Devising a Rule-Based Trading System for a Hedge Fund - Research Paper Example

--------------------- --------------------------- -------------------June 20007 Technical Analysis The foremost objective of this report was to devise a rule based trading system for a hedge fund. The basis for analysis was single scrip in which the fund was expected to be interested in a major way both as a buyer and a seller. The chosen scrip was Goldman Sacchs and its equity quotes over a select period formed the basis of the present report. The most critical assumption underlying the design of this trading system is that the fund is having a risk appetite that represents a judicious mix of risk assumption and risk aversion. This implied that it is assumed that the fund would definitely be interested in riding a wave but not to the peak but obtain gains much before the peak and go short somewhere between the bottom and the peak. Similarly the fund would not wait for the market to bottom out before taking a decision on going long and that it would go long once market moves down somewhere between the peak and the bottom. Either strategies would imply that the fund is not looking for excessive and speculative gains; nevertheless it does maintain inherent profit booking targets. The trading system explained below is based on trading rules that were tested for profits results based on this risk philosophy. Financial theory, taught in finance textbooks the globe over, normally exposes a student of finance to the concepts like the efficient market hypothesis and the economically rational individual. Bubbles and crashes seem to defy these two seminal concepts with an awkwardness equivalent to the awkwardness one would attach to those things on earth that defy gravity. Nevertheless such extreme stock market movements are a reality. Bubbles make investing decisions arduous as stock prices tend to deviate by substantial margins from their fundamental valuations. Investors relying on past company results and technical analysis are equally defeated in such situations as is the EMH.In fact, investors always act on the basis that they have an applicable construct to explain stock price movements and tend to input all available information collected under such constructs in their investment decisions (Poole 2000). Finance research has also held varying opinions on this issue. For instance, Biermann (1995) supports the idea that market prices are determined from backward looking investors than by those that indulge in predictions of all sorts. Others have, for example elaborated on the use of price to earnings ratios to determine excess market valuations. Some technical work has set to rest in a convincing manner the phenomenon of bubbles and bursts. For instance, Graham (1973) describes in details why markets fluctuate and how to deal with the violent fluctuations .Graham discusses five basic points to read into cross sectional view of market bubbles. Most of these points concern factors like growth and earnings and their impact on price movements and price levels. Graham (1973), in fact, provides a much better viewpoint on gauging market bubbles through an adaptive expectations model. The Efficient Markets Hypothesis (EMH) states that current prices always 'fully reflect' available information, so that the only reason prices change between time t and time t+1 is the arrival of new information. The EMH requires that only two necessary conditions be met. First, the market must be aware of all available information .The type of information available is determined by the strength of the EMH being tested. In a Weak Form EMH, current prices entirely reflect all that can be known from the study of historical prices and trading volumes. If the Weak Form is valid, technical analysis becomes ineffective. Any information contained in past prices has been analyzed and acted on by the market, so that shares are neither under-valued nor over-valued. In a Semi- Strong EMH, current prices efficiently adjust to information that is publicly available. If this form of the hypothesis holds true, then fundamental as well as technical analysis is also ineffective because all publicly available information has been thoroughly analyzed, assessed and acted upon. Finally, in a Strong Form EMH, current prices fully reflect all information, and not just that information which is to be found in the historical trading pattern or available publicly. Thus, if the Strong Form holds true, any attempt to make profitable use of monopolistic access to information is useless because this information has already been incorporated into the market price of the share. The second necessary condition is that of the rational expectations element of the EMH, or informational efficiency. It means that real returns can be randomly higher or lesser than expected returns, but on average, unexpected returns must be zero. The main implication of the rational expectations is that no system of trading rules can have higher expected returns than the equilibrium expected returns derived by the market. In other words in a perfect market scenario of RWT and varying degrees of market perfection in 3 forms of hypotheses under EMH the prices determined are efficient and there is no incentive on the market to either change prices or move away from equilibrium prices until unless some new unabsorbed information/event comes about making it necessary to move towards a new equilibrium. Based on the above theoretical discourse the present paper took up the equity trading data of Goldman Sacchs from the New York Stock Exchange for the period 31st December 2004 to 30th April 2007 comprising of 585 observations. It was decided to test the market on the basis of data that was available in reverse order of chronology. This meant that it was presumed that for establishing rules the training data more appropriate would be older data. Thus the oldest 234 observations beginning from the date 31-12-2004 were taken as the Training data. Thereafter the immediately succeeding 234 observations were taken as the Test data and the latest 117 observations till the date 30th April 2007 were taken as the prediction set to test the validity of the filter or the trading rules. These three data subsets formed roughly 40 %,, 40% and 20% of the total data set of observations on the equity prices of Goldman Sacchs on New York Stock exchange for the chosen period. Trading system was designed in two decisional halves. One set of rules recommended for a sell decision and the other set of riles recommended for a buy decision. Sell decisional rules were based on an analysis of the data on the daily high quotes of the scrip and the difference between the daily high and low quotes of the scrip. It was logically derived that for sell trading rules it was the high quotes that would offer more information than either the opening, low or closing quotes. However the low quotes, in conjunction with the high quotes afforded a signal which indicated at the widening or the narrowing of the market in order to go short. Thus percentage change in high quotes was reckoned as a sure shot signal for a decision to go short. Similarly the daily low quotes and high and low quotes differences were observed to have a reasonable pattern to signal the decisions to go long. The daily data of the high, low and the High-Low quotes' differences has been plotted in figure 1 below: Figure 1 : High,Low,High-Low of Goldman Sacchs for the Training Data The above technical analysis is carried in table 1 at Annexure A. This technical analysis threw up the following possible filter or trading rules for selling and buying decisions. Filter Rule 1: Sell whenever percentage change in the High quote exceeds 2% Filter Rule 2: Sell whenever the difference between the High and Low quotes exceeds $3. Filter Rule 3: Else Hold Filter Rule 4:Buy on the immediate next trading day whenever negative percentage change in the Low quote exceeds 2% Filter Rule 5: Buy on the immediate next trading day whenever the difference between the High and Low quotes exceeds $2.5. Filter Rule 6: Or else remain unbought It was observed from the table 1 analysis of the data that the fund would have taken appropriate short and long decisions based on these trading rules given the above assumptions about its trading philosophy and risk appetite. It was also observed that in most market turnarounds both the high quote percentage change and the High-Low quote differences based above trading rule came good as far as the going short decisions were concerned.Similaty the low quotes percentage change and the and the High-Low quote differences based above trading rule came good as far as the going long decisions were concerned in training data, on post facto basis. However when these rules were applied to the test data it was observed that in certain market changes these rules did not adequately signal the going short or long decisions. For instance on 14th March 2006 when the high quote registered a sudden jump of 4.58 % with High and Low quotes differences of $ 3.88 a short decision was imminent by the suggested trading rule. However the subsequent movement of the scrip revealed that the fund would have done better to hold on to the scrip as the scrip rose up to $152.66 from the sold price level of $ 149.50.This kind of price obtention was definitely in line even with the conservative risk philosophy assumed within the trading rule. Much more profits had it decided to hold back a short decision. In fact there appeared to new information that the market was building in and around this period in this scrip which was the cause for the outlier result to the trading rules. In this particular instance the fund would have made The data carrying the analysis of the test data is carried at table 2 in Annexure A. Table 3 carried at Annexure A reveals the results of the accuracy test of the above trading rules carried out on the prediction data set. The results confirm the fact that above trading rules do not adequately reflect new and additional information which the market discounts in the scrip prices ,in that, in such events a trading decision, based on above rules, would lead to booking of losses which could have been avoided. For instance the high quote of the scrip price prevailed at $ 215.23 on 16th April 2007 ,up from $ 207.95 as on 15th April 2007 ,registering an increase of 3.58 %.Given the above trading rule the scrip would have been sold at this price; however the data in Table 3 reveals that the scrip price rose up to $ 223.98 on 23rd April 2007.This sharp upward rise was definitely due to some additional and new information about the scrip which the filter rule was unable to capture. However, on 21st March 2007 the quote of the scrip price prevailed at $ 211.51 up from $ 204.43 as on 20th March 2007 ,registering an increase of 3.46 %;a trading rule based short decision was very much in line with the subsequent developments in the market. the scrip price rose very gradually after this sell decision to $211.73 on 27th March 2007 before it fell to a mere $208.67 on 28th March 2007.Thus the sell decision was very much in line with the risk philosophy of the fund as well as made for good profit booking by the fund. It was interesting to observe that in both of the above instances the above High-Low quote differences rule held good in that such difference prevailed very much above the level of $3. Thus a better modification of the latter rule would be that the High-Low price difference should not exceed the range of $3-$4.5 with the additional corollary that in case such a difference is noted much beyond the above range and if it plummets much below this range on next or coming trading days then most of the overbought inventory should be immediately disposed off. This would be a strategy in loss minimization while still riding the peak in the market. It goes without saying that subjectivity has its role to play in the above building of the differences' range given the risk philosophy of the fund. Prediction data revealed that while short decisions were largely covered by the trading rules; the trading rule concerning long decisions sadly misfired for most market movements. For instance when on March 5th 2007 the scrip low was quoted as $189.85 down from $195.59 on March 02,2007 -a reduction of 2.93 %-a trading decision to purchase the scrip on the next trading day i.e. March 6th 2007 would have afforded a price as high as .$193.70 .Similarly on February 27th ,2007 - the scrip low was quoted as $194.65 down from $212.66 on February 26th ,2007 -a reduction of 8.47 %-a trading decision to purchase the scrip on the next trading day i.e. February 28th ,2007 would have afforded a price as high as .$197.79 . In all these market downturns it is observed that it no longer makes sense to wait for the next trading day to arrive to avail a lower purchase price; rather it makes more sense to go for the kill on the same very day. However quick availability of the data would be an evident constraint for such a decision to come about. Thus the trading rules that can be recommended to the fund can be restated as follows Filter Rule 1: Sell whenever percentage change in the High quote exceeds 2% Filter Rule 2: Sell whenever the difference between the High and Low quotes exceeds the range of $3-$4.5 with the additional corollary that in case such a difference is noted much beyond the above range and if it plummets much below this range on next or coming trading days then most of the overbought inventory should be immediately disposed off. Filter Rule 3: Else Hold Filter Rule 4:Buy on the immediate next trading day whenever negative percentage change in the Low quote exceeds 2% Filter Rule 5: Buy on the same trading day whenever the difference between the High and Low quotes exceeds $2.5. Filter Rule 6: Or else remain unbought Works Cited Poole, William.(2000).Expectations. Twenty-second Henry Thorton Lecture. 28 November 2000. Bierman Jr, Harold.(1995).Bubbles, Theory, and Market Timing. Journal of Portfolio Management 22.1 : 54-61. Graham, Benjamin.(1973). The Intelligent Investor. 4 ed. New York: Harper & Row. Annexure A Table 1: Technical Analysis of the Goldman Sacchs Training Data. Training Dataset Date Open High %Change H-L Low %Change 11/30/2005 130.45 131.27 -0.87593 2.83 128.44 -0.47269 11/29/2005 132 132.43 -1.39241 3.38 129.05 -1.36808 11/28/2005 134.3 134.3 -0.43739 3.46 130.84 -2.38006 11/25/2005 134.2 134.89 -0.07408 0.86 134.03 1.070809 11/23/2005 132.61 134.99 1.503872 2.38 132.61 1.376042 11/22/2005 131.8 132.99 0.384964 2.18 130.81 0.24523 11/21/2005 131.25 132.48 0.439727 1.99 130.49 0.523843 11/18/2005 131.9 131.9 1.14255 2.09 129.81 1.525106 11/17/2005 128 130.41 1.51008 2.55 127.86 1.027181 11/16/2005 128.35 128.47 -0.99414 1.91 126.56 -0.39351 11/15/2005 129.7 129.76 -0.42971 2.7 127.06 -1.19751 11/14/2005 130.32 130.32 -0.23731 1.72 128.6 -0.5183 11/11/2005 129.45 130.63 0.230185 1.36 129.27 1.166067 11/10/2005 128.15 130.33 0.462499 2.55 127.78 0.219608 11/9/2005 127.84 129.73 1.067311 2.23 127.5 0.220091 11/8/2005 128.35 128.36 -2.52867 1.14 127.22 -1.12691 11/7/2005 130.5 131.69 0.388779 3.02 128.67 -0.17843 11/4/2005 129.75 131.18 0.907692 2.28 128.9 0.632368 11/3/2005 130 130 0.432633 1.91 128.09 1.65873 11/2/2005 126 129.44 2.009615 3.44 126 0.961538 11/1/2005 126.7 126.89 -0.38468 2.09 124.8 -0.12005 10/31/2005 125 127.38 2.108216 2.43 124.95 1.925116 10/28/2005 123.7 124.75 -0.1201 2.16 122.59 0.467137 10/27/2005 123.8 124.9 -0.07201 2.88 122.02 -0.51366 10/26/2005 123.25 124.99 0.120154 2.34 122.65 0.269784 10/25/2005 122.52 124.84 1.109581 2.52 122.32 2.61745 10/24/2005 119.7 123.47 2.908818 4.27 119.2 0.999831 10/21/2005 119.8 119.98 -1.72018 1.96 118.02 -0.58125 10/20/2005 119.98 122.08 0.618149 3.37 118.71 2.318566 10/19/2005 116.25 121.33 2.483318 5.31 116.02 -0.43766 10/18/2005 116.55 118.39 0.586236 1.86 116.53 0.517554 10/17/2005 115.99 117.7 2.463655 1.77 115.93 3.021417 10/14/2005 114.1 114.87 -1.17009 2.34 112.53 2.086546 10/13/2005 115.2 116.23 -2.05612 6 110.23 -2.90672 10/12/2005 117.55 118.67 -0.93497 5.14 113.53 -2.96581 10/11/2005 119.2 119.79 0.351847 2.79 117 -0.46789 10/10/2005 118 119.37 1.11817 1.82 117.55 0.298635 10/7/2005 117.25 118.05 -0.43016 0.85 117.2 0.834552 10/6/2005 117.7 118.56 -0.52857 2.33 116.23 -0.31732 10/5/2005 118.92 119.19 -2.02219 2.59 116.6 -1.76917 10/4/2005 120.9 121.65 -0.58025 2.95 118.7 -2.12731 10/3/2005 121.29 122.36 0.542317 1.08 121.28 0.397351 9/30/2005 120.89 121.7 0.189347 0.9 120.8 1.48702 9/29/2005 119.1 121.47 0.496401 2.44 119.03 -0.62615 9/28/2005 120.15 120.87 -0.08267 1.09 119.78 0.192388 9/27/2005 119.7 120.97 0.690861 1.42 119.55 0.209556 9/26/2005 119.95 120.14 0.191811 0.84 119.3 1.256153 9/23/2005 118.79 119.91 0.730847 2.09 117.82 2.496738 9/22/2005 115.68 119.04 1.215883 4.09 114.95 -0.44171 9/21/2005 116.13 117.61 -2.31728 2.15 115.46 -2.19399 9/20/2005 120.39 120.4 1.50059 2.35 118.05 0.880191 9/19/2005 118.1 118.62 0.101266 1.6 117.02 0.619089 9/16/2005 116.5 118.5 2.023246 2.2 116.3 1.2537 9/15/2005 115 116.15 -1.98312 1.29 114.86 -0.57133 9/14/2005 117.75 118.5 0.517432 2.98 115.52 -1.04506 9/13/2005 117.75 117.89 -0.49797 1.15 116.74 0.145835 9/12/2005 116.71 118.48 1.891985 1.91 116.57 1.013865 9/9/2005 115.5 116.28 0.501296 0.88 115.4 0.865309 9/8/2005 114.73 115.7 0.564972 1.29 114.41 0.069973 9/7/2005 114.59 115.05 0.113122 0.72 114.33 0.616034 9/6/2005 113.79 114.92 0.993057 1.29 113.63 0.798368 9/2/2005 113.3 113.79 -0.56798 1.06 112.73 1.012545 9/1/2005 111.7 114.44 2.636771 2.84 111.6 1.602331 8/31/2005 109.84 111.5 1.363636 1.66 109.84 0.900239 8/30/2005 109.9 110 -0.37134 1.14 108.86 -0.38433 8/29/2005 109.5 110.41 -0.26197 1.13 109.28 0.229295 8/26/2005 110.5 110.7 -0.04515 1.67 109.03 0.027523 8/25/2005 110.24 110.75 -1.73898 1.75 109 -0.90008 8/24/2005 111.79 112.71 0.633929 2.72 109.99 -0.97236 8/23/2005 111.5 112 -0.36474 0.93 111.07 -0.009 8/22/2005 111.8 112.41 0.509657 1.33 111.08 0.11717 8/19/2005 111.12 111.84 0.458098 0.89 110.95 0.662312 8/18/2005 110.89 111.33 -0.6603 1.11 110.22 0.009074 8/17/2005 111.85 112.07 -2.43754 1.86 110.21 -1.59821 8/16/2005 114.55 114.87 0.043546 2.87 112 -0.86741 8/15/2005 113.25 114.82 0.411019 1.84 112.98 0.070859 8/12/2005 113.18 114.35 0.061253 1.45 112.9 0.857602 8/11/2005 112.08 114.28 0.404147 2.34 111.94 0.107315 8/10/2005 111.98 113.82 1.970973 2 111.82 1.636066 8/9/2005 110.03 111.62 0.594809 1.6 110.02 0.337437 8/8/2005 110.03 110.96 1.056466 1.31 109.65 1.293303 8/5/2005 108.75 109.8 -0.2453 1.55 108.25 -0.45977 8/4/2005 110 110.07 -0.92709 1.32 108.75 -0.01839 8/3/2005 109.08 111.1 1.294675 2.33 108.77 1.417249 8/2/2005 107.25 109.68 1.3023 2.43 107.25 0.524885 8/1/2005 107.6 108.27 -1.12329 1.58 106.69 -0.69806 7/29/2005 109.42 109.5 -0.36397 2.06 107.44 -0.61055 7/28/2005 109.2 109.9 0.659461 1.8 108.1 0.764355 7/27/2005 107.95 109.18 0.423105 1.9 107.28 -0.26959 7/26/2005 108.53 108.72 -0.92044 1.15 107.57 -0.68322 7/25/2005 109.07 109.73 0.448554 1.42 108.31 0.585067 7/22/2005 107.94 109.24 -0.36483 1.56 107.68 -0.18539 7/21/2005 109.25 109.64 -0.30915 1.76 107.88 0.139237 7/20/2005 107.75 109.98 0.091008 2.25 107.73 -0.81937 7/19/2005 108.65 109.88 1.104159 1.26 108.62 1.051261 7/18/2005 107.95 108.68 -0.10111 1.19 107.49 -0.25981 7/15/2005 108.25 108.79 -0.37546 1.02 107.77 -0.41582 7/14/2005 108.95 109.2 0.682279 0.98 108.22 0.913838 7/13/2005 107.32 108.46 -0.20243 1.22 107.24 0.224299 7/12/2005 107 108.68 1.135306 1.68 107 1.306571 7/11/2005 105.66 107.46 1.530612 1.84 105.62 1.871142 7/8/2005 104.1 105.84 1.564149 2.16 103.68 1.627132 7/7/2005 102.35 104.21 0.134525 2.19 102.02 -0.9803 7/6/2005 103.03 104.07 0.356798 1.04 103.03 0.851605 7/5/2005 102.25 103.7 0.057893 1.54 102.16 -0.00979 7/1/2005 102.17 103.64 0.17398 1.47 102.17 0.393043 6/30/2005 103.28 103.46 -0.94782 1.69 101.77 -0.81863 6/29/2005 104.21 104.45 -0.4859 1.84 102.61 -0.66796 6/28/2005 103.5 104.96 1.224805 1.66 103.3 1.27451 6/27/2005 103 103.69 -0.00964 1.69 102 0.068675 6/24/2005 102.16 103.7 0.5527 1.77 101.93 0.029441 6/23/2005 102.3 103.13 -0.26112 1.23 101.9 -0.42994 6/22/2005 102.67 103.4 -0.38536 1.06 102.34 -0.21451 6/21/2005 103 103.8 -0.04815 1.24 102.56 -0.09741 6/20/2005 103.25 103.85 -0.37414 1.19 102.66 0.351906 6/17/2005 102.75 104.24 0.909971 1.94 102.3 3.647416 6/16/2005 100 103.3 3.683629 4.6 98.7 0.909927 6/15/2005 98.6 99.63 -0.53908 1.82 97.81 -0.44784 6/14/2005 99.65 100.17 0.400922 1.92 98.25 -0.16259 6/13/2005 98.78 99.77 -0.35953 1.36 98.41 -0.27361 6/10/2005 100.13 100.13 -0.22917 1.45 98.68 0.070987 6/9/2005 99.2 100.36 1.138769 1.75 98.61 0.264362 6/8/2005 99.1 99.23 -0.24128 0.88 98.35 0.071225 6/7/2005 99.2 99.47 0.698522 1.19 98.28 1.91849 6/6/2005 96.75 98.78 0.662387 2.35 96.43 -0.23795 6/3/2005 97.55 98.13 -0.3554 1.47 96.66 -0.58624 6/2/2005 98 98.48 -1.30287 1.25 97.23 0.53769 6/1/2005 97.4 99.78 2.26504 3.07 96.71 2.068602 5/31/2005 94.9 97.57 0.618748 2.82 94.75 -0.43085 5/27/2005 96.95 96.97 -1.21231 1.81 95.16 -0.91628 5/26/2005 98.05 98.16 -1.54463 2.12 96.04 -1.2239 5/25/2005 99.7 99.7 -0.79602 2.47 97.23 -1.48936 5/24/2005 100.5 100.5 -1.13133 1.8 98.7 -1.59521 5/23/2005 101.65 101.65 0.444664 1.35 100.3 0.75339 5/20/2005 99.95 101.2 0.696517 1.65 99.55 0.322483 5/19/2005 100 100.5 0.530159 1.27 99.23 0.741117 5/18/2005 99 99.97 1.368891 1.47 98.5 1.285347 5/17/2005 97.5 98.62 -0.67479 1.37 97.25 -0.56237 5/16/2005 98 99.29 -0.90818 1.49 97.8 1.431238 5/13/2005 99.5 100.2 -3.40307 3.78 96.42 -2.9394 5/12/2005 103.5 103.73 -0.29796 4.39 99.34 -2.57919 5/11/2005 102.55 104.04 -0.22058 2.07 101.97 0.157155 5/10/2005 104.22 104.27 -1.20334 2.46 101.81 -2.31242 5/9/2005 104.48 105.54 -0.60275 1.32 104.22 -0.26794 5/6/2005 105.75 106.18 -1.03458 1.68 104.5 -0.05738 5/5/2005 106.8 107.29 0.130658 2.73 104.56 -0.086 5/4/2005 105.2 107.15 2.1449 2.5 104.65 1.552644 5/3/2005 103.55 104.9 -0.8975 1.85 103.05 0.048544 5/2/2005 105.85 105.85 -1.33296 2.85 103 -1.43541 4/29/2005 107.13 107.28 -0.56539 2.78 104.5 -1.35926 4/28/2005 106.95 107.89 -0.24963 1.95 105.94 0.69385 4/27/2005 105.67 108.16 0.904935 2.95 105.21 0.085616 4/26/2005 105.74 107.19 0.733014 2.07 105.12 0.545194 4/25/2005 105.5 106.41 0.624113 1.86 104.55 1.298324 4/22/2005 105 105.75 -1.09428 2.54 103.21 -0.232 4/21/2005 105.5 106.92 0.028066 3.47 103.45 -0.59575 4/20/2005 106.7 106.89 -0.95441 2.82 104.07 -2.42828 4/19/2005 107.5 107.92 -0.06482 1.26 106.66 0.338664 4/18/2005 106.69 107.99 -0.99019 1.69 106.3 -0.17842 4/15/2005 108.35 109.07 -1.20471 2.58 106.49 -1.78917 4/14/2005 110.15 110.4 -1.42857 1.97 108.43 -1.18473 4/13/2005 111.77 112 -0.41789 2.27 109.73 -0.37225 4/12/2005 111.55 112.47 -1.1774 2.33 110.14 -1.59042 4/11/2005 113.45 113.81 -0.38512 1.89 111.92 -0.76255 4/8/2005 113.25 114.25 0.280874 1.47 112.78 0.516934 4/7/2005 112.5 113.93 1.145241 1.73 112.2 1.272678 4/6/2005 110.95 112.64 0.661305 1.85 110.79 0.307832 4/5/2005 110.95 111.9 0.511991 1.45 110.45 1.722232 4/4/2005 109.15 111.33 0.243112 2.75 108.58 0.249284 4/1/2005 110.74 111.06 0.725558 2.75 108.31 -0.68769 3/31/2005 110 110.26 0.327571 1.2 109.06 0.804141 3/30/2005 108.19 109.9 -0.65986 1.71 108.19 -0.1661 3/29/2005 109.68 110.63 0.581871 2.26 108.37 -0.16582 3/28/2005 108.95 109.99 0.447489 1.44 108.55 0.166098 3/24/2005 108.78 109.5 0.532501 1.13 108.37 0.809302 3/23/2005 107.6 108.92 -1.86503 1.42 107.5 -0.15789 3/22/2005 109.75 110.99 0.13533 3.32 107.67 -1.76095 3/21/2005 110.1 110.84 0.126468 1.24 109.6 0.03651 3/18/2005 109.7 110.7 -0.48544 1.14 109.56 1.023513 3/17/2005 109.97 111.24 0.596853 2.79 108.45 -0.13812 3/16/2005 110.54 110.58 -1.17962 1.98 108.6 -1.65716 3/15/2005 111.7 111.9 1.038375 1.47 110.43 1.256189 3/14/2005 109.81 110.75 -0.71717 1.69 109.06 0.137728 3/11/2005 111.34 111.55 -0.40179 2.64 108.91 -1.72352 3/10/2005 111.45 112 -0.44444 1.18 110.82 0 3/9/2005 112.5 112.5 -0.59203 1.68 110.82 -1.14184 3/8/2005 112.8 113.17 0.044201 1.07 112.1 0.511073 3/7/2005 111.95 113.12 0.257024 1.59 111.53 1.363265 3/4/2005 110.2 112.83 1.777016 2.8 110.03 0.944954 3/3/2005 110.4 110.86 -0.41322 1.86 109 -0.20143 3/2/2005 109.25 111.32 0.505598 2.1 109.22 0.765753 3/1/2005 108.39 110.76 0.590319 2.37 108.39 0.036917 2/28/2005 110 110.11 -0.12698 1.76 108.35 -0.16585 2/25/2005 108.73 110.25 0.952294 1.72 108.53 0.369925 2/24/2005 108.65 109.21 -0.1828 1.08 108.13 -0.03698 2/23/2005 108.62 109.41 0.137287 1.24 108.17 0.604539 2/22/2005 108.05 109.26 -1.38989 1.74 107.52 -0.99448 2/18/2005 110.65 110.8 -1.78176 2.2 108.6 -1.75502 2/17/2005 112.6 112.81 0.168709 2.27 110.54 -0.9587 2/16/2005 112.35 112.62 -0.50358 1.01 111.61 -0.57016 2/15/2005 112.5 113.19 -0.16758 0.94 112.25 0.501388 2/14/2005 112.78 113.38 -0.48275 1.69 111.69 -0.33907 2/11/2005 112.78 113.93 0.840857 1.86 112.07 0.286353 2/10/2005 111.8 112.98 -0.32642 1.23 111.75 0.359228 2/9/2005 112 113.35 1.26865 2 111.35 1.310163 2/8/2005 109.97 111.93 1.560657 2.02 109.91 0.530504 2/7/2005 110.02 110.21 -0.10876 0.88 109.33 0.570325 2/4/2005 108.74 110.33 1.275932 1.62 108.71 0.471349 2/3/2005 108.4 108.94 -0.02753 0.74 108.2 0.194462 2/2/2005 108.15 108.97 0.027538 0.98 107.99 0.643057 2/1/2005 107.65 108.94 0.898398 1.64 107.3 0.139991 1/31/2005 107.38 107.97 1.18077 0.82 107.15 3.028846 1/28/2005 104.65 106.71 2.27142 2.71 104 0.961072 1/27/2005 103.37 104.34 0.792117 1.33 103.01 1.198546 1/26/2005 103.18 103.52 -1.12703 1.73 101.79 -0.79914 1/25/2005 104.1 104.7 0.153051 2.09 102.61 -0.41731 1/24/2005 103.33 104.54 0 1.5 103.04 0.243214 1/21/2005 103.2 104.54 0.742026 1.75 102.79 -0.08748 1/20/2005 103.5 103.77 -0.90718 0.89 102.88 -0.89587 1/19/2005 104.33 104.72 -0.43735 0.91 103.81 0.241406 1/18/2005 103.6 105.18 0.7954 1.62 103.56 0.602293 1/14/2005 103.1 104.35 0.375144 1.41 102.94 0.155672 1/13/2005 102.8 103.96 -0.28774 1.18 102.78 0.361293 1/12/2005 104.1 104.26 -0.40122 1.85 102.41 -0.95745 1/11/2005 104.05 104.68 -0.71137 1.28 103.4 -0.83437 1/10/2005 104.28 105.43 -0.02845 1.16 104.27 -0.12452 1/7/2005 105.23 105.46 0.199525 1.06 104.4 0.471562 1/6/2005 103.96 105.25 0.257192 1.34 103.91 0.318594 1/5/2005 103.75 104.98 -0.20913 1.4 103.58 -0.31758 1/4/2005 104.8 105.2 -0.04751 1.29 103.91 -0.41211 1/3/2005 104.9 105.25 0.238095 0.91 104.34 0.288351 12/31/2004 104.92 105 0.96 104.04 Table 2: Technical Analysis of the Goldman Sacchs Test Data. Test Data Set Open High %Change H-L Low %Change 11/7/2006 190.2 191.42 -0.14606 2.86 188.56 0.468883 11/6/2006 187.68 191.7 1.455411 4.02 187.68 1.284404 11/3/2006 188.9 188.95 0.617711 3.65 185.3 1.423098 11/2/2006 184.51 187.79 -2.29957 5.09 182.7 -1.10961 11/1/2006 191 192.21 0.622971 7.46 184.75 -2.18657 10/31/2006 190 191.02 0.246654 2.14 188.88 1.167649 10/30/2006 188 190.55 -1.38695 3.85 186.7 -0.89708 10/27/2006 192.01 193.23 -0.19112 4.84 188.39 0.05311 10/26/2006 189.18 193.6 2.061258 5.31 188.29 0.603761 10/25/2006 188.64 189.69 0.76494 2.53 187.16 1.496746 10/24/2006 184.52 188.25 1.828312 3.85 184.4 2.325065 10/23/2006 180.23 184.87 2.313354 4.66 180.21 0.760414 10/20/2006 179.72 180.69 -1.06226 1.84 178.85 -0.58366 10/19/2006 181.25 182.63 -1.09396 2.73 179.9 -1.07231 10/18/2006 184.07 184.65 -0.03248 2.8 181.85 -0.15922 10/17/2006 184.22 184.71 -0.41514 2.57 182.14 -0.51887 10/16/2006 183.82 185.48 0.826267 2.39 183.09 1.350678 10/13/2006 181.21 183.96 1.121372 3.31 180.65 1.142153 10/12/2006 179.27 181.92 1.648321 3.31 178.61 1.052334 10/11/2006 177.3 178.97 -0.4893 2.22 176.75 -0.02263 10/10/2006 177.05 179.85 1.329652 3.06 176.79 0.838467 10/9/2006 175.4 177.49 0.846591 2.17 175.32 0.874568 10/6/2006 174.32 176 -0.29458 2.2 173.8 -0.50947 10/5/2006 176.52 176.52 -0.07925 1.83 174.69 0.796261 10/4/2006 173.31 176.66 1.295872 3.35 173.31 1.887125 10/3/2006 170.44 174.4 1.720618 4.3 170.1 0.943564 10/2/2006 168.51 171.45 0.175285 2.94 168.51 -0.34891 9/29/2006 170.05 171.15 0.676471 2.05 169.1 0.774732 9/28/2006 168.95 170 0.058858 2.2 167.8 0.328849 9/27/2006 168.93 169.9 -0.01177 2.65 167.25 0.137708 9/26/2006 167.94 169.92 0.295125 2.9 167.02 0.011976 9/25/2006 167.9 169.42 0.647538 2.42 167 0.748069 9/22/2006 166.95 168.33 -0.80146 2.57 165.76 -0.06029 9/21/2006 167.5 169.69 1.51352 3.83 165.86 0.992511 9/20/2006 164.63 167.16 1.790281 2.93 164.23 1.182922 9/19/2006 163.08 164.22 -0.35194 1.91 162.31 0.191358 9/18/2006 162.02 164.8 0.641221 2.8 162 0.297177 9/15/2006 162.5 163.75 0.349308 2.23 161.52 1.253761 9/14/2006 159.75 163.18 0.566991 3.66 159.52 1.728206 9/13/2006 157.7 162.26 1.571205 5.45 156.81 1.357378 9/12/2006 154.75 159.75 5.633803 5.04 154.71 3.727791 9/11/2006 149.25 151.23 0.152318 2.08 149.15 1.104935 9/8/2006 151 151 0.212371 3.48 147.52 -0.55949 9/7/2006 150.1 150.68 -0.50185 2.33 148.35 -1.04723 9/6/2006 150.65 151.44 -0.0462 1.52 149.92 0.583697 9/5/2006 149.75 151.51 1.391956 2.46 149.05 1.304968 9/1/2006 148.7 149.43 0.457143 2.3 147.13 0.040797 8/31/2006 147.07 148.75 0.670005 1.68 147.07 0.443928 8/30/2006 147.2 147.76 -1.35523 1.34 146.42 0.521763 8/29/2006 149.6 149.79 -0.49821 4.13 145.66 -1.50122 8/28/2006 148.25 150.54 -0.58116 2.66 147.88 -1.24875 8/25/2006 150.69 151.42 -1.41927 1.67 149.75 -0.66335 8/24/2006 153.55 153.6 -0.74313 2.85 150.75 -0.92014 8/23/2006 153.41 154.75 -0.16773 2.6 152.15 -0.58804 8/22/2006 154.36 155.01 0.492707 1.96 153.05 0.929834 8/21/2006 153.16 154.25 -0.3231 2.61 151.64 -0.88889 8/18/2006 154.45 154.75 -1.35144 1.75 153 -0.55249 8/17/2006 153.9 156.87 1.173815 3.02 153.85 0.739916 8/16/2006 153.95 155.05 0.688356 2.33 152.72 0.998611 8/15/2006 152.38 153.99 0.640481 2.78 151.21 1.191193 8/14/2006 152.48 153.01 0.091581 3.58 149.43 -0.37336 8/11/2006 152.35 152.87 0.493032 2.88 149.99 1.003367 8/10/2006 149.5 152.12 -1.06016 3.62 148.5 -0.73529 8/9/2006 153.5 153.75 -1.06178 4.15 149.6 -0.5914 8/8/2006 152.65 155.4 0.355182 4.91 150.49 -0.83685 8/7/2006 152.12 154.85 -0.92136 3.09 151.76 -0.26944 8/4/2006 154 156.29 2.050278 4.12 152.17 2.492086 8/3/2006 148.75 153.15 1.760797 4.68 148.47 0.630338 8/2/2006 150.26 150.5 -0.81719 2.96 147.54 -1.37041 8/1/2006 151.63 151.74 -1.29448 2.15 149.59 -0.71021 7/31/2006 151.6 153.73 0.905809 3.07 150.66 0.890645 7/28/2006 149.65 152.35 1.817817 3.02 149.33 1.178942 7/27/2006 148.7 149.63 0.544282 2.04 147.59 0.613539 7/26/2006 147.5 148.82 -0.56792 2.13 146.69 0.928856 7/25/2006 146.9 149.67 1.471186 4.33 145.34 1.593737 7/24/2006 143.3 147.5 1.682063 4.44 143.06 0.888575 7/21/2006 145.05 145.06 -1.85386 3.26 141.8 -2.2069 7/20/2006 146.7 147.8 -0.03382 2.8 145 1.611773 7/19/2006 142.7 147.85 3.76895 5.15 142.7 2.00143 7/18/2006 140.62 142.48 0.147607 2.58 139.9 0.502874 7/17/2006 140.1 142.27 -0.85714 3.07 139.2 0.165503 7/14/2006 143.1 143.5 -1.1708 4.53 138.97 -2.20267 7/13/2006 144.03 145.2 -2.70053 3.1 142.1 -2.04729 7/12/2006 148.7 149.23 0.154362 4.16 145.07 -1.00989 7/11/2006 148.4 149 -0.93744 2.45 146.55 -1.08666 7/10/2006 149.25 150.41 -0.0598 2.25 148.16 -0.18863 7/7/2006 150.01 150.5 -1.18188 2.06 148.44 -1.17177 7/6/2006 152.29 152.3 0.395517 2.1 150.2 0.133333 7/5/2006 151.7 151.7 -0.7134 1.7 150 -0.88542 7/3/2006 151.93 152.79 0.045836 1.45 151.34 1.230769 6/30/2006 152.2 152.72 0.341656 3.22 149.5 2.152374 6/29/2006 148.1 152.2 2.491582 5.85 146.35 0.882333 6/28/2006 147.41 148.5 -1.58394 3.43 145.07 -1.42022 6/27/2006 149.05 150.89 0.626876 3.73 147.16 -0.63471 6/26/2006 148.92 149.95 0.368139 1.85 148.1 0.604578 6/23/2006 147.85 149.4 -0.7309 2.19 147.21 0.176931 6/22/2006 149.71 150.5 0.119745 3.55 146.95 0.996564 6/21/2006 145.77 150.32 2.965957 4.82 145.5 1.330176 6/20/2006 144.65 145.99 0.164666 2.4 143.59 0.447709 6/19/2006 144.98 145.75 0.802268 2.8 142.95 0.238412 6/16/2006 143.3 144.59 -0.41325 1.98 142.61 1.813379 6/15/2006 140.4 145.19 2.419582 5.12 140.07 2.397836 6/14/2006 139.75 141.76 -2.57045 4.97 136.79 -0.88399 6/13/2006 144.5 145.5 -3.46338 7.49 138.01 -4.82069 6/12/2006 150.3 150.72 -0.9073 5.72 145 -2.67803 6/9/2006 151 152.1 0.949094 3.11 148.99 3.107266 6/8/2006 148.8 150.67 -1.21943 6.17 144.5 -2.56237 6/7/2006 149.25 152.53 0.309089 4.23 148.3 0.542373 6/6/2006 151.39 152.06 -2.70651 4.56 147.5 -1.56823 6/5/2006 154.95 156.29 -0.45223 6.44 149.85 -2.44141 6/2/2006 155.5 157 2.220197 3.4 153.6 2.270457 6/1/2006 150.92 153.59 0.787453 3.4 150.19 0.697285 5/31/2006 151.3 152.39 0.289569 3.24 149.15 -0.067 5/30/2006 151 151.95 -0.64731 2.7 149.25 -0.14719 5/26/2006 150 152.94 3.814825 3.47 149.47 3.310755 5/25/2006 145.2 147.32 1.188268 2.64 144.68 3.033756 5/24/2006 143.65 145.59 -2.20983 5.17 140.42 -2.28253 5/23/2006 148.05 148.88 0.249141 5.18 143.7 0.251151 5/22/2006 148.51 148.51 -1.28946 5.17 143.34 -2.32368 5/19/2006 148.3 150.45 0.133111 3.7 146.75 0.34188 5/18/2006 149.36 150.25 -0.59543 4 146.25 -0.5102 5/17/2006 150.85 151.15 -2.55303 4.15 147 -2.4034 5/16/2006 153.6 155.11 -1.20382 4.49 150.62 -0.32427 5/15/2006 154.6 157 -1.69067 5.89 151.11 -3.17806 5/12/2006 158.75 159.7 -2.91203 3.63 156.07 -1.59521 5/11/2006 164.38 164.49 -0.55619 5.89 158.6 -2.12897 5/10/2006 164.85 165.41 -0.51125 3.36 162.05 -1.00794 5/9/2006 163.75 166.26 -0.17412 2.56 163.7 0.924784 5/8/2006 164.39 166.55 1.18469 4.35 162.2 1.571795 5/5/2006 159.75 164.6 2.663257 4.91 159.69 1.06962 5/4/2006 159.16 160.33 0.300282 2.33 158 0.158479 5/3/2006 159.5 159.85 -0.09375 2.1 157.75 0.400967 5/2/2006 157.6 160 -1.03297 2.88 157.12 0.666325 5/1/2006 160.3 161.67 -1.95282 5.59 156.08 -1.61992 4/28/2006 163.81 164.89 -0.54286 6.24 158.65 -2.12832 4/27/2006 163.35 165.79 0.692378 3.69 162.1 -0.06165 4/26/2006 163.5 164.65 -0.57367 2.45 162.2 0.272008 4/25/2006 165.35 165.6 -0.40296 3.84 161.76 -1.06422 4/24/2006 165.5 166.27 -1.41705 2.77 163.5 -1.1009 4/21/2006 168.62 168.66 -0.38391 3.34 165.32 -0.44562 4/20/2006 166.06 169.31 1.038372 3.25 166.06 1.503667 4/19/2006 164.55 167.57 0.836442 3.97 163.6 1.41334 4/18/2006 162.75 166.18 1.819741 4.86 161.32 0.825 4/17/2006 160.25 163.21 2.204271 3.21 160 1.1378 4/13/2006 158.45 159.69 -0.38054 1.49 158.2 -0.12626 4/12/2006 159.63 160.3 -1.83711 1.9 158.4 -0.0694 4/11/2006 163 163.3 -0.45718 4.79 158.51 -1.821 4/10/2006 162.5 164.05 0.545477 2.6 161.45 0.975671 4/7/2006 162.04 163.16 0.672549 3.27 159.89 -0.11245 4/6/2006 160.07 162.07 0.092638 2 160.07 0.04375 4/5/2006 160.5 161.92 0.34705 1.92 160 1.18897 4/4/2006 158.12 161.36 0.925694 3.24 158.12 0.764721 4/3/2006 157.99 159.88 0.947089 2.96 156.92 0.4288 3/31/2006 157 158.38 -0.78306 2.13 156.25 0.346799 3/30/2006 157.73 159.63 1.307355 3.92 155.71 0.56187 3/29/2006 154.9 157.57 -0.15841 2.73 154.84 0.4411 3/28/2006 155.01 157.82 1.583419 3.66 154.16 1.334385 3/27/2006 152.13 155.36 1.828669 3.23 152.13 0.828473 3/24/2006 151.68 152.57 0.401421 1.69 150.88 0.285809 3/23/2006 151.17 151.96 -0.26254 1.51 150.45 1.449764 3/22/2006 148.3 152.36 0.236842 4.06 148.3 -0.47648 3/21/2006 151.61 152 -0.43233 2.99 149.01 -0.52737 3/20/2006 150.05 152.66 0.739079 2.86 149.8 1.195704 3/17/2006 148.25 151.54 1.235888 3.51 148.03 0.393354 3/16/2006 149.1 149.69 0.033414 2.24 147.45 -0.09486 3/15/2006 148.3 149.64 0.093645 2.05 147.59 1.352836 3/14/2006 145.92 149.5 4.582022 3.88 145.62 4.627102 3/13/2006 141.55 142.95 0.351 3.77 139.18 -0.69212 3/10/2006 141.63 142.45 -0.66248 2.3 140.15 -0.74363 3/9/2006 142.66 143.4 -0.87786 2.2 141.2 -0.04247 3/8/2006 143.55 144.67 0.145369 3.41 141.26 -1.33408 3/7/2006 144.37 144.46 -1.78134 1.29 143.17 -0.78997 3/6/2006 146.54 147.08 -0.27122 2.77 144.31 0.845563 3/3/2006 143.5 147.48 1.808643 4.38 143.1 0.604612 3/2/2006 143.07 144.86 0.779185 2.62 142.24 0.480362 3/1/2006 141.98 143.74 -0.29134 2.18 141.56 0.3189 2/28/2006 143.6 144.16 -0.75043 3.05 141.11 -1.55574 2/27/2006 144.81 145.25 -0.10316 1.91 143.34 0.202726 2/24/2006 143.05 145.4 -0.14422 2.35 143.05 -0.51464 2/23/2006 145.61 145.61 0.054971 1.82 143.79 0.39098 2/22/2006 143.45 145.53 -0.15094 2.3 143.23 0.153835 2/21/2006 145.56 145.75 -0.32143 2.74 143.01 -0.72886 2/17/2006 146.19 146.22 -0.08883 2.16 144.06 -0.10401 2/16/2006 146.1 146.35 0.584192 2.14 144.21 1.98727 2/15/2006 142 145.5 2.234401 4.1 141.4 1.895222 2/14/2006 141.2 142.32 0.366714 3.55 138.77 -0.27309 2/13/2006 139.65 141.8 -0.03525 2.65 139.15 0.979681 2/10/2006 140.67 141.85 -0.70004 4.05 137.8 -1.91473 2/9/2006 141.14 142.85 0.648207 2.36 140.49 0.839793 2/8/2006 140.1 141.93 -0.96295 2.61 139.32 -0.11471 2/7/2006 142.35 143.31 -0.54823 3.83 139.48 -1.49718 2/6/2006 142.61 144.1 0.68474 2.5 141.6 0.639659 2/3/2006 141.55 143.12 -0.45211 2.42 140.7 -0.49505 2/2/2006 142.27 143.77 0.573627 2.37 141.4 0.690736 2/1/2006 141.4 142.95 0.768363 2.52 140.43 1.430119 1/31/2006 139.73 141.86 0.867463 3.41 138.45 -0.18744 1/30/2006 139.55 140.64 0.636852 1.93 138.71 1.174325 1/27/2006 137.93 139.75 1.004626 2.65 137.1 3.074957 1/26/2006 133.01 138.36 3.222919 5.35 133.01 0.41522 1/25/2006 133.65 134.04 -0.03729 1.58 132.46 0.090676 1/24/2006 132.63 134.09 -0.06707 1.75 132.34 0.531753 1/23/2006 131.64 134.18 0.089512 2.54 131.64 0.297143 1/20/2006 132.85 134.06 -0.56371 2.81 131.25 -1.10014 1/19/2006 132.72 134.82 1.612903 2.11 132.71 1.297611 1/18/2006 131.06 132.68 -0.33802 1.67 131.01 0.321617 1/17/2006 131 133.13 -0.39653 2.54 130.59 -0.99318 1/13/2006 132.02 133.66 0.337812 1.76 131.9 0.395798 1/12/2006 131.4 133.21 -0.44096 1.83 131.38 -0.03044 1/11/2006 131.45 133.8 0.639338 2.38 131.42 1.076757 1/10/2006 130.05 132.95 1.7838 2.93 130.02 1.578125 1/9/2006 128.5 130.62 1.059961 2.62 128 0.557781 1/6/2006 127.29 129.25 1.515866 1.96 127.29 1.337473 1/5/2006 126 127.32 -1.23342 1.71 125.61 -0.60927 1/4/2006 127.35 128.91 -0.40946 2.53 126.38 1.730661 1/3/2006 126.7 129.44 1.069727 5.21 124.23 -1.94949 12/30/2005 127.15 128.07 -0.52043 1.37 126.7 -0.58847 12/29/2005 127.45 128.74 -0.05434 1.29 127.45 -0.14886 12/28/2005 128.3 128.81 -0.45595 1.17 127.64 -0.14863 12/27/2005 128.7 129.4 0.723904 1.57 127.83 0.33752 12/23/2005 127.95 128.47 0.17154 1.07 127.4 0.560423 12/22/2005 127.55 128.25 -0.03897 1.56 126.69 0.459916 12/21/2005 126.35 128.3 1.639864 2.19 126.11 1.423516 12/20/2005 124.7 126.23 -0.91837 1.89 124.34 -0.08839 12/19/2005 127.3 127.4 -0.35977 2.95 124.45 -1.31631 12/16/2005 127.66 127.86 -1.34259 1.75 126.11 -1.16771 12/15/2005 128.25 129.6 -1.74375 2 127.6 -1.35292 12/14/2005 131.08 131.9 0.007582 2.55 129.35 0.653646 12/13/2005 128.8 131.89 0.664021 3.38 128.51 0 12/12/2005 130.4 131.02 0.745867 2.51 128.51 0.0545 12/9/2005 129.15 130.05 0.023073 1.61 128.44 0.532248 12/8/2005 129.05 130.02 -0.8238 2.26 127.76 -0.84594 12/7/2005 130.68 131.1 -2.28086 2.25 128.85 -1.52847 12/6/2005 133.95 134.16 0.366574 3.31 130.85 1.10493 12/5/2005 130.75 133.67 1.449605 4.25 129.42 -0.45381 12/2/2005 130.15 131.76 0.075953 1.75 130.01 0.308618 12/1/2005 130.5 131.66 2.05 129.61 Table 3: Technical Analysis of the Goldman Sacchs Prediction Data. Prediction Data Set Date Open High %Change H-L Low 4/30/2007 224.36 224.98 -0.32342 6.5 218.48 -2.02251 4/27/2007 224.05 225.71 -0.39716 2.72 222.99 -0.52639 4/26/2007 225.9 226.61 0.247733 2.44 224.17 1.849159 4/25/2007 221.9 226.05 1.258735 5.95 220.1 0.635545 4/24/2007 222.75 223.24 -0.33039 4.53 218.71 -0.80279 4/23/2007 221 223.98 0.805617 3.5 220.48 0.96625 4/20/2007 221.23 222.19 0.216499 3.82 218.37 1.662011 4/19/2007 215.34 221.71 1.450535 6.91 214.8 0.387905 4/18/2007 214.1 218.54 0.770047 4.57 213.97 0.201367 4/17/2007 215.15 216.87 0.761976 3.33 213.54 2.604267 4/16/2007 208.24 215.23 3.500842 7.11 208.12 1.220758 4/13/2007 207.95 207.95 0.207209 2.34 205.61 0.107113 4/12/2007 206.25 207.52 -0.64634 2.13 205.39 -0.59048 4/11/2007 208.7 208.87 -0.44802 2.26 206.61 -0.76845 4/10/2007 208.3 209.81 -0.02859 1.6 208.21 0.366353 4/9/2007 208.57 209.87 0.657074 2.42 207.45 0.019285 4/5/2007 208.5 208.5 -0.69064 1.09 207.41 -0.38423 4/4/2007 209.45 209.95 0.095352 1.74 208.21 0.842737 4/3/2007 207 209.75 0.996726 3.28 206.47 1.564268 4/2/2007 207.67 207.68 -0.64584 4.39 203.29 -0.68881 3/30/2007 207.44 209.03 0.067021 4.33 204.7 -0.77557 3/29/2007 208.09 208.89 0.10543 2.59 206.3 0.053349 3/28/2007 208.21 208.67 -1.44524 2.48 206.19 -1.69257 3/27/2007 211.01 211.73 -0.23089 1.99 209.74 0.210225 3/26/2007 212.01 212.22 0.155741 2.92 209.3 -0.19551 3/23/2007 210.06 211.89 0.066116 2.18 209.71 0.200678 3/22/2007 211.7 211.75 0.11347 2.46 209.29 2.512735 3/21/2007 205.34 211.51 3.463288 7.35 204.16 1.069307 3/20/2007 202.49 204.43 0.953086 2.43 202 0.778288 3/19/2007 201.32 202.5 0.721214 2.06 200.44 1.094467 3/16/2007 200.79 201.05 -0.65227 2.78 198.27 -0.61654 3/15/2007 200 202.37 0.103878 2.87 199.5 0.992204 3/14/2007 200 202.16 -3.06866 4.62 197.54 -0.49365 3/13/2007 204.96 208.56 2.794618 10.04 198.52 -0.17097 3/12/2007 200 202.89 -0.04926 4.03 198.86 0 3/9/2007 202.95 202.99 0.48015 4.13 198.86 0.434343 3/8/2007 198.03 202.02 1.517588 4.02 198 1.278772 3/7/2007 197.48 199 0.403633 3.5 195.5 0.929272 3/6/2007 193.9 198.2 0.359512 4.5 193.7 2.027917 3/5/2007 193.55 197.49 -1.70715 7.64 189.85 -2.93471 3/2/2007 198.2 200.92 -0.87815 5.33 195.59 0.77803 3/1/2007 197.12 202.7 -0.56414 8.62 194.08 -1.87573 2/28/2007 200.4 203.85 -3.11312 6.06 197.79 1.613152 2/27/2007 209.75 210.4 -3.64977 15.75 194.65 -8.46892 2/26/2007 217.99 218.37 -0.65059 5.71 212.66 -1.34076 2/23/2007 219.16 219.8 -1.32435 4.25 215.55 -1.12385 2/22/2007 221 222.75 0.564334 4.75 218 -0.07334 2/21/2007 219.25 221.5 -0.18026 3.34 218.16 1.01403 2/20/2007 218.33 221.9 2.022989 5.93 215.97 0.441819 2/16/2007 215.96 217.5 -0.61232 2.48 215.02 -0.6423 2/15/2007 217.94 218.84 -0.11867 2.43 216.41 1.701208 2/14/2007 213.7 219.1 2.719175 6.31 212.79 1.102295 2/13/2007 211.98 213.3 -0.3271 2.83 210.47 0.285891 2/12/2007 213.75 214 -2.39898 4.13 209.87 -0.33716 2/9/2007 215.77 219.26 1.881883 8.68 210.58 0.366999 2/8/2007 212.09 215.21 -0.2965 5.4 209.81 -1.54388 2/7/2007 215.03 215.85 -0.00463 2.75 213.1 0.188058 2/6/2007 213.29 215.86 1.00131 3.16 212.7 0.567376 2/5/2007 213.3 213.72 -0.08415 2.22 211.5 0.236967 2/2/2007 211 213.9 0 2.9 211 0.60554 2/1/2007 213.44 213.9 0.540541 4.17 209.73 1.177095 1/31/2007 208.3 212.75 0.207244 5.46 207.29 -0.51831 1/30/2007 211.08 212.31 -1.28789 3.94 208.37 -0.83758 1/29/2007 213.9 215.08 0.08376 4.95 210.13 -0.22317 1/26/2007 214.56 214.9 -2.5441 4.3 210.6 -0.89878 1/25/2007 219.83 220.51 0.154426 8 212.51 -0.2441 1/24/2007 213.51 220.17 3.162778 7.14 213.03 1.129836 1/23/2007 212.82 213.42 0.079719 2.77 210.65 0.500954 1/22/2007 211.09 213.25 0.856035 3.65 209.6 0.363915 1/19/2007 209.08 211.44 -1.56883 2.6 208.84 -0.12434 1/18/2007 213.75 214.81 0.336307 5.71 209.1 -0.82997 1/17/2007 212.2 214.09 -0.48343 3.24 210.85 0 1/16/2007 210.85 215.13 0.424797 4.28 210.85 0.213878 1/12/2007 210.9 214.22 0.492565 3.82 210.4 1.348748 1/11/2007 208.34 213.17 2.269238 5.57 207.6 3.027295 1/10/2007 203.4 208.44 1.727672 6.94 201.5 -0.24752 1/9/2007 203.54 204.9 0.4658 2.9 202 1.968703 1/8/2007 199.05 203.95 1.975 5.85 198.1 0.101061 1/5/2007 198.43 200 -0.33388 2.1 197.9 -0.08583 1/4/2007 200.22 200.67 -1.30336 2.6 198.07 0.126378 1/3/2007 200.6 203.32 0.454545 5.5 197.82 -0.75256 12/29/2006 200.93 202.4 -0.03951 3.08 199.32 -0.22026 12/28/2006 202.33 202.48 0.093925 2.72 199.76 0.020028 12/27/2006 199.86 202.29 0.842473 2.57 199.72 0.721166 12/26/2006 198.9 200.6 0.728094 2.31 198.29 1.344168 12/22/2006 199.1 199.15 -1.74651 3.49 195.66 -1.03187 12/21/2006 202.36 202.69 -0.79291 4.99 197.7 -1.75909 12/20/2006 201.79 204.31 0.809197 3.07 201.24 0.404131 12/19/2006 201.98 202.67 -0.45189 2.24 200.43 0.395712 12/18/2006 200.5 203.59 0.812082 3.95 199.64 -0.08008 12/15/2006 200.61 201.95 0.572709 2.15 199.8 1.098011 12/14/2006 199.2 200.8 -0.48568 3.17 197.63 -0.18687 12/13/2006 200.72 201.78 -1.01545 3.78 198 -0.22173 12/12/2006 200.21 203.85 -0.80292 5.41 198.44 -1.6845 12/11/2006 205.5 205.5 0.116925 3.66 201.84 0.92 12/8/2006 200.24 205.26 -0.69666 5.26 200 0 12/7/2006 206.7 206.7 0.804682 6.7 200 -0.49751 12/6/2006 202 205.05 1.384425 4.05 201 1.407598 12/5/2006 199.7 202.25 1.084566 4.04 198.21 1.443267 12/4/2006 195.65 200.08 1.858168 4.69 195.39 2.020677 12/1/2006 195.7 196.43 -0.01018 4.91 191.52 -0.8593 11/30/2006 195.98 196.45 -1.50414 3.27 193.18 0.062157 11/29/2006 197.99 199.45 0.992455 6.39 193.06 0.814621 11/28/2006 193 197.49 -2.28105 5.99 191.5 -0.83372 11/27/2006 201.35 202.1 -0.6147 8.99 193.11 -3.03289 11/24/2006 200.23 203.35 0.434632 4.2 199.15 -0.42002 11/22/2006 200 202.47 1.29071 2.48 199.99 0.85733 11/21/2006 199 199.89 0.898491 1.6 198.29 1.671538 11/20/2006 195.35 198.11 0.563452 3.08 195.03 0.07697 11/17/2006 195.98 197 0.101626 2.12 194.88 0.453608 11/16/2006 194 196.8 1.276245 2.8 194 2.191319 11/15/2006 190.37 194.32 1.77019 4.48 189.84 2.394822 11/14/2006 188.4 190.94 0.600632 5.54 185.4 -0.97741 11/13/2006 187.65 189.8 1.459347 2.57 187.23 1.424702 11/10/2006 185.46 187.07 -1.02116 2.47 184.6 -0.09741 11/9/2006 188.4 189 -0.48441 4.22 184.78 -0.92225 11/8/2006 187.65 189.92 3.42 186.5 Read More