OPTIMAL PORTFOLIOS ON (IN)EFFICIENT MARKETS

Jan Hurt

Charles University of Prague, Czech Republic

This is a presentation version. Final version will be available till the middle of November.

1. Introduction

We study the performance of portfolios of assets from the point of view of an extended efficient market hypothesis. We assume that the investors make their decisions exclusively on the information based on the expected returns and the covariance structure of returns and that this information is available to all investors. Further, we suppose that the investors’ behaviour is rational in the following sense: (i) the investors choose portfolios with the highest expected return among those with the same risk, (ii) the investors choose portfolios with the smallest risk among those with the same expected return (risk aversion). Under these assumptions the whole market should be in an equilibrium.

In practice, even if data come from the set of highly rated companies, they exhibit severe violations from what might be considered as a rational behaviour of the market. In this contribution we analyze the impact of this inconsistency on the optimal portfolio selection and the influence upon the re-balancing portfolio. The data from the Mathematica FinancialData Integrated Data Source were used for numerical illustrations as well for encouragement for this presentation. 

In Section 2 we present some statistical characteristics of Dow Jones Industrial (DJI) and Standard & Poor’s indexes and prices of the companies in DJI. In Section 3 Markowitz type portfolios are constructed. The criterion is to minimize standard error of the portfolio return under the condition of prescribed minimum expected return. Both “short sales allowed” and “short sales not allowed” are considered. The data in this study cover the period January 1, 2009 to October 10, 2011, 700 trading days. Here we deal with daily returns but the methodology can be used for any other periods.

2. Preliminary analysis

Initialization

Since the real download of the data may not be reliable, we use already downloaded data for the convenience of a potential user. Commands for reading data from the Wolfram data-source is given in the Appendix. For life calculations it is therefore necessary to evaluate  cells in the following four subsubsections.

Dow Jones Industrial Members

membersDJI={"AA","AXP","BA","BAC","CAT","CSCO","CVX","DD","DIS","GE","HD","HPQ","IBM","INTC","JNJ","JPM","KFT","KO","MCD","MMM","MRK","MSFT","PFE","PG","T","TRV","UTX","VZ","WMT","XOM"};
Text@Grid[{Prepend[membersDJI,"Company"],Prepend[Range[Length[membersDJI]],"Number"]}//Transpose,Frame->All]

Names of companies in DJI:

DJI Index

indexDJI={{{2009,1,2},9034.69`},{{2009,1,5},8952.89`},{{2009,1,6},9015.1`},{{2009,1,7},8769.7`},{{2009,1,8},8742.46`},{{2009,1,9},8599.18`},{{2009,1,12},8473.97`},{{2009,1,13},8448.56`},{{2009,1,14},8200.14`},{{2009,1,15},8212.49`},{{2009,1,16},8281.22`},{{2009,1,20},7949.09`},{{2009,1,21},8228.1`},{{2009,1,22},8122.8`},{{2009,1,23},8077.56`},{{2009,1,26},8116.03`},{{2009,1,27},8174.73`},{{2009,1,28},8375.45`},{{2009,1,29},8149.01`},{{2009,1,30},8000.86`},{{2009,2,2},7936.83`},{{2009,2,3},8078.36`},{{2009,2,4},7956.66`},{{2009,2,5},8063.07`},{{2009,2,6},8280.59`},{{2009,2,9},8270.87`},{{2009,2,10},7888.88`},{{2009,2,11},7939.53`},{{2009,2,12},7932.76`},{{2009,2,13},7850.41`},{{2009,2,17},7552.6`},{{2009,2,18},7555.63`},{{2009,2,19},7465.95`},{{2009,2,20},7365.67`},{{2009,2,23},7114.78`},{{2009,2,24},7350.94`},{{2009,2,25},7270.89`},{{2009,2,26},7182.08`},{{2009,2,27},7062.93`},{{2009,3,2},6763.29`},{{2009,3,3},6726.02`},{{2009,3,4},6875.84`},{{2009,3,5},6594.44`},{{2009,3,6},6626.94`},{{2009,3,9},6547.05`},{{2009,3,10},6926.49`},{{2009,3,11},6930.4`},{{2009,3,12},7170.06`},{{2009,3,13},7223.98`},{{2009,3,16},7216.97`},{{2009,3,17},7395.7`},{{2009,3,18},7486.58`},{{2009,3,19},7400.8`},{{2009,3,20},7278.38`},{{2009,3,23},7775.86`},{{2009,3,24},7660.21`},{{2009,3,25},7749.81`},{{2009,3,26},7924.56`},{{2009,3,27},7776.18`},{{2009,3,30},7522.02`},{{2009,3,31},7608.92`},{{2009,4,1},7761.6`},{{2009,4,2},7978.08`},{{2009,4,3},8017.59`},{{2009,4,6},7975.85`},{{2009,4,7},7789.56`},{{2009,4,8},7837.11`},{{2009,4,9},8083.38`},{{2009,4,13},8057.81`},{{2009,4,14},7920.18`},{{2009,4,15},8029.62`},{{2009,4,16},8125.43`},{{2009,4,17},8131.33`},{{2009,4,20},7841.73`},{{2009,4,21},7969.56`},{{2009,4,22},7886.57`},{{2009,4,23},7957.06`},{{2009,4,24},8076.29`},{{2009,4,27},8025.`},{{2009,4,28},8016.95`},{{2009,4,29},8185.73`},{{2009,4,30},8168.12`},{{2009,5,1},8212.41`},{{2009,5,4},8426.74`},{{2009,5,5},8410.65`},{{2009,5,6},8512.28`},{{2009,5,7},8409.85`},{{2009,5,8},8574.65`},{{2009,5,11},8418.77`},{{2009,5,12},8469.11`},{{2009,5,13},8284.89`},{{2009,5,14},8331.32`},{{2009,5,15},8268.64`},{{2009,5,18},8504.08`},{{2009,5,19},8474.85`},{{2009,5,20},8422.04`},{{2009,5,21},8292.13`},{{2009,5,22},8277.32`},{{2009,5,26},8473.49`},{{2009,5,27},8300.02`},{{2009,5,28},8403.8`},{{2009,5,29},8500.33`},{{2009,6,1},8721.44`},{{2009,6,2},8740.87`},{{2009,6,3},8675.24`},{{2009,6,4},8750.24`},{{2009,6,5},8763.13`},{{2009,6,8},8764.49`},{{2009,6,9},8763.06`},{{2009,6,10},8739.02`},{{2009,6,11},8770.92`},{{2009,6,12},8799.26`},{{2009,6,15},8612.13`},{{2009,6,16},8504.67`},{{2009,6,17},8497.18`},{{2009,6,18},8555.6`},{{2009,6,19},8539.73`},{{2009,6,22},8339.01`},{{2009,6,23},8322.91`},{{2009,6,24},8299.86`},{{2009,6,25},8472.4`},{{2009,6,26},8438.39`},{{2009,6,29},8529.38`},{{2009,6,30},8447.`},{{2009,7,1},8504.06`},{{2009,7,2},8280.74`},{{2009,7,6},8324.87`},{{2009,7,7},8163.6`},{{2009,7,8},8178.41`},{{2009,7,9},8183.17`},{{2009,7,10},8146.52`},{{2009,7,13},8331.68`},{{2009,7,14},8359.49`},{{2009,7,15},8616.21`},{{2009,7,16},8711.82`},{{2009,7,17},8743.94`},{{2009,7,20},8848.15`},{{2009,7,21},8915.94`},{{2009,7,22},8881.26`},{{2009,7,23},9069.29`},{{2009,7,24},9093.24`},{{2009,7,27},9108.51`},{{2009,7,28},9096.72`},{{2009,7,29},9070.72`},{{2009,7,30},9154.46`},{{2009,7,31},9171.61`},{{2009,8,3},9286.56`},{{2009,8,4},9320.19`},{{2009,8,5},9280.97`},{{2009,8,6},9256.26`},{{2009,8,7},9370.07`},{{2009,8,10},9337.95`},{{2009,8,11},9241.45`},{{2009,8,12},9361.61`},{{2009,8,13},9398.19`},{{2009,8,14},9321.4`},{{2009,8,17},9135.34`},{{2009,8,18},9217.94`},{{2009,8,19},9279.16`},{{2009,8,20},9350.05`},{{2009,8,21},9505.96`},{{2009,8,24},9509.28`},{{2009,8,25},9539.29`},{{2009,8,26},9543.52`},{{2009,8,27},9580.63`},{{2009,8,28},9544.2`},{{2009,8,31},9496.28`},{{2009,9,1},9310.6`},{{2009,9,2},9280.67`},{{2009,9,3},9344.61`},{{2009,9,4},9441.27`},{{2009,9,8},9497.34`},{{2009,9,9},9547.22`},{{2009,9,10},9627.48`},{{2009,9,11},9605.41`},{{2009,9,14},9626.8`},{{2009,9,15},9683.41`},{{2009,9,16},9791.71`},{{2009,9,17},9783.92`},{{2009,9,18},9820.2`},{{2009,9,21},9778.86`},{{2009,9,22},9829.87`},{{2009,9,23},9748.55`},{{2009,9,24},9707.44`},{{2009,9,25},9665.19`},{{2009,9,28},9789.36`},{{2009,9,29},9742.2`},{{2009,9,30},9712.28`},{{2009,10,1},9509.28`},{{2009,10,2},9487.67`},{{2009,10,5},9599.75`},{{2009,10,6},9731.25`},{{2009,10,7},9725.58`},{{2009,10,8},9786.87`},{{2009,10,9},9864.94`},{{2009,10,12},9885.8`},{{2009,10,13},9871.06`},{{2009,10,14},10015.86`},{{2009,10,15},10062.94`},{{2009,10,16},9995.91`},{{2009,10,19},10092.19`},{{2009,10,20},10041.48`},{{2009,10,21},9949.36`},{{2009,10,22},10081.31`},{{2009,10,23},9972.18`},{{2009,10,26},9867.96`},{{2009,10,27},9882.17`},{{2009,10,28},9762.69`},{{2009,10,29},9962.58`},{{2009,10,30},9712.73`},{{2009,11,2},9789.44`},{{2009,11,3},9771.91`},{{2009,11,4},9802.14`},{{2009,11,5},10005.96`},{{2009,11,6},10023.42`},{{2009,11,9},10226.94`},{{2009,11,10},10246.97`},{{2009,11,11},10291.26`},{{2009,11,12},10197.47`},{{2009,11,13},10270.47`},{{2009,11,16},10406.96`},{{2009,11,17},10437.42`},{{2009,11,18},10426.31`},{{2009,11,19},10332.44`},{{2009,11,20},10318.16`},{{2009,11,23},10450.95`},{{2009,11,24},10433.71`},{{2009,11,25},10464.4`},{{2009,11,27},10309.92`},{{2009,11,30},10344.84`},{{2009,12,1},10471.58`},{{2009,12,2},10452.68`},{{2009,12,3},10366.15`},{{2009,12,4},10388.9`},{{2009,12,7},10390.11`},{{2009,12,8},10285.97`},{{2009,12,9},10337.05`},{{2009,12,10},10405.83`},{{2009,12,11},10471.5`},{{2009,12,14},10501.05`},{{2009,12,15},10452.`},{{2009,12,16},10441.12`},{{2009,12,17},10308.26`},{{2009,12,18},10328.89`},{{2009,12,21},10414.14`},{{2009,12,22},10464.93`},{{2009,12,23},10466.44`},{{2009,12,24},10520.1`},{{2009,12,28},10547.08`},{{2009,12,29},10545.41`},{{2009,12,30},10548.51`},{{2009,12,31},10428.05`},{{2010,1,4},10583.96`},{{2010,1,5},10572.02`},{{2010,1,6},10573.68`},{{2010,1,7},10606.86`},{{2010,1,8},10618.19`},{{2010,1,11},10663.99`},{{2010,1,12},10627.26`},{{2010,1,13},10680.77`},{{2010,1,14},10710.55`},{{2010,1,15},10609.65`},{{2010,1,19},10725.43`},{{2010,1,20},10603.15`},{{2010,1,21},10389.88`},{{2010,1,22},10172.98`},{{2010,1,25},10196.86`},{{2010,1,26},10194.29`},{{2010,1,27},10236.16`},{{2010,1,28},10120.46`},{{2010,1,29},10067.33`},{{2010,2,1},10185.53`},{{2010,2,2},10296.85`},{{2010,2,3},10270.55`},{{2010,2,4},10002.18`},{{2010,2,5},10012.23`},{{2010,2,8},9908.39`},{{2010,2,9},10058.64`},{{2010,2,10},10038.38`},{{2010,2,11},10144.19`},{{2010,2,12},10099.14`},{{2010,2,16},10268.81`},{{2010,2,17},10309.24`},{{2010,2,18},10392.9`},{{2010,2,19},10402.35`},{{2010,2,22},10383.38`},{{2010,2,23},10282.41`},{{2010,2,24},10374.16`},{{2010,2,25},10321.03`},{{2010,2,26},10325.26`},{{2010,3,1},10403.79`},{{2010,3,2},10405.98`},{{2010,3,3},10396.76`},{{2010,3,4},10444.14`},{{2010,3,5},10566.2`},{{2010,3,8},10552.52`},{{2010,3,9},10564.38`},{{2010,3,10},10567.33`},{{2010,3,11},10611.84`},{{2010,3,12},10624.69`},{{2010,3,15},10642.15`},{{2010,3,16},10685.98`},{{2010,3,17},10733.67`},{{2010,3,18},10779.17`},{{2010,3,19},10741.98`},{{2010,3,22},10785.89`},{{2010,3,23},10888.83`},{{2010,3,24},10836.15`},{{2010,3,25},10841.21`},{{2010,3,26},10850.36`},{{2010,3,29},10895.86`},{{2010,3,30},10907.42`},{{2010,3,31},10856.63`},{{2010,4,1},10927.07`},{{2010,4,5},10973.55`},{{2010,4,6},10969.99`},{{2010,4,7},10897.52`},{{2010,4,8},10927.07`},{{2010,4,9},10997.35`},{{2010,4,12},11005.97`},{{2010,4,13},11019.42`},{{2010,4,14},11123.11`},{{2010,4,15},11144.57`},{{2010,4,16},11018.66`},{{2010,4,19},11092.05`},{{2010,4,20},11117.06`},{{2010,4,21},11124.92`},{{2010,4,22},11134.29`},{{2010,4,23},11204.28`},{{2010,4,26},11205.03`},{{2010,4,27},10991.99`},{{2010,4,28},11045.27`},{{2010,4,29},11167.32`},{{2010,4,30},11008.61`},{{2010,5,3},11151.83`},{{2010,5,4},10926.77`},{{2010,5,5},10868.12`},{{2010,5,6},10520.32`},{{2010,5,7},10380.43`},{{2010,5,10},10785.14`},{{2010,5,11},10748.26`},{{2010,5,12},10896.91`},{{2010,5,13},10782.95`},{{2010,5,14},10620.16`},{{2010,5,17},10625.83`},{{2010,5,18},10510.95`},{{2010,5,19},10444.37`},{{2010,5,20},10068.01`},{{2010,5,21},10193.39`},{{2010,5,24},10066.57`},{{2010,5,25},10043.75`},{{2010,5,26},9974.45`},{{2010,5,27},10258.99`},{{2010,5,28},10136.63`},{{2010,6,1},10024.02`},{{2010,6,2},10249.54`},{{2010,6,3},10255.28`},{{2010,6,4},9931.97`},{{2010,6,7},9816.49`},{{2010,6,8},9939.98`},{{2010,6,9},9899.25`},{{2010,6,10},10172.53`},{{2010,6,11},10211.07`},{{2010,6,14},10190.89`},{{2010,6,15},10404.77`},{{2010,6,16},10409.46`},{{2010,6,17},10434.17`},{{2010,6,18},10450.64`},{{2010,6,21},10442.41`},{{2010,6,22},10293.52`},{{2010,6,23},10298.44`},{{2010,6,24},10152.8`},{{2010,6,25},10143.81`},{{2010,6,28},10138.52`},{{2010,6,29},9870.3`},{{2010,6,30},9774.02`},{{2010,7,1},9732.53`},{{2010,7,2},9686.48`},{{2010,7,6},9743.62`},{{2010,7,7},10018.28`},{{2010,7,8},10138.99`},{{2010,7,9},10198.03`},{{2010,7,12},10216.27`},{{2010,7,13},10363.02`},{{2010,7,14},10366.72`},{{2010,7,15},10359.31`},{{2010,7,16},10097.9`},{{2010,7,19},10154.43`},{{2010,7,20},10229.96`},{{2010,7,21},10120.53`},{{2010,7,22},10322.3`},{{2010,7,23},10424.62`},{{2010,7,26},10525.43`},{{2010,7,27},10537.69`},{{2010,7,28},10497.88`},{{2010,7,29},10467.16`},{{2010,7,30},10465.94`},{{2010,8,2},10674.38`},{{2010,8,3},10636.38`},{{2010,8,4},10680.43`},{{2010,8,5},10674.98`},{{2010,8,6},10653.56`},{{2010,8,9},10698.75`},{{2010,8,10},10644.25`},{{2010,8,11},10378.83`},{{2010,8,12},10319.95`},{{2010,8,13},10303.15`},{{2010,8,16},10302.01`},{{2010,8,17},10405.85`},{{2010,8,18},10415.54`},{{2010,8,19},10271.21`},{{2010,8,20},10213.62`},{{2010,8,23},10174.41`},{{2010,8,24},10040.45`},{{2010,8,25},10060.06`},{{2010,8,26},9985.81`},{{2010,8,27},10150.65`},{{2010,8,30},10009.73`},{{2010,8,31},10014.72`},{{2010,9,1},10269.47`},{{2010,9,2},10320.1`},{{2010,9,3},10447.93`},{{2010,9,7},10340.69`},{{2010,9,8},10387.01`},{{2010,9,9},10415.24`},{{2010,9,10},10462.77`},{{2010,9,13},10544.13`},{{2010,9,14},10526.49`},{{2010,9,15},10572.73`},{{2010,9,16},10594.83`},{{2010,9,17},10607.85`},{{2010,9,20},10753.62`},{{2010,9,21},10761.03`},{{2010,9,22},10739.31`},{{2010,9,23},10662.42`},{{2010,9,24},10860.26`},{{2010,9,27},10812.04`},{{2010,9,28},10858.14`},{{2010,9,29},10835.28`},{{2010,9,30},10788.05`},{{2010,10,1},10829.68`},{{2010,10,4},10751.27`},{{2010,10,5},10944.72`},{{2010,10,6},10967.65`},{{2010,10,7},10948.58`},{{2010,10,8},11006.48`},{{2010,10,11},11010.34`},{{2010,10,12},11020.4`},{{2010,10,13},11096.08`},{{2010,10,14},11096.92`},{{2010,10,15},11062.78`},{{2010,10,18},11143.69`},{{2010,10,19},10978.62`},{{2010,10,20},11107.97`},{{2010,10,21},11146.57`},{{2010,10,22},11132.56`},{{2010,10,25},11164.05`},{{2010,10,26},11169.46`},{{2010,10,27},11126.28`},{{2010,10,28},11113.95`},{{2010,10,29},11118.4`},{{2010,11,1},11124.62`},{{2010,11,2},11188.72`},{{2010,11,3},11215.13`},{{2010,11,4},11434.84`},{{2010,11,5},11444.08`},{{2010,11,8},11406.84`},{{2010,11,9},11346.75`},{{2010,11,10},11357.04`},{{2010,11,11},11283.1`},{{2010,11,12},11192.58`},{{2010,11,15},11201.97`},{{2010,11,16},11023.5`},{{2010,11,17},11007.88`},{{2010,11,18},11181.23`},{{2010,11,19},11203.55`},{{2010,11,22},11178.58`},{{2010,11,23},11036.37`},{{2010,11,24},11187.28`},{{2010,11,26},11092.`},{{2010,11,29},11052.49`},{{2010,11,30},11006.02`},{{2010,12,1},11255.78`},{{2010,12,2},11362.41`},{{2010,12,3},11382.09`},{{2010,12,6},11362.19`},{{2010,12,7},11359.16`},{{2010,12,8},11372.48`},{{2010,12,9},11370.06`},{{2010,12,10},11410.32`},{{2010,12,13},11428.56`},{{2010,12,14},11476.54`},{{2010,12,15},11457.47`},{{2010,12,16},11499.25`},{{2010,12,17},11491.91`},{{2010,12,20},11478.13`},{{2010,12,21},11533.16`},{{2010,12,22},11559.49`},{{2010,12,23},11573.49`},{{2010,12,27},11555.03`},{{2010,12,28},11575.54`},{{2010,12,29},11585.38`},{{2010,12,30},11569.71`},{{2010,12,31},11577.51`},{{2011,1,3},11670.75`},{{2011,1,4},11691.18`},{{2011,1,5},11722.89`},{{2011,1,6},11697.31`},{{2011,1,7},11674.76`},{{2011,1,10},11637.45`},{{2011,1,11},11671.88`},{{2011,1,12},11755.44`},{{2011,1,13},11731.9`},{{2011,1,14},11787.38`},{{2011,1,18},11837.93`},{{2011,1,19},11825.29`},{{2011,1,20},11822.8`},{{2011,1,21},11871.84`},{{2011,1,24},11980.52`},{{2011,1,25},11977.19`},{{2011,1,26},11985.44`},{{2011,1,27},11989.83`},{{2011,1,28},11823.7`},{{2011,1,31},11891.93`},{{2011,2,1},12040.16`},{{2011,2,2},12041.97`},{{2011,2,3},12062.26`},{{2011,2,4},12092.15`},{{2011,2,7},12161.63`},{{2011,2,8},12233.15`},{{2011,2,9},12239.89`},{{2011,2,10},12229.29`},{{2011,2,11},12273.26`},{{2011,2,14},12268.19`},{{2011,2,15},12226.64`},{{2011,2,16},12288.17`},{{2011,2,17},12318.14`},{{2011,2,18},12391.25`},{{2011,2,22},12212.79`},{{2011,2,23},12105.78`},{{2011,2,24},12068.5`},{{2011,2,25},12130.45`},{{2011,2,28},12226.34`},{{2011,3,1},12058.02`},{{2011,3,2},12066.8`},{{2011,3,3},12258.2`},{{2011,3,4},12169.88`},{{2011,3,7},12090.03`},{{2011,3,8},12214.38`},{{2011,3,9},12213.09`},{{2011,3,10},11984.61`},{{2011,3,11},12044.4`},{{2011,3,14},11993.16`},{{2011,3,15},11855.42`},{{2011,3,16},11613.3`},{{2011,3,17},11774.59`},{{2011,3,18},11858.52`},{{2011,3,21},12036.53`},{{2011,3,22},12018.63`},{{2011,3,23},12086.02`},{{2011,3,24},12170.56`},{{2011,3,25},12220.59`},{{2011,3,28},12197.88`},{{2011,3,29},12279.01`},{{2011,3,30},12350.61`},{{2011,3,31},12319.73`},{{2011,4,1},12376.72`},{{2011,4,4},12400.03`},{{2011,4,5},12393.9`},{{2011,4,6},12426.75`},{{2011,4,7},12409.49`},{{2011,4,8},12380.05`},{{2011,4,11},12381.11`},{{2011,4,12},12263.58`},{{2011,4,13},12270.99`},{{2011,4,14},12285.15`},{{2011,4,15},12341.83`},{{2011,4,18},12201.59`},{{2011,4,19},12266.75`},{{2011,4,20},12453.54`},{{2011,4,21},12505.99`},{{2011,4,25},12479.88`},{{2011,4,26},12595.37`},{{2011,4,27},12690.96`},{{2011,4,28},12763.31`},{{2011,4,29},12810.54`},{{2011,5,2},12807.36`},{{2011,5,3},12807.51`},{{2011,5,4},12723.58`},{{2011,5,5},12584.17`},{{2011,5,6},12638.74`},{{2011,5,9},12684.68`},{{2011,5,10},12760.36`},{{2011,5,11},12630.03`},{{2011,5,12},12695.92`},{{2011,5,13},12595.75`},{{2011,5,16},12548.37`},{{2011,5,17},12479.58`},{{2011,5,18},12560.18`},{{2011,5,19},12605.32`},{{2011,5,20},12512.04`},{{2011,5,23},12381.26`},{{2011,5,24},12356.21`},{{2011,5,25},12394.66`},{{2011,5,26},12402.76`},{{2011,5,27},12441.58`},{{2011,5,31},12569.79`},{{2011,6,1},12290.14`},{{2011,6,2},12248.55`},{{2011,6,3},12151.26`},{{2011,6,6},12089.96`},{{2011,6,7},12070.81`},{{2011,6,8},12048.94`},{{2011,6,9},12124.36`},{{2011,6,10},11951.91`},{{2011,6,13},11952.97`},{{2011,6,14},12076.11`},{{2011,6,15},11897.27`},{{2011,6,16},11961.52`},{{2011,6,17},12004.36`},{{2011,6,20},12080.38`},{{2011,6,21},12190.01`},{{2011,6,22},12109.67`},{{2011,6,23},12050.`},{{2011,6,24},11934.58`},{{2011,6,27},12043.56`},{{2011,6,28},12188.69`},{{2011,6,29},12261.42`},{{2011,6,30},12414.34`},{{2011,7,1},12582.77`},{{2011,7,5},12569.87`},{{2011,7,6},12626.02`},{{2011,7,7},12719.49`},{{2011,7,8},12657.2`},{{2011,7,11},12505.76`},{{2011,7,12},12446.88`},{{2011,7,13},12491.61`},{{2011,7,14},12437.12`},{{2011,7,15},12479.73`},{{2011,7,18},12385.16`},{{2011,7,19},12587.42`},{{2011,7,20},12571.91`},{{2011,7,21},12724.41`},{{2011,7,22},12681.16`},{{2011,7,25},12592.8`},{{2011,7,26},12501.3`},{{2011,7,27},12302.55`},{{2011,7,28},12240.11`},{{2011,7,29},12143.24`},{{2011,8,1},12132.49`},{{2011,8,2},11866.62`},{{2011,8,3},11896.44`},{{2011,8,4},11383.68`},{{2011,8,5},11444.61`},{{2011,8,8},10809.85`},{{2011,8,9},11239.77`},{{2011,8,10},10719.94`},{{2011,8,11},11143.31`},{{2011,8,12},11269.02`},{{2011,8,15},11482.9`},{{2011,8,16},11405.93`},{{2011,8,17},11410.21`},{{2011,8,18},10990.58`},{{2011,8,19},10817.65`},{{2011,8,22},10854.65`},{{2011,8,23},11176.76`},{{2011,8,24},11320.71`},{{2011,8,25},11149.82`},{{2011,8,26},11284.54`},{{2011,8,29},11539.25`},{{2011,8,30},11559.95`},{{2011,8,31},11613.53`},{{2011,9,1},11493.57`},{{2011,9,2},11240.26`},{{2011,9,6},11139.3`},{{2011,9,7},11414.86`},{{2011,9,8},11295.81`},{{2011,9,9},10992.13`},{{2011,9,12},11061.12`},{{2011,9,13},11105.85`},{{2011,9,14},11246.73`},{{2011,9,15},11433.18`},{{2011,9,16},11509.09`},{{2011,9,19},11401.01`},{{2011,9,20},11408.66`},{{2011,9,21},11124.84`},{{2011,9,22},10733.83`},{{2011,9,23},10771.48`},{{2011,9,26},11043.86`},{{2011,9,27},11190.69`},{{2011,9,28},11010.9`},{{2011,9,29},11153.98`},{{2011,9,30},10913.38`},{{2011,10,3},10655.3`},{{2011,10,4},10808.71`},{{2011,10,5},10939.95`},{{2011,10,6},11123.33`},{{2011,10,7},11103.12`},{{2011,10,10},11433.18`},{{2011,10,11},11416.3`}};

S&P Index

indexSP500={{{2009,1,2},931.8`},{{2009,1,5},927.45`},{{2009,1,6},934.7`},{{2009,1,7},906.65`},{{2009,1,8},909.73`},{{2009,1,9},890.35`},{{2009,1,12},870.26`},{{2009,1,13},871.79`},{{2009,1,14},842.62`},{{2009,1,15},843.74`},{{2009,1,16},850.12`},{{2009,1,20},805.22`},{{2009,1,21},840.24`},{{2009,1,22},827.5`},{{2009,1,23},831.95`},{{2009,1,26},836.57`},{{2009,1,27},845.71`},{{2009,1,28},874.09`},{{2009,1,29},845.14`},{{2009,1,30},825.88`},{{2009,2,2},825.44`},{{2009,2,3},838.51`},{{2009,2,4},832.23`},{{2009,2,5},845.85`},{{2009,2,6},868.6`},{{2009,2,9},869.89`},{{2009,2,10},827.16`},{{2009,2,11},833.74`},{{2009,2,12},835.19`},{{2009,2,13},826.84`},{{2009,2,17},789.17`},{{2009,2,18},788.42`},{{2009,2,19},778.94`},{{2009,2,20},770.05`},{{2009,2,23},743.33`},{{2009,2,24},773.14`},{{2009,2,25},764.9`},{{2009,2,26},752.83`},{{2009,2,27},735.09`},{{2009,3,2},700.82`},{{2009,3,3},696.33`},{{2009,3,4},712.87`},{{2009,3,5},682.55`},{{2009,3,6},683.38`},{{2009,3,9},676.53`},{{2009,3,10},719.6`},{{2009,3,11},721.36`},{{2009,3,12},750.74`},{{2009,3,13},756.55`},{{2009,3,16},753.89`},{{2009,3,17},778.12`},{{2009,3,18},794.35`},{{2009,3,19},784.04`},{{2009,3,20},768.54`},{{2009,3,23},822.92`},{{2009,3,24},806.12`},{{2009,3,25},813.88`},{{2009,3,26},832.86`},{{2009,3,27},815.94`},{{2009,3,30},787.53`},{{2009,3,31},797.87`},{{2009,4,1},811.08`},{{2009,4,2},834.38`},{{2009,4,3},842.5`},{{2009,4,6},835.48`},{{2009,4,7},815.55`},{{2009,4,8},825.16`},{{2009,4,9},856.56`},{{2009,4,13},858.73`},{{2009,4,14},841.5`},{{2009,4,15},852.06`},{{2009,4,16},865.3`},{{2009,4,17},869.6`},{{2009,4,20},832.39`},{{2009,4,21},850.08`},{{2009,4,22},843.55`},{{2009,4,23},851.92`},{{2009,4,24},866.23`},{{2009,4,27},857.51`},{{2009,4,28},855.16`},{{2009,4,29},873.64`},{{2009,4,30},872.81`},{{2009,5,1},877.52`},{{2009,5,4},907.24`},{{2009,5,5},903.8`},{{2009,5,6},919.53`},{{2009,5,7},907.39`},{{2009,5,8},929.23`},{{2009,5,11},909.24`},{{2009,5,12},908.35`},{{2009,5,13},883.92`},{{2009,5,14},893.07`},{{2009,5,15},882.88`},{{2009,5,18},909.71`},{{2009,5,19},908.13`},{{2009,5,20},903.47`},{{2009,5,21},888.33`},{{2009,5,22},887.`},{{2009,5,26},910.33`},{{2009,5,27},893.06`},{{2009,5,28},906.83`},{{2009,5,29},919.14`},{{2009,6,1},942.87`},{{2009,6,2},944.74`},{{2009,6,3},931.76`},{{2009,6,4},942.46`},{{2009,6,5},940.09`},{{2009,6,8},939.14`},{{2009,6,9},942.43`},{{2009,6,10},939.15`},{{2009,6,11},944.89`},{{2009,6,12},946.21`},{{2009,6,15},923.72`},{{2009,6,16},911.97`},{{2009,6,17},910.71`},{{2009,6,18},918.37`},{{2009,6,19},921.23`},{{2009,6,22},893.04`},{{2009,6,23},895.1`},{{2009,6,24},900.94`},{{2009,6,25},920.26`},{{2009,6,26},918.9`},{{2009,6,29},927.23`},{{2009,6,30},919.32`},{{2009,7,1},923.33`},{{2009,7,2},896.42`},{{2009,7,6},898.72`},{{2009,7,7},881.03`},{{2009,7,8},879.56`},{{2009,7,9},882.68`},{{2009,7,10},879.13`},{{2009,7,13},901.05`},{{2009,7,14},905.84`},{{2009,7,15},932.68`},{{2009,7,16},940.74`},{{2009,7,17},940.38`},{{2009,7,20},951.13`},{{2009,7,21},954.58`},{{2009,7,22},954.07`},{{2009,7,23},976.29`},{{2009,7,24},979.26`},{{2009,7,27},982.18`},{{2009,7,28},979.62`},{{2009,7,29},975.15`},{{2009,7,30},986.75`},{{2009,7,31},987.48`},{{2009,8,3},1002.63`},{{2009,8,4},1005.65`},{{2009,8,5},1002.72`},{{2009,8,6},997.08`},{{2009,8,7},1010.48`},{{2009,8,10},1007.1`},{{2009,8,11},994.35`},{{2009,8,12},1005.81`},{{2009,8,13},1012.73`},{{2009,8,14},1004.09`},{{2009,8,17},979.73`},{{2009,8,18},989.67`},{{2009,8,19},996.46`},{{2009,8,20},1007.37`},{{2009,8,21},1026.13`},{{2009,8,24},1025.57`},{{2009,8,25},1028.`},{{2009,8,26},1028.12`},{{2009,8,27},1030.98`},{{2009,8,28},1028.93`},{{2009,8,31},1020.62`},{{2009,9,1},998.04`},{{2009,9,2},994.75`},{{2009,9,3},1003.24`},{{2009,9,4},1016.4`},{{2009,9,8},1025.39`},{{2009,9,9},1033.37`},{{2009,9,10},1044.14`},{{2009,9,11},1042.73`},{{2009,9,14},1049.34`},{{2009,9,15},1052.63`},{{2009,9,16},1068.76`},{{2009,9,17},1065.49`},{{2009,9,18},1068.3`},{{2009,9,21},1064.66`},{{2009,9,22},1071.66`},{{2009,9,23},1060.87`},{{2009,9,24},1050.78`},{{2009,9,25},1044.38`},{{2009,9,28},1062.98`},{{2009,9,29},1060.61`},{{2009,9,30},1057.08`},{{2009,10,1},1029.85`},{{2009,10,2},1025.21`},{{2009,10,5},1040.46`},{{2009,10,6},1054.72`},{{2009,10,7},1057.58`},{{2009,10,8},1065.48`},{{2009,10,9},1071.49`},{{2009,10,12},1076.19`},{{2009,10,13},1073.19`},{{2009,10,14},1092.02`},{{2009,10,15},1096.56`},{{2009,10,16},1087.68`},{{2009,10,19},1097.91`},{{2009,10,20},1091.06`},{{2009,10,21},1081.4`},{{2009,10,22},1092.91`},{{2009,10,23},1079.6`},{{2009,10,26},1066.95`},{{2009,10,27},1063.41`},{{2009,10,28},1042.63`},{{2009,10,29},1066.11`},{{2009,10,30},1036.19`},{{2009,11,2},1042.88`},{{2009,11,3},1045.41`},{{2009,11,4},1046.5`},{{2009,11,5},1066.63`},{{2009,11,6},1069.3`},{{2009,11,9},1093.08`},{{2009,11,10},1093.01`},{{2009,11,11},1098.51`},{{2009,11,12},1087.24`},{{2009,11,13},1093.48`},{{2009,11,16},1109.3`},{{2009,11,17},1110.32`},{{2009,11,18},1109.8`},{{2009,11,19},1094.9`},{{2009,11,20},1091.38`},{{2009,11,23},1106.24`},{{2009,11,24},1105.65`},{{2009,11,25},1110.63`},{{2009,11,27},1091.49`},{{2009,11,30},1095.63`},{{2009,12,1},1108.86`},{{2009,12,2},1109.24`},{{2009,12,3},1099.92`},{{2009,12,4},1105.98`},{{2009,12,7},1103.25`},{{2009,12,8},1091.94`},{{2009,12,9},1095.95`},{{2009,12,10},1102.35`},{{2009,12,11},1106.41`},{{2009,12,14},1114.11`},{{2009,12,15},1107.93`},{{2009,12,16},1109.18`},{{2009,12,17},1096.08`},{{2009,12,18},1102.47`},{{2009,12,21},1114.05`},{{2009,12,22},1118.02`},{{2009,12,23},1120.59`},{{2009,12,24},1126.48`},{{2009,12,28},1127.78`},{{2009,12,29},1126.2`},{{2009,12,30},1126.42`},{{2009,12,31},1115.1`},{{2010,1,4},1132.99`},{{2010,1,5},1136.52`},{{2010,1,6},1137.14`},{{2010,1,7},1141.69`},{{2010,1,8},1144.98`},{{2010,1,11},1146.98`},{{2010,1,12},1136.22`},{{2010,1,13},1145.68`},{{2010,1,14},1148.46`},{{2010,1,15},1136.03`},{{2010,1,19},1150.23`},{{2010,1,20},1138.04`},{{2010,1,21},1116.48`},{{2010,1,22},1091.76`},{{2010,1,25},1096.78`},{{2010,1,26},1092.17`},{{2010,1,27},1097.5`},{{2010,1,28},1084.53`},{{2010,1,29},1073.87`},{{2010,2,1},1089.19`},{{2010,2,2},1103.32`},{{2010,2,3},1097.28`},{{2010,2,4},1063.11`},{{2010,2,5},1066.19`},{{2010,2,8},1056.74`},{{2010,2,9},1070.52`},{{2010,2,10},1068.13`},{{2010,2,11},1078.47`},{{2010,2,12},1075.51`},{{2010,2,16},1094.87`},{{2010,2,17},1099.51`},{{2010,2,18},1106.75`},{{2010,2,19},1109.17`},{{2010,2,22},1108.01`},{{2010,2,23},1094.6`},{{2010,2,24},1105.24`},{{2010,2,25},1102.94`},{{2010,2,26},1104.49`},{{2010,3,1},1115.71`},{{2010,3,2},1118.31`},{{2010,3,3},1118.79`},{{2010,3,4},1122.97`},{{2010,3,5},1138.7`},{{2010,3,8},1138.5`},{{2010,3,9},1140.45`},{{2010,3,10},1145.61`},{{2010,3,11},1150.24`},{{2010,3,12},1149.99`},{{2010,3,15},1150.51`},{{2010,3,16},1159.46`},{{2010,3,17},1166.21`},{{2010,3,18},1165.83`},{{2010,3,19},1159.9`},{{2010,3,22},1165.81`},{{2010,3,23},1174.17`},{{2010,3,24},1167.72`},{{2010,3,25},1165.73`},{{2010,3,26},1166.59`},{{2010,3,29},1173.22`},{{2010,3,30},1173.27`},{{2010,3,31},1169.43`},{{2010,4,1},1178.1`},{{2010,4,5},1187.44`},{{2010,4,6},1189.44`},{{2010,4,7},1182.45`},{{2010,4,8},1186.44`},{{2010,4,9},1194.37`},{{2010,4,12},1196.48`},{{2010,4,13},1197.3`},{{2010,4,14},1210.65`},{{2010,4,15},1211.67`},{{2010,4,16},1192.13`},{{2010,4,19},1197.52`},{{2010,4,20},1207.17`},{{2010,4,21},1205.94`},{{2010,4,22},1208.67`},{{2010,4,23},1217.28`},{{2010,4,26},1212.05`},{{2010,4,27},1183.71`},{{2010,4,28},1191.36`},{{2010,4,29},1206.78`},{{2010,4,30},1186.69`},{{2010,5,3},1202.26`},{{2010,5,4},1173.6`},{{2010,5,5},1165.87`},{{2010,5,6},1128.15`},{{2010,5,7},1110.88`},{{2010,5,10},1159.73`},{{2010,5,11},1155.79`},{{2010,5,12},1171.67`},{{2010,5,13},1157.44`},{{2010,5,14},1135.68`},{{2010,5,17},1136.94`},{{2010,5,18},1120.8`},{{2010,5,19},1115.05`},{{2010,5,20},1071.59`},{{2010,5,21},1087.69`},{{2010,5,24},1073.65`},{{2010,5,25},1074.03`},{{2010,5,26},1067.95`},{{2010,5,27},1103.06`},{{2010,5,28},1089.41`},{{2010,6,1},1070.71`},{{2010,6,2},1098.38`},{{2010,6,3},1102.83`},{{2010,6,4},1064.88`},{{2010,6,7},1050.47`},{{2010,6,8},1062.`},{{2010,6,9},1055.69`},{{2010,6,10},1086.84`},{{2010,6,11},1091.6`},{{2010,6,14},1089.63`},{{2010,6,15},1115.23`},{{2010,6,16},1114.61`},{{2010,6,17},1116.04`},{{2010,6,18},1117.51`},{{2010,6,21},1113.2`},{{2010,6,22},1095.31`},{{2010,6,23},1092.04`},{{2010,6,24},1073.69`},{{2010,6,25},1076.76`},{{2010,6,28},1074.57`},{{2010,6,29},1041.24`},{{2010,6,30},1030.71`},{{2010,7,1},1027.37`},{{2010,7,2},1022.58`},{{2010,7,6},1028.06`},{{2010,7,7},1060.27`},{{2010,7,8},1070.25`},{{2010,7,9},1077.96`},{{2010,7,12},1078.75`},{{2010,7,13},1095.34`},{{2010,7,14},1095.17`},{{2010,7,15},1096.48`},{{2010,7,16},1064.88`},{{2010,7,19},1071.25`},{{2010,7,20},1083.48`},{{2010,7,21},1069.59`},{{2010,7,22},1093.67`},{{2010,7,23},1102.66`},{{2010,7,26},1115.01`},{{2010,7,27},1113.84`},{{2010,7,28},1106.13`},{{2010,7,29},1101.53`},{{2010,7,30},1101.6`},{{2010,8,2},1125.86`},{{2010,8,3},1120.46`},{{2010,8,4},1127.24`},{{2010,8,5},1125.81`},{{2010,8,6},1121.64`},{{2010,8,9},1127.79`},{{2010,8,10},1121.06`},{{2010,8,11},1089.47`},{{2010,8,12},1083.61`},{{2010,8,13},1079.25`},{{2010,8,16},1079.38`},{{2010,8,17},1092.54`},{{2010,8,18},1094.16`},{{2010,8,19},1075.63`},{{2010,8,20},1071.69`},{{2010,8,23},1067.36`},{{2010,8,24},1051.87`},{{2010,8,25},1055.33`},{{2010,8,26},1047.22`},{{2010,8,27},1064.59`},{{2010,8,30},1048.92`},{{2010,8,31},1049.33`},{{2010,9,1},1080.29`},{{2010,9,2},1090.1`},{{2010,9,3},1104.51`},{{2010,9,7},1091.84`},{{2010,9,8},1098.87`},{{2010,9,9},1104.18`},{{2010,9,10},1109.55`},{{2010,9,13},1121.9`},{{2010,9,14},1121.1`},{{2010,9,15},1125.07`},{{2010,9,16},1124.66`},{{2010,9,17},1125.59`},{{2010,9,20},1142.71`},{{2010,9,21},1139.78`},{{2010,9,22},1134.28`},{{2010,9,23},1124.83`},{{2010,9,24},1148.67`},{{2010,9,27},1142.16`},{{2010,9,28},1147.7`},{{2010,9,29},1144.73`},{{2010,9,30},1141.2`},{{2010,10,1},1146.24`},{{2010,10,4},1137.03`},{{2010,10,5},1160.75`},{{2010,10,6},1159.97`},{{2010,10,7},1158.06`},{{2010,10,8},1165.15`},{{2010,10,11},1165.32`},{{2010,10,12},1169.77`},{{2010,10,13},1178.1`},{{2010,10,14},1173.81`},{{2010,10,15},1176.19`},{{2010,10,18},1184.71`},{{2010,10,19},1165.9`},{{2010,10,20},1178.17`},{{2010,10,21},1180.26`},{{2010,10,22},1183.08`},{{2010,10,25},1185.62`},{{2010,10,26},1185.64`},{{2010,10,27},1182.45`},{{2010,10,28},1183.78`},{{2010,10,29},1183.26`},{{2010,11,1},1184.38`},{{2010,11,2},1193.57`},{{2010,11,3},1197.96`},{{2010,11,4},1221.06`},{{2010,11,5},1225.85`},{{2010,11,8},1223.25`},{{2010,11,9},1213.4`},{{2010,11,10},1218.71`},{{2010,11,11},1213.54`},{{2010,11,12},1199.21`},{{2010,11,15},1197.75`},{{2010,11,16},1178.34`},{{2010,11,17},1178.59`},{{2010,11,18},1196.69`},{{2010,11,19},1199.73`},{{2010,11,22},1197.84`},{{2010,11,23},1180.73`},{{2010,11,24},1198.35`},{{2010,11,26},1189.4`},{{2010,11,29},1187.76`},{{2010,11,30},1180.55`},{{2010,12,1},1206.07`},{{2010,12,2},1221.53`},{{2010,12,3},1224.71`},{{2010,12,6},1223.12`},{{2010,12,7},1223.75`},{{2010,12,8},1228.28`},{{2010,12,9},1233.`},{{2010,12,10},1240.4`},{{2010,12,13},1240.46`},{{2010,12,14},1241.59`},{{2010,12,15},1235.23`},{{2010,12,16},1242.87`},{{2010,12,17},1243.91`},{{2010,12,20},1247.08`},{{2010,12,21},1254.6`},{{2010,12,22},1258.84`},{{2010,12,23},1256.77`},{{2010,12,27},1257.54`},{{2010,12,28},1258.51`},{{2010,12,29},1259.78`},{{2010,12,30},1257.88`},{{2010,12,31},1257.64`},{{2011,1,3},1271.87`},{{2011,1,4},1270.2`},{{2011,1,5},1276.56`},{{2011,1,6},1273.85`},{{2011,1,7},1271.5`},{{2011,1,10},1269.75`},{{2011,1,11},1274.48`},{{2011,1,12},1285.96`},{{2011,1,13},1283.76`},{{2011,1,14},1293.24`},{{2011,1,18},1295.02`},{{2011,1,19},1281.92`},{{2011,1,20},1280.26`},{{2011,1,21},1283.35`},{{2011,1,24},1290.84`},{{2011,1,25},1291.18`},{{2011,1,26},1296.63`},{{2011,1,27},1299.54`},{{2011,1,28},1276.34`},{{2011,1,31},1286.12`},{{2011,2,1},1307.59`},{{2011,2,2},1304.03`},{{2011,2,3},1307.1`},{{2011,2,4},1310.87`},{{2011,2,7},1319.05`},{{2011,2,8},1324.57`},{{2011,2,9},1320.88`},{{2011,2,10},1321.87`},{{2011,2,11},1329.15`},{{2011,2,14},1332.32`},{{2011,2,15},1328.01`},{{2011,2,16},1336.32`},{{2011,2,17},1340.43`},{{2011,2,18},1343.01`},{{2011,2,22},1315.44`},{{2011,2,23},1307.4`},{{2011,2,24},1306.1`},{{2011,2,25},1319.88`},{{2011,2,28},1327.22`},{{2011,3,1},1306.33`},{{2011,3,2},1308.44`},{{2011,3,3},1330.97`},{{2011,3,4},1321.15`},{{2011,3,7},1310.13`},{{2011,3,8},1321.82`},{{2011,3,9},1320.02`},{{2011,3,10},1295.11`},{{2011,3,11},1304.28`},{{2011,3,14},1296.39`},{{2011,3,15},1281.87`},{{2011,3,16},1256.88`},{{2011,3,17},1273.72`},{{2011,3,18},1279.21`},{{2011,3,21},1298.38`},{{2011,3,22},1293.77`},{{2011,3,23},1297.54`},{{2011,3,24},1309.66`},{{2011,3,25},1313.8`},{{2011,3,28},1310.19`},{{2011,3,29},1319.44`},{{2011,3,30},1328.26`},{{2011,3,31},1325.83`},{{2011,4,1},1332.41`},{{2011,4,4},1332.87`},{{2011,4,5},1332.63`},{{2011,4,6},1335.54`},{{2011,4,7},1333.51`},{{2011,4,8},1328.17`},{{2011,4,11},1324.46`},{{2011,4,12},1314.16`},{{2011,4,13},1314.41`},{{2011,4,14},1314.52`},{{2011,4,15},1319.68`},{{2011,4,18},1305.14`},{{2011,4,19},1312.62`},{{2011,4,20},1330.36`},{{2011,4,21},1337.38`},{{2011,4,25},1335.25`},{{2011,4,26},1347.24`},{{2011,4,27},1355.66`},{{2011,4,28},1360.48`},{{2011,4,29},1363.61`},{{2011,5,2},1361.22`},{{2011,5,3},1356.62`},{{2011,5,4},1347.32`},{{2011,5,5},1335.1`},{{2011,5,6},1340.2`},{{2011,5,9},1346.29`},{{2011,5,10},1357.16`},{{2011,5,11},1342.08`},{{2011,5,12},1348.65`},{{2011,5,13},1337.77`},{{2011,5,16},1329.47`},{{2011,5,17},1328.98`},{{2011,5,18},1340.68`},{{2011,5,19},1343.6`},{{2011,5,20},1333.27`},{{2011,5,23},1317.37`},{{2011,5,24},1316.28`},{{2011,5,25},1320.47`},{{2011,5,26},1325.69`},{{2011,5,27},1331.1`},{{2011,5,31},1345.2`},{{2011,6,1},1314.55`},{{2011,6,2},1312.94`},{{2011,6,3},1300.16`},{{2011,6,6},1286.17`},{{2011,6,7},1284.94`},{{2011,6,8},1279.56`},{{2011,6,9},1289.`},{{2011,6,10},1270.98`},{{2011,6,13},1271.83`},{{2011,6,14},1287.87`},{{2011,6,15},1265.42`},{{2011,6,16},1267.64`},{{2011,6,17},1271.5`},{{2011,6,20},1278.36`},{{2011,6,21},1295.52`},{{2011,6,22},1287.14`},{{2011,6,23},1283.5`},{{2011,6,24},1268.45`},{{2011,6,27},1280.1`},{{2011,6,28},1296.67`},{{2011,6,29},1307.41`},{{2011,6,30},1320.64`},{{2011,7,1},1339.67`},{{2011,7,5},1337.88`},{{2011,7,6},1339.22`},{{2011,7,7},1353.22`},{{2011,7,8},1343.8`},{{2011,7,11},1319.49`},{{2011,7,12},1313.64`},{{2011,7,13},1317.72`},{{2011,7,14},1308.87`},{{2011,7,15},1316.14`},{{2011,7,18},1305.44`},{{2011,7,19},1326.73`},{{2011,7,20},1325.84`},{{2011,7,21},1343.8`},{{2011,7,22},1345.02`},{{2011,7,25},1337.43`},{{2011,7,26},1331.94`},{{2011,7,27},1304.89`},{{2011,7,28},1300.67`},{{2011,7,29},1292.28`},{{2011,8,1},1286.94`},{{2011,8,2},1254.05`},{{2011,8,3},1260.34`},{{2011,8,4},1200.07`},{{2011,8,5},1199.38`},{{2011,8,8},1119.46`},{{2011,8,9},1172.53`},{{2011,8,10},1120.76`},{{2011,8,11},1172.64`},{{2011,8,12},1178.81`},{{2011,8,15},1204.49`},{{2011,8,16},1192.76`},{{2011,8,17},1193.89`},{{2011,8,18},1140.65`},{{2011,8,19},1123.53`},{{2011,8,22},1123.82`},{{2011,8,23},1162.35`},{{2011,8,24},1177.6`},{{2011,8,25},1159.27`},{{2011,8,26},1176.8`},{{2011,8,29},1210.08`},{{2011,8,30},1212.92`},{{2011,8,31},1218.89`},{{2011,9,1},1204.42`},{{2011,9,2},1173.97`},{{2011,9,6},1165.24`},{{2011,9,7},1198.62`},{{2011,9,8},1185.9`},{{2011,9,9},1154.23`},{{2011,9,12},1162.27`},{{2011,9,13},1172.87`},{{2011,9,14},1188.68`},{{2011,9,15},1209.11`},{{2011,9,16},1216.01`},{{2011,9,19},1204.09`},{{2011,9,20},1202.09`},{{2011,9,21},1166.76`},{{2011,9,22},1129.56`},{{2011,9,23},1136.43`},{{2011,9,26},1162.95`},{{2011,9,27},1175.38`},{{2011,9,28},1151.06`},{{2011,9,29},1160.4`},{{2011,9,30},1131.42`},{{2011,10,3},1099.23`},{{2011,10,4},1123.95`},{{2011,10,5},1144.03`},{{2011,10,6},1164.97`},{{2011,10,7},1155.46`},{{2011,10,10},1194.89`},{{2011,10,11},1195.54`}};

Tickers and prices of the companies

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},106.68`},{{2011,4,15},106.32`},{{2011,4,18},103.03`},{{2011,4,19},105.22`},{{2011,4,20},107.82`},{{2011,4,21},108.96`},{{2011,4,25},108.39`},{{2011,4,26},111.47`},{{2011,4,27},112.14`},{{2011,4,28},112.17`},{{2011,4,29},114.92`},{{2011,5,2},113.89`},{{2011,5,3},112.79`},{{2011,5,4},110.3`},{{2011,5,5},108.93`},{{2011,5,6},109.88`},{{2011,5,9},111.19`},{{2011,5,10},112.4`},{{2011,5,11},109.52`},{{2011,5,12},108.17`},{{2011,5,13},105.88`},{{2011,5,16},105.64`},{{2011,5,17},101.65`},{{2011,5,18},104.81`},{{2011,5,19},104.86`},{{2011,5,20},103.89`},{{2011,5,23},101.46`},{{2011,5,24},101.12`},{{2011,5,25},102.82`},{{2011,5,26},103.75`},{{2011,5,27},104.16`},{{2011,5,31},105.35`},{{2011,6,1},100.81`},{{2011,6,2},101.76`},{{2011,6,3},100.67`},{{2011,6,6},99.44`},{{2011,6,7},99.46`},{{2011,6,8},97.63`},{{2011,6,9},98.84`},{{2011,6,10},96.38`},{{2011,6,13},95.04`},{{2011,6,14},97.45`},{{2011,6,15},95.25`},{{2011,6,16},95.06`},{{2011,6,17},95.55`},{{2011,6,20},97.77`},{{2011,6,21},100.96`},{{2011,6,22},99.73`},{{2011,6,23},100.13`},{{2011,6,24},99.59`},{{2011,6,27},100.38`},{{2011,6,28},103.4`},{{2011,6,29},102.93`},{{2011,6,30},106.01`},{{2011,7,1},108.16`},{{2011,7,5},107.97`},{{2011,7,6},109.62`},{{2011,7,7},111.16`},{{2011,7,8},109.95`},{{2011,7,11},107.71`},{{2011,7,12},106.48`},{{2011,7,13},108.18`},{{2011,7,14},107.13`},{{2011,7,15},108.9`},{{2011,7,18},107.8`},{{2011,7,19},109.64`},{{2011,7,20},110.31`},{{2011,7,21},111.6`},{{2011,7,22},105.15`},{{2011,7,25},105.66`},{{2011,7,26},105.2`},{{2011,7,27},101.34`},{{2011,7,28},99.64`},{{2011,7,29},98.79`},{{2011,8,1},100.72`},{{2011,8,2},97.18`},{{2011,8,3},96.28`},{{2011,8,4},89.55`},{{2011,8,5},90.99`},{{2011,8,8},82.6`},{{2011,8,9},87.48`},{{2011,8,10},83.51`},{{2011,8,11},87.25`},{{2011,8,12},89.81`},{{2011,8,15},91.37`},{{2011,8,16},89.35`},{{2011,8,17},87.64`},{{2011,8,18},83.33`},{{2011,8,19},79.97`},{{2011,8,22},79.89`},{{2011,8,23},82.98`},{{2011,8,24},85.4`},{{2011,8,25},83.25`},{{2011,8,26},85.16`},{{2011,8,29},88.15`},{{2011,8,30},89.83`},{{2011,8,31},91.`},{{2011,9,1},88.55`},{{2011,9,2},85.38`},{{2011,9,6},85.7`},{{2011,9,7},88.69`},{{2011,9,8},87.04`},{{2011,9,9},83.96`},{{2011,9,12},83.87`},{{2011,9,13},85.02`},{{2011,9,14},85.45`},{{2011,9,15},86.6`},{{2011,9,16},85.9`},{{2011,9,19},84.6`},{{2011,9,20},83.66`},{{2011,9,21},79.36`},{{2011,9,22},73.9`},{{2011,9,23},73.86`},{{2011,9,26},76.85`},{{2011,9,27},77.67`},{{2011,9,28},75.08`},{{2011,9,29},75.39`},{{2011,9,30},73.84`},{{2011,10,3},70.55`},{{2011,10,4},72.54`},{{2011,10,5},74.26`},{{2011,10,6},77.09`},{{2011,10,7},75.52`},{{2011,10,10},79.13`},{{2011,10,11},80.66`}}},{"CSCO",{{{2009,1,2},16.77`},{{2009,1,5},16.92`},{{2009,1,6},17.59`},{{2009,1,7},17.13`},{{2009,1,8},17.34`},{{2009,1,9},16.51`},{{2009,1,12},16.22`},{{2009,1,13},16.27`},{{2009,1,14},15.56`},{{2009,1,15},15.63`},{{2009,1,16},15.64`},{{2009,1,20},14.84`},{{2009,1,21},15.52`},{{2009,1,22},15.2`},{{2009,1,23},15.71`},{{2009,1,26},16.12`},{{2009,1,27},16.54`},{{2009,1,28},16.69`},{{2009,1,29},15.75`},{{2009,1,30},14.8`},{{2009,2,2},15.14`},{{2009,2,3},15.45`},{{2009,2,4},15.66`},{{2009,2,5},16.17`},{{2009,2,6},16.85`},{{2009,2,9},16.66`},{{2009,2,10},15.87`},{{2009,2,11},15.99`},{{2009,2,12},16.02`},{{2009,2,13},15.92`},{{2009,2,17},15.12`},{{2009,2,18},15.2`},{{2009,2,19},14.87`},{{2009,2,20},14.91`},{{2009,2,23},14.2`},{{2009,2,24},14.82`},{{2009,2,25},14.6`},{{2009,2,26},14.33`},{{2009,2,27},14.41`},{{2009,3,2},14.16`},{{2009,3,3},14.23`},{{2009,3,4},15.08`},{{2009,3,5},14.39`},{{2009,3,6},14.02`},{{2009,3,9},13.47`},{{2009,3,10},14.48`},{{2009,3,11},14.85`},{{2009,3,12},15.34`},{{2009,3,13},15.34`},{{2009,3,16},15.28`},{{2009,3,17},15.96`},{{2009,3,18},16.32`},{{2009,3,19},16.05`},{{2009,3,20},15.73`},{{2009,3,23},16.79`},{{2009,3,24},16.49`},{{2009,3,25},16.38`},{{2009,3,26},17.12`},{{2009,3,27},16.76`},{{2009,3,30},16.13`},{{2009,3,31},16.58`},{{2009,4,1},17.26`},{{2009,4,2},17.94`},{{2009,4,3},17.96`},{{2009,4,6},17.33`},{{2009,4,7},16.66`},{{2009,4,8},16.94`},{{2009,4,9},17.62`},{{2009,4,13},17.69`},{{2009,4,14},17.73`},{{2009,4,15},17.36`},{{2009,4,16},17.88`},{{2009,4,17},17.79`},{{2009,4,20},17.12`},{{2009,4,21},17.49`},{{2009,4,22},17.24`},{{2009,4,23},17.42`},{{2009,4,24},18.21`},{{2009,4,27},18.16`},{{2009,4,28},18.46`},{{2009,4,29},19.03`},{{2009,4,30},19.1`},{{2009,5,1},19.36`},{{2009,5,4},19.28`},{{2009,5,5},19.41`},{{2009,5,6},19.39`},{{2009,5,7},18.74`},{{2009,5,8},18.52`},{{2009,5,11},18.4`},{{2009,5,12},18.51`},{{2009,5,13},17.85`},{{2009,5,14},17.89`},{{2009,5,15},17.72`},{{2009,5,18},18.51`},{{2009,5,19},18.67`},{{2009,5,20},18.39`},{{2009,5,21},17.9`},{{2009,5,22},17.7`},{{2009,5,26},18.28`},{{2009,5,27},18.02`},{{2009,5,28},18.3`},{{2009,5,29},18.29`},{{2009,6,1},19.28`},{{2009,6,2},19.39`},{{2009,6,3},19.14`},{{2009,6,4},19.45`},{{2009,6,5},19.65`},{{2009,6,8},19.65`},{{2009,6,9},19.86`},{{2009,6,10},19.73`},{{2009,6,11},19.88`},{{2009,6,12},19.69`},{{2009,6,15},19.14`},{{2009,6,16},18.87`},{{2009,6,17},1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011,4,19},66.16`},{{2011,4,20},66.91`},{{2011,4,21},66.94`},{{2011,4,25},66.8`},{{2011,4,26},66.`},{{2011,4,27},66.07`},{{2011,4,28},66.47`},{{2011,4,29},66.52`},{{2011,5,2},66.78`},{{2011,5,3},66.94`},{{2011,5,4},66.52`},{{2011,5,5},65.77`},{{2011,5,6},65.97`},{{2011,5,9},66.02`},{{2011,5,10},66.4`},{{2011,5,11},66.38`},{{2011,5,12},67.36`},{{2011,5,13},67.23`},{{2011,5,16},66.89`},{{2011,5,17},67.04`},{{2011,5,18},67.35`},{{2011,5,19},67.51`},{{2011,5,20},67.35`},{{2011,5,23},66.55`},{{2011,5,24},66.53`},{{2011,5,25},65.98`},{{2011,5,26},65.77`},{{2011,5,27},65.58`},{{2011,5,31},65.88`},{{2011,6,1},65.83`},{{2011,6,2},65.12`},{{2011,6,3},64.62`},{{2011,6,6},64.51`},{{2011,6,7},64.29`},{{2011,6,8},64.49`},{{2011,6,9},64.97`},{{2011,6,10},64.48`},{{2011,6,13},64.68`},{{2011,6,14},65.17`},{{2011,6,15},64.53`},{{2011,6,16},65.05`},{{2011,6,17},65.18`},{{2011,6,20},65.38`},{{2011,6,21},65.81`},{{2011,6,22},65.95`},{{2011,6,23},64.54`},{{2011,6,24},64.49`},{{2011,6,27},64.77`},{{2011,6,28},65.58`},{{2011,6,29},66.26`},{{2011,6,30},66.83`},{{2011,7,1},67.63`},{{2011,7,5},67.84`},{{2011,7,6},68.07`},{{2011,7,7},68.28`},{{2011,7,8},68.21`},{{2011,7,11},67.64`},{{2011,7,12},67.39`},{{2011,7,13},67.6`},{{2011,7,14},67.21`},{{2011,7,15},67.07`},{{2011,7,18},66.67`},{{2011,7,19},68.85`},{{2011,7,20},68.4`},{{2011,7,21},68.87`},{{2011,7,22},69.26`},{{2011,7,25},68.79`},{{2011,7,26},68.72`},{{2011,7,27},68.22`},{{2011,7,28},68.34`},{{2011,7,29},67.55`},{{2011,8,1},67.27`},{{2011,8,2},66.62`},{{2011,8,3},67.94`},{{2011,8,4},65.37`},{{2011,8,5},66.32`},{{2011,8,8},64.68`},{{2011,8,9},66.23`},{{2011,8,10},63.53`},{{2011,8,11},66.02`},{{2011,8,12},66.69`},{{2011,8,15},67.74`},{{2011,8,16},67.71`},{{2011,8,17},68.81`},{{2011,8,18},67.3`},{{2011,8,19},66.65`},{{2011,8,22},66.81`},{{2011,8,23},68.59`},{{2011,8,24},69.21`},{{2011,8,25},67.51`},{{2011,8,26},68.04`},{{2011,8,29},69.26`},{{2011,8,30},69.39`},{{2011,8,31},69.97`},{{2011,9,1},69.97`},{{2011,9,2},69.27`},{{2011,9,6},68.96`},{{2011,9,7},70.32`},{{2011,9,8},70.69`},{{2011,9,9},68.9`},{{2011,9,12},68.91`},{{2011,9,13},69.1`},{{2011,9,14},69.77`},{{2011,9,15},71.02`},{{2011,9,16},71.23`},{{2011,9,19},70.49`},{{2011,9,20},70.65`},{{2011,9,21},69.28`},{{2011,9,22},67.82`},{{2011,9,23},67.42`},{{2011,9,26},68.76`},{{2011,9,27},69.57`},{{2011,9,28},68.06`},{{2011,9,29},69.05`},{{2011,9,30},67.56`},{{2011,10,3},65.42`},{{2011,10,4},65.23`},{{2011,10,5},65.53`},{{2011,10,6},65.39`},{{2011,10,7},65.9`},{{2011,10,10},66.9`},{{2011,10,11},66.8`}}},{"MCD",{{{2009,1,2},58.31`},{{2009,1,5},58.13`},{{2009,1,6},56.83`},{{2009,1,7},56.01`},{{2009,1,8},55.35`},{{2009,1,9},54.94`},{{2009,1,12},55.02`},{{2009,1,13},54.26`},{{2009,1,14},52.44`},{{2009,1,15},53.03`},{{2009,1,16},54.58`},{{2009,1,20},52.2`},{{2009,1,21},53.69`},{{2009,1,22},53.71`},{{2009,1,23},53.07`},{{2009,1,26},53.41`},{{2009,1,27},53.52`},{{2009,1,28},54.15`},{{2009,1,29},53.18`},{{2009,1,30},53.07`},{{2009,2,2},52.96`},{{2009,2,3},53.85`},{{2009,2,4},52.92`},{{2009,2,5},53.38`},{{2009,2,6},53.47`},{{2009,2,9},53.98`},{{2009,2,10},52.39`},{{2009,2,11},52.21`},{{2009,2,12},52.1`},{{2009,2,13},51.96`},{{2009,2,17},50.93`},{{2009,2,18},51.59`},{{2009,2,19},50.59`},{{2009,2,20},49.91`},{{2009,2,23},49.27`},{{2009,2,24},50.08`},{{2009,2,25},49.65`},{{2009,2,26},48.19`},{{2009,2,27},48.23`},{{2009,3,2},47.86`},{{2009,3,3},48.4`},{{2009,3,4},49.06`},{{2009,3,5},46.95`},{{2009,3,6},48.11`},{{2009,3,9},48.3`},{{2009,3,10},48.56`},{{2009,3,11},47.11`},{{2009,3,12},48.16`},{{2009,3,13},48.35`},{{2009,3,16},47.72`},{{2009,3,17},49.52`},{{2009,3,18},51.16`},{{2009,3,19},50.5`},{{2009,3,20},49.11`},{{2009,3,23},50.92`},{{2009,3,24},49.44`},{{2009,3,25},50.78`},{{2009,3,26},51.75`},{{2009,3,27},50.78`},{{2009,3,30},49.77`},{{2009,3,31},50.37`},{{2009,4,1},50.99`},{{2009,4,2},52.02`},{{2009,4,3},52.29`},{{2009,4,6},51.64`},{{2009,4,7},51.14`},{{2009,4,8},51.29`},{{2009,4,9},52.31`},{{2009,4,13},51.8`},{{2009,4,14},50.61`},{{2009,4,15},49.8`},{{2009,4,16},50.49`},{{2009,4,17},51.78`},{{2009,4,20},51.08`},{{2009,4,21},51.35`},{{2009,4,22},50.08`},{{2009,4,23},51.05`},{{2009,4,24},50.13`},{{2009,4,27},50.3`},{{2009,4,28},50.34`},{{2009,4,29},50.23`},{{2009,4,30},49.19`},{{2009,5,1},48.37`},{{2009,5,4},48.71`},{{2009,5,5},49.07`},{{2009,5,6},49.56`},{{2009,5,7},49.29`},{{2009,5,8},50.7`},{{2009,5,11},50.22`},{{2009,5,12},49.82`},{{2009,5,13},49.38`},{{2009,5,14},49.45`},{{2009,5,15},49.35`},{{2009,5,18},50.03`},{{2009,5,19},49.73`},{{2009,5,20},51.93`},{{2009,5,21},51.41`},{{2009,5,22},52.69`},{{2009,5,26},54.32`},{{2009,5,27},53.38`},{{2009,5,28},53.66`},{{2009,5,29},54.46`},{{2009,6,1},55.25`},{{2009,6,2},55.74`},{{2009,6,3},56.3`},{{2009,6,4},56.07`},{{2009,6,5},55.72`},{{2009,6,8},54.65`},{{2009,6,9},54.99`},{{2009,6,10},54.32`},{{2009,6,11},53.68`},{{2009,6,12},54.32`},{{2009,6,15},53.78`},{{2009,6,16},53.12`},{{2009,6,17},53.4`},{{2009,6,18},54.13`},{{2009,6,19},54.14`},{{2009,6,22},53.24`},{{2009,6,23},52.83`},{{2009,6,24},52.4`},{{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010,8,10},33.84`},{{2010,8,11},33.01`},{{2010,8,12},33.15`},{{2010,8,13},33.11`},{{2010,8,16},33.09`},{{2010,8,17},33.63`},{{2010,8,18},33.46`},{{2010,8,19},32.84`},{{2010,8,20},32.58`},{{2010,8,23},33.09`},{{2010,8,24},32.58`},{{2010,8,25},32.68`},{{2010,8,26},32.62`},{{2010,8,27},33.11`},{{2010,8,30},32.86`},{{2010,8,31},33.27`},{{2010,9,1},33.7`},{{2010,9,2},33.45`},{{2010,9,3},33.67`},{{2010,9,7},33.55`},{{2010,9,8},33.88`},{{2010,9,9},34.14`},{{2010,9,10},34.68`},{{2010,9,13},34.63`},{{2010,9,14},34.91`},{{2010,9,15},34.91`},{{2010,9,16},34.83`},{{2010,9,17},34.73`},{{2010,9,20},34.93`},{{2010,9,21},35.11`},{{2010,9,22},35.34`},{{2010,9,23},35.05`},{{2010,9,24},35.7`},{{2010,9,27},35.5`},{{2010,9,28},35.61`},{{2010,9,29},35.49`},{{2010,9,30},35.19`},{{2010,10,1},34.99`},{{2010,10,4},34.91`},{{2010,10,5},35.39`},{{2010,10,6},35.38`},{{2010,10,7},35.1`},{{2010,10,8},35.29`},{{2010,10,11},35.24`},{{2010,10,12},35.03`},{{2010,10,13},35.53`},{{2010,10,14},35.52`},{{2010,10,15},35.33`},{{2010,10,18},35.59`},{{2010,10,19},34.91`},{{2010,10,20},35.36`},{{2010,10,21},35.47`},{{2010,10,22},35.47`},{{2010,10,25},35.78`},{{2010,10,26},35.44`},{{2010,10,27},34.86`},{{2010,10,28},35.32`},{{2010,10,29},34.71`},{{2010,11,1},34.66`},{{2010,11,2},35.`},{{2010,11,3},34.91`},{{2010,11,4},35.04`},{{2010,11,5},34.13`},{{2010,11,8},34.05`},{{2010,11,9},33.51`},{{2010,11,10},33.42`},{{2010,11,11},33.66`},{{2010,11,12},33.18`},{{2010,11,15},33.02`},{{2010,11,16},32.6`},{{2010,11,17},32.95`},{{2010,11,18},33.74`},{{2010,11,19},33.78`},{{2010,11,22},34.03`},{{2010,11,23},33.28`},{{2010,11,24},33.6`},{{2010,11,26},33.26`},{{2010,11,29},33.17`},{{2010,11,30},32.95`},{{2010,12,1},33.52`},{{2010,12,2},33.67`},{{2010,12,3},33.75`},{{2010,12,6},33.7`},{{2010,12,7},33.82`},{{2010,12,8},33.84`},{{2010,12,9},34.1`},{{2010,12,10},34.41`},{{2010,12,13},34.88`},{{2010,12,14},35.32`},{{2010,12,15},35.42`},{{2010,12,16},35.6`},{{2010,12,17},35.25`},{{2010,12,20},35.27`},{{2010,12,21},34.96`},{{2010,12,22},35.`},{{2010,12,23},35.06`},{{2010,12,27},35.01`},{{2010,12,28},34.98`},{{2010,12,29},34.99`},{{2010,12,30},34.79`},{{2010,12,31},34.82`},{{2011,1,3},34.82`},{{2011,1,4},35.12`},{{2011,1,5},35.33`},{{2011,1,6},35.81`},{{2011,1,7},36.09`},{{2011,1,10},35.94`},{{2011,1,11},35.7`},{{2011,1,12},35.9`},{{2011,1,13},33.52`},{{2011,1,14},33.07`},{{2011,1,18},32.73`},{{2011,1,19},32.77`},{{2011,1,20},32.9`},{{2011,1,21},32.76`},{{2011,1,24},32.66`},{{2011,1,25},32.23`},{{2011,1,26},32.08`},{{2011,1,27},32.13`},{{2011,1,28},31.95`},{{2011,1,31},32.05`},{{2011,2,1},32.85`},{{2011,2,2},32.68`},{{2011,2,3},31.79`},{{2011,2,4},31.78`},{{2011,2,7},31.89`},{{2011,2,8},32.15`},{{2011,2,9},31.97`},{{2011,2,10},31.92`},{{2011,2,11},31.95`},{{2011,2,14},31.71`},{{2011,2,15},31.68`},{{2011,2,16},31.85`},{{2011,2,17},31.98`},{{2011,2,18},31.74`},{{2011,2,22},31.25`},{{2011,2,23},31.01`},{{2011,2,24},30.95`},{{2011,2,25},31.1`},{{2011,2,28},31.47`},{{2011,3,1},31.36`},{{2011,3,2},31.48`},{{2011,3,3},31.98`},{{2011,3,4},31.94`},{{2011,3,7},31.72`},{{2011,3,8},31.87`},{{2011,3,9},32.17`},{{2011,3,10},31.79`},{{2011,3,11},31.99`},{{2011,3,14},31.65`},{{2011,3,15},31.14`},{{2011,3,16},30.38`},{{2011,3,17},30.73`},{{2011,3,18},31.19`},{{2011,3,21},31.66`},{{2011,3,22},31.8`},{{2011,3,23},31.9`},{{2011,3,24},31.98`},{{2011,3,25},31.84`},{{2011,3,28},31.72`},{{2011,3,29},32.04`},{{2011,3,30},32.55`},{{2011,3,31},32.27`},{{2011,4,1},32.33`},{{2011,4,4},32.52`},{{2011,4,5},32.41`},{{2011,4,6},32.6`},{{2011,4,7},32.58`},{{2011,4,8},32.91`},{{2011,4,11},32.84`},{{2011,4,12},32.81`},{{2011,4,13},32.72`},{{2011,4,14},33.1`},{{2011,4,15},33.73`},{{2011,4,18},33.17`},{{2011,4,19},32.99`},{{2011,4,20},33.28`},{{2011,4,21},33.28`},{{2011,4,25},33.56`},{{2011,4,26},34.27`},{{2011,4,27},34.83`},{{2011,4,28},34.97`},{{2011,4,29},35.14`},{{2011,5,2},35.49`},{{2011,5,3},35.59`},{{2011,5,4},35.74`},{{2011,5,5},35.44`},{{2011,5,6},35.57`},{{2011,5,9},35.66`},{{2011,5,10},35.94`},{{2011,5,11},35.81`},{{2011,5,12},36.36`},{{2011,5,13},36.25`},{{2011,5,16},36.46`},{{2011,5,17},36.43`},{{2011,5,18},36.74`},{{2011,5,19},36.54`},{{2011,5,20},36.23`},{{2011,5,23},36.07`},{{2011,5,24},36.04`},{{2011,5,25},35.87`},{{2011,5,26},35.56`},{{2011,5,27},35.4`},{{2011,5,31},35.92`},{{2011,6,1},35.44`},{{2011,6,2},35.34`},{{2011,6,3},35.02`},{{2011,6,6},34.76`},{{2011,6,7},34.77`},{{2011,6,8},34.99`},{{2011,6,9},35.19`},{{2011,6,10},34.65`},{{2011,6,13},34.91`},{{2011,6,14},35.22`},{{2011,6,15},34.75`},{{2011,6,16},34.76`},{{2011,6,17},34.97`},{{2011,6,20},35.36`},{{2011,6,21},35.36`},{{2011,6,22},35.05`},{{2011,6,23},34.55`},{{2011,6,24},34.14`},{{2011,6,27},34.12`},{{2011,6,28},34.5`},{{2011,6,29},34.68`},{{2011,6,30},34.87`},{{2011,7,1},35.18`},{{2011,7,5},35.07`},{{2011,7,6},35.11`},{{2011,7,7},35.31`},{{2011,7,8},35.69`},{{2011,7,11},35.26`},{{2011,7,12},35.21`},{{2011,7,13},35.6`},{{2011,7,14},35.88`},{{2011,7,15},35.5`},{{2011,7,18},35.07`},{{2011,7,19},35.36`},{{2011,7,20},35.17`},{{2011,7,21},35.75`},{{2011,7,22},35.66`},{{2011,7,25},35.46`},{{2011,7,26},35.36`},{{2011,7,27},34.77`},{{2011,7,28},34.52`},{{2011,7,29},33.72`},{{2011,8,1},33.04`},{{2011,8,2},32.51`},{{2011,8,3},32.31`},{{2011,8,4},31.14`},{{2011,8,5},31.33`},{{2011,8,8},29.58`},{{2011,8,9},30.85`},{{2011,8,10},29.46`},{{2011,8,11},30.83`},{{2011,8,12},30.97`},{{2011,8,15},31.75`},{{2011,8,16},31.72`},{{2011,8,17},31.82`},{{2011,8,18},30.69`},{{2011,8,19},30.89`},{{2011,8,22},30.94`},{{2011,8,23},31.56`},{{2011,8,24},31.85`},{{2011,8,25},31.48`},{{2011,8,26},31.54`},{{2011,8,29},32.07`},{{2011,8,30},32.31`},{{2011,8,31},32.71`},{{2011,9,1},32.51`},{{2011,9,2},31.99`},{{2011,9,6},31.87`},{{2011,9,7},32.57`},{{2011,9,8},32.39`},{{2011,9,9},31.46`},{{2011,9,12},31.62`},{{2011,9,13},31.74`},{{2011,9,14},32.12`},{{2011,9,15},32.49`},{{2011,9,16},32.68`},{{2011,9,19},32.25`},{{2011,9,20},32.5`},{{2011,9,21},31.85`},{{2011,9,22},31.13`},{{2011,9,23},31.05`},{{2011,9,26},31.61`},{{2011,9,27},32.14`},{{2011,9,28},31.94`},{{2011,9,29},32.66`},{{2011,9,30},32.7`},{{2011,10,3},31.57`},{{2011,10,4},31.35`},{{2011,10,5},31.46`},{{2011,10,6},31.42`},{{2011,10,7},31.61`},{{2011,10,10},32.35`},{{2011,10,11},31.93`}}},{"MSFT",{{{2009,1,2},19.1`},{{2009,1,5},19.28`},{{2009,1,6},19.5`},{{2009,1,7},18.33`},{{2009,1,8},18.9`},{{2009,1,9},18.34`},{{2009,1,12},18.29`},{{2009,1,13},18.62`},{{2009,1,14},17.93`},{{2009,1,15},18.07`},{{2009,1,16},18.52`},{{2009,1,20},17.36`},{{2009,1,21},18.21`},{{2009,1,22},16.07`},{{2009,1,23},16.16`},{{2009,1,26},16.56`},{{2009,1,27},16.59`},{{2009,1,28},16.95`},{{2009,1,29},16.52`},{{2009,1,30},16.06`},{{2009,2,2},16.75`},{{2009,2,3},17.38`},{{2009,2,4},17.5`},{{2009,2,5},17.89`},{{2009,2,6},18.47`},{{2009,2,9},18.26`},{{2009,2,10},17.66`},{{2009,2,11},18.05`},{{2009,2,12},18.09`},{{2009,2,13},17.93`},{{2009,2,17},17.11`},{{2009,2,18},17.14`},{{2009,2,19},16.94`},{{2009,2,20},17.03`},{{2009,2,23},16.28`},{{2009,2,24},16.24`},{{2009,2,25},16.04`},{{2009,2,26},15.53`},{{2009,2,27},15.28`},{{2009,3,2},14.93`},{{2009,3,3},15.02`},{{2009,3,4},15.25`},{{2009,3,5},14.44`},{{2009,3,6},14.45`},{{2009,3,9},14.33`},{{2009,3,10},15.59`},{{2009,3,11},16.18`},{{2009,3,12},16.09`},{{2009,3,13},15.75`},{{2009,3,16},15.37`},{{2009,3,17},15.98`},{{2009,3,18},16.04`},{{2009,3,19},16.21`},{{2009,3,20},16.14`},{{2009,3,23},17.34`},{{2009,3,24},16.96`},{{2009,3,25},16.91`},{{2009,3,26},17.81`},{{2009,3,27},17.15`},{{2009,3,30},16.53`},{{2009,3,31},17.38`},{{2009,4,1},18.26`},{{2009,4,2},18.25`},{{2009,4,3},17.73`},{{2009,4,6},17.74`},{{2009,4,7},17.74`},{{2009,4,8},18.15`},{{2009,4,9},18.6`},{{2009,4,13},18.53`},{{2009,4,14},18.3`},{{2009,4,15},17.81`},{{2009,4,16},18.69`},{{2009,4,17},18.16`},{{2009,4,20},17.6`},{{2009,4,21},17.94`},{{2009,4,22},17.76`},{{2009,4,23},17.9`},{{2009,4,24},19.78`},{{2009,4,27},19.3`},{{2009,4,28},18.85`},{{2009,4,29},19.15`},{{2009,4,30},19.16`},{{2009,5,1},19.14`},{{2009,5,4},19.1`},{{2009,5,5},18.72`},{{2009,5,6},18.72`},{{2009,5,7},18.27`},{{2009,5,8},18.37`},{{2009,5,11},18.27`},{{2009,5,12},18.81`},{{2009,5,13},18.68`},{{2009,5,14},18.97`},{{2009,5,15},19.12`},{{2009,5,18},19.48`},{{2009,5,19},19.33`},{{2009,5,20},19.4`},{{2009,5,21},18.87`},{{2009,5,22},18.8`},{{2009,5,26},19.36`},{{2009,5,27},19.16`},{{2009,5,28},19.47`},{{2009,5,29},19.88`},{{2009,6,1},20.37`},{{2009,6,2},20.37`},{{2009,6,3},20.68`},{{2009,6,4},20.78`},{{2009,6,5},21.07`},{{2009,6,8},20.99`},{{2009,6,9},21.02`},{{2009,6,10},21.46`},{{2009,6,11},21.73`},{{2009,6,12},22.21`},{{2009,6,15},22.29`},{{2009,6,16},22.32`},{{2009,6,17},22.54`},{{2009,6,18},22.37`},{{2009,6,19},22.91`},{{2009,6,22},22.16`},{{2009,6,23},22.22`},{{2009,6,24},22.34`},{{2009,6,25},22.64`},{{2009,6,26},22.23`},{{2009,6,29},22.71`},{{2009,6,30},22.63`},{{2009,7,1},22.88`},{{2009,7,2},22.24`},{{2009,7,6},22.08`},{{2009,7,7},21.45`},{{2009,7,8},21.47`},{{2009,7,9},21.36`},{{2009,7,10},21.31`},{{2009,7,13},22.11`},{{2009,7,14},22.`},{{2009,7,15},22.96`},{{2009,7,16},23.26`},{{2009,7,17},23.12`},{{2009,7,20},23.35`},{{2009,7,21},23.63`},{{2009,7,22},23.61`},{{2009,7,23},24.33`},{{2009,7,24},22.32`},{{2009,7,27},22.`},{{2009,7,28},22.34`},{{2009,7,29},22.65`},{{2009,7,30},22.66`},{{2009,7,31},22.39`},{{2009,8,3},22.68`},{{2009,8,4},22.63`},{{2009,8,5},22.66`},{{2009,8,6},22.33`},{{2009,8,7},22.43`},{{2009,8,10},22.29`},{{2009,8,11},22.02`},{{2009,8,12},22.4`},{{2009,8,13},22.48`},{{2009,8,14},22.55`},{{2009,8,17},22.13`},{{2009,8,18},22.57`},{{2009,8,19},22.64`},{{2009,8,20},22.66`},{{2009,8,21},23.37`},{{2009,8,24},23.59`},{{2009,8,25},23.59`},{{2009,8,26},23.5`},{{2009,8,27},23.63`},{{2009,8,28},23.62`},{{2009,8,31},23.59`},{{2009,9,1},22.97`},{{2009,9,2},22.84`},{{2009,9,3},23.08`},{{2009,9,4},23.57`},{{2009,9,8},23.76`},{{2009,9,9},23.72`},{{2009,9,10},23.93`},{{2009,9,11},23.8`},{{2009,9,14},23.93`},{{2009,9,15},24.12`},{{2009,9,16},24.12`},{{2009,9,17},24.22`},{{2009,9,18},24.18`},{{2009,9,21},24.22`},{{2009,9,22},24.67`},{{2009,9,23},24.61`},{{2009,9,24},24.83`},{{2009,9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19},24.05`},{{2011,8,22},23.98`},{{2011,8,23},24.72`},{{2011,8,24},24.9`},{{2011,8,25},24.57`},{{2011,8,26},25.25`},{{2011,8,29},25.84`},{{2011,8,30},26.23`},{{2011,8,31},26.6`},{{2011,9,1},26.21`},{{2011,9,2},25.8`},{{2011,9,6},25.51`},{{2011,9,7},26.`},{{2011,9,8},26.22`},{{2011,9,9},25.74`},{{2011,9,12},25.89`},{{2011,9,13},26.04`},{{2011,9,14},26.5`},{{2011,9,15},26.99`},{{2011,9,16},27.12`},{{2011,9,19},27.21`},{{2011,9,20},26.98`},{{2011,9,21},25.99`},{{2011,9,22},25.06`},{{2011,9,23},25.06`},{{2011,9,26},25.44`},{{2011,9,27},25.67`},{{2011,9,28},25.58`},{{2011,9,29},25.45`},{{2011,9,30},24.89`},{{2011,10,3},24.53`},{{2011,10,4},25.34`},{{2011,10,5},25.89`},{{2011,10,6},26.34`},{{2011,10,7},26.25`},{{2011,10,10},26.94`},{{2011,10,11},27.`}}},{"PFE",{{{2009,1,2},16.13`},{{2009,1,5},16.03`},{{2009,1,6},15.72`},{{2009,1,7},15.44`},{{2009,1,8},15.58`},{{2009,1,9},15.4`},{{2009,1,12},15.33`},{{2009,1,13},15.53`},{{2009,1,14},15.22`},{{2009,1,15},15.35`},{{2009,1,16},15.45`},{{2009,1,20},15.19`},{{2009,1,21},15.43`},{{2009,1,22},15.2`},{{2009,1,23},15.41`},{{2009,1,26},13.82`},{{2009,1,27},13.97`},{{2009,1,28},13.63`},{{2009,1,29},13.35`},{{2009,1,30},12.87`},{{2009,2,2},13.15`},{{2009,2,3},13.42`},{{2009,2,4},13.14`},{{2009,2,5},13.08`},{{2009,2,6},13.38`},{{2009,2,9},13.27`},{{2009,2,10},12.69`},{{2009,2,11},12.97`},{{2009,2,12},13.21`},{{2009,2,13},13.15`},{{2009,2,17},12.85`},{{2009,2,18},12.77`},{{2009,2,19},12.65`},{{2009,2,20},12.37`},{{2009,2,23},11.97`},{{2009,2,24},12.26`},{{2009,2,25},11.8`},{{2009,2,26},11.45`},{{2009,2,27},11.1`},{{2009,3,2},10.52`},{{2009,3,3},10.71`},{{2009,3,4},11.27`},{{2009,3,5},11.43`},{{2009,3,6},11.48`},{{2009,3,9},11.39`},{{2009,3,10},11.81`},{{2009,3,11},11.54`},{{2009,3,12},12.65`},{{2009,3,13},13.11`},{{2009,3,16},12.76`},{{2009,3,17},12.86`},{{2009,3,18},12.85`},{{2009,3,19},12.36`},{{2009,3,20},12.29`},{{2009,3,23},12.65`},{{2009,3,24},12.55`},{{2009,3,25},12.86`},{{2009,3,26},12.97`},{{2009,3,27},12.66`},{{2009,3,30},12.36`},{{2009,3,31},12.28`},{{2009,4,1},12.62`},{{2009,4,2},12.42`},{{2009,4,3},12.22`},{{2009,4,6},12.37`},{{2009,4,7},12.19`},{{2009,4,8},12.16`},{{2009,4,9},12.22`},{{2009,4,13},12.16`},{{2009,4,14},12.03`},{{2009,4,15},12.5`},{{2009,4,16},12.54`},{{2009,4,17},12.77`},{{2009,4,20},12.26`},{{2009,4,21},12.19`},{{2009,4,22},11.76`},{{2009,4,23},11.98`},{{2009,4,24},11.88`},{{2009,4,27},12.17`},{{2009,4,28},12.08`},{{2009,4,29},12.11`},{{2009,4,30},12.05`},{{2009,5,1},12.25`},{{2009,5,4},12.61`},{{2009,5,5},12.88`},{{2009,5,6},12.69`},{{2009,5,7},12.92`},{{2009,5,8},13.13`},{{2009,5,11},12.91`},{{2009,5,12},13.62`},{{2009,5,13},13.93`},{{2009,5,14},13.99`},{{2009,5,15},13.69`},{{2009,5,18},13.86`},{{2009,5,19},13.77`},{{2009,5,20},13.78`},{{2009,5,21},13.53`},{{2009,5,22},13.65`},{{2009,5,26},13.7`},{{2009,5,27},13.37`},{{2009,5,28},13.4`},{{2009,5,29},13.86`},{{2009,6,1},13.46`},{{2009,6,2},13.66`},{{2009,6,3},13.58`},{{2009,6,4},13.35`},{{2009,6,5},13.24`},{{2009,6,8},13.05`},{{2009,6,9},12.89`},{{2009,6,10},12.82`},{{2009,6,11},13.34`},{{2009,6,12},13.46`},{{2009,6,15},12.89`},{{2009,6,16},12.92`},{{2009,6,17},13.3`},{{2009,6,18},13.61`},{{2009,6,19},13.68`},{{2009,6,22},13.49`},{{2009,6,23},13.44`},{{2009,6,24},13.43`},{{2009,6,25},13.98`},{{2009,6,26},13.86`},{{2009,6,29},13.92`},{{2009,6,30},13.68`},{{2009,7,1},13.59`},{{2009,7,2},13.21`},{{2009,7,6},13.29`},{{2009,7,7},13.31`},{{2009,7,8},13.33`},{{2009,7,9},13.03`},{{2009,7,10},12.95`},{{2009,7,13},13.46`},{{2009,7,14},13.59`},{{2009,7,15},13.7`},{{2009,7,16},13.75`},{{2009,7,17},13.65`},{{2009,7,20},13.92`},{{2009,7,21},14.32`},{{2009,7,22},14.48`},{{2009,7,23},14.73`},{{2009,7,24},15.03`},{{2009,7,27},15.16`},{{2009,7,28},14.62`},{{2009,7,29},14.37`},{{2009,7,30},14.54`},{{2009,7,31},14.53`},{{2009,8,3},14.63`},{{2009,8,4},14.66`},{{2009,8,5},14.62`},{{2009,8,6},14.55`},{{2009,8,7},14.7`},{{2009,8,10},14.66`},{{2009,8,11},14.58`},{{2009,8,12},14.61`},{{2009,8,13},14.56`},{{2009,8,14},14.53`},{{2009,8,17},14.63`},{{2009,8,18},14.72`},{{2009,8,19},15.08`},{{2009,8,20},14.95`},{{2009,8,21},15.33`},{{2009,8,24},15.41`},{{2009,8,25},15.48`},{{2009,8,26},15.45`},{{2009,8,27},15.53`},{{2009,8,28},15.49`},{{2009,8,31},15.39`},{{2009,9,1},15.09`},{{2009,9,2},15.`},{{2009,9,3},14.81`},{{2009,9,4},15.1`},{{2009,9,8},14.93`},{{2009,9,9},14.9`},{{2009,9,10},15.05`},{{2009,9,11},14.97`},{{2009,9,14},15.07`},{{2009,9,15},14.93`},{{2009,9,16},15.13`},{{2009,9,17},15.04`},{{2009,9,18},15.21`},{{2009,9,21},15.33`},{{2009,9,22},15.48`},{{2009,9,23},15.14`},{{2009,9,24},15.15`},{{2009,9,25},15.11`},{{2009,9,28},15.27`},{{2009,9,29},15.45`},{{2009,9,30},15.25`},{{2009,10,1},15.03`},{{2009,10,2},14.88`},{{2009,10,5},15.11`},{{2009,10,6},15.46`},{{2009,10,7},15.38`},{{2009,10,8},15.39`},{{2009,10,9},15.59`},{{2009,10,12},15.75`},{{2009,10,13},15.46`},{{2009,10,14},16.`},{{2009,10,15},16.27`},{{2009,10,16},16.37`},{{2009,10,19},16.57`},{{2009,10,20},16.52`},{{2009,10,21},16.04`},{{2009,10,22},16.18`},{{2009,10,23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7`},{{2010,11,5},63.47`},{{2010,11,8},63.23`},{{2010,11,9},63.29`},{{2010,11,10},63.05`},{{2010,11,11},62.85`},{{2010,11,12},62.82`},{{2010,11,15},62.78`},{{2010,11,16},61.96`},{{2010,11,17},61.78`},{{2010,11,18},62.51`},{{2010,11,19},62.54`},{{2010,11,22},62.06`},{{2010,11,23},61.14`},{{2010,11,24},61.13`},{{2010,11,26},60.67`},{{2010,11,29},60.67`},{{2010,11,30},59.63`},{{2010,12,1},60.69`},{{2010,12,2},60.89`},{{2010,12,3},60.86`},{{2010,12,6},60.6`},{{2010,12,7},60.69`},{{2010,12,8},61.16`},{{2010,12,9},61.39`},{{2010,12,10},61.71`},{{2010,12,13},61.7`},{{2010,12,14},62.06`},{{2010,12,15},62.14`},{{2010,12,16},62.98`},{{2010,12,17},63.29`},{{2010,12,20},63.44`},{{2010,12,21},63.34`},{{2010,12,22},63.42`},{{2010,12,23},63.71`},{{2010,12,27},63.15`},{{2010,12,28},63.24`},{{2010,12,29},62.89`},{{2010,12,30},62.77`},{{2010,12,31},62.82`},{{2011,1,3},63.25`},{{2011,1,4},63.42`},{{2011,1,5},63.28`},{{2011,1,6},63.17`},{{2011,1,7},62.98`},{{2011,1,10},62.85`},{{2011,1,11},62.53`},{{2011,1,12},63.44`},{{2011,1,13},63.94`},{{2011,1,14},63.99`},{{2011,1,18},63.96`},{{2011,1,19},64.29`},{{2011,1,20},64.73`},{{2011,1,21},64.84`},{{2011,1,24},65.5`},{{2011,1,25},65.61`},{{2011,1,26},65.03`},{{2011,1,27},63.13`},{{2011,1,28},63.15`},{{2011,1,31},62.1`},{{2011,2,1},61.9`},{{2011,2,2},61.77`},{{2011,2,3},61.88`},{{2011,2,4},62.57`},{{2011,2,7},63.5`},{{2011,2,8},63.59`},{{2011,2,9},63.34`},{{2011,2,10},63.53`},{{2011,2,11},63.68`},{{2011,2,14},63.49`},{{2011,2,15},62.88`},{{2011,2,16},62.72`},{{2011,2,17},62.96`},{{2011,2,18},63.25`},{{2011,2,22},63.03`},{{2011,2,23},63.11`},{{2011,2,24},62.02`},{{2011,2,25},61.82`},{{2011,2,28},62.02`},{{2011,3,1},61.72`},{{2011,3,2},61.39`},{{2011,3,3},61.53`},{{2011,3,4},61.02`},{{2011,3,7},60.71`},{{2011,3,8},61.04`},{{2011,3,9},60.99`},{{2011,3,10},60.49`},{{2011,3,11},60.49`},{{2011,3,14},60.35`},{{2011,3,15},59.67`},{{2011,3,16},58.76`},{{2011,3,17},59.45`},{{2011,3,18},59.61`},{{2011,3,21},60.3`},{{2011,3,22},59.94`},{{2011,3,23},59.92`},{{2011,3,24},60.14`},{{2011,3,25},59.89`},{{2011,3,28},59.67`},{{2011,3,29},60.28`},{{2011,3,30},60.96`},{{2011,3,31},60.6`},{{2011,4,1},61.07`},{{2011,4,4},61.25`},{{2011,4,5},60.67`},{{2011,4,6},60.75`},{{2011,4,7},61.12`},{{2011,4,8},60.89`},{{2011,4,11},61.18`},{{2011,4,12},61.87`},{{2011,4,13},61.96`},{{2011,4,14},62.27`},{{2011,4,15},63.13`},{{2011,4,18},62.96`},{{2011,4,19},62.82`},{{2011,4,20},62.68`},{{2011,4,21},62.24`},{{2011,4,25},62.34`},{{2011,4,26},62.79`},{{2011,4,27},63.5`},{{2011,4,28},63.98`},{{2011,4,29},64.37`},{{2011,5,2},64.65`},{{2011,5,3},65.18`},{{2011,5,4},65.93`},{{2011,5,5},65.34`},{{2011,5,6},64.74`},{{2011,5,9},64.61`},{{2011,5,10},65.2`},{{2011,5,11},65.38`},{{2011,5,12},66.3`},{{2011,5,13},66.32`},{{2011,5,16},66.4`},{{2011,5,17},66.87`},{{2011,5,18},66.83`},{{2011,5,19},66.91`},{{2011,5,20},66.81`},{{2011,5,23},66.51`},{{2011,5,24},66.47`},{{2011,5,25},65.84`},{{2011,5,26},65.65`},{{2011,5,27},65.66`},{{2011,5,31},66.46`},{{2011,6,1},65.86`},{{2011,6,2},65.47`},{{2011,6,3},64.9`},{{2011,6,6},64.97`},{{2011,6,7},64.53`},{{2011,6,8},64.32`},{{2011,6,9},64.48`},{{2011,6,10},64.17`},{{2011,6,13},64.24`},{{2011,6,14},64.23`},{{2011,6,15},63.24`},{{2011,6,16},63.74`},{{2011,6,17},64.16`},{{2011,6,20},64.56`},{{2011,6,21},63.7`},{{2011,6,22},63.54`},{{2011,6,23},62.94`},{{2011,6,24},62.08`},{{2011,6,27},62.31`},{{2011,6,28},62.21`},{{2011,6,29},62.04`},{{2011,6,30},63.05`},{{2011,7,1},63.75`},{{2011,7,5},63.74`},{{2011,7,6},64.17`},{{2011,7,7},64.42`},{{2011,7,8},64.4`},{{2011,7,11},64.19`},{{2011,7,12},64.01`},{{2011,7,13},64.11`},{{2011,7,14},64.08`},{{2011,7,15},64.3`},{{2011,7,18},64.03`},{{2011,7,19},64.09`},{{2011,7,20},64.2`},{{2011,7,21},64.49`},{{2011,7,22},64.25`},{{2011,7,25},63.31`},{{2011,7,26},63.09`},{{2011,7,27},62.2`},{{2011,7,28},61.92`},{{2011,7,29},61.49`},{{2011,8,1},61.43`},{{2011,8,2},60.87`},{{2011,8,3},60.73`},{{2011,8,4},59.58`},{{2011,8,5},60.59`},{{2011,8,8},59.29`},{{2011,8,9},60.22`},{{2011,8,10},58.51`},{{2011,8,11},60.45`},{{2011,8,12},61.14`},{{2011,8,15},61.88`},{{2011,8,16},61.62`},{{2011,8,17},61.67`},{{2011,8,18},60.86`},{{2011,8,19},60.96`},{{2011,8,22},61.71`},{{2011,8,23},63.02`},{{2011,8,24},63.31`},{{2011,8,25},62.53`},{{2011,8,26},62.57`},{{2011,8,29},63.09`},{{2011,8,30},63.5`},{{2011,8,31},63.68`},{{2011,9,1},63.26`},{{2011,9,2},62.55`},{{2011,9,6},62.38`},{{2011,9,7},62.72`},{{2011,9,8},62.91`},{{2011,9,9},61.84`},{{2011,9,12},61.83`},{{2011,9,13},61.94`},{{2011,9,14},62.34`},{{2011,9,15},62.78`},{{2011,9,16},64.33`},{{2011,9,19},63.81`},{{2011,9,20},64.08`},{{2011,9,21},63.02`},{{2011,9,22},61.17`},{{2011,9,23},61.25`},{{2011,9,26},62.54`},{{2011,9,27},63.26`},{{2011,9,28},62.73`},{{2011,9,29},63.7`},{{2011,9,30},63.18`},{{2011,10,3},62.84`},{{2011,10,4},63.37`},{{2011,10,5},63.34`},{{2011,10,6},63.61`},{{2011,10,7},63.91`},{{2011,10,10},64.8`},{{2011,10,11},64.57`}}},{"T",{{{2009,1,2},24.51`},{{2009,1,5},23.68`},{{2009,1,6},23.58`},{{2009,1,7},23.`},{{2009,1,8},22.98`},{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6.72`},{{2010,12,7},26.94`},{{2010,12,8},27.03`},{{2010,12,9},27.21`},{{2010,12,10},27.27`},{{2010,12,13},27.17`},{{2010,12,14},27.7`},{{2010,12,15},27.5`},{{2010,12,16},27.6`},{{2010,12,17},27.58`},{{2010,12,20},27.5`},{{2010,12,21},27.44`},{{2010,12,22},27.5`},{{2010,12,23},27.57`},{{2010,12,27},27.61`},{{2010,12,28},27.6`},{{2010,12,29},27.67`},{{2010,12,30},27.69`},{{2010,12,31},27.74`},{{2011,1,3},28.01`},{{2011,1,4},28.21`},{{2011,1,5},28.3`},{{2011,1,6},27.92`},{{2011,1,7},27.63`},{{2011,1,10},27.14`},{{2011,1,11},26.73`},{{2011,1,12},26.86`},{{2011,1,13},26.9`},{{2011,1,14},27.23`},{{2011,1,18},27.13`},{{2011,1,19},27.13`},{{2011,1,20},27.04`},{{2011,1,21},27.13`},{{2011,1,24},27.28`},{{2011,1,25},27.55`},{{2011,1,26},27.52`},{{2011,1,27},26.94`},{{2011,1,28},26.33`},{{2011,1,31},26.36`},{{2011,2,1},26.69`},{{2011,2,2},26.5`},{{2011,2,3},26.81`},{{2011,2,4},26.79`},{{2011,2,7},26.78`},{{2011,2,8},26.73`},{{2011,2,9},26.79`},{{2011,2,10},27.05`},{{2011,2,11},27.27`},{{2011,2,14},27.26`},{{2011,2,15},27.05`},{{2011,2,16},27.11`},{{2011,2,17},27.3`},{{2011,2,18},27.36`},{{2011,2,22},27.01`},{{2011,2,23},26.85`},{{2011,2,24},26.74`},{{2011,2,25},26.94`},{{2011,2,28},27.18`},{{2011,3,1},26.9`},{{2011,3,2},26.98`},{{2011,3,3},26.94`},{{2011,3,4},26.74`},{{2011,3,7},26.72`},{{2011,3,8},27.25`},{{2011,3,9},27.58`},{{2011,3,10},27.4`},{{2011,3,11},27.26`},{{2011,3,14},27.`},{{2011,3,15},26.64`},{{2011,3,16},26.18`},{{2011,3,17},26.57`},{{2011,3,18},26.76`},{{2011,3,21},27.07`},{{2011,3,22},26.91`},{{2011,3,23},26.95`},{{2011,3,24},27.34`},{{2011,3,25},27.63`},{{2011,3,28},28.12`},{{2011,3,29},28.78`},{{2011,3,30},29.41`},{{2011,3,31},29.32`},{{2011,4,1},29.33`},{{2011,4,4},29.47`},{{2011,4,5},29.4`},{{2011,4,6},29.6`},{{2011,4,7},29.67`},{{2011,4,8},29.83`},{{2011,4,11},29.78`},{{2011,4,12},29.6`},{{2011,4,13},29.32`},{{2011,4,14},29.42`},{{2011,4,15},29.77`},{{2011,4,18},29.44`},{{2011,4,19},29.44`},{{2011,4,20},29.27`},{{2011,4,21},29.8`},{{2011,4,25},29.68`},{{2011,4,26},30.06`},{{2011,4,27},30.52`},{{2011,4,28},30.47`},{{2011,4,29},30.23`},{{2011,5,2},30.32`},{{2011,5,3},30.95`},{{2011,5,4},30.88`},{{2011,5,5},30.33`},{{2011,5,6},30.37`},{{2011,5,9},30.45`},{{2011,5,10},30.78`},{{2011,5,11},30.48`},{{2011,5,12},30.74`},{{2011,5,13},30.51`},{{2011,5,16},30.17`},{{2011,5,17},30.23`},{{2011,5,18},30.31`},{{2011,5,19},30.5`},{{2011,5,20},30.42`},{{2011,5,23},30.19`},{{2011,5,24},30.27`},{{2011,5,25},30.11`},{{2011,5,26},30.22`},{{2011,5,27},30.4`},{{2011,5,31},30.66`},{{2011,6,1},30.28`},{{2011,6,2},30.08`},{{2011,6,3},29.77`},{{2011,6,6},29.49`},{{2011,6,7},29.44`},{{2011,6,8},29.47`},{{2011,6,9},29.46`},{{2011,6,10},29.47`},{{2011,6,13},29.68`},{{2011,6,14},29.91`},{{2011,6,15},29.48`},{{2011,6,16},29.56`},{{2011,6,17},29.89`},{{2011,6,20},30.08`},{{2011,6,21},30.22`},{{2011,6,22},30.`},{{2011,6,23},29.84`},{{2011,6,24},29.57`},{{2011,6,27},29.88`},{{2011,6,28},30.13`},{{2011,6,29},30.37`},{{2011,6,30},30.51`},{{2011,7,1},30.77`},{{2011,7,5},30.73`},{{2011,7,6},30.76`},{{2011,7,7},30.76`},{{2011,7,8},30.67`},{{2011,7,11},30.33`},{{2011,7,12},30.3`},{{2011,7,13},30.35`},{{2011,7,14},30.12`},{{2011,7,15},29.85`},{{2011,7,18},29.66`},{{2011,7,19},29.87`},{{2011,7,20},29.77`},{{2011,7,21},29.82`},{{2011,7,22},29.86`},{{2011,7,25},29.46`},{{2011,7,26},29.49`},{{2011,7,27},29.5`},{{2011,7,28},28.82`},{{2011,7,29},28.82`},{{2011,8,1},29.07`},{{2011,8,2},28.74`},{{2011,8,3},29.05`},{{2011,8,4},28.34`},{{2011,8,5},28.49`},{{2011,8,8},27.28`},{{2011,8,9},28.41`},{{2011,8,10},27.46`},{{2011,8,11},28.01`},{{2011,8,12},27.79`},{{2011,8,15},28.37`},{{2011,8,16},28.35`},{{2011,8,17},28.73`},{{2011,8,18},28.03`},{{2011,8,19},27.56`},{{2011,8,22},28.02`},{{2011,8,23},28.54`},{{2011,8,24},28.98`},{{2011,8,25},28.62`},{{2011,8,26},28.6`},{{2011,8,29},28.82`},{{2011,8,30},29.17`},{{2011,8,31},28.05`},{{2011,9,1},27.84`},{{2011,9,2},27.62`},{{2011,9,6},27.41`},{{2011,9,7},27.7`},{{2011,9,8},27.54`},{{2011,9,9},27.12`},{{2011,9,12},27.46`},{{2011,9,13},27.69`},{{2011,9,14},27.83`},{{2011,9,15},28.11`},{{2011,9,16},28.5`},{{2011,9,19},28.15`},{{2011,9,20},28.41`},{{2011,9,21},27.87`},{{2011,9,22},27.33`},{{2011,9,23},27.43`},{{2011,9,26},27.91`},{{2011,9,27},28.23`},{{2011,9,28},28.12`},{{2011,9,29},28.4`},{{2011,9,30},28.09`},{{2011,10,3},27.73`},{{2011,10,4},27.88`},{{2011,10,5},28.31`},{{2011,10,6},28.41`},{{2011,10,7},28.44`},{{2011,10,10},29.17`},{{2011,10,11},28.77`}}},{"TRV",{{{2009,1,2},41.85`},{{2009,1,5},41.23`},{{2009,1,6},39.97`},{{2009,1,7},38.39`},{{2009,1,8},39.1`},{{2009,1,9},38.87`},{{2009,1,12},37.99`},{{2009,1,13},38.69`},{{2009,1,14},37.03`},{{2009,1,15},37.02`},{{2009,1,16},38.01`},{{2009,1,20},35.52`},{{2009,1,21},37.61`},{{2009,1,22},35.7`},{{2009,1,23},35.11`},{{2009,1,26},34.79`},{{2009,1,27},36.93`},{{2009,1,28},38.18`},{{2009,1,29},36.51`},{{2009,1,30},35.77`},{{2009,2,2},35.91`},{{2009,2,3},36.28`},{{2009,2,4},35.77`},{{2009,2,5},35.44`},{{2009,2,6},36.77`},{{2009,2,9},37.6`},{{2009,2,10},35.96`},{{20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.06`},{{2011,3,9},35.23`},{{2011,3,10},34.99`},{{2011,3,11},34.46`},{{2011,3,14},33.81`},{{2011,3,15},33.52`},{{2011,3,16},32.97`},{{2011,3,17},33.96`},{{2011,3,18},34.45`},{{2011,3,21},35.04`},{{2011,3,22},35.51`},{{2011,3,23},35.54`},{{2011,3,24},35.74`},{{2011,3,25},35.84`},{{2011,3,28},36.28`},{{2011,3,29},36.8`},{{2011,3,30},36.97`},{{2011,3,31},37.04`},{{2011,4,1},36.98`},{{2011,4,4},37.11`},{{2011,4,5},36.89`},{{2011,4,6},36.85`},{{2011,4,7},36.76`},{{2011,4,8},36.72`},{{2011,4,11},36.85`},{{2011,4,12},36.64`},{{2011,4,13},36.69`},{{2011,4,14},36.71`},{{2011,4,15},36.85`},{{2011,4,18},36.32`},{{2011,4,19},36.25`},{{2011,4,20},36.79`},{{2011,4,21},35.93`},{{2011,4,25},36.01`},{{2011,4,26},36.63`},{{2011,4,27},37.24`},{{2011,4,28},37.26`},{{2011,4,29},36.78`},{{2011,5,2},36.57`},{{2011,5,3},36.8`},{{2011,5,4},36.67`},{{2011,5,5},36.14`},{{2011,5,6},36.29`},{{2011,5,9},36.25`},{{2011,5,10},36.58`},{{2011,5,11},36.27`},{{2011,5,12},36.44`},{{2011,5,13},36.27`},{{2011,5,16},35.99`},{{2011,5,17},36.13`},{{2011,5,18},36.11`},{{2011,5,19},36.33`},{{2011,5,20},36.17`},{{2011,5,23},35.87`},{{2011,5,24},35.92`},{{2011,5,25},35.44`},{{2011,5,26},35.64`},{{2011,5,27},35.7`},{{2011,5,31},35.95`},{{2011,6,1},35.31`},{{2011,6,2},35.21`},{{2011,6,3},34.69`},{{2011,6,6},34.28`},{{2011,6,7},34.44`},{{2011,6,8},34.95`},{{2011,6,9},34.73`},{{2011,6,10},34.26`},{{2011,6,13},34.69`},{{2011,6,14},34.64`},{{2011,6,15},34.19`},{{2011,6,16},34.31`},{{2011,6,17},34.57`},{{2011,6,20},34.71`},{{2011,6,21},35.04`},{{2011,6,22},34.99`},{{2011,6,23},35.1`},{{2011,6,24},35.05`},{{2011,6,27},35.44`},{{2011,6,28},35.6`},{{2011,6,29},35.75`},{{2011,6,30},36.24`},{{2011,7,1},36.8`},{{2011,7,5},36.82`},{{2011,7,6},37.02`},{{2011,7,7},36.91`},{{2011,7,8},36.97`},{{2011,7,11},36.61`},{{2011,7,12},36.58`},{{2011,7,13},36.43`},{{2011,7,14},36.37`},{{2011,7,15},36.31`},{{2011,7,18},36.21`},{{2011,7,19},36.46`},{{2011,7,20},36.82`},{{2011,7,21},37.05`},{{2011,7,22},36.24`},{{2011,7,25},35.72`},{{2011,7,26},35.78`},{{2011,7,27},35.71`},{{2011,7,28},35.17`},{{2011,7,29},34.81`},{{2011,8,1},35.38`},{{2011,8,2},35.`},{{2011,8,3},35.48`},{{2011,8,4},34.44`},{{2011,8,5},34.57`},{{2011,8,8},32.67`},{{2011,8,9},33.82`},{{2011,8,10},33.2`},{{2011,8,11},34.14`},{{2011,8,12},33.83`},{{2011,8,15},34.57`},{{2011,8,16},34.4`},{{2011,8,17},35.12`},{{2011,8,18},34.59`},{{2011,8,19},34.23`},{{2011,8,22},34.34`},{{2011,8,23},35.47`},{{2011,8,24},35.97`},{{2011,8,25},35.28`},{{2011,8,26},35.27`},{{2011,8,29},35.64`},{{2011,8,30},35.81`},{{2011,8,31},35.67`},{{2011,9,1},35.39`},{{2011,9,2},35.07`},{{2011,9,6},34.74`},{{2011,9,7},35.13`},{{2011,9,8},34.89`},{{2011,9,9},34.76`},{{2011,9,12},34.77`},{{2011,9,13},35.01`},{{2011,9,14},35.11`},{{2011,9,15},35.69`},{{2011,9,16},36.22`},{{2011,9,19},35.78`},{{2011,9,20},35.91`},{{2011,9,21},35.35`},{{2011,9,22},35.1`},{{2011,9,23},35.39`},{{2011,9,26},35.86`},{{2011,9,27},36.38`},{{2011,9,28},36.33`},{{2011,9,29},36.64`},{{2011,9,30},36.29`},{{2011,10,3},35.84`},{{2011,10,4},35.9`},{{2011,10,5},35.77`},{{2011,10,6},35.91`},{{2011,10,7},36.16`},{{2011,10,10},36.9`},{{2011,10,11},36.5`}}},{"WMT",{{{2009,1,2},53.58`},{{2009,1,5},52.96`},{{2009,1,6},52.49`},{{2009,1,7},52.04`},{{2009,1,8},48.14`},{{2009,1,9},48.33`},{{2009,1,12},48.15`},{{2009,1,13},48.84`},{{2009,1,14},48.31`},{{2009,1,15},48.12`},{{2009,1,16},48.31`},{{2009,1,20},47.38`},{{2009,1,21},46.05`},{{2009,1,22},45.79`},{{2009,1,23},45.31`},{{2009,1,26},45.54`},{{2009,1,27},45.72`},{{2009,1,28},45.66`},{{2009,1,29},44.85`},{{2009,1,30},44.15`},{{2009,2,2},43.64`},{{2009,2,3},44.8`},{{2009,2,4},43.5`},{{2009,2,5},45.5`},{{2009,2,6},46.5`},{{2009,2,9},46.18`},{{2009,2,10},44.72`},{{2009,2,11},45.19`},{{2009,2,12},45.1`},{{2009,2,13},43.6`},{{2009,2,17},45.2`},{{2009,2,18},46.85`},{{2009,2,19},47.27`},{{2009,2,20},46.87`},{{2009,2,23},45.8`},{{2009,2,24},46.86`},{{2009,2,25},46.11`},{{2009,2,26},45.21`},{{2009,2,27},46.14`},{{2009,3,2},45.01`},{{2009,3,3},44.4`},{{2009,3,4},45.44`},{{2009,3,5},46.62`},{{2009,3,6},45.83`},{{2009,3,9},44.52`},{{2009,3,10},45.61`},{{2009,3,11},44.72`},{{2009,3,12},46.12`},{{2009,3,13},46.35`},{{2009,3,16},45.99`},{{2009,3,17},47.12`},{{2009,3,18},47.53`},{{2009,3,19},47.07`},{{2009,3,20},46.73`},{{2009,3,23},48.51`},{{2009,3,24},48.13`},{{2009,3,25},48.7`},{{2009,3,26},49.72`},{{2009,3,27},49.54`},{{2009,3,30},48.77`},{{2009,3,31},49.09`},{{2009,4,1},49.77`},{{2009,4,2},50.55`},{{2009,4,3},50.7`},{{2009,4,6},50.35`},{{2009,4,7},49.37`},{{2009,4,8},49.58`},{{2009,4,9},47.74`},{{2009,4,13},48.56`},{{2009,4,14},48.17`},{{2009,4,15},48.33`},{{2009,4,16},47.85`},{{2009,4,17},47.3`},{{2009,4,20},46.43`},{{2009,4,21},46.96`},{{2009,4,22},46.14`},{{2009,4,23},46.04`},{{2009,4,24},45.11`},{{2009,4,27},45.71`},{{2009,4,28},45.67`},{{2009,4,29},47.54`},{{2009,4,30},47.49`},{{2009,5,1},47.16`},{{2009,5,4},47.91`},{{2009,5,5},47.55`},{{2009,5,6},46.65`},{{2009,5,7},47.01`},{{2009,5,8},47.25`},{{2009,5,11},47.71`},{{2009,5,12},47.96`},{{2009,5,13},47.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2009,6,15},68.84`},{{2009,6,16},67.72`},{{2009,6,17},67.53`},{{2009,6,18},67.54`},{{2009,6,19},67.18`},{{2009,6,22},65.09`},{{2009,6,23},65.19`},{{2009,6,24},64.72`},{{2009,6,25},66.07`},{{2009,6,26},65.29`},{{2009,6,29},66.73`},{{2009,6,30},66.1`},{{2009,7,1},66.71`},{{2009,7,2},64.76`},{{2009,7,6},64.39`},{{2009,7,7},62.93`},{{2009,7,8},62.65`},{{2009,7,9},62.37`},{{2009,7,10},61.57`},{{2009,7,13},62.12`},{{2009,7,14},62.61`},{{2009,7,15},64.71`},{{2009,7,16},64.73`},{{2009,7,17},64.78`},{{2009,7,20},65.18`},{{2009,7,21},66.63`},{{2009,7,22},66.17`},{{2009,7,23},67.71`},{{2009,7,24},68.35`},{{2009,7,27},68.78`},{{2009,7,28},67.97`},{{2009,7,29},67.54`},{{2009,7,30},66.86`},{{2009,7,31},66.55`},{{2009,8,3},66.8`},{{2009,8,4},66.75`},{{2009,8,5},66.21`},{{2009,8,6},65.93`},{{2009,8,7},65.68`},{{2009,8,10},65.41`},{{2009,8,11},64.81`},{{2009,8,12},65.74`},{{2009,8,13},65.4`},{{2009,8,14},64.88`},{{2009,8,17},63.31`},{{2009,8,18},63.25`},{{2009,8,19},64.69`},{{2009,8,20},65.25`},{{2009,8,21},66.51`},{{2009,8,24},67.82`},{{2009,8,25},67.23`},{{2009,8,26},67.89`},{{2009,8,27},67.41`},{{2009,8,28},66.7`},{{2009,8,31},65.78`},{{2009,9,1},65.08`},{{2009,9,2},64.86`},{{2009,9,3},64.93`},{{2009,9,4},65.81`},{{2009,9,8},67.21`},{{2009,9,9},67.06`},{{2009,9,10},67.21`},{{2009,9,11},66.57`},{{2009,9,14},66.59`},{{2009,9,15},66.1`},{{2009,9,16},66.91`},{{2009,9,17},66.44`},{{2009,9,18},66.58`},{{2009,9,21},66.18`},{{2009,9,22},66.43`},{{2009,9,23},65.64`},{{2009,9,24},65.57`},{{2009,9,25},65.35`},{{2009,9,28},66.2`},{{2009,9,29},65.7`},{{2009,9,30},65.27`},{{2009,10,1},63.99`},{{2009,10,2},63.33`},{{2009,10,5},64.29`},{{2009,10,6},65.31`},{{2009,10,7},65.32`},{{2009,10,8},65.68`},{{2009,10,9},65.89`},{{2009,10,12},66.71`},{{2009,10,13},66.84`},{{2009,10,14},68.34`},{{2009,10,15},69.38`},{{2009,10,16},69.56`},{{2009,10,19},70.03`},{{2009,10,20},69.46`},{{2009,10,21},69.74`},{{2009,10,22},70.81`},{{2009,10,23},69.98`},{{2009,10,26},69.66`},{{2009,10,27},71.26`},{{2009,10,28},70.24`},{{2009,10,29},70.35`},{{2009,10,30},68.18`},{{2009,11,2},68.63`},{{2009,11,3},68.24`},{{2009,11,4},67.82`},{{2009,11,5},68.97`},{{2009,11,6},69.04`},{{2009,11,9},69.7`},{{2009,11,10},69.47`},{{2009,11,11},69.76`},{{2009,11,12},68.79`},{{2009,11,13},69.34`},{{2009,11,16},71.21`},{{2009,11,17},71.79`},{{2009,11,18},72.02`},{{2009,11,19},71.42`},{{2009,11,20},71.17`},{{2009,11,23},72.43`},{{2009,11,24},72.69`},{{2009,11,25},73.17`},{{2009,11,27},71.63`},{{2009,11,30},71.83`},{{2009,12,1},72.75`},{{2009,12,2},72.52`},{{2009,12,3},71.75`},{{2009,12,4},71.04`},{{2009,12,7},70.58`},{{2009,12,8},69.8`},{{2009,12,9},69.64`},{{2009,12,10},69.27`},{{2009,12,11},69.68`},{{2009,12,14},66.68`},{{2009,12,15},66.18`},{{2009,12,16},65.47`},{{2009,12,17},65.27`},{{2009,12,18},65.26`},{{2009,12,21},65.55`},{{2009,12,22},65.61`},{{2009,12,23},65.31`},{{2009,12,24},65.69`},{{2009,12,28},66.1`},{{2009,12,29},65.87`},{{2009,12,30},65.8`},{{2009,12,31},65.24`},{{2010,1,4},66.16`},{{2010,1,5},66.42`},{{2010,1,6},66.99`},{{2010,1,7},66.78`},{{2010,1,8},66.52`},{{2010,1,11},67.26`},{{2010,1,12},66.93`},{{2010,1,13},66.66`},{{2010,1,14},66.67`},{{2010,1,15},66.12`},{{2010,1,19},66.28`},{{2010,1,20},65.09`},{{2010,1,21},63.82`},{{2010,1,22},63.24`},{{2010,1,25},63.`},{{2010,1,26},63.07`},{{2010,1,27},62.71`},{{2010,1,28},62.15`},{{2010,1,29},61.65`},{{2010,2,1},63.32`},{{2010,2,2},64.07`},{{2010,2,3},63.72`},{{2010,2,4},61.92`},{{2010,2,5},62.`},{{2010,2,8},61.97`},{{2010,2,9},62.79`},{{2010,2,10},62.45`},{{2010,2,11},62.83`},{{2010,2,12},62.4`},{{2010,2,16},63.83`},{{2010,2,17},63.33`},{{2010,2,18},63.52`},{{2010,2,19},63.43`},{{2010,2,22},62.98`},{{2010,2,23},62.54`},{{2010,2,24},63.13`},{{2010,2,25},62.73`},{{2010,2,26},62.6`},{{2010,3,1},62.98`},{{2010,3,2},63.07`},{{2010,3,3},63.01`},{{2010,3,4},62.98`},{{2010,3,5},64.01`},{{2010,3,8},64.02`},{{2010,3,9},64.31`},{{2010,3,10},64.73`},{{2010,3,11},64.73`},{{2010,3,12},64.33`},{{2010,3,15},63.85`},{{2010,3,16},64.11`},{{2010,3,17},64.87`},{{2010,3,18},64.9`},{{2010,3,19},64.56`},{{2010,3,22},64.49`},{{2010,3,23},64.47`},{{2010,3,24},64.04`},{{2010,3,25},63.85`},{{2010,3,26},64.08`},{{2010,3,29},64.81`},{{2010,3,30},64.57`},{{2010,3,31},64.5`},{{2010,4,1},65.11`},{{2010,4,5},65.67`},{{2010,4,6},65.39`},{{2010,4,7},64.85`},{{2010,4,8},65.35`},{{2010,4,9},66.22`},{{2010,4,12},66.17`},{{2010,4,13},66.12`},{{2010,4,14},66.07`},{{2010,4,15},65.74`},{{2010,4,16},65.42`},{{2010,4,19},65.71`},{{2010,4,20},66.42`},{{2010,4,21},66.37`},{{2010,4,22},66.03`},{{2010,4,23},66.68`},{{2010,4,26},66.73`},{{2010,4,27},65.75`},{{2010,4,28},66.63`},{{2010,4,29},66.12`},{{2010,4,30},65.26`},{{2010,5,3},65.33`},{{2010,5,4},64.01`},{{2010,5,5},63.72`},{{2010,5,6},61.53`},{{2010,5,7},61.35`},{{2010,5,10},62.82`},{{2010,5,11},62.5`},{{2010,5,12},62.93`},{{2010,5,13},62.77`},{{2010,5,14},61.66`},{{2010,5,17},61.34`},{{2010,5,18},60.88`},{{2010,5,19},60.55`},{{2010,5,20},58.49`},{{2010,5,21},59.03`},{{2010,5,24},58.36`},{{2010,5,25},57.89`},{{2010,5,26},57.51`},{{2010,5,27},59.59`},{{2010,5,28},58.62`},{{2010,6,1},57.45`},{{2010,6,2},58.92`},{{2010,6,3},59.69`},{{2010,6,4},57.72`},{{2010,6,7},57.5`},{{2010,6,8},59.38`},{{2010,6,9},58.2`},{{2010,6,10},60.01`},{{2010,6,11},59.98`},{{2010,6,14},59.5`},{{2010,6,15},60.61`},{{2010,6,16},60.61`},{{2010,6,17},60.7`},{{2010,6,18},61.18`},{{2010,6,21},61.21`},{{2010,6,22},60.06`},{{2010,6,23},59.24`},{{2010,6,24},58.24`},{{2010,6,25},57.3`},{{2010,6,28},56.69`},{{2010,6,29},55.55`},{{2010,6,30},55.33`},{{2010,7,1},54.89`},{{2010,7,2},54.85`},{{2010,7,6},55.71`},{{2010,7,7},56.65`},{{2010,7,8},57.02`},{{2010,7,9},56.99`},{{2010,7,12},57.15`},{{2010,7,13},57.61`},{{2010,7,14},57.46`},{{2010,7,15},57.47`},{{2010,7,16},56.2`},{{2010,7,19},56.65`},{{2010,7,20},57.16`},{{2010,7,21},56.4`},{{2010,7,22},57.57`},{{2010,7,23},57.9`},{{2010,7,26},58.55`},{{2010,7,27},58.96`},{{2010,7,28},59.06`},{{2010,7,29},58.5`},{{2010,7,30},57.86`},{{2010,8,2},60.06`},{{2010,8,3},60.81`},{{2010,8,4},60.81`},{{2010,8,5},60.8`},{{2010,8,6},60.08`},{{2010,8,9},60.55`},{{2010,8,10},60.05`},{{2010,8,11},58.97`},{{2010,8,12},58.82`},{{2010,8,13},58.5`},{{2010,8,16},58.47`},{{2010,8,17},59.39`},{{2010,8,18},58.74`},{{2010,8,19},57.9`},{{2010,8,20},57.51`},{{2010,8,23},58.1`},{{2010,8,24},57.56`},{{2010,8,25},57.53`},{{2010,8,26},57.11`},{{2010,8,27},58.4`},{{2010,8,30},57.61`},{{2010,8,31},57.72`},{{2010,9,1},59.48`},{{2010,9,2},59.63`},{{2010,9,3},59.88`},{{2010,9,7},59.13`},{{2010,9,8},59.32`},{{2010,9,9},59.62`},{{2010,9,10},59.76`},{{2010,9,13},59.57`},{{2010,9,14},59.58`},{{2010,9,15},59.57`},{{2010,9,16},59.54`},{{2010,9,17},59.35`},{{2010,9,20},60.1`},{{2010,9,21},60.09`},{{2010,9,22},60.01`},{{2010,9,23},59.71`},{{2010,9,24},60.3`},{{2010,9,27},60.26`},{{2010,9,28},60.6`},{{2010,9,29},60.14`},{{2010,9,30},60.34`},{{2010,10,1},61.07`},{{2010,10,4},60.73`},{{2010,10,5},61.77`},{{2010,10,6},62.44`},{{2010,10,7},62.35`},{{2010,10,8},62.87`},{{2010,10,11},63.03`},{{2010,10,12},63.18`},{{2010,10,13},63.51`},{{2010,10,14},63.77`},{{2010,10,15},63.66`},{{2010,10,18},64.72`},{{2010,10,19},63.59`},{{2010,10,20},64.46`},{{2010,10,21},64.76`},{{2010,10,22},64.78`},{{2010,10,25},64.64`},{{2010,10,26},64.97`},{{2010,10,27},64.13`},{{2010,10,28},64.66`},{{2010,10,29},64.93`},{{2010,11,1},65.38`},{{2010,11,2},66.25`},{{2010,11,3},66.37`},{{2010,11,4},67.75`},{{2010,11,5},68.36`},{{2010,11,8},68.67`},{{2010,11,9},69.41`},{{2010,11,10},69.9`},{{2010,11,11},70.58`},{{2010,11,12},69.76`},{{2010,11,15},69.26`},{{2010,11,16},67.74`},{{2010,11,17},67.81`},{{2010,11,18},69.09`},{{2010,11,19},69.32`},{{2010,11,22},68.97`},{{2010,11,23},67.78`},{{2010,11,24},68.67`},{{2010,11,26},68.03`},{{2010,11,29},68.25`},{{2010,11,30},68.35`},{{2010,12,1},70.09`},{{2010,12,2},70.24`},{{2010,12,3},69.96`},{{2010,12,6},70.07`},{{2010,12,7},70.22`},{{2010,12,8},70.6`},{{2010,12,9},70.75`},{{2010,12,10},70.93`},{{2010,12,13},71.11`},{{2010,12,14},70.93`},{{2010,12,15},70.6`},{{2010,12,16},70.97`},{{2010,12,17},70.92`},{{2010,12,20},70.97`},{{2010,12,21},71.46`},{{2010,12,22},71.54`},{{2010,12,23},71.93`},{{2010,12,27},71.74`},{{2010,12,28},72.15`},{{2010,12,29},72.1`},{{2010,12,30},72.09`},{{2010,12,31},71.85`},{{2011,1,3},73.26`},{{2011,1,4},73.6`},{{2011,1,5},73.4`},{{2011,1,6},73.88`},{{2011,1,7},74.28`},{{2011,1,10},73.83`},{{2011,1,11},74.38`},{{2011,1,12},75.25`},{{2011,1,13},75.38`},{{2011,1,14},76.49`},{{2011,1,18},77.35`},{{2011,1,19},76.88`},{{2011,1,20},76.4`},{{2011,1,21},77.61`},{{2011,1,24},77.23`},{{2011,1,25},77.32`},{{2011,1,26},78.28`},{{2011,1,27},78.49`},{{2011,1,28},77.62`},{{2011,1,31},79.28`},{{2011,2,1},82.45`},{{2011,2,2},81.96`},{{2011,2,3},81.99`},{{2011,2,4},81.84`},{{2011,2,7},82.47`},{{2011,2,8},81.97`},{{2011,2,9},81.55`},{{2011,2,10},82.19`},{{2011,2,11},81.81`},{{2011,2,14},83.88`},{{2011,2,15},81.96`},{{2011,2,16},82.67`},{{2011,2,17},82.86`},{{2011,2,18},83.47`},{{2011,2,22},84.4`},{{2011,2,23},86.01`},{{2011,2,24},84.92`},{{2011,2,25},84.3`},{{2011,2,28},84.49`},{{2011,3,1},83.77`},{{2011,3,2},84.05`},{{2011,3,3},84.78`},{{2011,3,4},84.05`},{{2011,3,7},83.69`},{{2011,3,8},83.57`},{{2011,3,9},83.35`},{{2011,3,10},80.39`},{{2011,3,11},81.12`},{{2011,3,14},81.38`},{{2011,3,15},80.4`},{{2011,3,16},78.35`},{{2011,3,17},80.17`},{{2011,3,18},79.87`},{{2011,3,21},81.83`},{{2011,3,22},81.56`},{{2011,3,23},81.6`},{{2011,3,24},81.72`},{{2011,3,25},82.6`},{{2011,3,28},82.45`},{{2011,3,29},82.24`},{{2011,3,30},83.46`},{{2011,3,31},83.11`},{{2011,4,1},83.65`},{{2011,4,4},83.84`},{{2011,4,5},84.38`},{{2011,4,6},84.14`},{{2011,4,7},84.72`},{{2011,4,8},84.9`},{{2011,4,11},84.12`},{{2011,4,12},82.17`},{{2011,4,13},82.15`},{{2011,4,14},82.43`},{{2011,4,15},83.26`},{{2011,4,18},82.09`},{{2011,4,19},82.78`},{{2011,4,20},84.61`},{{2011,4,21},85.31`},{{2011,4,25},85.17`},{{2011,4,26},86.36`},{{2011,4,27},86.71`},{{2011,4,28},86.28`},{{2011,4,29},86.91`},{{2011,5,2},85.91`},{{2011,5,3},84.58`},{{2011,5,4},83.78`},{{2011,5,5},81.62`},{{2011,5,6},81.68`},{{2011,5,9},82.17`},{{2011,5,10},82.33`},{{2011,5,11},80.59`},{{2011,5,12},80.52`},{{2011,5,13},80.34`},{{2011,5,16},79.71`},{{2011,5,17},79.88`},{{2011,5,18},81.2`},{{2011,5,19},81.79`},{{2011,5,20},81.03`},{{2011,5,23},80.14`},{{2011,5,24},80.76`},{{2011,5,25},81.42`},{{2011,5,26},81.85`},{{2011,5,27},82.09`},{{2011,5,31},82.92`},{{2011,6,1},81.49`},{{2011,6,2},80.8`},{{2011,6,3},80.65`},{{2011,6,6},79.76`},{{2011,6,7},79.48`},{{2011,6,8},80.23`},{{2011,6,9},80.65`},{{2011,6,10},79.26`},{{2011,6,13},78.71`},{{2011,6,14},79.85`},{{2011,6,15},78.14`},{{2011,6,16},78.7`},{{2011,6,17},78.5`},{{2011,6,20},79.19`},{{2011,6,21},80.04`},{{2011,6,22},79.3`},{{2011,6,23},77.93`},{{2011,6,24},76.28`},{{2011,6,27},77.41`},{{2011,6,28},79.11`},{{2011,6,29},79.72`},{{2011,6,30},80.85`},{{2011,7,1},81.47`},{{2011,7,5},81.06`},{{2011,7,6},81.03`},{{2011,7,7},81.82`},{{2011,7,8},81.88`},{{2011,7,11},81.36`},{{2011,7,12},81.35`},{{2011,7,13},81.94`},{{2011,7,14},81.7`},{{2011,7,15},82.46`},{{2011,7,18},82.11`},{{2011,7,19},83.08`},{{2011,7,20},82.75`},{{2011,7,21},84.46`},{{2011,7,22},84.66`},{{2011,7,25},84.02`},{{2011,7,26},83.82`},{{2011,7,27},82.76`},{{2011,7,28},80.93`},{{2011,7,29},79.27`},{{2011,8,1},79.08`},{{2011,8,2},77.33`},{{2011,8,3},77.21`},{{2011,8,4},73.36`},{{2011,8,5},74.33`},{{2011,8,8},69.73`},{{2011,8,9},71.17`},{{2011,8,10},68.03`},{{2011,8,11},71.58`},{{2011,8,12},72.`},{{2011,8,15},74.29`},{{2011,8,16},73.5`},{{2011,8,17},74.16`},{{2011,8,18},70.94`},{{2011,8,19},69.8`},{{2011,8,22},70.18`},{{2011,8,23},73.66`},{{2011,8,24},73.54`},{{2011,8,25},71.77`},{{2011,8,26},72.64`},{{2011,8,29},74.12`},{{2011,8,30},73.91`},{{2011,8,31},74.02`},{{2011,9,1},73.49`},{{2011,9,2},72.14`},{{2011,9,6},71.15`},{{2011,9,7},73.65`},{{2011,9,8},72.82`},{{2011,9,9},71.01`},{{2011,9,12},71.84`},{{2011,9,13},71.65`},{{2011,9,14},72.64`},{{2011,9,15},74.01`},{{2011,9,16},74.55`},{{2011,9,19},73.7`},{{2011,9,20},74.01`},{{2011,9,21},71.97`},{{2011,9,22},69.24`},{{2011,9,23},69.31`},{{2011,9,26},71.72`},{{2011,9,27},72.91`},{{2011,9,28},72.07`},{{2011,9,29},73.88`},{{2011,9,30},72.63`},{{2011,10,3},71.15`},{{2011,10,4},72.83`},{{2011,10,5},73.95`},{{2011,10,6},73.89`},{{2011,10,7},73.56`},{{2011,10,10},76.28`},{{2011,10,11},76.27`}}}};

tickersandpricesCompaniesread

Preliminary calculations

Returns, logreturns

Clear[returns,logreturns];
returns[prices_]:=((Rest[prices]-Most[prices])/(Most[prices]))
logreturns[prices_]:=Log[((Rest[prices])/(Most[prices]))]

tickersandpricesCompanies//Dimensions
(* AT&T is company number 25 *)
tickersandpricesCompanies[[25,2]]//Dimensions
tickersandpricesCompanies[[25,2]]//First
DateListPlot[tickersandpricesCompanies[[25,2]],Joined->True]

Extraction of prices, calculation of returns and logreturns

pricesDJI=(indexDJI//Transpose)[[2,All]];
pricesSP500=(indexSP500//Transpose)[[2,All]];
pricesCompanies=Table[Map[Last,Map[Last,tickersandpricesCompanies][[i]]],{i,Length[membersDJI]}];

Maximum correlation coefficients in the rows:

Map[Max,Correlation[pricesCompanies//Transpose]-IdentityMatrix[Length[pricesCompanies]]]

The correlation matrix is very badly conditioned.

Det@Correlation[pricesCompanies//Transpose]

Short look on the indices (independence, trend, normality)

{DateListPlot[{indexDJI,indexSP500},Joined->True],DateListPlot[indexSP500,Joined->True]}

Relative development of DJI and S&P (both indices equal 1 at startdate)

ListPlot[{(pricesDJI/(pricesDJI[[1]])),(pricesSP500/(pricesSP500[[1]]))},Joined->True]

Print[Style["Correlation between DJI and S&P500 = ",14,Brown,FontFamily->"Times"],Correlation[pricesDJI,pricesSP500]]

returnsDJI=returns[pricesDJI];returnsSP500=returns[pricesSP500];
Print[Style["Mean of returns DJI:   ",14,Brown,FontFamily->"Times"],Mean[returnsDJI]]
logreturnsDJI=logreturns[pricesDJI];logreturnsSP500=logreturns[pricesSP500];
ListPlot[returnsDJI,Joined->True,PlotRange->All,PlotLabel->Style["DJI returns",24,FontFamily->"Times"]]
Print[Style["Serial correlation for returns and logreturns DJI: ",14,Brown,FontFamily->"Times"],{Correlation[Most[returnsDJI],Rest[returnsDJI]],Correlation[Most[logreturnsDJI],Rest[logreturnsDJI]]}]
Print[Style["Serial correlation for returns and logreturns SP500: ",14,Brown,FontFamily->"Times"],{Correlation[Most[returnsSP500],Rest[returnsSP500]],
Correlation[Most[logreturnsSP500],Rest[logreturnsSP500]]}]

Rank correlation for testing independence:

Clear[SpearmanRankCorrelationTest];
(* Returns the p-values either in the printed form or as a pair *)
Needs["MultivariateStatistics`"];
Needs["HypothesisTesting`"];
SpearmanRankCorrelationTest[list1_,list2_,print_:True]:=Module[{rs,t,n,tspt,tspn},
n=Length[list1];
rs=SpearmanRankCorrelation[list1,list2];
t=rs(Sqrt[((n-2)/(1-(rs^2)))]);
tspt=TwoSidedPValue/.StudentTPValue[Abs[t],n-2,TwoSided->True];
tspn=TwoSidedPValue/.NormalPValue[(Sqrt[n-1])Abs[rs],TwoSided->True];
Which[print==True,Print["p-value based on t-approximation = ",tspt,"\np-value based on normal approximation = ",tspn],
print== False,{tspt,tspn}]]

SpearmanRankCorrelationTest[Most[logreturnsDJI],Rest[logreturnsDJI]]

Trend

Test of goodness of fit with a normal distribution

DistributionFitTest[returnsDJI]
ℋreturnsDJI=DistributionFitTest[returnsDJI,NormalDistribution[μ,σ],"HypothesisTestData"];
ℋreturnsDJI["FittedDistributionParameters"]

ℋreturnsDJI["TestDataTable",All]

Show[Histogram[returnsDJI,Automatic,"ProbabilityDensity"],Plot[PDF[ℋreturnsDJI["FittedDistribution"],x],{x,-0.05,0.05}],PlotLabel->Style["DJI returns",24,FontFamily->"Times"]]

Leptokurtosis is obvious.

Short look on the prices (independence, trend, normality)

returnsCompanies=Map[returns,pricesCompanies];
logreturnsCompanies=Map[logreturns,pricesCompanies];
Map[ListPlot[#[[2]],Joined->True,PlotRange->All,PlotLabel->#[[1]]]&,{membersDJI,returnsCompanies}//Transpose]
Print[Style["Serial correlation for returns and logreturns Companies ",14,Brown]];Text@Grid[Map[{#[[1]],Correlation[Most[#[[2]]],Rest[#[[2]]]],Correlation[Most[#[[3]]],Rest[#[[3]]]]}&,{membersDJI,returnsCompanies,logreturnsCompanies}//Transpose],Frame->All]

Spearman correlation tests
p-values for Student t and normal approximation, respectively

Text@Grid[srcompanies=Map[{#[[1]],srct=SpearmanRankCorrelationTest[Most[#[[2]]],Rest[#[[2]]],False];srct//First,srct//Last}&,{membersDJI,logreturnsCompanies}//Transpose],Frame->All]

The companies with significant values on level 5 per cent:

Text@Grid[Sort[Select[srcompanies,#[[2]]≤0.05&],#1[[2]]<#2[[2]]&],Frame->All]

We see that returns of some companies may be considered as independent, some of them not.

Means and covariances

meansreturnsCompanies=Mean[returnsCompanies//Transpose];
covariancesreturnsCompanies=Covariance[returnsCompanies//Transpose];
standarderrorsreturnsCompanies=(Sqrt[Diagonal[covariancesreturnsCompanies]]);

Companies sorted by mean returns

Text@Grid[Map[{#[[1]],#[[2]],#[[3]]}&,Sort[{membersDJI,meansreturnsCompanies,standarderrorsreturnsCompanies}//Transpose,#1[[2]]<#2[[2]]&]],Frame->All]

Plot in σ-μ plane

ListPlot[{standarderrorsreturnsCompanies,meansreturnsCompanies}//Transpose,AxesLabel->{σ,μ},PlotStyle->{PointSize[0.02]}]

Companies sorted by Sharpe ratio μ/σ

Text@Grid[Sort[Map[{#[[1]],#[[2]]/#[[3]]}&,{membersDJI,meansreturnsCompanies,standarderrorsreturnsCompanies}//Transpose],#1[[2]]<#2[[2]]&],Frame->All]

3. Portfolio construction

Mean-variance portfolios

Definition of variables

variables=Map[Subscript[x,#]&,membersDJI]

Short sales allowed, exact solution

The exact solution is obtained by the method of Lagrange multipliers which leads to the following procedure. Here μ is the exact required return. The output of the portfolio is {μ,σ,x}, where μ is the (prescribed) return on the portfolio, σ its risk (standard error of the return), and x is the optimal portfolio.

Clear[optimalPortfolioExact];
optimalPortfolioExact[μ_(*required return *),means_,covariances_,variables_]:=
Module[{n,ones,A,B,C,Δ,δ,xx1,xx2,inverse,weights},
n=Length[variables];ones=Table[1,{n}];
inverse=Inverse[covariances];
A=ones.inverse.ones;B=ones.inverse.means;C=means.inverse.means;Δ=A C-(B^2);
xx1=((inverse.ones)/A);xx2=((inverse.means)/B);
δ=A(C-μ B)/Δ;
weights=δ xx1+(1-δ)xx2;
{weights.means,(Sqrt[weights.covariances.weights]),Thread[variables->weights]}//Simplify
]

exactShortAllowed=optimalPortfolioExact[(*0.001*)μ,meansreturnsCompanies,covariancesreturnsCompanies,variables]//Simplify
Print[Style["Sum of the weights is  ",12],Total[variables/.(exactShortAllowed//Last)]]
Print[Style["The risk and mean of the minimum-variance portfolio are\n  ",12],FindMinimum[{exactShortAllowed[[2]],μ≥0},μ]]

parexact=ParametricPlot[{exactShortAllowed[[2]],μ},{μ,0.00036,0.001849},AxesOrigin->{0.007,0.00036},AxesLabel->{σ,μ},PlotLabel->Style["Efficient frontier",18],AspectRatio->0.5]

Short sales allowed numerically

We consider 4 cases (here (Subscript[x, 1]),...,(Subscript[x, n])  are the weights in portfolio and (Subscript[r, 1]),...,(Subscript[r, n]) are the expected returns of the respective assets, μ prescribed expected return) : 
{equal, equal} means (∑_(i=1)^n)(Subscript[x, i])=1,  (∑_(i=1)^n)(Subscript[x, i])(Subscript[r, i])=μ
{equal, unequal}  means (∑_(i=1)^n)(Subscript[x, i])=1,  (∑_(i=1)^n)(Subscript[x, i])(Subscript[r, i])≥μ
{unequal, equal}  means (∑_(i=1)^n)(Subscript[x, i])≤1,  (∑_(i=1)^n)(Subscript[x, i])(Subscript[r, i])=μ
{unequal, unequal}  means (∑_(i=1)^n)(Subscript[x, i])≤1,  (∑_(i=1)^n)(Subscript[x, i])(Subscript[r, i])≥μ.

On efficient markets all four cases are equivalent. Form the numerical point of view the last case (inequalities) is recommendable.

Off[FindMinimum::precw]

Example of {equal, equal}

(* μ == 0.001 *)spendingAllShortAllowed=FindMinimum[{variables.covariancesreturnsCompanies.variables,Total[variables]==1&&meansreturnsCompanies.variables==0.001},variables]

Case {equal, equal}

parequaleaqual=ParametricPlot[{Sqrt[(FindMinimum[{variables.covariancesreturnsCompanies.variables,Total[variables]==1&&meansreturnsCompanies.variables==μ},variables]//First)]//Evaluate,μ},{μ,0.00036,0.001849},AxesOrigin->{0.007,0.00036},AxesLabel->{σ,μ},PlotLabel->Style["Efficient frontier numerically",18],AspectRatio->0.5]

The coincidence with the exact solution is perfect:

Show[{parexact,parequaleaqual}]

Case {equal, unequal}

parequaluneaqual=ParametricPlot[{Sqrt[(FindMinimum[{variables.covariancesreturnsCompanies.variables,Total[variables]==1&&meansreturnsCompanies.variables≥μ},variables,WorkingPrecision->25]//First)]//Evaluate,μ},{μ,0.00036,0.001849},AxesOrigin->{0.007,0.00036},AxesLabel->{σ,μ},PlotLabel->Style["Frontier with minimum prescribed return",18],AspectRatio->0.5,PlotStyle->{Red}]

Comparison with the efficient frontier

Show[{parequaluneaqual,parexact}]

Case {unequal, equal}
Not necessarily spend all the wealth. Inequality in total (it may be not a good strategy to spend all your wealth on an inefficient market):

parunequaleaqual=ParametricPlot[{Sqrt[(FindMinimum[{variables.covariancesreturnsCompanies.variables,Total[variables]≤1&&meansreturnsCompanies.variables==μ},variables]//First)]//Evaluate,μ},{μ,0.00036,0.001849},AxesOrigin->{0.002,0.00036},AxesLabel->{σ,μ},PlotLabel->Style["Frontier with exact prescribed return\nnot necesserily spending all wealth",18],AspectRatio->0.5,PlotStyle->{Red}]

Comparison with the efficient frontier

Show[{parunequaleaqual,parexact}]

parunequaluneaqual=ParametricPlot[{Sqrt[(FindMinimum[{variables.covariancesreturnsCompanies.variables,Total[variables]≤1&&meansreturnsCompanies.variables≥μ},variables,WorkingPrecision->25]//First)]//Evaluate,μ},{μ,0.00036,0.001849},AxesOrigin->{0.002,0.00036},AxesLabel->{σ,μ},PlotLabel->Style["Frontier with minimum prescribed return\nnot necesserily spending all wealth",18],AspectRatio->0.5,PlotStyle->{Red}]

Comparison with the efficient frontier

Show[{parunequaluneaqual,parexact}]

Short sales not allowed

Case {equal, equal}

Example of  {equal, equal} with μ=0.001 
In this case we need to increase precision by setting WorkingPrecision -> 25. Observe the substantial difference.

spendingAllNoShortAllowed=FindMinimum[{variables.covariancesreturnsCompanies.variables,Total[variables]==1&&meansreturnsCompanies.variables==0.001&&Apply[And,Thread[variables≥0]]},variables]
spendingAllNoShortAllowedPrecision25=FindMinimum[{variables.covariancesreturnsCompanies.variables,Total[variables]==1&&meansreturnsCompanies.variables==0.001&&Apply[And,Thread[variables≥0]]},variables,WorkingPrecision->25]//Chop[#,(10^(-5))]&

Case {equal, equal}

parequaleaqualNoShortAllowed=ParametricPlot[{Sqrt[(FindMinimum[{variables.covariancesreturnsCompanies.variables,Total[variables]==1&&meansreturnsCompanies.variables==μ&&Apply[And,Thread[variables≥0]]},variables,WorkingPrecision->25]//First)]//Evaluate,μ},{μ,0.00036,0.001849},AxesOrigin->{0.007,0.00036},AxesLabel->{σ,μ},PlotLabel->Style["Efficient frontier numerically",18],AspectRatio->0.5]

Comparison with the efficient frontier the short sales are allowed:

Show[parequaleaqualNoShortAllowed,parexact]

Case {equal, unequal}

parequaluneaqualNoShortAllowed=ParametricPlot[{Sqrt[(FindMinimum[{variables.covariancesreturnsCompanies.variables,Total[variables]==1&&meansreturnsCompanies.variables≥μ&&Apply[And,Thread[variables≥0]]},variables,WorkingPrecision->25]//First)]//Evaluate,μ},{μ,0.00036,0.001849},AxesOrigin->{0.007,0.00036},AxesLabel->{σ,μ},PlotLabel->Style["Frontier with minimum prescribed return",18],AspectRatio->0.5,PlotStyle->{Red}]

Comparison with the efficient frontier

Show[parequaluneaqualNoShortAllowed,parequaleaqualNoShortAllowed]

Case {unequal, equal}

pareunqualeaqualNoShortAllowed=ParametricPlot[{Sqrt[(FindMinimum[{variables.covariancesreturnsCompanies.variables,Total[variables]≤1&&meansreturnsCompanies.variables==μ&&Apply[And,Thread[variables≥0]]},variables,WorkingPrecision->25]//First)]//Evaluate,μ},{μ,0.00036,0.001849},AxesOrigin->{0.007,0.00036},AxesLabel->{σ,μ},PlotLabel->Style["Frontier with exact prescribed return\nnot necesserily spending all wealth",18],AspectRatio->0.5,PlotStyle->{Red}]

Comparison with the efficient frontier

Show[pareunqualeaqualNoShortAllowed,parequaleaqualNoShortAllowed]

Case {unequal, uneaqual}

parunequaluneaqualNoShortAllowed=ParametricPlot[{Sqrt[(FindMinimum[{variables.covariancesreturnsCompanies.variables,Total[variables]≤ 1&&meansreturnsCompanies.variables≥μ&&Apply[And,Thread[variables≥0]]},variables,WorkingPrecision->25]//First)]//Evaluate,μ},{μ,0.00036,0.001849},AxesOrigin->{0.007,0.00036},AxesLabel->{σ,μ},PlotLabel->Style["Frontier with minimum prescribed return\nnot necesserily spending all wealth",18],AspectRatio->0.5,PlotStyle->{Red}]

Comparison with the efficient frontier

Show[parunequaluneaqualNoShortAllowed,parequaleaqualNoShortAllowed]

4.Appendix

Here we give commands for reading the data.

startingdate={2009,1,1};
enddate={2011,10,11};

Dow Jones Industrial Members

membersDJIread=FinancialData["^DJI","Members"];

(Map[{#,FinancialData[#,"Name"]}&,membersDJI])//TableForm

Reading data from FinancialData

indexDJIread=FinancialData["^DJI",{startingdate,enddate}];
indexSP500read=FinancialData["SP500",{startingdate,enddate}];
tickersandpricesCompaniesread=Map[{#,FinancialData[#,{startingdate,enddate}]}&,membersDJI];

Checking the dimensions

Length@indexDJIread
Length@indexSP500read
Map[Length[#[[2]]]&,tickersandpricesCompaniesread]

In Section Preliminary calculations we just set indexDJI = indexDJIread &c. by hard copy.

5. Acknowledgments

The research has been supported by Grant of Czech Ministry of Education MSM 0021620839, Methods of modern mathematics and their applications.

6. Author’s address

Jan Hurt
Department of Statistics
Faculty of Mathematics and Physics
Charles University of Prague
Sokolovska 83
186 75 PRAGUE 8
Czech Republic
e-mail: hurt@karlin.mff.cuni.cz

7. References

[1] Dupačová, J., Hurt, J., Štěpán, J.: Stochastic Modeling in Economics and Finance. Kluwer, Dordrecht 2002.

[2] http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield

[3] Hamrick, J., Cawley, J.: Expected Returns of the Dow Industrials, Fama-French Model. Wolfram Demonstrations Project.
http://demonstrations.wolfram.com/ExpectedReturnsOfTheDowIndustrialsFamaFrenchModel/

[4] Hamrick, J., Cawley, J.: Expected Returns of the Dow Industrials, Beta Model. Wolfram Demonstrations Project.
http://demonstrations.wolfram.com/ExpectedReturnsOfTheDowIndustrialsBetaModel/

[5] Maclachlan, F.: Three-Asset Efficient Frontier. Wolfram Demonstrations Project.