Forecasting Crude Oil Volatility - Dissertation Example

? Forecasting Crude Oil (Spot Price) Volatility Table of Contents METHODOLOGY AND DATA 2 Introduction 2 Volatility clustering 4 Data for GARCH Models 6 Estimation 10 Models Used in the Study 11 GARCH (1,1) Model 12 EWMA is considered to be a special type of GARCH(1,1) 15 EGARCH (1,1) Model 15 Data and Sample Size Selection 17 There are four main benchmarks within the global arena in respect to international trading: West Texas Intermediate (WTI), Brent, Dubai, and Tapis. Whereas WTI is a reference to the USA crude oil, Brent is for North Sea, Dubai for Middle and Far East, and Tapis is for Asia-Pacific region. In this paper, data is obtained from WTI for the crude oil spot prices between January 1986 and October 2012. The crude oil spot prices used in testing of the identified GARCH models are daily prices. Daily prices for crude oils are effective in volatility forecasting. 17 It was also imperative to use the two cluster analysis in the paper. 17 In the case of GARCH to obtain the unknowns the formula was applied where the initial value Xk was taken to be 25.56 where a= 0.001 (fixed) 17 b= 0.00 18 c= 0.00 18 In using the same formula the values for a, b and c were P-GARCH established to be 18 a= 0.001(fixed) 18 b= 0.394 18 c= 0.050 18 Xk= 25.56 18 For GARCH GJR, the values were found to be 18 a=0.001 (fixed) 18 b= 0.488 18 c= 0.110 18 Xk= 25.56 18 for E GARCH a=0.001 (fixed) 18 b= 0.488 18 c= 0.11 18 From the findings captured in the spread sheet, we can derive various important factors about the GARCH family models and answer important questions arising from the same. These are 19 The data should be within range in order to get rid of outlier values.The data is reliable since the projection/ forecasted values are within limit. There are no outlier values as a result of projection. 19 The null hypothesis – Garch models predict uniformly 19 Alternative hypothesis- GARCH models predictions differ. Based on the results, it is clear that there exists variations among the four models. Thus it is rational to conclude that the alternative hypothesis holds. 19 The best model should be as closer to the baseline as possible. GARCH is a replica of the baseline and hence cannot be taken to be the best.Of the four GJR GARCH varies the least from the baseline hence is the best. 19 EGARCH has the largest variation from the baseline hence is the worst. 19 20 BIBLIOGRAPHY 20 APPENDICES………………………………………………………………………………….20 METHODOLOGY AND DATA Introduction Volatility is a concept that refers to the spread of all possible outcomes within an uncertain variable. Finance discipline has various uncertain variables such as prices of products, returns on assets, and share prices amongst others (Olowe, 2010). Modeling and forecasting of volatility have been attributed to increasing uncertainty in financial aspects and components (Day & Lewis, 1993). Oil price fluctuations in the global arena experience significant uncertainties thereby invoking interests amongst financial and market participants (Kang, Kang, & Yoon, 2009). The main reasons explaining such significant interest include the fact that oil price fluctuations affect decision making process for both producers and consumers in addition to investors’ decisions. Whereas oil price fluctuations affect strategic planning and appraisal of projects for producers and consumers, investors continue to face challenges in investment, allocation of portfolios, and management of risks decisions (Campbell, Lo, & MacKinlay, 1997). Policy and decision making within the oil markets require accurate forecasting of the crude oil prices (Olowe, 2010). Attaining accurate and adequate forecasting require adequate and accurate data. In most cases, daily prices of crude oil are used to predict or forecast volatility (uncertainty) for purposes of developing effective policies and decision making processes (Campbell, Lo, & MacKinlay, 1997). Forecasting volatility of crude oil prices have been done for a long time via the structural models. However, structural models for forecasting uncertainty in the prices of crude oil are prone to greater challenges of complexity and existence of known and unknown variables to be used (Lee & Zyren, 2007). As a result, structural models have yielded inaccurate volatility forecasts for crude oil prices thereby influencing financial and oil market participants and other stakeholders to use other volatility forecasting models. One of the most widely used volatility forecasting model is the family of Generalized Autoregressive Conditional Heteroskedasticity (GARCH). According to Sadorsky (2009); Agnolucci (2009); and Kang, Kang, and Yoon (2009), GARCH family of models is extensively used due to the fact that they (GARCH models) provide close to accurate forecasting as well as taken into considerations the estimations of VaR (Value-at-Risk). Even though there have been extensive research studies aimed at identifying the most appropriate GARCH model capable of giving a volatility forecast that is the best out-of-sample, it is clear that no GARCH model has consistently been dominant (Olowe, 2010). Figure 1 provides a table identifying some of the researchers who have employed GARCH models to forecast volatility but have ended up with different best models amongst the tested ones (Kumar, 1992). Nevertheless, the superiority of any applicable GARCH model depends on the loss function in question (Campbell, Lo, & MacKinlay, 1997). There are different forms of GARCH models: GARCH 1, 1, EGARCH, GJR GARCH, and P GARCH. It is important however to conduct a test on these forms of GARCH model in a bid to identifying one that successfully predict the level of volatility in the oil market based on crude oil spot prices. Date Study Models used Best Model Identified 2009 Kang et al GARCH, IGARCH, cGARCH, and FIGARCH cGARCH, and FIGARCH 2009 Cheong GARCH, AGARCH, FIGARCH, and FIAGARCH GARCH 2010 Agnolucci GARCH, cGARCH, TGARCH, amongst others cGARCH 2006 Mohammadi and Su GARCH, APARCH, EGARCH, and FIGARCH APARCH 2010 Wei et al 9 models tested No superior 2012 Wang and Wu Univariant and multivariant MVGARCH models Figure 1: Table providing models tested by previous researchers The methodology section below explains the models selected for this study. Andersen and Bollerslev (1998) proved that volatility models are an extremely efficient way of forecast of conditional variance through use of intra-period returns to measure time- varying volatility. This paper also attempts the same approach in an effort to compare the different volatility within and without the GARCH family. There are at least 330 volatility estimation. The GARCH models however reign supreme in the view of many econometricians. The models are characterized by an ability to accurately capture volatility clustering. They are therefore widely used for accounting in time-series data especially where nonuniform variance is involved. MATLAB, SPSS and other related computational toolboxes are used to perform GARCH estimation, forecasting, and simulation. Financial Toolboxes allow one to work with a univariate GARCH process. It is therefore possible to simulate GARCH(p, q) processes, Estimate the parameters of any univariate GARCH(p, q) model that has Gaussian innovations and Forecast conditional variances. Volatility clustering Volatility clustering is the phenomenon of alternation between periods of calm and others of high volatility is an attribute of any sample of market data.  However, no explanation of the same has been universally accepted. Generalized AutoRegressive Conditional Heteroskedasticity (GARCH ) models volatility clustering without attempting to explain it.  The figure below is an example of a GARCH volatility model. Figure 1: S&P 500 volatility until late 2011 as estimated by a garch(1,1) model. From the figure, it is apparent that volatility is time- dynamic.  Data for GARCH Models A GARCH estimator uses daily data as its natural frequency of data.  Alternatively monthly data can be used though the smooths are sometimes out of the data. Intraday data can also be used but it gets complicated.  There is alternation of data volatility  is highly dependent on the market where the trading occurs. A good example of the complication is the intraday Value at Risk. All the data collected should be used for daily GARCH daily recording Figure III: Volatility of MMM as estimated by a GARCH (1,1) model. The real data contains many shocks of all sizes. Volatility resulting from announcements and not shocks, build up with nearing of announcement time and then declines after the results are known. GARCH model estimation mostly comes in handy in the estimation of the rate of decay. Due to the nature of decay, the models require a wide range of data. However, the tens of thousands of observations that would be ideal for the models are practically impossible due to the periodical changes in markets. It is also a practical impossibility to collect such a large amount of observations. To achieve a balance therefore, 2000 observations are made daily. Using less than 1000 observations means that the information on parameters may fail to be accurate.  The best model to pick is one with persistence that is nearly right and whose alpha1 parameter ranges between 0 and 0.1, while the beta1 parameter lies between 0.9 and 1. Estimation A GARCH (1,1) model is certainly not the best.  However, we shall use not as a representative of the GARCH family since it is the one in highest use and in most case achieves the objectives. The GARCH (1,1) model also has many features that identify is as the average GARCH model. GARCH models almost always use estimation via maximum likelihood.  This approach creates a big optimization problem.  That is because it dictates that a lot of data has to be collected. That aside, implementations of GARCH require thorough watching out for the likelihood optimization.  Returns lack a normal distribution. They have quite long tails.  These long tails are entirely caused by the GARCH effects. In this case, GARCH models are ideal for use.  Longer tailed Methodology It is undisputable that there are numerous models for forecasting volatility of crude oil prices within the global market. However, these models can successfully predict the levels of volatility in the oil market only to certain extents (Sadorsky, 2009). It is important to establish a model that will have the most accurate prediction of volatility within the oil market (Agnolucci, 2009). Notably, in order to identify such models there is need for adequate testing. This research aims at testing various models to establish their extent to successfully predicting the levels of volatility within the oil market. The models to be used include GARCH (1,1), and EGARCH (1,1). The selection of these models is based on the fact that they are generalized, autoregressive, conditional, and their Heteroskedasticity property (Cheong, 2009; Olowe, 2010; & Agnolucci 2009). Specific reasons for choosing the specific models for testing are described in the following section. Data applicable for testing the two GARCH models will be obtained from WTI, which is one of the world’s benchmarks on international trading. Once the daily crude oil prices are obtained, they will be transformed into econometrically analyzable form for purposes of testing the two GARCH models. It is important to note that most of the data will be analyzed through Microsoft Excel. The results will be presented in form of tables, graphs, and related figures. From the tables, graphs, and related figures displaying the analysis of the data, the paper will provide a deeper evaluation or discussion of the same. Formulas for the two models are described in the following section. What’s more, this chapter also describes how the approximately 6,760 daily prices of crude oil obtained from WTI will be sampled in order to obtain a more sizable data to use in testing the two GARCH models. A concluding remark based on the purpose of testing will then be provided at the end of the chapter. Models Used in the Study GARCH (1,1), and EGARCH (1,1) are mostly commonly used models in forecasting volatility of crude oil prices. Selection of these two models is based on the fact that there is no serial correction within tests and corrections as portrayed in the empirical studies (Agnolucci, 2009). In addition, the homoscedastic errors obtained from the GARCH (1,1) and EGARCH (1,1) are normally and independently distributed. That is, GARCH (1,1) Model Generalized Autoregressive Conditional Heteroscedastic (GARCH) model is regarded as an extension of the Engle’s ARCH model that has been commonly applied in understanding variance of heteroscedasticity. In this perspective, GARCH model has been selected for testing based on the fact that it depends on the p past conditional variances in addition to the q past squared associated innovations (Cheong, 2009). The GARCH (p,q) model refers to any autoregressive moving average model that is used within conditional variances. GARCH (1,1) model takes into consideration of the fact that conditional variance of a given set of data varies over time for non-negative function as given by the formula (Sadorsky, 2009): Considering the fact that GARCH model takes into consideration the fact that conditional variance vary over time, it is important to note that the idea can be expressed as follows: From the above formula it is clear that Zt is independently and identically a normal distribution with a mean of zero and unit variance (Lee & Zyren, 2007). The mean of zero and unit variance can be tested through the Students t-test and the GED (Generalized Error Distribution) for purposes of allowing for flatter tails, which make the forecasting more successful. It therefore follows that the distribution of conditional upon the history is normal having a variance that is demoted as ht and a mean of zero (Sadorsky, 2009). In addition, it is also true from these concepts that the unconditional variance of is constant based on the iterated expectations law stating that (Cheong, 2009): . Following through the above concepts and formulas, the formula for obtaining GARCH (1,1) model is represented by (Agnolucci, 2009): Where, is a condition that has to be met given the fact that GARCH (1,1) is developed on the basis of nonnegative conditional variance amongst the data set employed in the process of forecasting the volatility of the crude oil prices (Lee & Zyren, 2007). In addition, the variance (ht) is a function of an intercept (?), a shock from the prior period (?) and the variance from last period (?) (Agnolucci, 2009). It is important to note that the above is a model of GARCH model considers the past shocks in forecasting the volatility of the crude oil prices in question. Based on various empirical research regarding GARCH (1,1) model, this study aims at establishing the evidence towards accepting the strengths of the model. Some of the strengths under investigations in this study include the fact that GARCH (1,1) has the possibility of reducing possible number of parameters needed for purposes of estimation given that it takes into account specific data and information of conditional variance lags (Cheong, 2009). Again, GARCH (1,1) model will be tested if it has the capability of successfully capturing various stylized facts regarding asset returns (Sadorsky, 2009). Such ability makes GARCH model to capture fat-tailed returns as well as volatility clustering as discussed above. What’s more, the test will identify whether there is a possibility of modifying the model to capture more elements or properties of the data set under scrutiny. Since GARCH model is essentially ARCH (?), the test aims at finding out if it is true that GARCH (1,1) can easily be employed in removing empirical complications within data set under study.  From the explanation above, one can deduce that GARCH is based on the idea that volatility is a function of lagged variances and lagged squared returns. The illustration below (i-1) can be taken to be the most recent period. Ui-1 is the volatility of the most recent period’s returns (Standard deviation).   Lagged Periodic Returns squared Ui-12 Ui-22 Ui-32 Weights ?1 ?2 ?3 Lagged Variance ?i-1 ?i-2 ?i-3 Weights ?1 ?2 ?3 A GARCH(p,q) model where (p) is the number of squared returns lagged and (q) is the number of variances lagged is obtained by adding a constant A GARCH(1,1) model is unique in that it lags only on one squared return and in only one of the variances. The meaning of (1,1) is in fact derived from her. This notwithstanding, the terms and the constant need to be weighted too. In the long-run the constant is the average variance that exerts a downward pull on the time series. The more the weight assigned to the long-run variance, the less the time series is persistent and the more the time series is gravitated toward the mean and the more a tendency toward "regression to the mean” is exhibited. GARCH(1,1) has three basic terms. Each of these is an independent weighting factor that is multiplied by, the long-run variance, a single lagged variance, and: a single squared lagged return. EWMA is considered to be a special type of GARCH(1,1) EWMA is a GARCH (1,1) whose weight that has been assigned to the model’s long run variance has been set to zero i.e. gamma= 0. This will in effect mean that the time series will not show mean revision. Also, in EWMA alpha and beta add up to one. The current volatility becomes: EGARCH (1,1) Model Exponential Generalized Autoregressive Conditional Heteroscedastic (EGARCH) is a variant GARCH model aimed at modeling logarithm of the process of conditional variance. In addition, EGARCH has additional leverage terms capable of capturing all the volatility clustering that are associated with asymmetry (Cheong, 2009). EGARCH has been incorporated in this study for test based on the fact that it takes into considerations various effects of changes in prices within the financial markets with respect to crude oil. EGARCH is built on the conditional variance attained as a result of price effects. Despite numerous studies, the following test will establish the evidence in supporting of EGARCH model. The formula for the EGARCH model is given by: The above formula can also be given as, Where, and is the standardized residual. ? is the asymmetric component The EGARCH model deviates from other GARCH models in that: EGARCH model volatility measured by the particular conditional variance is explicitly a multiplicative function of the lagged innovations.. Volatility reacts asymmetrically to either positive or negative news. . EGARCH models do not benefit from parameter restrictions. This reduces possible instabilities and subsequently reduces optimization routines. QML estimators’ theoretical properties of EGARCH models are clarified only to a very small extent. If wt= w =0 and . Then ?t2 is stationary and strictly ergodic. It has also been proved that unconditional variance exists when Zt has a GED with parameter, ? ? 1 which in essence determines how thick the tails are. GED is actually leptokurtic when ? ? 2 The normal distribution is the case where GED (?=2). Top of Form Data and Sample Size Selection There are four main benchmarks within the global arena in respect to international trading: West Texas Intermediate (WTI), Brent, Dubai, and Tapis. Whereas WTI is a reference to the USA crude oil, Brent is for North Sea, Dubai for Middle and Far East, and Tapis is for Asia-Pacific region. In this paper, data is obtained from WTI for the crude oil spot prices between January 1986 and October 2012. The crude oil spot prices used in testing of the identified GARCH models are daily prices. Daily prices for crude oils are effective in volatility forecasting. Working The following formula was consequently obtained and used to estimate the parameters It was also imperative to use the two cluster analysis in the paper. In the case of GARCH to obtain the unknowns the formula was applied where the initial value Xk was taken to be 25.56 where a= 0.001 (fixed) b= 0.00 c= 0.00 In using the same formula the values for a, b and c were P-GARCH established to be a= 0.001(fixed) b= 0.394 c= 0.050 Xk= 25.56 For GARCH GJR, the values were found to be a=0.001 (fixed) b= 0.488 c= 0.110 Xk= 25.56 for E GARCH a=0.001 (fixed) b= 0.488 c= 0.11 From the findings captured in the spread sheet, we can derive various important factors about the GARCH family models and answer important questions arising from the same. These are The data should be within range in order to get rid of outlier values.The data is reliable since the projection/ forecasted values are within limit. There are no outlier values as a result of projection. The null hypothesis – Garch models predict uniformly Alternative hypothesis- GARCH models predictions differ. Based on the results, it is clear that there exists variations among the four models. Thus it is rational to conclude that the alternative hypothesis holds. The best model should be as closer to the baseline as possible. GARCH is a replica of the baseline and hence cannot be taken to be the best.Of the four GJR GARCH varies the least from the baseline hence is the best. EGARCH has the largest variation from the baseline hence is the worst. BIBLIOGRAPHY Agnolucci, P., 2009, Volatility in crude oil futures: A comparison of the predictive ability of GARCH and implied volatility models, Energy Economics, Vol., 31, Pp., 316-321. Cheong, C.W. (2009), ‘Modelling and forecasting crude oil markets using ARCH-type model, Energy Policy, Vol., 37, Pp., 2346-2355. Kang, S.H., Kang, S.M. and Yoon, S.M., 2009, Forecasting volatility of crude oil markets, Energy Economics, Vol., 31, Pp., 119-125. Mohammadi, H. and Su, L., 2010, International evidence on crude oil price dynamics: Applications of ARIMA-GARCH models, Energy Economics, in press. Sadorsky, P., 2006, Modeling and forecasting petroleum futures volatility, Energy Economics, Vol., 28, Pp., 467-488. Day, T. E. & Lewis, C. M., 1993, “Forecasting Futures Markets Volatility”, The Journal of Derivatives, Winter, Pp., 33 -50. Campbell, J. Y., Lo, A. W., and MacKinlay, A. C., 1997, The Econometrics of Financial Markets, Princeton, NJ: Princeton University Press. Kumar, M.S. 1992, "The Forecasting Accuracy of Crude Oil Futures Prices", International Monetary Fund. Staff Papers - International Monetary Fund, vol. 39, no. 2, pp. 432-432. Lee, T. K. & Zyren, J., 2007, "Volatility Relationship between Crude Oil and Petroleum Products", Atlantic Economic Journal, vol. 35, no. 1, pp. 97-97. Olowe, R. A. 2010, "Oil Price Volatility, Global Financial Crisis and The Month-of-the-Year Effect", International Journal of Business and Management, vol. 5, no. 11, pp. 156-170. APPENDICES The table above was used in obtaining the parameter On applying the formula through the use of excel the findings were as follows Data 1: Crude Oil Source key RWTC Date Cushing, OK WTI Spot Price FOB (Dollars per Barrel) E GARCH • GJR GARCH • P GARCH GARCH Jan 02, 1986 25.56 22.46182002 24.79620802 23.90770002 25.56 Jan 03, 1986 26 22.85342002 25.23136802 24.32570002 26 Jan 06, 1986 26.53 23.32512002 25.75553802 24.82920002 26.53 Jan 07, 1986 25.85 22.71992002 25.08301802 24.18320002 25.85 Jan 08, 1986 25.87 22.73772002 25.10279802 24.20220002 25.87 Jan 09, 1986 26.03 22.88012002 25.26103802 24.35420002 26.03 Jan 10, 1986 25.65 22.54192002 24.88521802 23.99320002 25.65 Jan 13, 1986 25.08 22.03462002 24.32148802 23.45170002 25.08 Jan 14, 1986 24.97 21.93672002 24.21269802 23.34720002 24.97 Jan 15, 1986 25.18 22.12362002 24.42038802 23.54670002 25.18 Jan 16, 1986 23.98 21.05562002 23.23358802 22.40670002 23.98 Jan 17, 1986 23.63 20.74412002 22.88743802 22.07420002 23.63 Jan 20, 1986 21.33 18.69712002 20.61273802 19.88920002 21.33 Jan 21, 1986 20.61 18.05632002 19.90065802 19.20520002 20.61 Jan 22, 1986 20.25 17.73592003 19.54461803 18.86320003 20.25 Jan 23, 1986 19.93 17.45112003 19.22813803 18.55920003 19.93 Jan 24, 1986 19.45 17.02392003 18.75341803 18.10320003 19.45 Jan 27, 1986 20.87 18.28772002 20.15779802 19.45220002 20.87 Jan 28, 1986 19.45 17.02392003 18.75341803 18.10320003 19.45 Jan 29, 1986 19.61 17.16632003 18.91165803 18.25520003 19.61 Jan 30, 1986 19.58 17.13962003 18.88198803 18.22670003 19.58 Jan 31, 1986 18.95 16.57892003 18.25891803 17.62820003 18.95 Feb 03, 1986 17.42 15.21722003 16.74574803 16.17470003 17.42 Feb 04, 1986 15.58 13.57962003 14.92598803 14.42670003 15.58 Feb 05, 1986 16.28 14.20262003 15.61828803 15.09170003 16.28 Feb 06, 1986 16.6 14.48742003 15.93476803 15.39570003 16.6 Feb 07, 1986 17.7 15.46642003 17.02266803 16.44070003 17.7 Feb 10, 1986 16.78 14.64762003 16.11278803 15.56670003 16.78 Feb 11, 1986 16.28 14.20262003 15.61828803 15.09170003 16.28 Feb 12, 1986 15.74 13.72202003 15.08422803 14.57870003 15.74 Feb 13, 1986 16.43 14.33612003 15.76663803 15.23420003 16.43 Feb 14, 1986 16.03 13.98012003 15.37103803 14.85420003 16.03 Feb 18, 1986 14.7 12.79642003 14.05566804 13.59070003 14.7 Feb 19, 1986 15.08 13.13462003 14.43148803 13.95170003 15.08 Feb 20, 1986 14.13 12.28912004 13.49193804 13.04920004 14.13 Feb 21, 1986 13.63 11.84412004 12.99743804 12.57420004 13.63 Feb 24, 1986 14.68 12.77862003 14.03588804 13.57170003 14.68 Feb 25, 1986 14.68 12.77862003 14.03588804 13.57170003 14.68 Feb 26, 1986 14.62 12.72522003 13.97654804 13.51470004 14.62 Feb 27, 1986 14.05 12.21792004 13.41281804 12.97320004 14.05 Feb 28, 1986 13.23 11.48812004 12.60183804 12.19420004 13.23 Mar 03, 1986 11.98 10.37562004 11.36558804 11.00670004 11.98 Mar 04, 1986 11.98 10.37562004 11.36558804 11.00670004 11.98 Mar 05, 1986 12.03 10.42012004 11.41503804 11.05420004 12.03 Mar 06, 1986 13.13 11.39912004 12.50293804 12.09920004 13.13 Mar 07, 1986 12.24 10.60702004 11.62272804 11.25370004 12.24 Mar 10, 1986 12.94 11.23002004 12.31502804 11.91870004 12.94 Mar 11, 1986 13.23 11.48812004 12.60183804 12.19420004 13.23 Mar 12, 1986 14.05 12.21792004 13.41281804 12.97320004 14.05 Mar 13, 1986 12.6 10.92742004 11.97876804 11.59570004 12.6 Mar 14, 1986 12.55 10.88292004 11.92931804 11.54820004 12.55 Mar 17, 1986 13.28 11.53262004 12.65128804 12.24170004 13.28 Mar 18, 1986 14.03 12.20012004 13.39303804 12.95420004 14.03 Mar 19, 1986 13.25 11.50592004 12.62161804 12.21320004 13.25 Mar 20, 1986 12.75 11.06092004 12.12711804 11.73820004 12.75 Mar 21, 1986 13.95 12.12892004 13.31391804 12.87820004 13.95 Mar 24, 1986 12.2 10.57142004 11.58316804 11.21570004 12.2 Mar 25, 1986 12.43 10.77612004 11.81063804 11.43420004 12.43 Mar 26, 1986 12.03 10.42012004 11.41503804 11.05420004 12.03 Mar 27, 1986 11.35 9.814920045 10.74251805 10.40820005 11.35 Mar 31, 1986 10.25 8.83592005 9.654618051 9.363200051 10.25 Apr 01, 1986 11.13 9.619120046 10.52493805 10.19920005 11.13 Apr 02, 1986 11.35 9.814920045 10.74251805 10.40820005 11.35 Apr 03, 1986 11.7 10.12642004 11.08866804 10.74070004 11.7 Apr 04, 1986 12.75 11.06092004 12.12711804 11.73820004 12.75 Apr 07, 1986 14.39 12.52052004 13.74907804 13.29620004 14.39 Apr 08, 1986 12.83 11.13212004 12.20623804 11.81420004 12.83 Apr 09, 1986 13 11.28342004 12.37436804 11.97570004 13 Apr 10, 1986 13.45 11.68392004 12.81941804 12.40320004 13.45 Apr 11, 1986 13.63 11.84412004 12.99743804 12.57420004 13.63 Apr 14, 1986 12.94 11.23002004 12.31502804 11.91870004 12.94 Apr 15, 1986 12.72 11.03422004 12.09744804 11.70970004 12.72 Apr 16, 1986 11.5 9.948420045 10.89086805 10.55070005 11.5 Apr 17, 1986 11.75 10.17092004 11.13811804 10.78820004 11.75 Apr 18, 1986 11.88 10.28662004 11.26668804 10.91170004 11.88 Apr 21, 1986 12.48 10.82062004 11.86008804 11.48170004 12.48 Apr 22, 1986 13.13 11.39912004 12.50293804 12.09920004 13.13 Apr 23, 1986 13.7 11.90642004 13.06666804 12.64070004 13.7 Apr 24, 1986 13.65 11.86192004 13.01721804 12.59320004 13.65 Apr 25, 1986 14.23 12.37812004 13.59083804 13.14420004 14.23 Apr 28, 1986 13.34 11.58602004 12.71062804 12.29870004 13.34 Apr 29, 1986 13.63 11.84412004 12.99743804 12.57420004 13.63 Apr 30, 1986 13.38 11.62162004 12.75018804 12.33670004 13.38 May 01, 1986 13.8 11.99542004 13.16556804 12.73570004 13.8 May 02, 1986 14.65 12.75192003 14.00621804 13.54320004 14.65 May 05, 1986 14.32 12.45822004 13.67984804 13.22970004 14.32 May 06, 1986 14.43 12.55612004 13.78863804 13.33420004 14.43 May 07, 1986 15.13 13.17912003 14.48093803 13.99920003 15.13 May 08, 1986 15.7 13.68642003 15.04466803 14.54070003 15.7 May 09, 1986 15.83 13.80212003 15.17323803 14.66420003 15.83 May 12, 1986 15.75 13.73092003 15.09411803 14.58820003 15.75 May 13, 1986 15.65 13.64192003 14.99521803 14.49320003 15.65 May 14, 1986 15.53 13.53512003 14.87653803 14.37920003 15.53 May 15, 1986 15.68 13.66862003 15.02488803 14.52170003 15.68 May 16, 1986 16.08 14.02462003 15.42048803 14.90170003 16.08 May 19, 1986 17.13 14.95912003 16.45893803 15.89920003 17.13 May 20, 1986 16.18 14.11362003 15.51938803 14.99670003 16.18 May 21, 1986 15.53 13.53512003 14.87653803 14.37920003 15.53 May 22, 1986 16.04 13.98902003 15.38092803 14.86370003 16.04 May 23, 1986 16.95 14.79892003 16.28091803 15.72820003 16.95 May 27, 1986 15.1 13.15242003 14.45126803 13.97070003 15.1 May 28, 1986 14.65 12.75192003 14.00621804 13.54320004 14.65 May 29, 1986 14.5 12.61842004 13.85786804 13.40070004 14.5 May 30, 1986 14.3 12.44042004 13.66006804 13.21070004 14.3 Jun 02, 1986 13.8 11.99542004 13.16556804 12.73570004 13.8 Jun 03, 1986 13.35 11.59492004 12.72051804 12.30820004 13.35 Jun 04, 1986 13.15 11.41692004 12.52271804 12.11820004 13.15 Jun 05, 1986 13.21 11.47032004 12.58205804 12.17520004 13.21 Jun 06, 1986 12.73 11.04312004 12.10733804 11.71920004 12.73 Jun 09, 1986 12.61 10.93632004 11.98865804 11.60520004 12.61 Jun 10, 1986 12.38 10.73162004 11.76118804 11.38670004 12.38 Jun 11, 1986 13.52 11.74622004 12.88864804 12.46970004 13.52 Jun 12, 1986 13.69 11.89752004 13.05677804 12.63120004 13.69 Jun 13, 1986 13.83 12.02212004 13.19523804 12.76420004 13.83 Jun 16, 1986 13.65 11.86192004 13.01721804 12.59320004 13.65 Jun 17, 1986 13.65 11.86192004 13.01721804 12.59320004 13.65 Jun 18, 1986 13.62 11.83522004 12.98754804 12.56470004 13.62 Jun 19, 1986 13.73 11.93312004 13.09633804 12.66920004 13.73 Jun 20, 1986 14.44 12.56502004 13.79852804 13.34370004 14.44 Jun 23, 1986 14.05 12.21792004 13.41281804 12.97320004 14.05 Jun 24, 1986 13.98 12.15562004 13.34358804 12.90670004 13.98 Jun 25, 1986 13.23 11.48812004 12.60183804 12.19420004 13.23 Jun 26, 1986 13.14 11.40802004 12.51282804 12.10870004 13.14 Jun 27, 1986 13.38 11.62162004 12.75018804 12.33670004 13.38 Jun 30, 1986 12.8 11.10542004 12.17656804 11.78570004 12.8 Jul 01, 1986 12.39 10.74052004 11.77107804 11.39620004 12.39 Jul 02, 1986 12.04 10.42902004 11.42492804 11.06370004 12.04 Jul 03, 1986 11.7 10.12642004 11.08866804 10.74070004 11.7 Jul 07, 1986 11.18 9.663620046 10.57438805 10.24670005 11.18 Jul 08, 1986 11.19 9.672520046 10.58427805 10.25620005 11.19 Jul 09, 1986 11 9.503420047 10.39636805 10.07570005 11 Jul 10, 1986 11.13 9.619120046 10.52493805 10.19920005 11.13 Jul 11, 1986 11.13 9.619120046 10.52493805 10.19920005 11.13 Jul 14, 1986 11.23 9.708120046 10.62383805 10.29420005 11.23 Jul 15, 1986 11.85 10.25992004 11.23701804 10.88320004 11.85 Jul 16, 1986 12.68 10.99862004 12.05788804 11.67170004 12.68 Jul 17, 1986 12.3 10.66042004 11.68206804 11.31070004 12.3 Jul 18, 1986 12.8 11.10542004 12.17656804 11.78570004 12.8 Jul 21, 1986 13.07 11.34572004 12.44359804 12.04220004 13.07 Jul 22, 1986 10.88 9.396620047 10.27768805 9.961700048 10.88 Jul 23, 1986 10.83 9.352120048 10.22823805 9.914200048 10.83 Jul 24, 1986 10.95 9.458920047 10.34691805 10.02820005 10.95 Jul 25, 1986 10.83 9.352120048 10.22823805 9.914200048 10.83 Jul 28, 1986 11.09 9.583520046 10.48537805 10.16120005 11.09 Jul 29, 1986 11.63 10.06412004 11.01943804 10.67420004 11.63 Jul 30, 1986 11.73 10.15312004 11.11833804 10.76920004 11.73 Jul 31, 1986 11.23 9.708120046 10.62383805 10.29420005 11.23 Aug 01, 1986 11.56 10.00182004 10.95020805 10.60770004 11.56 Aug 04, 1986 14 12.17342004 13.36336804 12.92570004 14 Aug 05, 1986 14.35 12.48492004 13.70951804 13.25820004 14.35 Aug 06, 1986 14.8 12.88542003 14.15456803 13.68570003 14.8 Aug 07, 1986 15.18 13.22362003 14.53038803 14.04670003 15.18 Aug 08, 1986 14.83 12.91212003 14.18423803 13.71420003 14.83 Aug 11, 1986 14.92 12.99222003 14.27324803 13.79970003 14.92 Aug 12, 1986 15.5 13.50842003 14.84686803 14.35070003 15.5 Aug 13, 1986 15.28 13.31262003 14.62928803 14.14170003 15.28 Aug 14, 1986 15.43 13.44612003 14.77763803 14.28420003 15.43 Aug 15, 1986 15.83 13.80212003 15.17323803 14.66420003 15.83 Aug 18, 1986 15.58 13.57962003 14.92598803 14.42670003 15.58 Aug 19, 1986 14.98 13.04562003 14.33258803 13.85670003 14.98 Aug 20, 1986 15.23 13.26812003 14.57983803 14.09420003 15.23 Aug 21, 1986 15.23 13.26812003 14.57983803 14.09420003 15.23 Aug 22, 1986 15.48 13.49062003 14.82708803 14.33170003 15.48 Aug 25, 1986 15.48 13.49062003 14.82708803 14.33170003 15.48 Aug 26, 1986 15.78 13.75762003 15.12378803 14.61670003 15.78 Aug 27, 1986 15.83 13.80212003 15.17323803 14.66420003 15.83 Aug 28, 1986 15.83 13.80212003 15.17323803 14.66420003 15.83 Aug 29, 1986 15.93 13.89112003 15.27213803 14.75920003 15.93 Sep 02, 1986 16.43 14.33612003 15.76663803 15.23420003 16.43 Sep 03, 1986 16.03 13.98012003 15.37103803 14.85420003 16.03 Sep 04, 1986 16.18 14.11362003 15.51938803 14.99670003 16.18 Sep 05, 1986 15.63 13.62412003 14.97543803 14.47420003 15.63 Sep 08, 1986 15.63 13.62412003 14.97543803 14.47420003 15.63 Sep 09, 1986 15 13.06342003 14.35236803 13.87570003 15 Sep 10, 1986 14.9 12.97442003 14.25346803 13.78070003 14.9 Sep 11, 1986 15.05 13.10792003 14.40181803 13.92320003 15.05 Sep 12, 1986 15.06 13.11682003 14.41170803 13.93270003 15.06 Sep 15, 1986 14.31 12.44932004 13.66995804 13.22020004 14.31 Sep 16, 1986 13.8 11.99542004 13.16556804 12.73570004 13.8 Sep 17, 1986 14.03 12.20012004 13.39303804 12.95420004 14.03 Sep 18, 1986 14.55 12.66292004 13.90731804 13.44820004 14.55 Sep 19, 1986 14.47 12.59172004 13.82819804 13.37220004 14.47 Sep 22, 1986 13.94 12.12002004 13.30402804 12.86870004 13.94 Sep 23, 1986 14.3 12.44042004 13.66006804 13.21070004 14.3 Sep 24, 1986 14.55 12.66292004 13.90731804 13.44820004 14.55 Sep 25, 1986 14.28 12.42262004 13.64028804 13.19170004 14.28 Sep 26, 1986 14.43 12.55612004 13.78863804 13.33420004 14.43 Sep 29, 1986 14.93 13.00112003 14.28313803 13.80920003 14.93 Sep 30, 1986 14.7 12.79642003 14.05566804 13.59070003 14.7 Oct 01, 1986 15.23 13.26812003 14.57983803 14.09420003 15.23 Oct 02, 1986 15.38 13.40162003 14.72818803 14.23670003 15.38 Oct 03, 1986 14.86 12.93882003 14.21390803 13.74270003 14.86 Oct 06, 1986 14.83 12.91212003 14.18423803 13.71420003 14.83 Oct 07, 1986 15.6 13.59742003 14.94576803 14.44570003 15.6 Oct 08, 1986 15.35 13.37492003 14.69851803 14.20820003 15.35 Oct 09, 1986 15.05 13.10792003 14.40181803 13.92320003 15.05 Oct 10, 1986 14.98 13.04562003 14.33258803 13.85670003 14.98 Oct 14, 1986 14.55 12.66292004 13.90731804 13.44820004 14.55 Oct 15, 1986 14.83 12.91212003 14.18423803 13.71420003 14.83 Oct 16, 1986 14.53 12.64512004 13.88753804 13.42920004 14.53 Oct 17, 1986 14.85 12.92992003 14.20401803 13.73320003 14.85 Oct 20, 1986 15.17 13.21472003 14.52049803 14.03720003 15.17 Oct 21, 1986 15.22 13.25922003 14.56994803 14.08470003 15.22 Oct 22, 1986 14.85 12.92992003 14.20401803 13.73320003 14.85 Oct 23, 1986 14.88 12.95662003 14.23368803 13.76170003 14.88 Oct 24, 1986 14.93 13.00112003 14.28313803 13.80920003 14.93 Oct 27, 1986 14.4 12.52942004 13.75896804 13.30570004 14.4 Oct 28, 1986 14.18 12.33362004 13.54138804 13.09670004 14.18 Oct 29, 1986 13.73 11.93312004 13.09633804 12.66920004 13.73 Oct 30, 1986 15.08 13.13462003 14.43148803 13.95170003 15.08 Oct 31, 1986 15.25 13.28592003 14.59961803 14.11320003 15.25 Nov 03, 1986 14.7 12.79642003 14.05566804 13.59070003 14.7 Nov 04, 1986 15.05 13.10792003 14.40181803 13.92320003 15.05 Nov 05, 1986 14.93 13.00112003 14.28313803 13.80920003 14.93 Nov 06, 1986 15.08 13.13462003 14.43148803 13.95170003 15.08 Nov 07, 1986 15.15 13.19692003 14.50071803 14.01820003 15.15 Nov 10, 1986 15.3 13.33042003 14.64906803 14.16070003 15.3 Nov 11, 1986 15.39 13.41052003 14.73807803 14.24620003 15.39 Nov 12, 1986 15.33 13.35712003 14.67873803 14.18920003 15.33 Nov 13, 1986 15.55 13.55292003 14.89631803 14.39820003 15.55 Nov 14, 1986 15.68 13.66862003 15.02488803 14.52170003 15.68 Nov 17, 1986 15.62 13.61522003 14.96554803 14.46470003 15.62 Nov 18, 1986 15.65 13.64192003 14.99521803 14.49320003 15.65 Nov 19, 1986 15.52 13.52622003 14.86664803 14.36970003 15.52 Nov 20, 1986 15.1 13.15242003 14.45126803 13.97070003 15.1 Nov 21, 1986 15.13 13.17912003 14.48093803 13.99920003 15.13 Nov 24, 1986 14.98 13.04562003 14.33258803 13.85670003 14.98 Nov 25, 1986 15.05 13.10792003 14.40181803 13.92320003 15.05 Nov 26, 1986 15 13.06342003 14.35236803 13.87570003 15 Nov 28, 1986 15 13.06342003 14.35236803 13.87570003 15 Dec 01, 1986 15.29 13.32152003 14.63917803 14.15120003 15.29 Dec 02, 1986 15.22 13.25922003 14.56994803 14.08470003 15.22 Dec 03, 1986 15.13 13.17912003 14.48093803 13.99920003 15.13 Dec 04, 1986 15.2 13.24142003 14.55016803 14.06570003 15.2 Dec 05, 1986 15.14 13.18802003 14.49082803 14.00870003 15.14 Dec 08, 1986 15.01 13.07232003 14.36225803 13.88520003 15.01 Dec 09, 1986 14.93 13.00112003 14.28313803 13.80920003 14.93 Dec 10, 1986 15.12 13.17022003 14.47104803 13.98970003 15.12 Dec 11, 1986 15.49 13.49952003 14.83697803 14.34120003 15.49 Dec 12, 1986 16.13 14.06912003 15.46993803 14.94920003 16.13 Dec 15, 1986 16.38 14.29162003 15.71718803 15.18670003 16.38 Dec 16, 1986 16.11 14.05132003 15.45015803 14.93020003 16.11 Dec 17, 1986 15.83 13.80212003 15.17323803 14.66420003 15.83 Dec 18, 1986 16.28 14.20262003 15.61828803 15.09170003 16.28 Dec 19, 1986 16.55 14.44292003 15.88531803 15.34820003 16.55 Dec 22, 1986 16.95 14.79892003 16.28091803 15.72820003 16.95 Dec 23, 1986 16.93 14.78112003 16.26113803 15.70920003 16.93 Dec 24, 1986 17.26 15.07482003 16.58750803 16.02270003 17.26 Dec 29, 1986 17.65 15.42192003 16.97321803 16.39320003 17.65 Dec 30, 1986 17.73 15.49312003 17.05233803 16.46920003 17.73 Dec 31, 1986 17.93 15.67112003 17.25013803 16.65920003 17.93 Jan 02, 1987 18.13 15.84912003 17.44793803 16.84920003 18.13 Jan 05, 1987 17.98 15.71562003 17.29958803 16.70670003 17.98 Jan 06, 1987 18.21 15.92032003 17.52705803 16.92520003 18.21 Jan 07, 1987 18.28 15.98262003 17.59628803 16.99170003 18.28 Jan 08, 1987 18.63 16.29412003 17.94243803 17.32420003 18.63 Jan 09, 1987 18.78 16.42762003 18.09078803 17.46670003 18.78 Jan 12, 1987 19 16.62342003 18.30836803 17.67570003 19 Jan 13, 1987 18.86 16.49882003 18.16990803 17.54270003 18.86 Jan 14, 1987 19.13 16.73912003 18.43693803 17.79920003 19.13 Jan 15, 1987 19.09 16.70352003 18.39737803 17.76120003 19.09 Jan 16, 1987 19.13 16.73912003 18.43693803 17.79920003 19.13 Jan 19, 1987 18.7 16.35642003 18.01166803 17.39070003 18.7 Jan 20, 1987 18.73 16.38312003 18.04133803 17.41920003 18.73 Jan 21, 1987 18.6 16.26742003 17.91276803 17.29570003 18.6 Jan 22, 1987 18.76 16.40982003 18.07100803 17.44770003 18.76 Jan 23, 1987 18.59 16.25852003 17.90287803 17.28620003 18.59 Jan 26, 1987 18.63 16.29412003 17.94243803 17.32420003 18.63 Jan 27, 1987 18.48 16.16062003 17.79408803 17.18170003 18.48 Jan 28, 1987 18.56 16.23182003 17.87320803 17.25770003 18.56 Jan 29, 1987 18.68 16.33862003 17.99188803 17.37170003 18.68 Jan 30, 1987 18.73 16.38312003 18.04133803 17.41920003 18.73 Feb 02, 1987 18.59 16.25852003 17.90287803 17.28620003 18.59 Feb 03, 1987 18.38 16.07162003 17.69518803 17.08670003 18.38 Feb 04, 1987 18.26 15.96482003 17.57650803 16.97270003 18.26 Feb 05, 1987 18.56 16.23182003 17.87320803 17.25770003 18.56 Feb 06, 1987 18.44 16.12502003 17.75452803 17.14370003 18.44 Feb 09, 1987 18.37 16.06272003 17.68529803 17.07720003 18.37 Feb 10, 1987 18.43 16.11612003 17.74463803 17.13420003 18.43 Feb 11, 1987 18.03 15.76012003 17.34903803 16.75420003 18.03 Feb 12, 1987 18.05 15.77792003 17.36881803 16.77320003 18.05 Feb 13, 1987 17.83 15.58212003 17.15123803 16.56420003 17.83 Feb 17, 1987 17.78 15.53762003 17.10178803 16.51670003 17.78 Feb 18, 1987 17.44 15.23502003 16.76552803 16.19370003 17.44 Feb 19, 1987 17.48 15.27062003 16.80508803 16.23170003 17.48 Feb 20, 1987 17.83 15.58212003 17.15123803 16.56420003 17.83 Feb 23, 1987 17.15 14.97692003 16.47871803 15.91820003 17.15 Feb 24, 1987 16.75 14.62092003 16.08311803 15.53820003 16.75 Feb 25, 1987 16.43 14.33612003 15.76663803 15.23420003 16.43 Feb 26, 1987 16.98 14.82562003 16.31058803 15.75670003 16.98 Feb 27, 1987 16.45 14.35392003 15.78641803 15.25320003 16.45 Mar 02, 1987 16.43 14.33612003 15.76663803 15.23420003 16.43 Mar 03, 1987 17.4 15.19942003 16.72596803 16.15570003 17.4 Mar 04, 1987 17.4 15.19942003 16.72596803 16.15570003 17.4 Mar 05, 1987 18 15.73342003 17.31936803 16.72570003 18 Mar 06, 1987 18.13 15.84912003 17.44793803 16.84920003 18.13 Mar 09, 1987 18.13 15.84912003 17.44793803 16.84920003 18.13 Mar 10, 1987 18.27 15.97372003 17.58639803 16.98220003 18.27 Mar 11, 1987 18.33 16.02712003 17.64573803 17.03920003 18.33 Mar 12, 1987 18.42 16.10722003 17.73474803 17.12470003 18.42 Mar 13, 1987 18.39 16.08052003 17.70507803 17.09620003 18.39 Mar 16, 1987 18.61 16.27632003 17.92265803 17.30520003 18.61 Mar 17, 1987 18.94 16.57002003 18.24902803 17.61870003 18.94 Mar 18, 1987 18.75 16.40092003 18.06111803 17.43820003 18.75 Mar 19, 1987 18.61 16.27632003 17.92265803 17.30520003 18.61 Mar 20, 1987 18.7 16.35642003 18.01166803 17.39070003 18.7 Mar 23, 1987 18.6 16.26742003 17.91276803 17.29570003 18.6 Mar 25, 1987 18.48 16.16062003 17.79408803 17.18170003 18.48 Mar 26, 1987 18.63 16.29412003 17.94243803 17.32420003 18.63 Mar 27, 1987 18.65 16.31192003 17.96221803 17.34320003 18.65 Mar 30, 1987 18.67 16.32972003 17.98199803 17.36220003 18.67 Mar 31, 1987 18.82 16.46322003 18.13034803 17.50470003 18.82 Apr 01, 1987 18.78 16.42762003 18.09078803 17.46670003 18.78 Apr 02, 1987 18.9 16.53442003 18.20946803 17.58070003 18.9 Apr 03, 1987 18.68 16.33862003 17.99188803 17.37170003 18.68 Apr 06, 1987 18.71 16.36532003 18.02155803 17.40020003 18.71 Apr 07, 1987 18.69 16.34752003 18.00177803 17.38120003 18.69 Apr 08, 1987 18.68 16.33862003 17.99188803 17.37170003 18.68 Apr 09, 1987 18.64 16.30302003 17.95232803 17.33370003 18.64 Apr 10, 1987 18.26 15.96482003 17.57650803 16.97270003 18.26 Apr 13, 1987 18.07 15.79572003 17.38859803 16.79220003 18.07 Apr 14, 1987 18.09 15.81352003 17.40837803 16.81120003 18.09 Apr 15, 1987 18.46 16.14282003 17.77430803 17.16270003 18.46 Apr 16, 1987 18.58 16.24962003 17.89298803 17.27670003 18.58 Apr 20, 1987 18.66 16.32082003 17.97210803 17.35270003 18.66 Apr 21, 1987 18.97 16.59672003 18.27869803 17.64720003 18.97 Apr 22, 1987 19.03 16.65012003 18.33803803 17.70420003 19.03 Apr 23, 1987 19.03 16.65012003 18.33803803 17.70420003 19.03 Apr 24, 1987 19.01 16.63232003 18.31825803 17.68520003 19.01 Apr 27, 1987 18.83 16.47212003 18.14023803 17.51420003 18.83 Apr 28, 1987 18.73 16.38312003 18.04133803 17.41920003 18.73 Apr 29, 1987 18.66 16.32082003 17.97210803 17.35270003 18.66 Apr 30, 1987 18.76 16.40982003 18.07100803 17.44770003 18.76 May 01, 1987 18.84 16.48102003 18.15012803 17.52370003 18.84 May 04, 1987 18.93 16.56112003 18.23913803 17.60920003 18.93 May 05, 1987 19.18 16.78362003 18.48638803 17.84670003 19.18 May 06, 1987 19.22 16.81922003 18.52594803 17.88470003 19.22 May 07, 1987 19.08 16.69462003 18.38748803 17.75170003 19.08 May 08, 1987 19.28 16.87262003 18.58528803 17.94170003 19.28 May 11, 1987 19.43 17.00612003 18.73363803 18.08420003 19.43 May 12, 1987 19.37 16.95272003 18.67429803 18.02720003 19.37 May 13, 1987 19.39 16.97052003 18.69407803 18.04620003 19.39 May 14, 1987 19.56 17.12182003 18.86220803 18.20770003 19.56 May 15, 1987 19.84 17.37102003 19.13912803 18.47370003 19.84 May 18, 1987 19.91 17.43332003 19.20835803 18.54020003 19.91 May 19, 1987 19.97 17.48672003 19.26769803 18.59720003 19.97 May 20, 1987 19.75 17.29092003 19.05011803 18.38820003 19.75 May 21, 1987 19.95 17.46892003 19.24791803 18.57820003 19.95 May 22, 1987 19.68 17.22862003 18.98088803 18.32170003 19.68 May 25, 1987 0.357421553 0.493369025 0.413701269 0.001 May 26, 1987 19.35 16.93492003 18.65451803 18.00820003 19.35 May 27, 1987 19.38 16.96162003 18.68418803 18.03670003 19.38 May 28, 1987 19.28 16.87262003 18.58528803 17.94170003 19.28 May 29, 1987 19.36 16.94382003 18.66440803 18.01770003 19.36 Jun 01, 1987 19.55 17.11292003 18.85231803 18.19820003 19.55 Jun 02, 1987 19.7 17.24642003 19.00066803 18.34070003 19.7 Jun 03, 1987 19.87 17.39772003 19.16879803 18.50220003 19.87 Jun 04, 1987 19.75 17.29092003 19.05011803 18.38820003 19.75 Jun 05, 1987 19.79 17.32652003 19.08967803 18.42620003 19.79 Jun 08, 1987 19.94 17.46002003 19.23802803 18.56870003 19.94 Jun 09, 1987 19.84 17.37102003 19.13912803 18.47370003 19.84 Jun 10, 1987 19.83 17.36212003 19.12923803 18.46420003 19.83 Jun 11, 1987 19.85 17.37992003 19.14901803 18.48320003 19.85 Jun 12, 1987 19.93 17.45112003 19.22813803 18.55920003 19.93 Jun 15, 1987 20.07 17.57572003 19.36659803 18.69220003 20.07 Jun 16, 1987 20.27 17.75372003 19.56439803 18.88220003 20.27 Jun 17, 1987 20.41 17.87832002 19.70285803 19.01520002 20.41 Jun 18, 1987 20.5 17.95842002 19.79186802 19.10070002 20.5 Jun 19, 1987 20.65 18.09192002 19.94021802 19.24320002 20.65 Jun 22, 1987 20.49 17.94952002 19.78197802 19.09120002 20.49 Jun 23, 1987 19.95 17.46892003 19.24791803 18.57820003 19.95 Jun 24, 1987 20.13 17.62912003 19.42593803 18.74920003 20.13 Jun 25, 1987 20.15 17.64692003 19.44571803 18.76820003 20.15 Jun 26, 1987 20.34 17.81602002 19.63362803 18.94870003 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0.413701269 0.001 Jul 05, 1988 15.11 13.16132003 14.46115803 13.98020003 15.11 Jul 06, 1988 15.44 13.45502003 14.78752803 14.29370003 15.44 Jul 07, 1988 15.83 13.80212003 15.17323803 14.66420003 15.83 Jul 08, 1988 15.42 13.43722003 14.76774803 14.27470003 15.42 Jul 11, 1988 14.56 12.67182004 13.91720804 13.45770004 14.56 Jul 12, 1988 14.61 12.71632003 13.96665804 13.50520004 14.61 Jul 13, 1988 14.35 12.48492004 13.70951804 13.25820004 14.35 Jul 14, 1988 14.84 12.92102003 14.19412803 13.72370003 14.84 Jul 15, 1988 14.85 12.92992003 14.20401803 13.73320003 14.85 Jul 18, 1988 15.84 13.81102003 15.18312803 14.67370003 15.84 Jul 19, 1988 15.16 13.20582003 14.51060803 14.02770003 15.16 Jul 20, 1988 15.76 13.73982003 15.10400803 14.59770003 15.76 Jul 21, 1988 16.28 14.20262003 15.61828803 15.09170003 16.28 Jul 22, 1988 16.27 14.19372003 15.60839803 15.08220003 16.27 Jul 25, 1988 16.09 14.03352003 15.43037803 14.91120003 16.09 Jul 26, 1988 15.99 13.94452003 15.33147803 14.81620003 15.99 Jul 27, 1988 16.18 14.11362003 15.51938803 14.99670003 16.18 Jul 28, 1988 16.08 14.02462003 15.42048803 14.90170003 16.08 Jul 29, 1988 16.37 14.28272003 15.70729803 15.17720003 16.37 Aug 01, 1988 16.07 14.01572003 15.41059803 14.89220003 16.07 Aug 02, 1988 15.57 13.57072003 14.91609803 14.41720003 15.57 Aug 03, 1988 15.2 13.24142003 14.55016803 14.06570003 15.2 Aug 04, 1988 15.12 13.17022003 14.47104803 13.98970003 15.12 Aug 05, 1988 15.31 13.33932003 14.65895803 14.17020003 15.31 Aug 08, 1988 15.84 13.81102003 15.18312803 14.67370003 15.84 Aug 09, 1988 15.56 13.56182003 14.90620803 14.40770003 15.56 Aug 10, 1988 15.65 13.64192003 14.99521803 14.49320003 15.65 Aug 11, 1988 15.75 13.73092003 15.09411803 14.58820003 15.75 Aug 12, 1988 15.54 13.54402003 14.88642803 14.38870003 15.54 Aug 15, 1988 15.59 13.58852003 14.93587803 14.43620003 15.59 Aug 16, 1988 15.51 13.51732003 14.85675803 14.36020003 15.51 Aug 17, 1988 15.46 13.47282003 14.80730803 14.31270003 15.46 Aug 18, 1988 15.59 13.58852003 14.93587803 14.43620003 15.59 Aug 19, 1988 15.77 13.74872003 15.11389803 14.60720003 15.77 Aug 22, 1988 15.75 13.73092003 15.09411803 14.58820003 15.75 Aug 23, 1988 15.71 13.69532003 15.05455803 14.55020003 15.71 Aug 24, 1988 15.55 13.55292003 14.89631803 14.39820003 15.55 Aug 25, 1988 15.33 13.35712003 14.67873803 14.18920003 15.33 Aug 26, 1988 15.35 13.37492003 14.69851803 14.20820003 15.35 Aug 29, 1988 15.24 13.27702003 14.58972803 14.10370003 15.24 Aug 30, 1988 15.39 13.41052003 14.73807803 14.24620003 15.39 Aug 31, 1988 15.19 13.23252003 14.54027803 14.05620003 15.19 Sep 01, 1988 15.05 13.10792003 14.40181803 13.92320003 15.05 Sep 02, 1988 14.79 12.87652003 14.14467803 13.67620003 14.79 Sep 05, 1988 14.79 12.87652003 14.14467803 13.67620003 14.79 Sep 06, 1988 14.25 12.39592004 13.61061804 13.16320004 14.25 Sep 07, 1988 14.29 12.43152004 13.65017804 13.20120004 14.29 Sep 08, 1988 14.51 12.62732004 13.86775804 13.41020004 14.51 Sep 09, 1988 14.14 12.29802004 13.50182804 13.05870004 14.14 Sep 12, 1988 14.48 12.60062004 13.83808804 13.38170004 14.48 Sep 13, 1988 14.55 12.66292004 13.90731804 13.44820004 14.55 Sep 14, 1988 15.38 13.40162003 14.72818803 14.23670003 15.38 Sep 15, 1988 14.86 12.93882003 14.21390803 13.74270003 14.86 Sep 16, 1988 14.5 12.61842004 13.85786804 13.40070004 14.5 Sep 19, 1988 14.72 12.81422003 14.07544804 13.60970003 14.72 Sep 20, 1988 15.08 13.13462003 14.43148803 13.95170003 15.08 Sep 21, 1988 15.19 13.23252003 14.54027803 14.05620003 15.19 Sep 22, 1988 15.25 13.28592003 14.59961803 14.11320003 15.25 Sep 23, 1988 14.26 12.40482004 13. 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