10.17. 🤔 Monte Carlo Simulations

A lot of scientific work can be done with simulations. Most drugs today are not tested on animals, or even manufactured in meatspace without significant testing via simulation in cyberspace. Investment strategies are simulated Millions of times to predict the most likely outcome, bridge designs, new computers, new cars, man many other things are designed and simulated in the computer before anything physical is created. Steve Jobs is said to have told his idol Seymour Cray that he used a Cray supercomputer to help design and model the latest Mac, to which Cray is reported to have replied ‘that’s great I just bought a Mac to help me design the next Cray.’

In this project we are going to investigate the Monte-Carlo simulation, named after the famous gambling city in Monaco.

We will do three simulations in this project. The first to help us calculate the value of pi. The second to predict the price of a stock, and the third to explore the “Monty Hall Paradox”

10.17.1. Approximating Pi

As you may recall from trigonometry pi is an irrational number with a decimal that goes on forever without repeating. There is no simple fraction that precisely equals pi, and there are many different formulas and techniques for approximating the value of pi such as the Leibniz formula:

\[\frac{\pi}{4} = \frac{1}{1} - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} ...\]

While calculating infinite sums might be fun, and Python can certainly handle it, The Monte Carlo simulation is definitely more fun and a lot more intuitive to understand.

Suppose you are throwing darts at a dartboard. Many of the darts are going to hit the board and some are going to miss. We are interested in exploring the ratio of the number of darts that hit the dartboard to the overall number of darts you throw: \(darts\_on\_board / total\_darts\). Not too bad so far, but how do we get from here to a value for pi?

Let me describe our simulation a little more precisely.

  1. Our dartboard is a ‘unit circle’ that is a circle centered at 0,0 with a radius of 1.0.
  2. Our dartboard is in the middle of a square that is 2 x 2 and there is a “magical force field” that ensures that all the darts either land on the dartboard or on the 2x2 square.
  3. We can simulate the throwing of the darts (and our force field) by using our random number generator to chose a random x coordinate between -1 and +1 and a random y coordinate between -2 and +2. This will tell us exactly where the dart lands.
  4. We know that a dart lands on the board if its distance to 0,0 is less than or equal to 1.0. \(d = \sqrt{x^2 + y^2}\) We know this because the radius of our dart board is 1.0.
  5. Since the area of the circle is \(\pi r^2\) the area of a unit circle is just \(\pi\) the area of the 2x2 square that contains our dart board is 4. So, the ratio of the number of darts that hit the dart board to the total number of darts we throw is \(\frac{\pi}{4}\). If we calculate the ratio and multiply by 4 we get \(\pi\)!!

What is even more fun is to use our turtle graphics package to simulate animate this simulation. Every time we throw a dart we make a dot on the screen where it lands. If you color the darts that hit the dart board blue and the darts that miss red you will definitely see a circle emerge as the simulation progresses.

Lets start with the animation part before we do too much math. You should also review the win.setworldcoordinates function so that we can plot our darts using real numbers between -1 and 1. Then before you plot a point check to see if the distance to 0,0 is less than or equal to 1 and set the color accordingly. Try to simulate about 1000 dart throws and see what you get.

Now that you have the animation working you can add in the counting and make a calculation of the value of pi. You can speed up the animation considerably with the use of the tracer function. Ordinarily the turtle draws the picture incrementally every time you perform a drawing operation. For example a straight line of 100 might be drawn in 10 segments with a small pause between each segment. The tracer(skips,pause) function allows you to say only perform every skips updates and to wait for only pause milliseconds. One funny side effect of this is that in a few odd cases your picture might look incomplete so if you use this its a good idea to also call update at the end of all your drawing to be sure you have the full picture.

Probably your first try with 1000 or 2000 repetitions will get you to around 3.1 or so. If you want to get a lot closer to the actual value for pi 3.1415926… then you will need to repeat the simulation itself several hundred or a thousand times and take the average of the predictions. To keep in practice with your graphing, you can keep track of each value for pi in a list and make a histogram of the predicted values for pi. It should be a nice “bell shape” with the center close to 3.14. You can experiment and compare notes with other students to try different values for the number of darts to throw and the number of experiments to try.

Note

Extending the Time Limit

When doing a long running simulation like the pi calculation you may run up against the time limit we have set for your program. 25 seconds. to increase the time you can do the following in your program:

import sys
sys.setExecutionLimit(60000)

That ups the time limit to 60 seconds. The value you pass is in milliseconds.

10.17.2. Predicting Stock Prices

Next we want to turn our attention to doing a monte carlo simulation of a stock price. Many money managers do a very similar simulation for their clients to help them with financial planning for retirement or saving for a college education.

The idea behind a stock simulation derives from Burton Malkiel’s random walk theory. In the random walk theory we flip a coin, if the coin is heads then the stock goes up a little bit, but if the coin is tails the stock goes down a little bit. How much the stock goes up or down will be determined based on analyzing how much it typically changes from day to day in the past.

Lets begin by first reading the stock data from a CSV file. You can see the columns below for the data which is real historical data. You could obtain this data from a number of different sources and use your own favorite stock if you would like. You’ll notice there are two columns for the closing price of the stock: Close and Adj Close. We are interested in the Adj Close column as that adjusts the stock price for future splits. A split happens when a company decides to lower their price by increasing the number of shares. A two for one split is common, so when a split happens, instead of 1 share at $60.00 per share you now have 2 shares at $30.00. You can see how on a graph this would make it look like the price was cut in half.

Data file: AAPL_train.csv
Date,Open,High,Low,Close,Adj Close,Volume
2006-12-01,13.114285,13.190000,12.871428,91.320000,13.045714,198769900
2006-12-04,13.125714,13.150000,12.928572,91.120003,13.017143,177384200
2006-12-05,13.092857,13.190000,12.981428,91.269997,13.038571,165709600
2006-12-06,12.948571,13.055715,12.810000,89.830002,12.832857,159546100
2006-12-07,12.861428,12.928572,12.414286,87.040001,12.434286,251206900
2006-12-08,12.461429,12.770000,12.428572,88.259995,12.608571,196069300
2006-12-11,12.700000,12.757143,12.578571,88.750000,12.678572,124945100
2006-12-12,12.658571,12.691428,12.218572,86.139999,12.305715,256655000
2006-12-13,12.564285,12.724286,12.450000,89.050003,12.721429,214263000
2006-12-14,12.721429,12.857142,12.608571,88.549995,12.650000,208082700
2006-12-15,12.717143,12.745714,12.475715,87.720001,12.531428,184984800
2006-12-18,12.518572,12.571428,12.084286,85.470001,12.210000,180394200
2006-12-19,12.104285,12.382857,11.945714,86.309998,12.330000,227851400
2006-12-20,12.352858,12.381429,12.105714,84.759995,12.108571,141922900
2006-12-21,12.100000,12.211429,11.742857,82.900002,11.842857,225899800
2006-12-22,11.922857,12.005714,11.657143,82.199997,11.742857,153325900
2006-12-26,11.735714,11.795714,11.555715,81.510002,11.644286,122672200
2006-12-27,11.164286,11.714286,10.967143,81.520004,11.645715,483938700
2006-12-28,11.460000,11.607142,11.378572,80.870003,11.552857,279969200
2006-12-29,11.992857,12.200000,11.908571,84.839996,12.120000,269107300
2007-01-03,12.327143,12.368571,11.700000,83.800003,11.971429,309579900
2007-01-04,12.007143,12.278571,11.974286,85.659996,12.237143,211815100
2007-01-05,12.252857,12.314285,12.057143,85.049995,12.150000,208685400
2007-01-08,12.280000,12.361428,12.182858,85.470001,12.210000,199276700
2007-01-09,12.350000,13.282857,12.164286,92.570000,13.224286,837324600
2007-01-10,13.535714,13.971429,13.350000,97.000000,13.857142,738220000
2007-01-11,13.705714,13.825714,13.585714,95.800003,13.685715,360063200
2007-01-12,13.512857,13.580000,13.318571,94.620003,13.517143,328172600
2007-01-16,13.668571,13.892858,13.635715,97.099998,13.871428,311019100
2007-01-17,13.937143,13.942857,13.545714,94.949997,13.564285,411565000
2007-01-18,13.157143,13.158571,12.721429,89.070000,12.724286,591151400
2007-01-19,12.661428,12.807143,12.588572,88.500000,12.642858,341118400
2007-01-22,12.734285,12.737143,12.235714,86.789993,12.398571,363506500
2007-01-23,12.247143,12.501429,12.215714,85.699997,12.242857,301856100
2007-01-24,12.382857,12.450000,12.297143,86.700005,12.385715,231953400
2007-01-25,12.444285,12.642858,12.290000,86.250000,12.321428,226493400
2007-01-26,12.444285,12.481428,12.141429,85.379997,12.197143,246718500
2007-01-29,12.328571,12.378572,12.218572,85.939995,12.277143,225416100
2007-01-30,12.347143,12.355714,12.178572,85.550003,12.221429,144492600
2007-01-31,12.122857,12.285714,12.050000,85.729996,12.247143,214017300
2007-02-01,12.318571,12.324286,12.105714,84.739998,12.105714,166085500
2007-02-02,12.017143,12.178572,11.957143,84.750000,12.107142,155382500
2007-02-05,12.042857,12.175714,11.991428,83.940002,11.991428,144713100
2007-02-06,12.064285,12.067142,11.837143,84.149994,12.021428,216098400
2007-02-07,12.068571,12.340000,11.935715,86.150002,12.307143,266706300
2007-02-08,12.204286,12.358571,12.201428,86.180000,12.311429,169757700
2007-02-09,12.268572,12.314285,11.887143,83.270004,11.895715,215135200
2007-02-12,12.061429,12.168571,11.947143,84.879997,12.125714,181017900
2007-02-13,12.165714,12.184286,12.042857,84.700005,12.100000,145246500
2007-02-14,12.090000,12.234285,12.081429,85.300003,12.185715,126995400
2007-02-15,12.205714,12.231428,12.111428,85.209999,12.172857,90915300
2007-02-16,12.178572,12.201428,12.094286,84.830002,12.118571,99967000
2007-02-20,12.092857,12.308572,12.022857,85.899994,12.271428,154425600
2007-02-21,12.282857,12.784286,12.280000,89.199997,12.742857,288828400
2007-02-22,12.971429,12.972857,12.647142,89.510002,12.787143,209556200
2007-02-23,12.737143,12.905714,12.692857,89.070000,12.724286,129473400
2007-02-26,12.834286,12.857142,12.515715,88.510002,12.644286,153962200
2007-02-27,12.328571,12.440000,11.915714,83.930000,11.990000,286453300
2007-02-28,11.857142,12.228572,11.857142,84.610001,12.087143,229868800
2007-03-01,12.004286,12.615714,11.964286,87.060005,12.437143,353882200
2007-03-02,12.395715,12.505714,12.172857,85.409996,12.201428,215000100
2007-03-05,12.270000,12.664286,12.251429,86.320000,12.331429,209724900
2007-03-06,12.542857,12.615714,12.485714,88.190002,12.598572,180796700
2007-03-07,12.578571,12.710000,12.492857,87.720001,12.531428,156571100
2007-03-08,12.655714,12.674286,12.494286,88.000000,12.571428,127752800
2007-03-09,12.685715,12.692857,12.485714,87.970001,12.567142,112959000
2007-03-12,12.581429,12.855714,12.570000,89.870003,12.838572,182352100
2007-03-13,12.772857,12.942857,12.628572,88.400002,12.628572,216972700
2007-03-14,12.657143,12.857142,12.560000,90.000000,12.857142,199146500
2007-03-15,12.851429,12.908571,12.758572,89.570000,12.795714,139874700
2007-03-16,12.791429,12.855714,12.760000,89.590004,12.798572,142926000
2007-03-19,12.891429,13.078571,12.798572,91.130005,13.018572,178240300
2007-03-20,13.050000,13.120000,13.008572,91.479996,13.068571,122229100
2007-03-21,13.141429,13.428572,13.092857,93.869995,13.410000,171724000
2007-03-22,13.390000,13.480000,13.285714,93.959999,13.422857,140373100
2007-03-23,13.335714,13.438571,13.328571,93.519997,13.360000,112721000
2007-03-26,13.427143,13.700000,13.328571,95.849998,13.692857,216246800
2007-03-27,13.672857,13.832857,13.571428,95.459999,13.637143,233013200
2007-03-28,13.554286,13.628572,13.307143,93.239998,13.320000,235584300
2007-03-29,13.455714,13.455714,13.175714,93.750000,13.392858,181430900
2007-03-30,13.468572,13.525714,13.250000,92.909996,13.272857,150139500
2007-04-02,13.448571,13.464286,13.288571,93.650002,13.378572,125498100
2007-04-03,13.448571,13.604285,13.394286,94.500000,13.500000,145983600
2007-04-04,13.562857,13.591429,13.447143,94.270004,13.467143,119196000
2007-04-05,13.445714,13.525714,13.360000,94.680000,13.525714,88879000
2007-04-09,13.601429,13.614285,13.291429,93.650002,13.378572,103335400
2007-04-10,13.381429,13.465714,13.344286,94.250000,13.464286,88116700
2007-04-11,13.414286,13.421429,13.190000,92.590004,13.227143,137254600
2007-04-12,13.148571,13.187143,12.960000,92.190002,13.170000,164168900
2007-04-13,12.985714,13.057143,12.865714,90.240005,12.891429,179985400
2007-04-16,12.938571,13.071428,12.892858,91.430000,13.061429,152258400
2007-04-17,13.142858,13.185715,12.814285,90.349998,12.907143,187980100
2007-04-18,12.880000,12.978572,12.800000,90.400002,12.914286,116011000
2007-04-19,12.884286,13.035714,12.832857,90.270004,12.895715,106478400
2007-04-20,12.984285,13.025714,12.935715,90.970001,12.995714,130694900
2007-04-23,13.084286,13.400000,13.060000,93.509995,13.358571,195072500
2007-04-24,13.422857,13.770000,13.042857,93.239998,13.320000,263813200
2007-04-25,13.461429,13.628572,13.400000,95.349998,13.621428,296786000
2007-04-26,14.511429,14.642858,14.042857,98.839996,14.120000,434444500
2007-04-27,14.025714,14.278571,13.955714,99.919998,14.274285,174850900
2007-04-30,14.298572,14.428572,14.238571,99.800003,14.257143,154127400
2007-05-01,14.227143,14.335714,14.078571,99.470001,14.210000,133130900
2007-05-02,14.235714,14.362857,14.210000,100.389999,14.341429,126286300
2007-05-03,14.390000,14.492857,14.287143,100.400002,14.342857,144019400
2007-05-04,14.400000,14.514286,14.357142,100.809998,14.401428,95496800
2007-05-07,14.440000,14.907143,14.430000,103.919998,14.845715,215389300
2007-05-08,14.781428,15.021428,14.774285,105.059998,15.008572,195999300
2007-05-09,14.987143,15.280000,14.984285,106.880005,15.268572,179439400
2007-05-10,15.232857,15.548572,15.131429,107.339996,15.334286,299314400
2007-05-11,15.391429,15.590000,15.254286,108.739998,15.534286,163424100
2007-05-14,15.660000,15.714286,15.464286,109.360001,15.622857,162986600
2007-05-15,15.652857,15.742857,15.211429,107.519997,15.360000,238628600
2007-05-16,15.504286,15.547143,14.774285,107.339996,15.334286,281691900
2007-05-17,15.307143,15.695714,15.307143,109.440002,15.634286,183822800
2007-05-18,15.747143,15.805715,15.681429,110.020004,15.717143,155336300
2007-05-21,15.758572,16.064285,15.721429,111.979996,15.997143,159973100
2007-05-22,16.070000,16.250000,16.001429,113.539993,16.219999,143102400
2007-05-23,16.288572,16.428572,16.084286,112.889992,16.127142,227843700
2007-05-24,16.115715,16.351429,15.767143,110.689995,15.812857,221840500
2007-05-25,16.000000,16.254286,15.928572,113.619995,16.231428,158239900
2007-05-29,16.350000,16.408571,16.098572,114.349998,16.335714,161423500
2007-05-30,16.328571,16.982857,16.218571,118.769997,16.967142,369611200
2007-05-31,17.152857,17.452858,17.077143,121.189995,17.312857,324266600
2007-06-01,17.299999,17.312857,16.898571,118.400002,16.914286,221315500
2007-06-04,16.947144,17.389999,16.842857,121.330002,17.332857,221668300
2007-06-05,17.344286,17.527143,17.214285,122.670006,17.524286,230196400
2007-06-06,17.471428,17.721428,17.421429,123.639999,17.662857,278060300
2007-06-07,17.855715,18.230000,17.598572,124.069992,17.724285,478769900
2007-06-08,17.974285,17.975714,17.469999,124.490005,17.784286,310420600
2007-06-11,18.000000,18.021429,17.077143,120.190002,17.170000,468564600
2007-06-12,17.049999,17.387142,16.901428,120.380005,17.197144,356641600
2007-06-13,17.307142,17.312857,16.485714,117.500008,16.785715,430338300
2007-06-14,16.742857,17.064285,16.631428,118.749992,16.964285,243316500
2007-06-15,17.231428,17.238571,17.122858,120.499992,17.214285,202804700
2007-06-18,17.611429,17.882856,17.505714,125.090004,17.870001,227651200
2007-06-19,17.812857,17.858572,17.558571,123.660004,17.665714,235756500
2007-06-20,17.695715,17.808571,17.357143,121.550003,17.364286,224378000
2007-06-21,17.385714,17.755714,17.245714,123.900009,17.700001,216761300
2007-06-22,17.692858,17.778572,17.482857,123.000000,17.571428,157969000
2007-06-25,17.741428,17.870001,17.294285,122.339996,17.477142,241350900
2007-06-26,17.711428,17.714285,16.959999,119.650002,17.092857,336251300
2007-06-27,17.230000,17.434286,17.037144,121.889999,17.412857,243674200
2007-06-28,17.480000,17.498571,17.142857,120.559998,17.222857,209535900
2007-06-29,17.424286,17.714285,17.298571,122.040001,17.434286,284460400
2007-07-02,17.292856,17.441429,17.042856,121.259995,17.322857,248715600
2007-07-03,17.428572,18.200001,17.357143,127.169998,18.167143,290620400
2007-07-05,18.400000,18.995714,18.384285,132.750000,18.964285,363262900
2007-07-06,19.018572,19.048571,18.628571,132.300003,18.900000,218673700
2007-07-09,18.911428,18.985714,18.454287,130.330002,18.618572,248955000
2007-07-10,18.411428,19.214285,18.401428,132.350006,18.907143,313751900
2007-07-11,18.867144,19.100000,18.758572,132.389999,18.912857,205443000
2007-07-12,19.121429,19.177143,18.912857,134.069992,19.152857,176152200
2007-07-13,19.290001,19.692858,19.217142,137.729996,19.675714,226901500
2007-07-16,19.770000,19.997143,19.642857,138.099991,19.728571,234028200
2007-07-17,19.757143,19.942858,19.642857,138.910004,19.844286,177489900
2007-07-18,19.741428,19.777143,19.434286,138.119995,19.731428,189214200
2007-07-19,20.042856,20.115715,19.950001,140.000000,20.000000,183222900
2007-07-20,20.235714,20.597143,20.000000,143.750000,20.535715,291943400
2007-07-23,20.472857,20.745714,20.132856,143.700012,20.528572,259122500
2007-07-24,19.840000,20.142857,19.164286,134.889999,19.270000,448823200
2007-07-25,19.621429,19.765715,19.285715,137.260010,19.608572,374045700
2007-07-26,20.844286,21.214285,19.565714,146.000000,20.857143,546657300
2007-07-27,20.884285,21.274286,20.540001,143.849991,20.549999,290274600
2007-07-30,20.618572,20.778572,19.938572,141.430008,20.204287,276747100
2007-07-31,20.424286,20.497143,18.788572,131.759995,18.822857,440598200
2007-08-01,19.091429,19.340000,18.252857,135.000000,19.285715,437539200
2007-08-02,19.521429,19.565714,19.164286,136.490005,19.498571,213161200
2007-08-03,19.322857,19.421429,18.785715,131.850006,18.835714,169796900
2007-08-06,18.985714,19.324286,18.328571,135.250000,19.321428,231292600
2007-08-07,19.277143,19.605715,18.947144,135.029999,19.290001,237484100
2007-08-08,19.537144,19.551428,18.857143,134.009995,19.144285,202024200
2007-08-09,18.730000,19.000000,17.870001,126.389999,18.055714,281348900
2007-08-10,17.588572,18.250000,17.185715,125.000000,17.857143,352687300
2007-08-13,18.331429,18.478571,18.071428,127.790001,18.255714,188227900
2007-08-14,18.327143,18.328571,17.672857,124.029999,17.718571,184751700
2007-08-15,17.534286,17.837143,17.092857,119.899994,17.128571,248213000
2007-08-16,16.715714,16.928572,15.945714,117.049995,16.721428,466672500
2007-08-17,17.430000,17.642857,17.117144,122.060005,17.437143,298765600
2007-08-20,17.708570,17.785715,17.214285,122.219994,17.459999,200829300
2007-08-21,17.458570,18.422857,17.285715,127.569992,18.224285,325761800
2007-08-22,18.745714,18.964285,18.618572,132.510010,18.930000,265441400
2007-08-23,19.012857,19.048571,18.537144,131.069992,18.724285,216709500
2007-08-24,18.647142,19.338572,18.544285,135.300003,19.328571,227958500
2007-08-27,19.055714,19.237143,18.871429,132.250000,18.892857,176859900
2007-08-28,18.712856,18.915714,18.090000,126.820007,18.117144,294841400
2007-08-29,18.554285,19.168571,18.505714,134.080002,19.154285,291715200
2007-08-30,18.952858,19.750000,18.900000,136.250000,19.464285,358895600
2007-08-31,19.927143,19.950001,19.629999,138.480011,19.782858,219221800
2007-09-04,19.991428,20.818571,19.977142,144.160004,20.594286,329210700
2007-09-05,20.709999,20.834286,19.442858,136.760010,19.537144,582055600
2007-09-06,19.365715,19.652857,18.958570,135.010010,19.287144,475315400
2007-09-07,18.858572,18.900000,18.571428,131.770004,18.824286,357644000
2007-09-10,19.570000,19.719999,19.135714,136.710007,19.530001,371959700
2007-09-11,19.700001,19.757143,19.107143,135.490005,19.355715,242971400
2007-09-12,19.427143,19.914286,19.392857,136.849991,19.549999,255692500
2007-09-13,19.832857,19.857143,19.521429,137.199997,19.600000,164040800
2007-09-14,19.510000,19.854286,19.457144,138.809998,19.830000,151830000
2007-09-17,19.855715,20.084286,19.657143,138.410004,19.772858,198342900
2007-09-18,19.865715,20.407143,19.690001,140.919998,20.131428,266022400
2007-09-19,20.431429,20.451429,19.914286,140.770004,20.110001,256720100
2007-09-20,20.021429,20.255714,19.902857,140.309998,20.044285,172960200
2007-09-21,20.162857,20.664286,20.044285,144.149994,20.592857,284720100
2007-09-24,20.961428,21.407143,20.950001,148.279999,21.182858,263040400
2007-09-25,20.977142,21.888571,20.974285,153.179993,21.882856,298137700
2007-09-26,22.067142,22.142857,21.607143,152.770004,21.824286,243817000
2007-09-27,21.967142,22.074286,21.760000,154.500000,22.071428,164549700
2007-09-28,21.920000,22.085714,21.821428,153.470001,21.924286,153775300
2007-10-01,22.090000,22.487143,21.847143,156.339996,22.334286,209267100
2007-10-02,22.364286,22.655714,22.270000,158.449997,22.635714,198017400
2007-10-03,22.540001,22.740000,22.430000,157.919998,22.559999,173129600
2007-10-04,22.571428,22.582857,21.928572,156.239990,22.320000,164239600
2007-10-05,22.624287,23.082857,22.528572,161.449997,23.064285,235867800
2007-10-08,23.355715,23.987143,23.281429,167.910004,23.987143,208982200
2007-10-09,24.314285,24.444286,23.811428,167.860001,23.980000,276071600
2007-10-10,23.935715,23.982857,23.657143,166.789993,23.827143,166897500
2007-10-11,24.212856,24.554285,21.887142,162.229996,23.175714,410998000
2007-10-12,23.287144,23.897142,23.114286,167.250000,23.892857,247044000
2007-10-15,23.997143,24.224285,23.357143,166.980011,23.854286,269482500
2007-10-16,23.648571,24.311428,23.592857,169.580002,24.225714,266957600
2007-10-17,24.670000,24.719999,24.168571,172.750000,24.678572,281903300
2007-10-18,24.500000,24.884285,24.435715,173.500000,24.785715,205919000
2007-10-19,24.891428,24.947144,24.285715,170.419998,24.345715,322945000
2007-10-22,24.335714,24.985714,24.280001,174.360001,24.908571,412374900
2007-10-23,26.937143,26.942858,26.108572,186.160004,26.594286,448791000
2007-10-24,26.544285,26.744286,25.605715,185.929993,26.561428,322120400
2007-10-25,26.410000,26.557142,25.951429,182.779999,26.111429,243400500
2007-10-26,26.469999,26.481428,26.125713,184.699997,26.385714,176719200
2007-10-29,26.492857,26.655714,26.385714,185.089996,26.441429,135138500
2007-10-30,26.597143,27.052856,26.389999,187.000000,26.714285,234853500
2007-10-31,26.804285,27.160000,26.421429,189.949997,27.135714,208327700
2007-11-01,26.942858,27.157143,25.714285,187.440002,26.777143,201259100
2007-11-02,27.030001,27.062857,26.212856,187.869995,26.838572,250528600
2007-11-05,26.469999,26.994286,26.320000,186.180008,26.597143,201044200
2007-11-06,26.721428,27.428572,26.467142,191.789993,27.398571,238681800
2007-11-07,27.230000,27.525715,26.590000,186.300003,26.614286,248581900
2007-11-08,26.667143,26.700001,23.967142,175.470001,25.067142,472594500
2007-11-09,24.450001,25.017143,23.601429,165.370010,23.624287,381595200
2007-11-12,23.611429,23.957144,21.518572,153.759995,21.965714,442266300
2007-11-13,22.978571,24.425714,21.965714,169.960007,24.280001,434861700
2007-11-14,25.308571,25.367144,23.391428,166.110001,23.730000,362292000
2007-11-15,23.770000,24.227142,22.900000,164.299988,23.471428,371852600
2007-11-16,23.614286,23.860001,22.761429,166.389999,23.770000,345873500
2007-11-19,23.728571,24.028572,23.157143,163.949997,23.421429,288607200
2007-11-20,23.667143,24.541430,23.361429,168.850006,24.121429,385910700
2007-11-21,23.691429,24.621429,23.524286,168.459991,24.065714,304452400
2007-11-23,24.571428,24.578571,24.250000,171.540009,24.505714,116439400
2007-11-26,24.798571,25.324286,24.621429,172.539993,24.648571,326438700
2007-11-27,25.031429,25.112858,24.287144,174.809998,24.972857,329257600
2007-11-28,25.260000,25.799999,25.049999,180.220001,25.745714,287728000
2007-11-29,25.632856,26.452858,25.592857,184.289993,26.327143,262731700
2007-11-30,26.762857,26.814285,25.671429,182.220001,26.031429,296950500
2007-12-03,25.980000,26.305714,25.385714,178.860001,25.551428,240367400
2007-12-04,25.307142,25.842857,25.284286,179.809998,25.687143,193449900
2007-12-05,26.127142,26.571428,26.058571,185.500000,26.500000,223100500
2007-12-06,26.598572,27.157143,26.588572,189.949997,27.135714,224952700
2007-12-07,27.219999,27.855715,26.862858,194.300003,27.757143,266516600
2007-12-10,27.655714,27.951429,27.527143,194.209991,27.744286,180594400
2007-12-11,27.821428,28.118572,26.770000,188.540009,26.934286,277731300
2007-12-12,27.634285,27.782858,26.537144,190.860001,27.265715,306415200
2007-12-13,27.170000,27.445715,26.831429,191.830002,27.404285,216154400
2007-12-14,27.195715,27.600000,27.077143,190.389999,27.198572,168578200
2007-12-17,27.245714,27.521429,26.139999,184.399994,26.342857,256173400
2007-12-18,26.645714,26.761429,25.514286,182.979996,26.139999,305650800
2007-12-19,26.139999,26.377142,25.842857,183.119995,26.160000,206869600
2007-12-20,26.490000,26.832857,26.190001,187.209991,26.744286,193514300
2007-12-21,27.160000,27.701429,27.127142,193.910004,27.701429,248490200
2007-12-24,27.861429,28.475714,27.827143,198.800003,28.400000,120050700
2007-12-26,28.430000,28.708570,28.117144,198.949997,28.421429,175933100
2007-12-27,28.421429,28.994286,28.257143,198.570007,28.367144,198881900
2007-12-28,28.655714,28.794285,28.125713,199.829987,28.547142,174911800
2007-12-31,28.500000,28.642857,28.250000,198.079987,28.297142,134833300
2008-01-02,28.467142,28.608572,27.507143,194.839996,27.834286,269794700
2008-01-03,27.915714,28.198572,27.527143,194.930008,27.847143,210516600
2008-01-04,27.350000,27.571428,25.555714,180.049988,25.721428,363958000
2008-01-07,25.892857,26.228571,24.318571,177.639999,25.377142,518048300
2008-01-08,25.734285,26.065714,24.400000,171.250000,24.464285,380954000
2008-01-09,24.471428,25.642857,24.042856,179.399994,25.628571,453470500
2008-01-10,25.368572,25.857143,25.058571,178.020004,25.431429,370743800
2008-01-11,25.142857,25.407143,24.285715,172.690002,24.670000,308071400
2008-01-14,25.360001,25.631428,25.024286,178.779999,25.540001,275112600
2008-01-15,25.388571,25.602858,23.522858,169.039993,24.148571,585819500
2008-01-16,23.604286,24.144285,22.385714,159.639999,22.805714,553461300
2008-01-17,23.072857,23.622858,22.631428,160.889999,22.984285,439464900
2008-01-18,23.101429,23.678572,22.801428,161.360001,23.051428,431085900
2008-01-22,21.151428,22.854286,20.857143,155.639999,22.234285,608688500
2008-01-23,19.455715,20.000000,18.020000,139.070007,19.867144,843242400
2008-01-24,19.998571,20.100000,18.858572,135.600006,19.371429,501466700
2008-01-25,19.855715,19.870001,18.515715,130.009995,18.572857,388684800
2008-01-28,18.308571,19.028572,18.064285,130.009995,18.572857,368711000
2008-01-29,18.735714,18.969999,18.435715,131.540009,18.791430,274995700
2008-01-30,18.767143,19.350000,18.571428,132.179993,18.882856,310762900
2008-01-31,18.492857,19.521429,18.485714,135.360001,19.337143,336418600
2008-02-01,19.462856,19.512857,18.882856,133.750000,19.107143,252686000
2008-02-04,19.172857,19.414286,18.774286,131.649994,18.807142,224808500
2008-02-05,18.632856,19.142857,18.414286,129.360001,18.480000,285260500
2008-02-06,18.690001,18.845715,17.395714,122.000000,17.428572,393318100
2008-02-07,17.138571,17.825714,16.752857,121.239998,17.320000,520832900
2008-02-08,17.440001,17.957144,17.371429,125.480003,17.925714,338993200
2008-02-11,18.287144,18.568571,18.171429,129.449997,18.492857,300358100
2008-02-12,18.671429,18.714285,17.660000,124.860001,17.837143,306495000
2008-02-13,18.097143,18.540001,17.947144,129.399994,18.485714,242133500
2008-02-14,18.485714,18.685715,18.144285,127.459991,18.208570,238524300
2008-02-15,18.038572,18.154285,17.722857,124.629997,17.804285,225325100
2008-02-19,17.998571,18.107143,17.348572,122.180008,17.454287,251261500
2008-02-20,17.457144,17.799999,17.382856,123.820007,17.688572,241859800
2008-02-21,18.007143,18.067142,17.265715,121.540009,17.362858,234528700
2008-02-22,17.497143,17.501429,16.552856,119.459999,17.065714,382469500
2008-02-25,16.941429,17.167143,16.665714,119.740005,17.105715,314193600
2008-02-26,16.805714,17.298571,16.491428,119.150002,17.021429,376222000
2008-02-27,16.889999,17.578571,16.870001,122.959999,17.565714,368784500
2008-02-28,18.171429,18.885714,17.967142,129.910004,18.558571,404563600
2008-02-29,18.469999,18.601429,17.828571,125.020004,17.860001,313870200
2008-03-03,17.777143,17.997143,16.857143,121.729996,17.389999,398260800
2008-03-04,17.427143,17.840000,17.200001,124.619995,17.802856,446345900
2008-03-05,17.654285,17.877142,17.464285,124.490005,17.784286,305459000
2008-03-06,17.801428,18.214285,17.258572,120.930008,17.275715,368424700
2008-03-07,17.201429,17.568571,17.007143,122.249992,17.464285,307615700
2008-03-10,17.425714,17.637142,17.052856,119.690002,17.098572,249897200
2008-03-11,17.728571,18.211428,17.428572,127.350006,18.192858,290985800
2008-03-12,18.148571,18.382856,17.881428,126.029999,18.004286,264907300
2008-03-13,17.728571,18.500000,17.571428,127.940002,18.277143,315525700
2008-03-14,18.554285,18.614286,17.742857,126.610001,18.087143,289160200
2008-03-17,17.507143,18.370001,17.507143,126.730003,18.104286,268149700
2008-03-18,18.454287,19.000000,18.381428,132.819992,18.974285,301280000
2008-03-19,19.017143,19.184286,18.524286,129.669998,18.524286,252634200
2008-03-20,18.731428,19.041430,18.454287,133.270004,19.038572,227196900
2008-03-24,19.144285,20.121429,19.091429,139.529999,19.932858,266730100
2008-03-25,19.994286,20.442858,19.618572,140.979996,20.139999,263097800
2008-03-26,20.124287,20.820000,20.091429,145.059998,20.722857,295521100
2008-03-27,20.707144,20.758572,19.998571,140.250000,20.035715,249957400
2008-03-28,20.257143,20.664286,20.228571,143.010010,20.430000,178652600
2008-03-31,20.467142,20.815714,20.360001,143.500000,20.500000,192016300
2008-04-01,20.900000,21.379999,20.515715,149.529999,21.361429,258141800
2008-04-02,21.254286,21.600000,20.835714,147.489990,21.070000,261242100
2008-04-03,21.008572,21.947144,21.000000,151.610001,21.658571,262892000
2008-04-04,21.741428,22.101429,21.535715,153.080002,21.868572,213604300
2008-04-07,22.304285,22.812857,22.158571,155.889999,22.270000,289581600
2008-04-08,21.935715,22.350000,21.760000,152.839996,21.834286,253573600
2008-04-09,21.901428,21.984285,21.494286,151.440002,21.634285,218349600
2008-04-10,21.590000,22.202858,21.514286,154.550003,22.078571,238940800
2008-04-11,21.817142,21.900000,20.914286,147.139999,21.020000,302519000
2008-04-14,20.967142,21.321428,20.648571,147.779999,21.111429,211271900
2008-04-15,21.342857,21.388571,20.817142,148.380005,21.197144,174509300
2008-04-16,21.674286,22.014286,21.517143,153.700012,21.957144,198943500
2008-04-17,22.024286,22.285715,21.907143,154.489990,22.070000,176066800
2008-04-18,22.731428,23.180000,22.625713,161.040009,23.005714,256691400
2008-04-21,23.172857,24.071428,23.108572,168.160004,24.022858,259788200
2008-04-22,23.914286,24.000000,22.584286,160.199997,22.885714,359893100
2008-04-23,23.435715,23.548571,23.011429,162.889999,23.270000,376047700
2008-04-24,23.620001,24.282858,22.741428,168.940002,24.134285,424016600
2008-04-25,24.385714,24.442858,23.774286,169.729996,24.247143,248118500
2008-04-28,24.250000,24.821428,24.161428,172.240005,24.605715,196803600
2008-04-29,24.444286,25.094286,24.321428,175.050003,25.007143,230869100
2008-04-30,25.170000,25.714285,24.702858,173.949997,24.850000,284881100
2008-05-01,24.994286,25.714285,24.980000,180.000000,25.714285,225894200
2008-05-02,25.741428,25.988571,25.507143,180.940002,25.848572,251520500
2008-05-05,25.988571,26.472857,25.864286,184.729996,26.389999,213639300
2008-05-06,26.379999,26.731428,26.025715,186.660004,26.665714,229717600
2008-05-07,26.578571,26.885714,25.791430,182.589996,26.084286,289283400
2008-05-08,26.252857,26.642857,26.152857,185.059998,26.437143,224771400
2008-05-09,26.165714,26.321428,25.910000,183.450012,26.207144,168268100
2008-05-12,26.458570,26.981428,26.121429,188.159988,26.879999,204640800
2008-05-13,26.944286,27.350000,26.837143,189.959991,27.137142,205809100
2008-05-14,27.318571,27.462856,26.510000,186.260010,26.608572,229205900
2008-05-15,26.687143,27.128571,26.314285,189.730011,27.104286,218302000
2008-05-16,27.158571,27.185715,26.714285,187.619995,26.802856,191442300
2008-05-19,26.837143,26.955715,25.900000,183.599991,26.228571,236455100
2008-05-20,25.974285,26.594286,25.731428,185.899994,26.557142,242462500
2008-05-21,26.524286,26.850000,25.178572,178.190002,25.455715,289414300
2008-05-22,25.608572,25.904285,24.571428,177.049988,25.292856,301683900
2008-05-23,25.824286,25.998571,25.400000,181.169998,25.881428,226729300
2008-05-27,26.107143,26.632856,25.977142,186.429993,26.632856,197476300
2008-05-28,26.772858,26.850000,26.245714,187.009995,26.715714,185994900
2008-05-29,26.680000,26.885714,26.500000,186.690002,26.670000,161796600
2008-05-30,26.778572,27.077143,26.768572,188.750000,26.964285,152546100
2008-06-02,26.942858,27.092857,26.361429,186.100006,26.585714,169960000
2008-06-03,26.694286,26.885714,26.048571,185.369995,26.481428,187630100
2008-06-04,26.288572,26.727142,26.175714,185.190002,26.455715,181745900
2008-06-05,26.620001,27.120001,26.528572,189.429993,27.061428,188861400
2008-06-06,26.857143,27.135714,26.507143,185.639999,26.520000,241605700
2008-06-09,26.398571,26.420000,25.107143,181.610001,25.944286,472098200
2008-06-10,25.787144,26.682858,25.574286,185.639999,26.520000,285235300
2008-06-11,26.334286,26.571428,25.655714,180.809998,25.830000,240387700
2008-06-12,25.927143,26.085714,24.457144,173.259995,24.751429,327083400
2008-06-13,24.520000,24.879999,23.615715,172.370010,24.624287,336489300
2008-06-16,24.471428,25.414286,24.152857,176.839996,25.262857,262932600
2008-06-17,25.442858,25.998571,25.344286,181.429993,25.918571,224914200
2008-06-18,25.874287,26.028572,25.335714,178.750000,25.535715,202867000
2008-06-19,25.507143,26.048571,25.257143,180.899994,25.842857,197987300
2008-06-20,25.621429,25.857143,25.000000,175.270004,25.038572,222091800
2008-06-23,24.962856,25.125713,24.508572,173.160004,24.737143,161445200
2008-06-24,24.624287,25.111429,24.518572,173.250000,24.750000,155486800
2008-06-25,24.944286,25.547142,24.840000,177.389999,25.341429,161112700
2008-06-26,24.867144,24.977142,24.001429,168.260010,24.037144,217402500
2008-06-27,23.787144,24.367144,23.450001,170.089996,24.298571,260562400
2008-06-30,24.312857,24.571428,23.802856,167.440002,23.920000,171049200
2008-07-01,23.461428,24.959999,23.428572,174.680008,24.954287,277820200
2008-07-02,25.028572,25.350000,24.025715,168.180008,24.025715,209379800
2008-07-03,24.227142,24.595715,23.678572,170.119995,24.302856,130840500
2008-07-07,24.737143,25.304285,24.557142,175.160004,25.022858,205097900
2008-07-08,25.057142,25.671429,24.677143,179.550003,25.650000,222087600
2008-07-09,25.742857,25.844286,24.877142,174.250000,24.892857,223944000
2008-07-10,24.988571,25.334286,24.481428,176.630005,25.232857,210172200
2008-07-11,25.067142,25.301428,24.428572,172.580002,24.654285,232502900
2008-07-14,25.605715,25.614286,24.725714,173.880005,24.840000,221513600
2008-07-15,24.639999,24.820000,23.770000,169.639999,24.234285,260010800
2008-07-16,24.314285,24.704287,24.085714,172.809998,24.687143,186947600
2008-07-17,24.871429,24.997143,24.484285,171.809998,24.544285,189381500
2008-07-18,24.074286,24.235714,23.571428,165.149994,23.592857,217103600
2008-07-21,23.842857,23.928572,23.017143,166.290009,23.755714,340117400
2008-07-22,21.285715,23.251429,20.932858,162.019989,23.145714,469898100
2008-07-23,23.570000,24.052856,23.080000,166.259995,23.751429,265442100
2008-07-24,23.474285,23.608572,22.635714,159.029999,22.718571,209904800
2008-07-25,22.914286,23.285715,22.664286,162.119995,23.160000,158409300
2008-07-28,23.191429,23.209999,22.002857,154.399994,22.057142,195178200
2008-07-29,22.201429,22.778572,21.950001,157.080002,22.440001,171017700
2008-07-30,22.540001,22.927143,22.297142,159.880005,22.840000,181295800
2008-07-31,22.505714,23.171429,22.425714,158.950012,22.707144,159374600
2008-08-01,22.842857,22.855715,22.250000,156.659988,22.379999,136159800
2008-08-04,22.371429,22.557142,21.844286,153.229996,21.889999,148131900
2008-08-05,22.202858,22.971428,22.117144,160.639999,22.948572,172092900
2008-08-06,22.852858,23.914286,22.571428,164.190002,23.455715,197852200
2008-08-07,23.244286,23.735714,23.071428,163.570007,23.367144,168093100
2008-08-08,23.408571,24.235714,23.392857,169.549988,24.221428,178499300
2008-08-11,24.295713,25.214285,24.238571,173.559998,24.794285,222826100
2008-08-12,24.788572,25.612858,24.787144,176.729996,25.247143,209069700
2008-08-13,25.425714,25.714285,25.128571,179.300003,25.614286,210586600
2008-08-14,25.475714,25.778572,25.405714,179.320007,25.617144,177825200
2008-08-15,25.577143,25.678572,25.007143,175.740005,25.105715,177062900
2008-08-18,25.081429,25.401428,24.831429,175.389999,25.055714,138003600
2008-08-19,24.934286,25.295713,24.544285,173.529999,24.790001,154051100
2008-08-20,24.967142,25.277143,24.801428,175.840012,25.120001,126737800
2008-08-21,24.924286,25.064285,24.555714,174.289993,24.898571,134936200
2008-08-22,25.117144,25.357143,25.081429,176.790009,25.255714,109902800
2008-08-25,25.164286,25.175714,24.522858,172.550003,24.650000,121106300
2008-08-26,24.680000,24.982857,24.658571,173.639999,24.805714,111387500
2008-08-27,24.758572,25.108572,24.598572,174.670013,24.952858,119445200
2008-08-28,25.040001,25.178572,24.678572,173.739990,24.820000,107846200
2008-08-29,24.708570,24.785715,24.148571,169.529999,24.218571,149822400
2008-09-02,24.628571,24.785715,23.571428,166.190002,23.741428,195190800
2008-09-03,23.834286,24.097143,23.428572,166.960007,23.851429,183708700
2008-09-04,23.694286,23.987143,22.972857,161.220001,23.031429,185846500
2008-09-05,22.655714,23.200001,22.521429,160.179993,22.882856,196721000
2008-09-08,23.510000,23.555714,21.637142,157.919998,22.559999,261494800
2008-09-09,22.408571,22.851429,21.398571,151.679993,21.668571,311256400
2008-09-10,21.760000,22.141428,21.257143,151.610001,21.658571,243285700
2008-09-11,21.168571,21.855715,20.857143,152.649994,21.807142,242783800
2008-09-12,21.558571,21.558571,20.928572,148.940002,21.277143,198256800
2008-09-15,20.290001,21.098572,20.051428,140.360001,20.051428,230158600
2008-09-16,19.122858,20.357143,18.878571,139.880005,19.982857,299959100
2008-09-17,19.784286,19.787144,18.261429,127.830002,18.261429,300113800
2008-09-18,18.652857,19.347143,17.240000,134.089996,19.155714,419063400
2008-09-19,20.371429,20.600000,19.472857,140.909988,20.129999,357718900
2008-09-22,19.991428,20.035715,18.665714,131.049988,18.721428,214178300
2008-09-23,18.835714,19.400000,18.094286,126.840004,18.120001,320091100
2008-09-24,18.181429,18.707144,17.878571,128.709991,18.387142,261753800
2008-09-25,18.542856,19.255714,18.360001,131.930008,18.847143,251511400
2008-09-26,17.844286,18.542856,17.571428,128.239990,18.320000,281612800
2008-09-29,17.088572,17.097143,14.370000,105.260002,15.037143,655514300
2008-09-30,15.464286,16.428572,15.185715,113.659996,16.237143,406670600
2008-10-01,15.988571,16.051428,15.341429,109.120003,15.588572,324121000
2008-10-02,15.430000,15.541429,14.285714,100.099998,14.300000,402341100
2008-10-03,14.857142,15.214286,13.521428,97.070000,13.867143,573599600
2008-10-06,13.137143,14.111428,12.505714,98.139999,14.020000,526854300
2008-10-07,14.354285,14.500000,12.707143,89.159996,12.737143,469693000
2008-10-08,12.272857,13.761429,12.240000,89.790001,12.827143,551935300
2008-10-09,13.335714,13.685715,12.371428,88.740005,12.677143,404345900
2008-10-10,12.242857,14.285714,12.142858,96.800003,13.828571,554824900
2008-10-13,14.935715,15.790000,14.431429,110.260002,15.751429,384769000
2008-10-14,16.608572,16.628571,14.734285,104.080002,14.868571,495248600
2008-10-15,14.834286,15.285714,13.984285,97.949997,13.992857,396043900
2008-10-16,14.252857,14.775714,13.105714,101.889999,14.555715,495130300
2008-10-17,14.228572,14.577143,12.270000,97.400002,13.914286,440556900
2008-10-20,14.254286,14.290000,13.377143,98.439995,14.062857,387292500
2008-10-21,13.850000,13.985714,13.022857,91.489998,13.070000,548415000
2008-10-22,13.910000,14.464286,13.275714,96.870003,13.838572,562202200
2008-10-23,13.787143,14.178572,13.128572,98.229996,14.032857,418857600
2008-10-24,12.904285,13.985714,12.872857,96.380005,13.768572,397514600
2008-10-27,13.581429,13.947143,13.122857,92.089996,13.155714,302192800
2008-10-28,13.632857,14.357142,13.195714,99.909996,14.272857,408533300
2008-10-29,14.408571,15.648571,14.277143,104.550003,14.935715,487744600
2008-10-30,15.461429,16.027143,15.372857,111.040001,15.862857,409522400
2008-10-31,15.342857,15.825714,15.020000,107.589996,15.370000,414939000
2008-11-03,15.132857,15.585714,14.980000,106.959999,15.280000,264484500
2008-11-04,15.712857,15.970000,15.238571,110.989998,15.855714,349670300
2008-11-05,15.558572,15.674286,14.712857,103.300003,14.757143,314113800
2008-11-06,14.435715,14.682858,14.000000,99.099998,14.157143,329768600
2008-11-07,14.177143,14.264286,13.674286,98.239998,14.034286,273813400
2008-11-10,14.310000,14.342857,13.500000,95.879997,13.697143,280955500
2008-11-11,13.544286,13.881429,13.180000,94.769997,13.538571,306134500
2008-11-12,13.204286,13.320000,12.858571,90.120003,12.874286,294744100
2008-11-13,12.838572,13.777143,12.288571,96.439995,13.777143,463521800
2008-11-14,13.394286,13.427143,12.857142,90.240005,12.891429,351316700
2008-11-17,12.640000,12.935715,12.465714,88.139999,12.591429,290631600
2008-11-18,12.805715,12.998571,12.408571,89.910004,12.844286,302423800
2008-11-19,12.777143,13.082857,12.315714,86.290001,12.327143,292975200
2008-11-20,12.177143,12.350000,11.428572,80.489998,11.498571,429203600
2008-11-21,11.704286,12.017143,11.305715,82.580002,11.797143,392317800
2008-11-24,12.172857,13.541429,12.120000,92.949997,13.278571,360564400
2008-11-25,13.518572,13.530000,12.594286,90.800003,12.971429,308823200
2008-11-26,12.845715,13.607142,12.835714,95.000000,13.571428,224959000
2008-11-28,13.528571,13.537143,13.122857,92.669998,13.238571,74443600
2008-12-01,13.042857,13.181429,12.702857,88.930000,12.704286,230941900
2008-12-02,12.861428,13.235714,12.357142,92.470001,13.210000,287180600
2008-12-03,12.771428,13.747143,12.685715,95.900002,13.700000,334670000
2008-12-04,13.490000,13.601429,12.722857,91.410004,13.058572,272842500
2008-12-05,12.907143,13.498571,12.694285,94.000000,13.428572,260948800
2008-12-08,13.897142,14.400000,13.685715,99.720001,14.245714,296285500
2008-12-09,14.005714,14.800000,13.887143,100.059998,14.294286,300874000
2008-12-10,13.981428,14.212857,13.785714,98.209999,14.030000,234511900
2008-12-11,13.907143,14.462857,13.547143,95.000000,13.571428,260154300
2008-12-12,13.257143,14.142858,13.218572,98.269997,14.038571,260293600
2008-12-15,13.712857,13.744286,13.285714,94.750000,13.535714,222939500
2008-12-16,13.425714,13.782857,13.250000,95.430000,13.632857,273376600
2008-12-17,13.004286,13.014286,12.574286,89.159996,12.737143,323465100
2008-12-18,12.758572,12.975715,12.634286,89.430000,12.775714,214354000
2008-12-19,12.848572,12.991428,12.685715,90.000000,12.857142,200480000
2008-12-22,12.860000,12.861428,12.098572,85.739998,12.248571,211185100
2008-12-23,12.410000,12.552857,12.271428,86.380005,12.340000,158757900
2008-12-24,12.305715,12.321428,12.078571,85.039993,12.148571,67833500
2008-12-26,12.377143,12.488571,12.177143,85.809998,12.258572,77081200
2008-12-29,12.360000,12.517143,12.152857,86.610001,12.372857,171500000
2008-12-30,12.488571,12.578571,12.102858,86.290001,12.327143,241900400
2008-12-31,12.281428,12.534286,12.191428,85.349998,12.192857,151885300
2009-01-02,12.268572,13.005714,12.165714,90.750000,12.964286,186503800
2009-01-05,13.310000,13.740000,13.244286,94.580002,13.511429,295402100
2009-01-06,13.707143,13.881429,13.198571,93.019997,13.288571,322327600
2009-01-07,13.115714,13.214286,12.894286,91.010002,13.001429,188262200
2009-01-08,12.918571,13.307143,12.862857,92.699997,13.242857,168375200
2009-01-09,13.315714,13.340000,12.877143,90.579994,12.940000,136711400
2009-01-12,12.922857,12.998571,12.507143,88.660004,12.665714,154429100
2009-01-13,12.605714,12.820000,12.335714,87.709999,12.530000,199599400
2009-01-14,12.320000,12.464286,12.102858,85.329994,12.190000,255416000
2009-01-15,11.510000,12.017143,11.435715,83.379997,11.911428,457908500
2009-01-16,12.042857,12.054286,11.485714,82.330002,11.761429,261906400
2009-01-20,11.704286,11.714286,11.171429,78.199997,11.171429,229978700
2009-01-21,11.341429,11.840000,11.330000,82.830002,11.832857,272317500
2009-01-22,12.577143,12.857142,12.260000,88.360001,12.622857,352382100
2009-01-23,12.402857,12.838572,12.357142,88.360001,12.622857,190942500
2009-01-26,12.694285,12.995714,12.614285,89.639999,12.805715,173059600
2009-01-27,12.884286,13.078571,12.820000,90.730003,12.961429,154509600
2009-01-28,13.160000,13.571428,13.071428,94.199997,13.457143,215351500
2009-01-29,13.298572,13.477143,13.228572,93.000000,13.285714,148182300
2009-01-30,13.228572,13.374286,12.858571,90.129997,12.875714,162869700
2009-02-02,12.728572,13.142858,12.700000,91.509995,13.072857,139561800
2009-02-03,13.131429,13.340000,12.897142,92.979996,13.282857,149827300
2009-02-04,13.317142,13.750000,13.300000,93.549995,13.364285,202105400
2009-02-05,13.252857,13.892858,13.231428,96.459999,13.780000,187311600
2009-02-06,13.860000,14.285714,13.857142,99.720001,14.245714,171802400
2009-02-09,14.285714,14.714286,14.214286,102.510002,14.644286,178752700
2009-02-10,14.475715,14.644286,13.865714,97.830002,13.975715,212265200
2009-02-11,13.767143,14.044286,13.681429,96.820000,13.831429,168743400
2009-02-12,13.690000,14.250000,13.690000,99.270004,14.181429,204297100
2009-02-13,14.141429,14.277143,14.017143,99.160004,14.165714,152244400
2009-02-17,13.838572,13.862857,13.468572,94.529999,13.504286,169559600
2009-02-18,13.578571,13.692857,13.245714,94.369995,13.481428,171194800
2009-02-19,13.338572,13.464286,12.872857,90.639999,12.948571,230701100
2009-02-20,12.771428,13.200000,12.714286,91.199997,13.028571,187579000
2009-02-23,13.092857,13.142858,12.358571,86.949997,12.421429,196745500
2009-02-24,12.492857,12.984285,12.428572,90.250000,12.892858,201776400
2009-02-25,12.837143,13.274285,12.750000,91.159996,13.022857,208263300
2009-02-26,13.142858,13.274285,12.708571,89.190002,12.741428,157467100
2009-02-27,12.561429,13.042857,12.524285,89.309998,12.758572,176664600
2009-03-02,12.588572,13.028571,12.524285,87.939995,12.562857,192732400
2009-03-03,12.704286,12.962857,12.554286,88.370003,12.624286,181085100
2009-03-04,12.882857,13.252857,12.778571,91.169998,13.024285,185350900
2009-03-05,12.922857,13.124286,12.635715,88.839996,12.691428,176724800
2009-03-06,12.620000,12.628572,11.761429,85.300003,12.185715,252786800
2009-03-09,12.025714,12.514286,11.795714,83.110001,11.872857,174574400
2009-03-10,12.124286,12.738571,12.051429,88.629997,12.661428,211064700
2009-03-11,12.830000,13.438571,12.797143,92.680000,13.240000,211593200
2009-03-12,13.271428,13.797143,13.142858,96.350006,13.764286,192114300
2009-03-13,13.757143,13.885715,13.572857,95.930000,13.704286,150292100
2009-03-16,13.790000,13.912857,13.454286,95.419998,13.631429,199311000
2009-03-17,13.605714,14.241428,13.581429,99.659996,14.237143,196661500
2009-03-18,14.272857,14.782857,14.245714,101.520004,14.502857,199009300
2009-03-19,14.550000,14.742857,14.321428,101.620003,14.517143,125045200
2009-03-20,14.584286,14.730000,14.367143,101.590004,14.512857,173896800
2009-03-23,14.672857,15.451428,14.535714,107.660004,15.380000,166599300
2009-03-24,15.194285,15.634286,15.055715,106.500000,15.214286,160153000
2009-03-25,15.368571,15.480000,14.837143,106.489998,15.212857,161654500
2009-03-26,15.404285,15.711429,15.368571,109.869995,15.695714,154063000
2009-03-27,15.461429,15.504286,15.200000,106.850006,15.264286,123218200
2009-03-30,14.930000,15.001429,14.658571,104.490005,14.927143,125699000
2009-03-31,15.064285,15.350000,15.000000,105.120003,15.017143,142520000
2009-04-01,14.870000,15.571428,14.841429,108.689995,15.527143,147343000
2009-04-02,15.734285,16.392857,15.682858,112.710007,16.101429,203091700
2009-04-03,16.312857,16.590000,16.217142,115.989998,16.570000,159060300
2009-04-06,16.420000,16.964285,16.182858,118.449997,16.921429,164516100
2009-04-07,16.647142,16.667143,16.312857,115.000000,16.428572,134145200
2009-04-08,16.490000,16.684286,16.368572,116.320007,16.617144,113907500
2009-04-09,16.917143,17.142857,16.851429,119.570000,17.081429,132689200
2009-04-13,17.144285,17.282858,17.000000,120.220001,17.174286,97309100
2009-04-14,17.081429,17.167143,16.750000,118.309998,16.901428,113655500
2009-04-15,16.742857,16.892857,16.537144,117.639999,16.805714,103220600
2009-04-16,17.027143,17.592857,16.969999,121.450005,17.350000,148361500
2009-04-17,17.311428,17.750000,17.178572,123.419998,17.631428,124373900
2009-04-20,17.389999,17.570000,17.022858,120.499992,17.214285,116616500
2009-04-21,16.984285,17.448572,16.942858,121.759995,17.394285,117671400
2009-04-22,17.518572,17.907143,17.314285,121.510002,17.358572,234691800
2009-04-23,18.088572,18.171429,17.644285,125.400002,17.914286,236289200
2009-04-24,17.805714,17.877142,17.567142,123.900009,17.700001,135191000
2009-04-27,17.557142,17.857143,17.522858,124.729996,17.818571,120172500
2009-04-28,17.621429,18.030001,17.608572,123.900009,17.700001,113964200
2009-04-29,17.835714,18.121429,17.690001,125.139992,17.877142,114527700
2009-04-30,18.031429,18.142857,17.845715,125.829994,17.975714,124622400
2009-05-01,17.971428,18.278572,17.971428,127.240005,18.177143,99379000
2009-05-04,18.320000,18.892857,18.240000,132.070007,18.867144,152339600
2009-05-05,18.821428,18.980000,18.731428,132.709991,18.958570,99563800
2009-05-06,19.047142,19.071428,18.602858,132.500000,18.928572,118384700
2009-05-07,18.904285,18.912857,18.271429,129.059998,18.437143,132944000
2009-05-08,18.434286,18.747143,18.037144,129.190002,18.455715,116991000
2009-05-11,18.195715,18.708570,18.160000,129.570007,18.510000,101164700
2009-05-12,18.508572,18.530001,17.607143,124.420006,17.774286,152370400
2009-05-13,17.601429,17.717142,17.054285,119.489998,17.070000,148992900
2009-05-14,17.111429,17.647142,17.100000,122.949997,17.564285,111956600
2009-05-15,17.474285,17.802856,17.372858,122.419998,17.488571,91891800
2009-05-18,17.675714,18.100000,17.367144,126.650002,18.092857,114710400
2009-05-19,18.117144,18.472857,17.962856,127.450005,18.207144,93105600
2009-05-20,18.232857,18.458570,17.900000,125.869995,17.981428,97146000
2009-05-21,17.878571,18.111429,17.555714,124.180000,17.740000,101986500
2009-05-22,17.721428,17.740000,17.392857,122.500000,17.500000,74499600
2009-05-26,17.822857,18.690001,17.792856,130.779999,18.682858,159231800
2009-05-27,18.825714,19.282858,18.701429,133.050003,19.007143,161605500
2009-05-28,19.064285,19.341429,18.861429,135.069992,19.295713,121888200
2009-05-29,19.341429,19.414286,19.121429,135.809998,19.401428,114133600
2009-06-01,19.495714,19.998571,19.428572,139.350006,19.907143,113124900
2009-06-02,19.855715,20.191429,19.764286,139.490005,19.927143,114055900
2009-06-03,20.000000,20.158571,19.867144,140.949997,20.135714,141299900
2009-06-04,20.018572,20.597143,20.005714,143.740005,20.534286,137658500
2009-06-05,20.758572,20.914286,20.458570,144.669998,20.667143,158179000
2009-06-08,20.545713,20.604286,19.918571,143.849991,20.549999,232913100
2009-06-09,20.544285,20.651428,20.078571,142.720001,20.388571,169241100
2009-06-10,20.325714,20.335714,19.757143,140.250000,20.035715,172155900
2009-06-11,19.935715,20.222857,19.792856,139.949997,19.992857,131205900
2009-06-12,19.830000,19.871429,19.434286,136.970001,19.567142,140771400
2009-06-15,19.430000,19.561428,19.270000,136.089996,19.441429,134937600
2009-06-16,19.522858,19.781429,19.442858,136.349991,19.478571,128701300
2009-06-17,19.524286,19.635714,19.218571,135.580002,19.368572,142853200
2009-06-18,19.444286,19.714285,19.370001,135.880005,19.411428,106920100
2009-06-19,19.724285,19.928572,19.557142,139.479996,19.925714,180464200
2009-06-22,20.095715,20.222857,19.475714,137.370010,19.624287,158728500
2009-06-23,19.485714,19.564285,18.982857,134.009995,19.144285,176633100
2009-06-24,19.345715,19.642857,19.265715,136.220001,19.459999,121381400
2009-06-25,19.392857,20.028572,19.315714,139.860001,19.980000,147361900
2009-06-26,19.969999,20.508572,19.962856,142.440002,20.348572,109846100
2009-06-29,20.494286,20.564285,20.219999,141.970001,20.281429,141904000
2009-06-30,20.368572,20.542856,20.257143,142.430008,20.347143,108556000
2009-07-01,20.500000,20.665714,20.360001,142.830002,20.404285,103544700
2009-07-02,20.178572,20.404285,19.969999,140.020004,20.002857,92619800
2009-07-06,19.814285,19.855715,19.464285,138.610001,19.801428,124672100
2009-07-07,19.782858,19.954287,19.311428,135.399994,19.342857,115399200
2009-07-08,19.417143,19.719999,19.202858,137.220001,19.602858,143982300
2009-07-09,19.680000,19.712856,19.418571,136.360001,19.480000,85756300
2009-07-10,19.477142,19.852858,19.474285,138.520004,19.788572,111318900
2009-07-13,19.934286,20.334286,19.647142,142.339996,20.334286,120875300
2009-07-14,20.290001,20.454287,20.165714,142.270004,20.324286,86811900
2009-07-15,20.719999,21.000000,20.617144,146.880005,20.982857,121396800
2009-07-16,20.822857,21.145714,20.795713,147.520004,21.074286,98392700
2009-07-17,21.297142,21.717142,21.232857,151.750000,21.678572,150538500
2009-07-20,21.895714,22.148571,21.555714,152.910004,21.844286,183881600
2009-07-21,21.898571,21.918571,21.392857,151.509995,21.644285,218695400
2009-07-22,22.541430,22.675714,22.301428,156.739990,22.391428,218526000
2009-07-23,22.375713,22.634285,22.222857,157.819992,22.545713,131740700
2009-07-24,22.421429,22.857143,22.357143,159.990005,22.855715,109590600
2009-07-27,22.881428,22.982857,22.465714,160.100006,22.871429,108327800
2009-07-28,22.697144,22.871429,22.514286,160.000000,22.857143,90888700
2009-07-29,22.700001,22.921429,22.607143,160.029999,22.861429,95539500
2009-07-30,23.100000,23.531429,23.071428,162.790009,23.255714,117401200
2009-07-31,23.284286,23.571428,23.272858,163.389999,23.341429,105634200
2009-08-03,23.601429,23.805714,23.552856,166.430008,23.775715,98560000
2009-08-04,23.561428,23.652857,23.458570,165.550003,23.650000,98952700
2009-08-05,23.678572,23.912857,23.458570,165.110001,23.587143,105795900
2009-08-06,23.654285,23.787144,23.298571,163.910004,23.415714,85404200
2009-08-07,23.641428,23.799999,23.542856,165.509995,23.644285,96838700
2009-08-10,23.665714,23.799999,23.379999,164.720001,23.531429,75073600
2009-08-11,23.384285,23.482857,23.125713,162.830002,23.261429,88835600
2009-08-12,23.221428,23.815714,23.208570,165.309998,23.615715,111267800
2009-08-13,23.807142,24.095715,23.785715,168.419998,24.059999,109995200
2009-08-14,23.991428,24.032858,23.647142,166.779999,23.825714,76454000
2009-08-17,23.364286,23.370001,22.774286,159.589996,22.798571,131095300
2009-08-18,23.090000,23.462856,23.058571,164.000000,23.428572,107788100
2009-08-19,23.250000,23.614286,23.207144,164.600006,23.514286,103317900
2009-08-20,23.568571,23.817142,23.515715,166.330002,23.761429,85507800
2009-08-21,23.950001,24.195715,23.828571,169.220001,24.174286,104018600
2009-08-24,24.302856,24.387142,24.038572,169.059998,24.151428,101732400
2009-08-25,24.208570,24.420000,24.161428,169.400009,24.200001,81088700
2009-08-26,24.131428,24.221428,23.822857,167.410004,23.915714,75999700
2009-08-27,24.107143,24.224285,23.547142,169.450012,24.207144,112295400
2009-08-28,24.610001,24.641428,24.075714,170.049988,24.292856,113425200
2009-08-31,24.022858,24.121429,23.785715,168.210007,24.030001,77834400
2009-09-01,23.998571,24.285715,23.562857,165.300003,23.614286,117257000
2009-09-02,23.517143,23.944286,23.444286,165.180008,23.597143,91062300
2009-09-03,23.777143,23.871429,23.571428,166.549988,23.792856,73488800
2009-09-04,23.897142,24.385714,23.870001,170.309998,24.330000,93657200
2009-09-08,24.711428,24.734285,24.571428,172.930008,24.704287,78761900
2009-09-09,24.682858,24.924286,24.242857,171.139999,24.448572,202771800
2009-09-10,24.580000,24.750000,24.401428,172.559998,24.651428,122783500
2009-09-11,24.701429,24.740000,24.410000,172.160004,24.594286,87240300
2009-09-14,24.404285,24.842857,24.321428,173.720001,24.817142,80502800
2009-09-15,24.862858,25.092857,24.798571,175.160004,25.022858,106617700
2009-09-16,25.427143,26.107143,25.411428,181.869995,25.981428,188505800
2009-09-17,25.997143,26.684286,25.995714,184.550003,26.364286,202643000
2009-09-18,26.547142,26.650000,26.394285,185.020004,26.431429,150395700
2009-09-21,26.327143,26.451429,25.945715,184.020004,26.288572,109428900
2009-09-22,26.455715,26.482857,26.121429,184.480011,26.354286,89188400
2009-09-23,26.485714,26.985714,26.432858,185.500000,26.500000,148390900
2009-09-24,26.742857,26.814285,26.110001,183.820007,26.260000,137720100
2009-09-25,26.001429,26.500000,25.920000,182.369995,26.052856,111309800
2009-09-28,26.267143,26.668571,26.190001,186.149994,26.592857,84361200
2009-09-29,26.675714,26.771429,26.330000,185.380005,26.482857,86346400
2009-09-30,26.590000,26.635714,26.087143,185.349991,26.478571,134896300
2009-10-01,26.478571,26.602858,25.814285,180.860001,25.837143,131177900
2009-10-02,25.915714,26.562857,25.907143,184.899994,26.414286,138327000
2009-10-05,26.600000,26.694286,26.324286,186.020004,26.574286,105783300
2009-10-06,26.820000,27.144285,26.757143,190.009995,27.144285,151271400
2009-10-07,27.108572,27.221428,27.004286,190.250000,27.178572,116417000
2009-10-08,27.237143,27.350000,26.984285,189.270004,27.038572,109552800
2009-10-09,26.995714,27.242857,26.945715,190.470001,27.209999,73318000
2009-10-12,27.288572,27.358572,27.091429,190.809998,27.258572,72006200
2009-10-13,27.232857,27.309999,27.100000,190.019989,27.145714,87005100
2009-10-14,27.464285,27.474285,27.175714,191.289993,27.327143,93877700
2009-10-15,27.090000,27.274286,27.075714,190.559998,27.222857,93389100
2009-10-16,27.049999,27.194286,26.834286,188.050003,26.864286,107856700
2009-10-19,26.835714,27.142857,26.507143,189.860001,27.122858,235557700
2009-10-20,28.657143,28.821428,28.264286,198.759995,28.394285,285259800
2009-10-21,28.502857,29.815714,28.461428,204.919998,29.274286,298431700
2009-10-22,29.242857,29.692858,28.930000,205.199997,29.314285,197848000
2009-10-23,29.385714,29.400000,29.032858,203.940002,29.134285,105196700
2009-10-26,29.095715,29.535715,28.585714,202.479996,28.925714,121084600
2009-10-27,28.808571,28.972857,28.064285,197.370010,28.195715,189137900
2009-10-28,28.244286,28.288572,27.299999,192.399994,27.485714,204596700
2009-10-29,27.857143,28.115715,27.448572,196.349991,28.049999,142567600
2009-10-30,28.008572,28.114286,26.881428,188.500000,26.928572,179381300
2009-11-02,27.114286,27.554285,26.510000,189.309998,27.044285,169745800
2009-11-03,26.835714,27.074286,26.559999,188.750000,26.964285,130635400
2009-11-04,27.247143,27.692858,27.175714,190.809998,27.258572,121882600
2009-11-05,27.485714,27.857143,27.402857,194.029999,27.718571,96200300
2009-11-06,27.501429,27.884285,27.485714,194.339996,27.762857,73774400
2009-11-09,28.134285,28.842857,28.037144,201.460007,28.780001,132213900
2009-11-10,28.717142,29.282858,28.715714,202.979996,28.997143,100298800
2009-11-11,29.222857,29.285715,28.832857,203.250000,29.035715,110967500
2009-11-12,29.020000,29.267143,28.775715,201.990005,28.855715,90932800
2009-11-13,28.981428,29.261429,28.867144,204.450012,29.207144,85810200
2009-11-16,29.354286,29.714285,29.287144,206.630005,29.518572,121301600
2009-11-17,29.440001,29.634285,29.285715,207.000000,29.571428,99128400
2009-11-18,29.505714,29.571428,29.142857,205.960007,29.422857,93580200
2009-11-19,29.230000,29.230000,28.542856,200.509995,28.644285,135581600
2009-11-20,28.450001,28.627142,28.251429,199.919998,28.559999,101666600
2009-11-23,29.000000,29.428572,28.992857,205.880005,29.411428,118724200
2009-11-24,29.332857,29.411428,28.985714,204.440002,29.205715,79609600
2009-11-25,29.342857,29.378571,29.108572,204.190002,29.170000,71613500
2009-11-27,28.459999,28.994286,28.338572,200.589996,28.655714,73814300
2009-11-30,28.730000,28.811428,28.395714,199.910004,28.558571,106214500
2009-12-01,28.891428,28.967142,28.118572,196.970001,28.138571,116440800
2009-12-02,28.422857,28.774286,27.964285,196.230011,28.032858,178815000
2009-12-03,28.202858,28.425714,28.038572,196.479996,28.068571,112179900
2009-12-04,28.528572,28.554285,27.182858,193.320007,27.617144,206721200
2009-12-07,27.617144,27.681429,26.954287,188.949997,26.992857,178689700
2009-12-08,27.051428,27.478571,26.957144,189.870010,27.124287,172599700
2009-12-09,27.325714,28.308571,27.187143,197.800003,28.257143,171195500
2009-12-10,28.500000,28.528572,28.017143,196.429993,28.061428,122417400
2009-12-11,28.254286,28.285715,27.632856,194.669998,27.809999,107443700
2009-12-14,27.910000,28.204287,27.508572,196.979996,28.139999,123947600
2009-12-15,27.975714,28.215714,27.610001,194.169998,27.738571,104864900
2009-12-16,27.871429,28.071428,27.792856,195.029999,27.861429,88246200
2009-12-17,27.751429,27.857143,27.285715,191.860001,27.408571,97209700
2009-12-18,27.595715,27.928572,27.514286,195.429993,27.918571,152192600
2009-12-21,28.007143,28.535715,27.952858,198.229996,28.318571,152976600
2009-12-22,28.491428,28.692858,28.379999,200.360001,28.622858,87378900
2009-12-23,28.742857,28.911428,28.687143,202.100006,28.871429,86381400
2009-12-24,29.078571,29.907143,29.049999,209.040009,29.862858,125222300
2009-12-28,30.245714,30.564285,29.944286,211.610001,30.230000,161141400
2009-12-29,30.375713,30.388571,29.818571,209.100006,29.871429,111301400
2009-12-30,29.832857,30.285715,29.758572,211.639999,30.234285,103021100
2009-12-31,30.447144,30.478571,30.080000,210.730011,30.104286,88102700
2010-01-04,30.490000,30.642857,30.340000,214.009995,30.572857,123432400
2010-01-05,30.657143,30.798571,30.464285,214.379990,30.625713,150476200
2010-01-06,30.625713,30.747143,30.107143,210.970001,30.138571,138040000
2010-01-07,30.250000,30.285715,29.864286,210.580002,30.082857,119282800
2010-01-08,30.042856,30.285715,29.865715,211.980011,30.282858,111902700
2010-01-11,30.400000,30.428572,29.778572,210.110001,30.015715,115557400
2010-01-12,29.884285,29.967142,29.488571,207.720001,29.674286,148614900
2010-01-13,29.695715,30.132856,29.157143,210.649994,30.092857,151473000
2010-01-14,30.015715,30.065714,29.860001,209.429993,29.918571,108223500
2010-01-15,30.132856,30.228571,29.410000,205.929993,29.418571,148516900
2010-01-19,29.761429,30.741428,29.605715,215.039993,30.719999,182501900
2010-01-20,30.701429,30.792856,29.928572,211.729996,30.247143,153038200
2010-01-21,30.297142,30.472857,29.601429,208.069992,29.724285,152038600
2010-01-22,29.540001,29.642857,28.165714,197.750000,28.250000,220441900
2010-01-25,28.930000,29.242857,28.598572,203.070007,29.010000,266424900
2010-01-26,29.421429,30.530001,28.940001,205.940002,29.420000,466777500
2010-01-27,29.549999,30.082857,28.504286,207.880005,29.697144,430642100
2010-01-28,29.275715,29.357143,28.385714,199.289993,28.469999,293375600
2010-01-29,28.725714,28.885714,27.178572,192.059998,27.437143,311488100
2010-02-01,27.481428,28.000000,27.328571,194.729996,27.818571,187469100
2010-02-02,27.987143,28.045713,27.625713,195.860001,27.980000,174585600
2010-02-03,27.881428,28.600000,27.774286,199.229996,28.461428,153832000
2010-02-04,28.104286,28.338572,27.367144,192.050003,27.435715,189413000
2010-02-05,27.518572,28.000000,27.264286,195.460007,27.922857,212576700
2010-02-08,27.955715,28.268572,27.714285,194.119995,27.731428,119567700
2010-02-09,28.059999,28.214285,27.821428,196.190002,28.027143,158221700
2010-02-10,27.984285,28.085714,27.751429,195.120010,27.874287,92590400
2010-02-11,27.840000,28.535715,27.722857,198.669998,28.381428,137586400
2010-02-12,28.301428,28.805714,27.928572,200.379990,28.625713,163867200
2010-02-16,28.848572,29.098572,28.788572,203.399994,29.057142,135934400
2010-02-17,29.170000,29.187143,28.694286,202.550003,28.935715,109099200
2010-02-18,28.804285,29.127142,28.702858,202.929993,28.990000,105706300
2010-02-19,28.837143,29.028572,28.730000,201.669998,28.809999,103867400
2010-02-22,28.905714,28.928572,28.455715,200.419998,28.631428,97640900
2010-02-23,28.571428,28.761429,27.958570,197.059998,28.151428,143773700
2010-02-24,28.318571,28.777143,28.262857,200.660004,28.665714,115141600
2010-02-25,28.197144,28.980000,28.127142,202.000000,28.857143,166281500
2010-02-26,28.911428,29.309999,28.857143,204.619995,29.231428,126865200
2010-03-01,29.392857,29.928572,29.350000,208.990005,29.855715,137523400
2010-03-02,29.990000,30.118572,29.677143,208.850006,29.835714,141636600
2010-03-03,29.848572,29.981428,29.705715,209.330002,29.904285,93013200
2010-03-04,29.897142,30.131428,29.804285,210.710007,30.101429,91510300
2010-03-05,30.705715,31.385714,30.661428,218.950012,31.278572,224905100
2010-03-08,31.430000,31.441429,31.178572,219.079987,31.297142,107472400
2010-03-09,31.187143,32.142857,31.127142,223.020004,31.860001,230064800
2010-03-10,31.975714,32.211430,31.885714,224.839996,32.119999,149054500
2010-03-11,31.987143,32.214287,31.902857,225.500000,32.214287,101425100
2010-03-12,32.481430,32.532856,32.250000,226.600006,32.371429,104080900
2010-03-15,32.197144,32.214287,31.464285,223.839996,31.977142,123375700
2010-03-16,32.025715,32.139999,31.787144,224.449997,32.064285,111727000
2010-03-17,32.128571,32.349998,31.895714,224.119995,32.017143,112739200
2010-03-18,32.014286,32.142857,31.801428,224.649994,32.092857,85527400
2010-03-19,32.112858,32.177143,31.604286,222.250000,31.750000,139861400
2010-03-22,31.495714,32.285713,31.450001,224.750000,32.107143,114104900
2010-03-23,32.234287,32.682858,32.014286,228.359985,32.622856,150607800
2010-03-24,32.520000,32.885715,32.501427,229.369995,32.767143,149445100
2010-03-25,32.988571,32.995716,32.321430,226.649994,32.378571,135571100
2010-03-26,32.707142,33.135715,32.650002,230.899994,32.985714,160218800
2010-03-29,33.285713,33.410000,33.088570,232.389984,33.198570,135186100
2010-03-30,33.799999,33.925713,33.464287,235.849991,33.692856,131827500
2010-03-31,33.641430,33.801430,33.494286,235.000015,33.571430,107664900
2010-04-01,33.915714,34.104286,33.250000,235.970001,33.709999,150786300
2010-04-05,33.568573,34.072857,33.538570,238.489990,34.070000,171126900
2010-04-06,34.028572,34.320000,33.857143,239.540009,34.220001,111754300
2010-04-07,34.221428,34.560001,34.094284,240.600006,34.371429,157125500
2010-04-08,34.348572,34.505714,34.005714,239.950012,34.278572,143247300
2010-04-09,34.490002,34.555714,34.351429,241.789993,34.541428,83545700
2010-04-12,34.599998,34.724285,34.544285,242.290009,34.612858,83256600
2010-04-13,34.551430,34.685715,34.444286,242.430008,34.632858,76552700
2010-04-14,35.040001,35.115715,34.867142,245.690002,35.098572,101019100
2010-04-15,35.111427,35.575714,35.072857,248.920013,35.560001,94196200
2010-04-16,35.509998,35.877144,34.935715,247.399994,35.342857,187636400
2010-04-19,35.290001,35.412857,34.538570,247.070007,35.295715,141731100
2010-04-20,35.505714,35.607143,34.708572,244.589996,34.941429,184581600
2010-04-21,36.971428,37.178570,36.532856,259.220001,37.031429,245597800
2010-04-22,36.891430,38.107143,36.599998,266.470001,38.067142,198356200
2010-04-23,38.284286,38.882858,38.142857,270.829987,38.689999,199238900
2010-04-26,38.840000,38.922855,38.312859,269.500000,38.500000,119767200
2010-04-27,38.181427,38.262856,37.217144,262.039978,37.434284,177335900
2010-04-28,37.607143,37.714287,36.630001,261.600006,37.371429,189600600
2010-04-29,37.574287,38.571430,37.430000,268.640015,38.377144,139710200
2010-04-30,38.472858,38.652859,37.285713,261.089996,37.298573,135615900
2010-05-03,37.691429,38.268570,37.554287,266.350006,38.049999,113585500
2010-05-04,37.555714,37.612858,36.678570,258.679993,36.954285,180954900
2010-05-05,36.147144,36.877144,35.532856,255.989990,36.570000,220775800
2010-05-06,36.261429,36.892857,28.464285,246.249985,35.178570,321465200
2010-05-07,34.815716,35.224285,32.172855,235.860001,33.694286,419004600
2010-05-10,35.750000,36.378571,35.504284,253.990005,36.284286,246076600
2010-05-11,35.977142,37.127144,35.785713,256.519989,36.645714,212226700
2010-05-12,37.034286,37.590000,36.957142,262.089996,37.441429,163594900
2010-05-13,37.602856,37.857143,36.628571,258.360016,36.908573,149928100
2010-05-14,36.451427,36.639999,35.642857,253.819992,36.259998,189840700
2010-05-17,36.385715,36.597141,35.387142,254.220001,36.317142,190708700
2010-05-18,36.711430,36.935715,35.751427,252.360016,36.051430,195669600
2010-05-19,35.642857,36.131428,34.978573,248.339996,35.477142,256431700
2010-05-20,34.554287,34.835712,33.744286,237.759995,33.965714,320728800
2010-05-21,33.259998,34.928570,33.049999,242.319992,34.617142,305972800
2010-05-24,35.325714,35.842857,35.180000,246.759979,35.251427,188559700
2010-05-25,34.192856,35.251427,33.880001,245.220001,35.031429,262001600
2010-05-26,35.725716,36.018570,34.821430,244.109985,34.872856,212663500
2010-05-27,35.799999,36.270000,35.587143,253.349991,36.192856,166570600
2010-05-28,37.055714,37.057144,36.192856,256.880005,36.697144,203903700
2010-06-01,37.098572,37.991428,36.994286,260.830017,37.261429,219118200
2010-06-02,37.791428,37.828571,37.189999,263.949982,37.707142,172137000
2010-06-03,37.882858,37.935715,37.201427,263.119995,37.588570,162526700
2010-06-04,36.887142,37.414288,36.375713,255.960007,36.565716,189576100
2010-06-07,36.898571,37.021427,35.792858,250.940002,35.848572,221735500
2010-06-08,36.177143,36.257141,35.092857,249.330002,35.618572,250192600
2010-06-09,35.924286,35.985714,34.641430,243.200012,34.742859,213657500
2010-06-10,34.977142,35.854286,34.599998,250.510010,35.787144,194089000
2010-06-11,35.461430,36.265713,35.338570,253.509995,36.215714,136439800
2010-06-14,36.565716,37.021427,36.287144,254.279999,36.325714,150740100
2010-06-15,36.520000,37.121429,36.500000,259.690002,37.098572,146268500
2010-06-16,37.299999,38.250000,37.232857,267.250000,38.178570,195919500
2010-06-17,38.657143,38.985714,38.500000,271.869995,38.838570,218213800
2010-06-18,38.892857,39.285713,38.774284,274.070007,39.152859,196155400
2010-06-21,39.669998,39.858570,38.389999,270.170013,38.595715,194122600
2010-06-22,38.880001,39.424286,38.785713,273.850006,39.121429,179315500
2010-06-23,39.225716,39.237144,38.271427,270.970001,38.709999,192114300
2010-06-24,38.714287,39.028572,38.299999,269.000000,38.428570,178569300
2010-06-25,38.580002,38.610001,37.972858,266.699982,38.099998,137485600
2010-06-28,38.132858,38.535713,37.788570,268.299988,38.328571,146237000
2010-06-29,37.731430,37.770000,36.328571,256.170013,36.595715,283336200
2010-06-30,36.672855,36.852856,35.715714,251.529999,35.932858,184863000
2010-07-01,36.328571,36.400002,34.745716,248.479996,35.497143,255724000
2010-07-02,35.784286,35.847141,34.742859,246.939987,35.277142,173460700
2010-07-06,35.857143,36.114285,35.165714,248.629990,35.518570,153808900
2010-07-07,35.784286,36.967144,35.678570,258.670013,36.952858,163639000
2010-07-08,37.497143,37.557144,36.412857,258.089996,36.869999,184536100
2010-07-09,36.698570,37.128571,36.451427,259.619995,37.088570,108330600
2010-07-12,36.932858,37.407143,36.408573,257.290009,36.755714,140719600
2010-07-13,36.617142,36.628571,35.204285,251.799988,35.971428,297731000
2010-07-14,35.625713,36.542858,35.571430,252.730011,36.104286,203011900
2010-07-15,35.461430,36.709999,35.328571,251.449997,35.921429,206216500
2010-07-16,36.168571,36.424286,35.487144,249.900009,35.700001,259964600
2010-07-19,35.697144,35.697144,34.228573,245.580017,35.082859,256119500
2010-07-20,34.700001,36.128571,34.287144,251.890015,35.984287,268737700
2010-07-21,37.869999,37.878571,36.285713,254.239990,36.320000,296417800
2010-07-22,36.811428,37.142857,36.472858,259.019989,37.002857,161329700
2010-07-23,36.727142,37.197144,36.611427,259.940002,37.134285,133347200
2010-07-26,37.142857,37.157143,36.815716,259.279999,37.040001,105137900
2010-07-27,37.267143,37.828571,37.185715,264.080017,37.725716,146192900
2010-07-28,37.667141,37.998573,37.178570,260.959991,37.279999,129996300
2010-07-29,37.244286,37.521427,36.585712,258.109985,36.872856,160951700
2010-07-30,36.555714,37.099998,36.414288,257.250000,36.750000,112052500
2010-08-02,37.205715,37.512856,37.088570,261.850006,37.407143,107013900
2010-08-03,37.287144,37.608570,37.060001,261.929993,37.418571,104413400
2010-08-04,37.548573,37.754284,37.187141,262.980011,37.568573,105093800
2010-08-05,37.389999,37.597141,37.221428,261.700012,37.385715,72274300
2010-08-06,37.111427,37.355713,36.804287,260.090027,37.155716,111224400
2010-08-09,37.354286,37.450001,37.081429,261.750000,37.392857,75782000
2010-08-10,37.121429,37.207142,36.792858,259.410004,37.058571,112980000
2010-08-11,36.485714,36.527142,35.687141,250.190002,35.741428,155013600
2010-08-12,35.241428,36.157143,35.160000,251.790009,35.970001,133730100
2010-08-13,35.950001,35.982857,35.584286,249.099991,35.585712,88717300
2010-08-16,35.368572,35.715714,35.231430,247.640015,35.377144,79607500
2010-08-17,35.725716,36.375713,35.599998,251.970016,35.995716,105660100
2010-08-18,36.051430,36.381428,35.939999,253.070007,36.152859,84924000
2010-08-19,36.119999,36.211430,35.525715,249.880005,35.697144,106676500
2010-08-20,35.627144,36.274284,35.571430,249.639999,35.662857,96057500
2010-08-23,35.970001,36.000000,35.035713,245.799988,35.114285,103510400
2010-08-24,34.667141,34.714287,34.092857,239.930008,34.275715,150641400
2010-08-25,34.005714,34.855713,33.885715,242.889984,34.698570,149216900
2010-08-26,35.064285,35.107143,34.325714,240.279999,34.325714,116626300
2010-08-27,34.535713,34.658573,33.651428,241.619995,34.517143,137097800
2010-08-30,34.394287,35.107143,34.382858,242.500000,34.642857,95822300
2010-08-31,34.549999,34.937141,34.335712,243.100006,34.728573,105196700
2010-09-01,35.352856,35.922855,35.182858,250.330002,35.761429,174259400
2010-09-02,35.894287,36.024284,35.509998,252.169983,36.024284,103856900
2010-09-03,36.441429,36.968571,36.357143,258.770020,36.967144,130197200
2010-09-07,36.662857,37.075714,36.607143,257.809998,36.830002,85639400
2010-09-08,37.111427,37.770000,37.014286,262.920013,37.560001,131637800
2010-09-09,37.862858,38.074287,37.560001,263.070007,37.581429,109643800
2010-09-10,37.598572,37.785713,37.342857,263.410004,37.630001,96885600
2010-09-13,37.974285,38.325714,37.965714,267.040009,38.148571,97195000
2010-09-14,38.029999,38.452858,37.931427,268.059998,38.294285,102037600
2010-09-15,38.310001,38.625713,38.262856,270.220001,38.602856,107342200
2010-09-16,38.605713,39.524284,38.500000,276.569977,39.509998,163025800
2010-09-17,39.669998,39.708572,39.097141,275.369995,39.338570,158619300
2010-09-20,39.439999,40.540001,39.407143,283.230011,40.461430,164669400
2010-09-21,40.551430,41.049999,40.398571,283.769989,40.538570,167018600
2010-09-22,40.387142,41.139999,40.344284,287.750000,41.107143,146322400
2010-09-23,40.904285,41.822857,40.857143,288.919983,41.274284,196529200
2010-09-24,41.728573,41.932858,41.507141,292.319977,41.759998,162372000
2010-09-27,41.997143,42.104286,41.572857,291.159973,41.594284,120708700
2010-09-28,41.681427,41.681427,39.285713,286.859985,40.980000,258760600
2010-09-29,41.032856,41.401428,40.857143,287.369995,41.052856,117411000
2010-09-30,41.285713,41.428570,40.178570,283.750000,40.535713,168347900
2010-10-01,40.878571,40.939999,40.192856,282.520020,40.360001,112035700
2010-10-04,40.228573,40.414288,39.681427,278.639984,39.805714,108825500
2010-10-05,40.285713,41.349998,40.259998,288.940002,41.277142,125491800
2010-10-06,41.369999,41.712856,40.751427,289.190002,41.312859,167717200
2010-10-07,41.477142,41.497143,40.987144,289.220001,41.317142,102099900
2010-10-08,41.672855,42.071430,41.428570,294.069977,42.009998,164600800
2010-10-11,42.105713,42.462856,42.085712,295.360016,42.194286,106938300
2010-10-12,42.201427,42.785713,41.784286,298.540009,42.648571,139636000
2010-10-13,42.885715,43.137142,42.828571,300.140015,42.877144,157523100
2010-10-14,43.098572,43.209999,42.914288,302.309998,43.187141,108824100
2010-10-15,43.919998,45.000000,43.558571,314.739990,44.962856,230548500
2010-10-18,45.495716,45.571430,44.898571,318.000000,45.428570,273252700
2010-10-19,43.342857,44.824287,42.860001,309.489990,44.212856,308196000
2010-10-20,44.142857,44.892857,43.838570,310.529999,44.361427,180406100
2010-10-21,44.622856,44.962856,43.828571,309.520020,44.217144,137865000
2010-10-22,44.152859,44.291428,43.757141,307.470001,43.924286,93194500
2010-10-25,44.155716,44.514286,44.062859,308.839996,44.119999,98115500
2010-10-26,43.838570,44.248573,43.664288,308.049988,44.007141,98232400
2010-10-27,43.950001,44.271427,43.657143,307.830017,43.975716,99750700
2010-10-28,43.992859,44.000000,42.985714,305.239990,43.605713,137762800
2010-10-29,43.461430,43.697144,42.981430,300.980011,42.997143,107627800
2010-11-01,43.174286,43.657143,43.171429,304.179993,43.454285,105972300
2010-11-02,43.857143,44.312859,43.857143,309.360016,44.194286,108482500
2010-11-03,44.481430,44.697144,44.075714,312.799988,44.685715,127087100
2010-11-04,45.064285,45.740002,45.004284,318.270020,45.467144,160622000
2010-11-05,45.427143,45.652859,45.250000,317.130005,45.304287,90313300
2010-11-08,45.314285,45.681427,45.251427,318.619995,45.517143,70439600
2010-11-09,45.864285,45.900002,44.928570,316.079987,45.154285,95886000
2010-11-10,45.234287,45.538570,44.792858,318.029999,45.432858,96056800
2010-11-11,45.000000,45.485714,44.892857,316.649994,45.235714,90321000
2010-11-12,45.142857,45.214287,43.375713,308.029999,44.004284,198961700
2010-11-15,44.065716,44.362858,43.752857,307.040009,43.862858,100901500
2010-11-16,43.674286,43.942856,42.759998,301.589996,43.084286,164412500
2010-11-17,43.028572,43.427143,42.537144,300.500000,42.928570,119862400
2010-11-18,43.599998,44.238571,43.527142,308.429993,44.061428,123622800
2010-11-19,43.995716,44.057144,43.605713,306.730011,43.818573,96210800

First, lets use Altair to graph the closing price of the stock over 1000 days.

Once you have your initial graph lets look at how much the stock changes from day to day. To do this we will make a new list of numbers where we take the price from day N and subtract the price from day N-1. Next we’ll use Altair to graph these changes to see if we can detect any pattern in how the stock changes from day to day. In fact it should look quite random.

Now that we have the deltas and have confirmed a random behavior from day to day let’s make a histogram to see the distribution of the daily changes. Hey its bell shaped!

Now we will compute some statistics – the mean change from day to day as well as the standard deviation of the changes. We want to know the standard deviation because we will use that to determine how much our stock might go up or down on any given day. You should get a mean of about 0.03 and a standard deviation of 0.548

Let’s Predict

Armed with the information from above we can make predictions for the next 250 days. We have the real data for the next 250 days below so we can see how accurate we are. To do this we’ll use the random.gauss function from the random module. This function returns a random number where the numbers are distributed according to a bell shaped curve, that is most of the numbers will be close the mean and some will be closer to the boundaries defined by our standard deviation. The gauss function takes two parameters: the mean si first and the standard deviation is next.

To predict the next 250 days we’ll take the closing price of our last day as the starting point and then add whatever value we get from our call to random.gauss(mean,std) This gives us a prediction for the next day. To predict the day after we use the first predicted value as our starting point and then add a random amount to that. We can repeat this 250 times to get our final prediction.

When professional money managers do this they will run the calculation a few hundred thousand times or even a million times and they will keep track of the worst case – that is the lowest closing price at the end of the 250 day period, the best case – the highest closing price at the end of the 250 day period, and the median case. That is the closing price that falls in the middle of all the possible closing prices.

You probably don’t want to run this a million times in your browser but let us give it a try for 10,000 times. What is your worst case, best case and average price for the final price.

Once you have those values you can use the real numbers below and compare your prediction to see how well you did. You can also join forces with the rest of your class to see if you did even better as a group.

Data file: AAPL_test.csv
Date,Open,High,Low,Close,Adj Close,Volume
2010-11-22,43.811428,44.765713,43.695713,313.359985,44.765713,98268800
2010-11-23,44.349998,44.535713,43.794285,308.730011,44.104286,129861900
2010-11-24,44.571430,45.057144,44.535713,314.799988,44.971428,103431300
2010-11-26,44.820000,45.385715,44.705715,315.000000,45.000000,59396400
2010-11-29,45.071430,45.354286,44.482857,316.869995,45.267143,111446300
2010-11-30,44.791428,44.908573,44.410000,311.149994,44.450001,125464500
2010-12-01,45.038570,45.392857,45.000000,316.399994,45.200001,115437700
2010-12-02,45.361427,45.571430,44.984287,318.149994,45.450001,115709300
2010-12-03,45.287144,45.521427,45.191429,317.440002,45.348572,85523200
2010-12-06,45.520000,46.047142,45.488571,320.149994,45.735714,112120400
2010-12-07,46.257141,46.284286,45.445713,318.210022,45.458572,97863500
2010-12-08,45.661430,45.860001,45.301430,321.009979,45.858570,80483900
2010-12-09,46.018570,46.071430,45.574287,319.760010,45.680000,73537800
2010-12-10,45.664288,45.864285,45.514286,320.559998,45.794285,65627800
2010-12-13,46.338570,46.437141,45.857143,321.670013,45.952858,109953900
2010-12-14,45.961430,46.077145,45.571430,320.290009,45.755714,87752000
2010-12-15,45.714287,46.142857,45.598572,320.359985,45.765713,104328000
2010-12-16,45.869999,46.087143,45.728573,321.250000,45.892857,80507700
2010-12-17,45.947144,45.970001,45.747143,320.610016,45.801430,96732300
2010-12-20,45.942856,46.178570,45.461430,322.209991,46.029999,96402600
2010-12-21,46.142857,46.341427,46.007141,324.200012,46.314285,64088500
2010-12-22,46.337143,46.531429,46.221428,325.160004,46.451427,66480400
2010-12-23,46.428570,46.450001,46.167141,323.600006,46.228573,55789300
2010-12-27,46.121429,46.491428,45.931427,324.679993,46.382858,62454000
2010-12-28,46.558571,46.665714,46.437141,325.470001,46.495716,43981000
2010-12-29,46.602856,46.635715,46.442856,325.290009,46.470001,40784800
2010-12-30,46.497143,46.501427,46.150002,323.660004,46.237144,39373600
2010-12-31,46.135715,46.211430,45.901428,322.559998,46.080002,48377000
2011-01-03,46.520000,47.180000,46.405716,329.570007,47.081429,111284600
2011-01-04,47.491428,47.500000,46.878571,331.290009,47.327145,77270200
2011-01-05,47.078571,47.762856,47.071430,334.000000,47.714287,63879900
2011-01-06,47.817142,47.892857,47.557144,333.729980,47.675713,75107200
2011-01-07,47.712856,48.049999,47.414288,336.119995,48.017143,77982800
2011-01-10,48.404285,49.032856,48.167141,342.450012,48.921429,112140000
2011-01-11,49.268570,49.279999,48.495716,341.639984,48.805714,111027000
2011-01-12,49.035713,49.204285,48.857143,344.420013,49.202858,75647600
2011-01-13,49.308571,49.520000,49.121429,345.679993,49.382858,74195100
2011-01-14,49.412857,49.782856,49.205715,348.479980,49.782856,77210000
2011-01-18,47.074287,49.251427,46.571430,340.650024,48.664288,470249500
2011-01-19,49.764286,49.799999,48.125713,338.840027,48.405716,283903200
2011-01-20,48.061428,48.328571,47.160000,332.679993,47.525715,191197300
2011-01-21,47.681427,47.840000,46.661430,326.720001,46.674286,188600300
2011-01-24,46.695713,48.207142,46.674286,337.449982,48.207142,143670800
2011-01-25,48.047142,48.777142,47.795715,341.399994,48.771427,136717000
2011-01-26,48.994286,49.371429,48.785713,343.850006,49.121429,126718900
2011-01-27,49.111427,49.241428,48.975716,343.209991,49.029999,71256500
2011-01-28,49.167141,49.200001,47.647144,336.100006,48.014286,148014300
2011-01-31,47.971428,48.577145,47.757141,339.320007,48.474285,94311700
2011-02-01,48.757141,49.378571,48.711430,345.029999,49.290001,106658300
2011-02-02,49.207142,49.321430,49.078571,344.320007,49.188572,64738800
2011-02-03,49.114285,49.177143,48.364285,343.440002,49.062859,98449400
2011-02-04,49.091427,49.528572,49.072857,346.500000,49.500000,80460100
2011-02-07,49.698570,50.464287,49.662857,351.880005,50.268570,121255400
2011-02-08,50.525715,50.788570,50.307144,355.200012,50.742859,95260200
2011-02-09,50.741428,51.285713,50.695713,358.160004,51.165714,120686300
2011-02-10,51.055714,51.428570,49.714287,354.540009,50.648571,232137500
2011-02-11,50.678570,51.114285,50.505714,356.850006,50.978573,91893200
2011-02-14,50.970001,51.354286,50.958572,359.179993,51.311428,77604100
2011-02-15,51.312859,51.424286,51.078571,359.900024,51.414288,71043700
2011-02-16,51.542858,52.128571,51.500000,363.130005,51.875713,120289400
2011-02-17,51.035713,51.467144,50.931427,358.299988,51.185715,132645800
2011-02-18,51.244286,51.357143,49.931427,350.559998,50.080002,204014300
2011-02-22,48.878571,49.342857,48.245716,338.609985,48.372856,218138900
2011-02-23,48.395714,49.234287,48.372856,342.619995,48.945713,167963600
2011-02-24,49.145714,49.307144,48.338570,342.880005,48.982857,124975200
2011-02-25,49.322857,49.775715,49.257141,348.160004,49.737144,95004700
2011-02-28,50.177143,50.721428,50.160000,353.210022,50.458572,100768500
2011-03-01,50.781429,50.817142,49.668571,349.309998,49.901428,114034200
2011-03-02,49.994286,50.621429,49.771427,352.119995,50.302856,150647700
2011-03-03,51.027142,51.398571,50.845715,359.559998,51.365715,125197100
2011-03-04,51.438572,51.470001,51.107143,360.000000,51.428570,113316700
2011-03-07,51.628571,51.667141,50.187141,355.359985,50.765713,136530800
2011-03-08,50.701427,51.057144,50.321430,355.760010,50.822857,89079200
2011-03-09,50.669998,50.680000,50.085712,352.470001,50.352856,113326500
2011-03-10,49.874287,49.967144,49.271427,346.669983,49.524284,126884800
2011-03-11,49.332859,50.331429,49.285713,351.989990,50.284286,117770100
2011-03-14,50.454285,50.925713,50.187141,353.559998,50.508572,108989300
2011-03-15,48.871429,49.691429,48.585712,345.429993,49.347141,180270300
2011-03-16,48.857143,49.000000,46.608570,330.010010,47.144287,290502800
2011-03-17,48.118572,48.515713,47.237144,334.639984,47.805714,164855600
2011-03-18,48.161430,48.314285,47.142857,330.669983,47.238571,188303500
2011-03-21,47.998573,48.534286,47.894287,339.299988,48.471428,102350500
2011-03-22,48.937141,48.945713,48.448570,341.200012,48.742859,81480700
2011-03-23,48.468571,48.602856,47.992859,339.190002,48.455715,93249100
2011-03-24,48.835712,49.428570,48.408573,344.970001,49.281429,101178000
2011-03-25,49.724285,50.294285,49.574287,351.540009,50.220001,112227500
2011-03-28,50.450001,50.617142,50.062859,350.440002,50.062859,77338800
2011-03-29,49.665714,50.137142,49.437141,350.959991,50.137142,88225200
2011-03-30,50.091427,50.125713,49.634285,348.630005,49.804287,82351500
2011-03-31,49.480000,49.971428,49.437141,348.510010,49.787144,68504800
2011-04-01,50.158573,50.227142,49.042858,344.559998,49.222858,104665400
2011-04-04,49.187141,49.228573,48.342857,341.190002,48.741428,115021200
2011-04-05,48.141430,48.892857,48.000000,338.890015,48.412857,120682800
2011-04-06,48.745716,49.128571,48.162857,338.039978,48.291428,100634800
2011-04-07,48.299999,48.632858,48.004284,338.079987,48.297142,93361800
2011-04-08,48.560001,48.592857,47.707142,335.059998,47.865715,94383800
2011-04-11,47.722858,47.952858,47.145714,330.799988,47.257141,99736700
2011-04-12,47.212856,47.675713,47.171429,332.399994,47.485714,106409800
2011-04-13,47.860001,48.020000,47.502857,336.130005,48.018570,86555000
2011-04-14,47.828571,48.000000,47.437141,332.419983,47.488571,75450200
2011-04-15,47.614285,47.662857,46.685715,327.459991,46.779999,113401400
2011-04-18,46.585712,47.461430,45.737144,331.850006,47.407143,152474700
2011-04-19,47.585712,48.282856,47.387142,337.859985,48.265713,104844600
2011-04-20,49.072857,49.392857,48.785713,342.410004,48.915714,175166600
2011-04-21,50.714287,50.732857,49.788570,350.699982,50.099998,188452600
2011-04-25,50.048573,50.535713,50.042858,353.010010,50.430000,66636500
2011-04-26,50.517143,50.712856,49.907143,350.420013,50.060001,84700000
2011-04-27,50.320000,50.335712,49.585712,350.149994,50.021427,89053300
2011-04-28,49.455715,49.964287,49.360001,346.750000,49.535713,90239800
2011-04-29,49.540001,50.564285,49.524284,350.130005,50.018570,251586300
2011-05-02,49.962856,50.067142,49.357143,346.279999,49.468571,110678400
2011-05-03,49.712856,49.984287,49.374287,348.200012,49.742859,78337000
2011-05-04,49.751427,50.261429,49.554287,349.570007,49.938572,97312600
2011-05-05,49.771427,50.135715,49.435715,346.750000,49.535713,83992300
2011-05-06,49.955715,50.000000,49.458572,346.660004,49.522858,70033600
2011-05-09,49.694286,49.885715,49.504284,347.600006,49.657143,51186800
2011-05-10,49.841427,49.955715,49.522858,349.450012,49.921429,70522900
2011-05-11,49.860001,50.000000,49.320000,347.230011,49.604286,84000000
2011-05-12,49.445713,49.588570,48.895714,346.569977,49.509998,80500000
2011-05-13,49.380001,49.464287,48.621429,340.500000,48.642857,81529000
2011-05-16,48.457142,48.745716,47.514286,333.299988,47.614285,112443800
2011-05-17,47.428570,48.020000,47.247143,336.140015,48.020000,113083600
2011-05-18,48.067142,48.721428,48.000000,339.869995,48.552856,83694100
2011-05-19,48.868572,48.915714,48.381428,340.529999,48.647144,65292500
2011-05-20,48.508572,48.707142,47.860001,335.220001,47.888573,84492100
2011-05-23,47.138573,47.997143,47.060001,334.399994,47.771427,95900000
2011-05-24,47.928570,47.985714,47.334286,332.190002,47.455715,80481800
2011-05-25,47.632858,48.365715,47.549999,336.779999,48.111427,73556000
2011-05-26,47.995716,48.127144,47.775715,335.000000,47.857143,55640200
2011-05-27,47.828571,48.232857,47.758572,337.410004,48.201427,50899800
2011-05-31,48.728573,49.689999,48.714287,347.829987,49.689999,104438600
2011-06-01,49.838570,50.304287,49.235714,345.509979,49.358570,138670700
2011-06-02,49.500000,49.711430,49.185715,346.099976,49.442856,84695800
2011-06-03,49.025715,49.332859,48.858570,343.440002,49.062859,78312500
2011-06-06,49.385715,49.578571,48.258572,338.039978,48.291428,115485300
2011-06-07,48.310001,48.317142,47.414288,332.039978,47.434284,132446300
2011-06-08,47.397144,47.828571,47.235714,332.239990,47.462856,83430900
2011-06-09,47.607143,47.667141,47.250000,331.489990,47.355713,68772200
2011-06-10,47.221428,47.380001,46.501427,325.900024,46.557144,108488800
2011-06-13,46.742859,46.901428,46.438572,326.600006,46.657143,82368300
2011-06-14,47.142857,47.607143,47.044285,332.440002,47.491428,83642300
2011-06-15,47.107143,47.185715,46.411430,326.750000,46.678570,99799000
2011-06-16,46.700001,46.954285,45.475716,325.160004,46.451427,127647800
2011-06-17,46.998573,47.035713,45.622856,320.259979,45.751427,153755000
2011-06-20,45.337143,45.385715,44.357143,315.320007,45.045715,160161400
2011-06-21,45.240002,46.542858,45.028572,325.299988,46.471428,123345600
2011-06-22,46.451427,46.985714,46.054287,322.609985,46.087143,97645800
2011-06-23,45.562859,47.384285,45.445713,331.230011,47.318573,139939800
2011-06-24,47.338570,47.592857,46.441429,326.350006,46.621429,109951800
2011-06-27,46.798573,47.700001,46.750000,332.039978,47.434284,84953400
2011-06-28,47.664288,48.099998,47.634285,335.260010,47.894287,73574900
2011-06-29,48.005714,48.052856,47.411430,334.040009,47.720001,88136300
2011-06-30,47.814285,48.018570,47.548573,335.670013,47.952858,80738700
2011-07-01,47.992859,49.071430,47.742859,343.260010,49.037144,108828300
2011-07-05,49.000000,49.975716,48.928570,349.429993,49.918571,88763500
2011-07-06,49.849998,50.585712,49.529999,351.759979,50.251427,111156500
2011-07-07,50.667141,51.142857,50.571430,357.200012,51.028572,99915900
2011-07-08,50.477142,51.428570,50.314285,359.709991,51.387142,122408300
2011-07-11,50.905716,51.395714,50.402859,354.000000,50.571430,110668600
2011-07-12,50.504284,51.097141,49.802856,353.750000,50.535713,112902300
2011-07-13,51.189999,51.428570,50.911430,358.019989,51.145714,97909700
2011-07-14,51.572857,51.658573,50.905716,357.770020,51.110001,107633400
2011-07-15,51.595715,52.142857,51.310001,364.919983,52.131428,121116800
2011-07-18,52.204285,53.521427,52.182858,373.800018,53.400002,143163300
2011-07-19,54.000000,54.092857,53.331429,376.849976,53.835712,204786400
2011-07-20,56.588570,56.610001,55.142857,386.899994,55.271427,235335100
2011-07-21,55.278572,55.722858,54.842857,387.290009,55.327145,131633600
2011-07-22,55.474285,56.435715,55.392857,393.299988,56.185715,129182200
2011-07-25,55.764286,57.142857,55.660000,398.500000,56.928570,147451500
2011-07-26,57.142857,57.785713,57.097141,403.410004,57.630001,119145600
2011-07-27,57.227142,57.520000,56.021427,392.589996,56.084286,164831100
2011-07-28,55.945713,56.712856,55.447144,391.820007,55.974285,148508500
2011-07-29,55.377144,56.450001,54.857143,390.479980,55.782856,158146100
2011-08-01,56.825714,57.071430,56.052856,396.750000,56.678570,153209000
2011-08-02,56.807144,56.842857,55.478573,388.910004,55.558571,159884900
2011-08-03,55.854286,56.221428,54.605713,392.570007,56.081429,183127000
2011-08-04,55.630001,55.902859,53.907143,377.369995,53.910000,217851900
2011-08-05,54.348572,54.785713,51.795715,373.619995,53.374287,301147700
2011-08-08,51.669998,52.538570,50.431427,353.210022,50.458572,285958400
2011-08-09,51.614285,53.515713,50.714287,374.010010,53.430000,270645900
2011-08-10,53.021427,53.521427,51.785713,363.690002,51.955715,219664200
2011-08-11,52.931427,53.635715,52.102856,373.700012,53.385715,185492300
2011-08-12,54.009998,54.234287,53.461430,376.989990,53.855713,132244000
2011-08-15,54.232857,54.995716,54.012856,383.410004,54.772858,115136000
2011-08-16,54.502857,54.767143,53.722858,380.480011,54.354286,124687500
2011-08-17,54.615715,54.931427,54.000000,380.440002,54.348572,110515300
2011-08-18,52.977142,53.235714,51.624287,366.050018,52.292858,212858800
2011-08-19,51.738571,52.428570,50.857143,356.029999,50.861427,193972100
2011-08-22,52.072857,52.125713,50.727142,356.440002,50.919998,133828800
2011-08-23,51.471428,53.377144,51.000000,373.600006,53.371429,164208800
2011-08-24,53.352856,54.137142,52.942856,376.180023,53.740002,156566900
2011-08-25,52.154285,53.635715,52.142857,373.720001,53.388573,217836500
2011-08-26,53.024284,54.828571,52.971428,383.579987,54.797142,160369300
2011-08-29,55.454285,55.928570,55.428570,389.970001,55.709999,101317300
2011-08-30,55.464287,55.977142,55.172855,389.989990,55.712856,104480600
2011-08-31,55.795715,56.011429,54.551430,384.830017,54.975716,130646600
2011-09-01,55.117142,55.334286,54.388573,381.029999,54.432858,85931300
2011-09-02,53.534286,54.000000,53.118572,374.049988,53.435715,109734800
2011-09-06,52.481430,54.332859,52.354286,379.740021,54.248573,127424500
2011-09-07,55.080002,55.085712,54.571430,383.929993,54.847141,87644200
2011-09-08,54.628571,55.515713,54.615715,384.140015,54.877144,104039600
2011-09-09,54.847141,55.142857,53.574287,377.479980,53.925713,141203300
2011-09-12,53.285713,54.411430,53.128571,379.940002,54.277142,116958100
2011-09-13,54.591427,55.172855,54.321430,384.619995,54.945713,110140100
2011-09-14,55.288570,56.029999,55.108570,389.299988,55.614285,133681100
2011-09-15,55.918571,56.237144,55.700001,392.959991,56.137142,104454700
2011-09-16,56.505714,57.214287,56.432858,400.500000,57.214287,174628300
2011-09-19,56.714287,59.032856,56.457142,411.630005,58.804287,205965200
2011-09-20,59.321430,60.408573,58.741428,413.450012,59.064285,193938500
2011-09-21,59.948570,60.227142,58.857143,412.140015,58.877144,151494000
2011-09-22,57.290001,58.545715,56.671429,401.820007,57.402859,242120200
2011-09-23,57.182858,58.105713,57.121429,404.299988,57.757141,136569300
2011-09-26,57.122856,57.711430,55.900002,403.170013,57.595715,203219100
2011-09-27,58.389999,58.464287,56.865715,399.260010,57.037144,158124400
2011-09-28,57.169998,57.677143,56.644287,397.010010,56.715714,107409400
2011-09-29,57.417141,57.458572,55.172855,390.570007,55.795715,162771700
2011-09-30,55.302856,55.555714,54.454285,381.320007,54.474285,136910200
2011-10-03,54.338570,54.662857,53.310001,374.600006,53.514286,167274800
2011-10-04,53.509998,54.542858,50.605713,372.500000,53.214287,308419300
2011-10-05,52.551430,54.259998,51.471428,378.250000,54.035713,196617400
2011-10-06,53.332859,54.968571,53.114285,377.369995,53.910000,203145600
2011-10-07,53.682858,53.962856,52.641430,369.799988,52.828571,133864500
2011-10-10,54.155716,55.544285,54.029999,388.809998,55.544285,110628700
2011-10-11,56.081429,57.597141,55.928570,400.289978,57.184284,151421900
2011-10-12,58.191429,58.464287,57.162857,402.190002,57.455715,155571500
2011-10-13,57.854286,58.347141,57.549999,408.429993,58.347141,106546300
2011-10-14,59.547142,60.285713,59.324287,422.000000,60.285713,143341800
2011-10-17,60.248573,60.957142,59.419998,419.990021,59.998573,171511200
2011-10-18,60.251427,60.687141,59.427143,422.239990,60.320000,220400600
2011-10-19,57.335712,58.345715,56.828571,398.619995,56.945713,276014900
2011-10-20,57.142857,57.192856,56.315716,395.309998,56.472858,137317600
2011-10-21,56.871429,57.020000,55.821430,392.869995,56.124287,155311100
2011-10-24,56.597141,58.071430,56.485714,405.770020,57.967144,125534500
2011-10-25,57.861427,58.078571,56.768570,397.770020,56.824287,107606800
2011-10-26,57.394287,57.507141,56.164288,400.600006,57.228573,114076200
2011-10-27,58.222858,58.428570,57.412857,404.690002,57.812859,123666200
2011-10-28,57.571430,58.049999,57.501427,404.949982,57.849998,80710700
2011-10-31,57.488571,58.475716,57.292858,404.779999,57.825714,96375300
2011-11-01,56.772858,57.071430,56.174286,396.510010,56.644287,132947500
2011-11-02,57.155716,57.205715,56.444286,397.410004,56.772858,81837700
2011-11-03,57.009998,57.628571,56.480000,403.070007,57.581429,110346600
2011-11-04,57.432858,57.634285,57.022858,400.239990,57.177143,75557300
2011-11-07,57.130001,57.142857,56.590000,399.730011,57.104286,67568900
2011-11-08,57.458572,58.285713,57.365715,406.229980,58.032856,100110500
2011-11-09,56.709999,57.270000,56.318573,395.279999,56.468571,139671000
2011-11-10,56.718571,56.744286,54.592857,385.220001,55.031429,186188100
2011-11-11,55.230000,55.528572,54.322857,384.619995,54.945713,163446500
2011-11-14,54.788570,55.035713,54.028572,379.260010,54.180000,108226300
2011-11-15,54.400002,55.642857,54.207142,388.829987,55.547142,107702700
2011-11-16,55.607143,55.877144,54.902859,384.770020,54.967144,8730260

10.17.3. Monty Hall Challenge

This is a pretty famous problem that can even get experienced statisticians arguing with each other. It comes from the famous game show of the 70’s called Let’s make a deal. Here’s a video, but please don’t throw away an entire half hour, you can get the gist of it in a few minutes. And then skip ahead to the end to see the “Big Deal of the Day” at around 18:30.

The big deal of the day works like this. There is usually one big prize, and two booby prizes, such as a goat. You can choose to get the whatever is behind door number 1, door number 2, or door number 3. Once you have picked your door then Monty will reveal what is behind one of the other doors. He won’t reveal the grand prize but he might show you the goat. Then Monty will give you the opportunity to switch your door. The question is, should you switch? Do you increase your odds of getting the grand prize by switching doors? Does it stay the same? Or, do your odds of winning go down if you switch? If you have already heard this keep it to yourself and let everyone make their best guess before find out the truth.

The math behind this is pretty complicated, but now that you are an experienced Monte Carlo simulator you can solve this one. With some Python code. Using the random number generator you can put a prize behind a door. Then using the random number generator you can let the ‘contestant’ pick a door. You will then remove a door using the rule that you cannot reveal the grand prize. Then you can simulate what happens if the contestant switches doors or not. You can do this 10,000 times to determine the odds of winning if you switch and the odds of winning of you stick. Since this is meant to be the challenge section I’ll leave it at that and you can start coding.

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