dec-11 13 0 121.00 2.460 0.810 Put 2 16-Dec-11 13 0 122.00 2.980 1.810 Put 3 16-Dec-11 13 0 123.00 3.550 2.810 Put 4 16-Dec-11 13 1 124.00 4.280 3.810 7. Option Strategy Long Call Condor For the long call condor strategy, profits are low while the losses are also minimized. Maximum profit is found at a sorted option price of $120.86, where the total profits are $63. Maximum losses are found at all levels outside of the sorted option price range of $118 to $127, with losses being $23 at this range.
ption Expire Remaining Contracts Exercise Last Trade Min Value Call 1 16-Dec-11 13 1 120.00 2.340 0.190 Call 2 16-Dec-11 13-1 121.00 1.790 0.000 Call 3 16-Dec-11 13-1 123.00 0.910 0.000 Call 4 16-Dec-11 13 1 124.00 0.590 0.000 Put 1 16-Dec-11 13 0 121.00 2.460 0.810 Put 2 16-Dec-11 13 0 122.00 2.980 1.810 Put 3 16-Dec-11 13 0 123.00 3.550 2.810 Put 4 16-Dec-11 13 0 124.00 4.280 3.810 V- Options Based Management Summary 1. For the micro-hedging part of the portfolio we used Apple Inc. as our underlying security. One of the reasons we choose Apple Inc. was because it holds the fourth largest position, by portfolio weight, at 11.262%. It also has the largest market capitalization of any
security in our portfolio, that s because he has the largest market capitalization of any stock in the world. Based on our findings, and our assumption of the market, we believe Apple inc. to have a 2-3% increase from now until the end of the option expiration December 18 th 2011. Using the information gathered to form our assumption we feel it would be best to use a profit-enhancing objective with the security. If we take the high side of our prediction, a 3% increase, the stock would be at or around $400 on expiration date. After looking at the various option strategies we created with the security, we feel that implementing a Collar strategy will give us the best chance to increase our profits. If our assumptions on the market change, due to market conditions, and unforeseeable actions, we also have constructed a risk-mitigation strategy with the security. Using the long call butterfly allows us to generate a profit no matter which way the stock goes, but limits our profitability. Each contract has the possibility of gaining a maximum of $236.79 and a minimum of $105.00. 2. For the macro-hedge part of the portfolio we used the Dow Jones Industrial Average as our base index. With only 5 of the 30 securities chosen for our portfolio listed in the Dow Jones, we felt we needed to gain more exposure on the index. It also would allow us to increase our profits on the portfolio, as well as provide some protection to the down side. Since our portfolio is made up of 30 securities we felt that using a risk-mitigation profit protecting strategy, would be our best fit here. Since we do predict the market to have a 1-2% increase over the next month we looked at our various strategies that would allow us to gain a profit for a minimal move in the markets. With the option index trading at( or around given a certain time) 121.75, a 1-2% move in either direction leaves at 119.36 and 124.185 on the high side The long call condor gives us an opportunity to collect profits if the option index is from a price range of 119-126. If we use our exact strategy above with a contract multiplier of 100, we can expect to gain a maximum of $6,300 and a potential loss, if outside of the price range stated, of $2,300. Part B: Futures-Based Risk Mitigation Strategies: 1 a) The market index used was the Dow Jones Industrial. Due to most of the stocks in our portfolio being located in different indices, all but 5, the Dow Jones Industrial was used to hedge against so that if our stocks went up we had the opportunity for increased profits if the Dow went down. If the NASDAQ was chosen we would risk losing more if stocks fell in price. Therefore our strategy was profit enhancement driven. b) The Dow Jones mini $5 futures contract is a type of option for which the underlying assets are the Dow Jones Industrial average. The option has a 5 times multiplier, which means that
Value each option contract on the index controls 5 times the value of the index. This gives the option holder more leverage on his/her investment compared to cash index options at a lower cost. 2 a) The hedge ratio is a ratio comparing the value of a position protected via a hedge with the size of the entire position itself. A hedge ratio shows how exposed an investment is to risk. Therefore the optimal hedge ratio was found with call 1 at 0.54082. This means that 54% of the call is protected from risk. Put 4 was the worst at -0.96767. b) c) For wealth change, the managed portfolio net value changes by $50,980, the dynamic hedge open changes by $664,185, and the gain over base is $81,795. 3 a) i) The Indexed Portfolio v/s the Market Index Value Portfolio Indexed Value v/s Market Index Value 12,200 12,000 11,800 11,600 11,400 11,200 11,000 10,800 10,600 10,400 10,200 10,000 9,800 9/9/11 9/16/11 9/23/11 9/30/11 10/7/11 10/14/11 10/21/11 10/28/11 11/4/11 11/11/11 11/18/11 11/25/11 ----- Market Index Value ----- Portfolio Index Value This graph is showing that the market started at a value of 11,000 while our portfolio started with a value of 10,700. On October 1 st and November 24 th they were farthest apart with the market at a value of 10,600 and the portfolio a value of 9,800 on October 1 st and then on November 24 th with a market value of 11,200 and the portfolio a value of 10,200. They were closest on November 6 th when the Market had a value of 11,600 and the portfolio had a value of 11,400. This is actually when the portfolio index value peaked. It ended with a market value of 12,000
Returns Portfolio Value Index Value and portfolio value of 11,000. Overall the indexed values are showing the relative increase or decrease in the value from the base period. In the end both the market and portfolio had increased in value and showed similar trends. ii) Portfolio Value v/s Index Value Portfolio Value v/s Index Value 2,000,000 12,200 1,800,000 1,600,000 12,100 12,000 11,900 1,400,000 11,800 11,700 1,200,000 11,600 1,000,000 11,500 11,400 800,000 600,000 11,300 11,200 11,100 400,000 200,000 11,000 10,900 10,800 0 10,700 09/06/11 09/14/11 09/22/11 09/30/11 10/08/11 10/16/11 10/24/11 11/01/11 11/09/11 11/17/11 11/25/11 12/03/11 Portfolio Value Dow Jones Industrials Value Optimal Portfolio Value The portfolio value is the value of the managed portfolio on the historical date. It peaked on 10/26/11 with a value of nearly 1,800,000. This was when the index value peaked as well at 12,200. Both were at the lowest on 10/2/11 when the portfolio had a value of just under 1,600,000 and the index had a value of 10,700. Therefore 10/26/11 was the best day and 10/2/11 was the worst. The index value was much more variable than the portfolio value. b) i) Portfolio Returns vs. Index Returns Portfolio Returns v/s Index Returns 0.05 0.00-0.05 09/14/11 09/22/11 09/30/11 10/08/11 10/16/11 10/24/11 11/01/11 11/09/11 11/17/11 11/25/11 12/03/11 Portfolio Interim Return Dow Jones Industrials Interim Return Optimal Portfolio Interim Return The portfolio returns and index returns were almost identical. According to the graph the best returns were on 10/10/11 at a value of 0.05. This was seen again in late November and early December. The lowest returns were on 9/22/11 at a value of -0.04. The portfolio primarily showed positive returns and both showed similar trends.
Value ii) Valuation Trend Portfolio, Index & Optimal Value 2,000,000 1,800,000 1,600,000 1,400,000 1,200,000 1,000,000 800,000 600,000 400,000 200,000 0 09/06/11 09/14/11 09/22/11 09/30/11 10/08/11 10/16/11 10/24/11 11/01/11 11/09/11 11/17/11 11/25/11 12/03/11 12,200 12,100 12,000 11,900 11,800 11,700 11,600 11,500 11,400 11,300 11,200 11,100 11,000 10,900 10,800 10,700 Portfolio Value Dow Jones Industrials Value Optimal Portfolio Value The Portfolio value v/s Index Value shows the greatest variation while the portfolio returns v/s index returns is the most constant. iii) Technical Trends Both the Bollinger-bands and momentum trends varied between 11,500 and just under 10,000. The momentum price trend was lowest on 10/3/11 at a value of around 9,500. The Bollinger Band trend was lowest around the same date. The Momentum price trend peaked at 11,500 on 12/1/11 while the Bollinger Band trend peaked at 11,400 on 10/28/11.
c) The Sharpe, or reward-to-variability, ratio is a direct measure of reward to risk. The numerator s (r p -R f ) while the denominator is the standard deviation of r p. The ratio examines the excess return (numerator) per unit of total risk. When comparing two or more assest with the same expected return, the one with the higher Sharpe ratio gives more return for each unit of risk. The portfolio had a Share ratio of 13.84 while the market index was at 29.28. Therefore the market index gives more return for each unit of risk. The Treynor ratio is also a direct measure of reward to risk. The numerator is identical to that used in the Sharpe measure. The denominator is the portfolio beta. This measure reports the amount of excess return per unit of systematic risk. The managed portfolio had a ratio of 0.25 while the market index was at 0.50. The market had higher excess returns per unit of systematic risk. d) Value at risk is the maximum probable loss of an investment over a specific period of time at a given confidence level (5%). It estimates an expected maximum loss for a portfolio given a time horizon and a level of statistical significance. The managed portfolio had a value of risk of $394.14 at 3.58% while the market index was $386.02 at 3.21%. This means that the portfolio has a 95% that the daily loss will not exceed $394.14 and the market $386.02. Therefore the market is safer. e) Conditional value at risk is the conditional expectation of the loss above VaR for a given time horizon at a specified confidence level (1%). It quantifies the dangers beyond VaR. The managed portfolio was $485.56 at 4.41% while the market was $494.95 at 4.12%. There is only a 1% chance that losses will exceed $484.56 for the portfolio and $494.95 for the market. The portfolio is safer when it comes to larger losses. f) Omega is a performance measure that incorporates all the distributional characteristics of a return series. It is a function of the return level and requires no parametric assumptions on the distribution of returns. It measures the total impact of the statistical moments. The portfolio had a value of 0.96 and the market had a value of 0.93. The higher omega value for the portfolio means that there is more density return on the right of the threshold r than on the left. Everything else equal, a high Omega means that returns on the left of the threshold (i.e. extreme negative returns), are not further away from the threshold than on the right.
g) Sharpe-Omegas numerators is the expected return of the portfolio less a threshold return level. The denominator is equal to a put price on the instrument at the threshold rate. The portfolio had a value of 0.04 and the market had a value of 0.09. The portfolio has higher asset volatility due to the lower sharpe-omega value. 4. See attached document 5. As a group we prefer to use option contracts as our hedging instrument. We feel that not only are the enormity of types of option strategies that we can use to either increase profits or use for risk-mitigation, but they are easier to maintain and implement. Part C: Automated Trader: 1. Summary: Our portfolio when we entered in all 30 securities was valued at 1,646,144 and now as up to date as 12/6/2011 at 4:00pm is 1,743,201 giving us an increase of 5.8% a. IMAX- The reason we choose IMAX for our presentation is because it has gained the most by % from time of investment. IMAX is an entertainment company that has cinemas all around the world, as well as other photographic equipment. We bought the stock at a purchase price of $18.80 and the most recent price was $21.20. That is a gain of 2.40 or 12%. The action that caused this was analyst upgrade, Benjamin Mogil of Stifel Nicholas, as he said that he expected screen installations to come in higher than
expected for the upcoming quarter. He also raised his price target to $25.00 for the stock. Also I d like to make note that this stocks short interest percentage is relatively high at, 4,738,442, and the days to cover is about 6.89. This sets up IMAX for a possible short squeeze candidate and may push the stock even higher in the near term. Also we d like to note that IMAX has a big motion picture being released next week, Mission Impossible Ghost Protocol, which may also contribute to a rise in stock price in the near term. b. The only stock of the 30 we choose to build our portfolio that has lost us money is Lululemon Athletica Inc... They are producers of high-end yoga and fitness pants for both men and women. Recently they came out with their quarterly earnings that did not meet expectations of the analysts. This caused a severe drop in price, resulting in the loss of $800.00 in our portfolio. We purchased the stock at 47.76 and the stocks most recent price was 46.16. Note* as you went over with us in close at 5:45 links were down on the automated trader so obtaining other information was un-obtainable.