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{"sheet":"AAPL and Google","index":0,"n_rows":71,"n_cols":7,"rows_kept":71,"cut":false,"hidden":false,"merged":[[0,0,0,6]]}
["PRICES AND RETURNS FOR APPLE AND GOOGLE\nJune 2007 - June 2012"]
["Monthly mean",{"$f":"AVERAGE(E11:E71)","v":2.6092535382995975E-2},{"$f":"AVERAGE(F11:F71)","v":-2.4269022221436731E-3},{"$f":"getformula(C2)","v":"<--  =AVERAGE(F11:F71)"}]
["Monthly variance",{"$f":"_xlfn.VAR.S(E11:E71)","v":1.2477690692371124E-2},{"$f":"_xlfn.VAR.S(F11:F71)","v":1.0175180168436861E-2},{"$f":"getformula(C3)","v":"<--  =VAR.S(F11:F71)"}]
["Monthly standard deviation",{"$f":"_xlfn.STDEV.S(E11:E71)","v":0.11170358406233492},{"$f":"_xlfn.STDEV.S(F11:F71)","v":0.10087209806699204},{"$f":"getformula(C4)","v":"<--  =STDEV.S(F11:F71)"}]
[]
["Annual mean",{"$f":"12*B2","v":0.31311042459595173},{"$f":"12*C2","v":-2.9122826665724078E-2},{"$f":"getformula(C6)","v":"<--  =12*C2"}]
["Annual variance",{"$f":"12*B3","v":0.14973228830845348},{"$f":"12*C3","v":0.12210216202124233},{"$f":"getformula(C7)","v":"<--  =12*C3"}]
["Annual standard deviation",{"$f":"SQRT(12)*B4","v":0.38695256596701033},{"$f":"SQRT(12)*C4","v":0.34943119783620108},{"$f":"getformula(C8)","v":"<--  =SQRT(12)*C4"}]
[]
["Date","AAPL","Google",null,"AAPL","Google"]
["2007-06-01",122.04,580.11]
["2007-07-02",131.76,645.9,null,{"$f":"LN(B12/B11)","v":7.6633226020915893E-2},0.10742695230781683,{"$f":"getformula(F12)","v":"<--  =LN(C12/C11)"}]
["2007-08-01",138.47999999999999,599.39,null,4.9743824998568914E-2,-7.4732221645049529E-2,{"$f":"getformula(F13)","v":"<--  =LN(C13/C12)"}]
["2007-09-04",153.47,592.64,null,0.10277919731904972,-1.1325339375617659E-2,"<--  =LN(C14/C13)"]
["2007-10-01",189.95,515.04,null,0.21325577144663097,-0.14034256446726184,"<--  =LN(C15/C14)"]
["2007-11-01",182.22,540.96,null,-4.1546131347922108E-2,4.9100771409077877E-2,"<--  =LN(C16/C15)"]
["2007-12-03",198.08,603.69000000000005,null,8.3456241210519033E-2,0.10971548218681069,"<--  =LN(C17/C16)"]
["2008-01-02",135.36000000000001,506.38,null,-0.38073309363831809,-0.17577344556712143,"<--  =LN(C18/C17)"]
["2008-02-01",125.02,529.02,null,-7.9464171354247048E-2,4.3738862747725364E-2,"<--  =LN(C19/C18)"]
["2008-03-03",143.5,544.1,null,0.13786131069600946,2.8106815164888964E-2,"<--  =LN(C20/C19)"]
["2008-04-01",173.95,586.76,null,0.1924328663982752,7.5482824127682258E-2,"<--  =LN(C21/C20)"]
["2008-05-01",188.75,613.4,null,8.1655486531183152E-2,4.440137406058902E-2,"<--  =LN(C22/C21)"]
["2008-06-02",167.44,600.36,null,-0.1197983099913898,-2.148777639203717E-2,"<--  =LN(C23/C22)"]
["2008-07-01",158.94999999999999,593.97,null,-5.2035390780932597E-2,-1.0700662251397116E-2,"<--  =LN(C24/C23)"]
["2008-08-01",169.53,555.71,null,6.4440214953050093E-2,-6.6582237591538612E-2,"<--  =LN(C25/C24)"]
["2008-09-02",113.66,613.70000000000005,null,-0.39981836644088625,9.9259633949873111E-2,"<--  =LN(C26/C25)"]
["2008-10-01",107.59,525.79,null,-5.4883829263157574E-2,-0.15460431591839269,"<--  =LN(C27/C26)"]
["2008-11-03",92.67,450.02,null,-0.1492829110072178,-0.15560986725547385,"<--  =LN(C28/C27)"]
["2008-12-01",85.35,484.85,null,-8.2284346358150504E-2,7.4547538529370433E-2,"<--  =LN(C29/C28)"]
["2009-01-02",90.13,444.95,null,5.4492623327868875E-2,-8.5877648447684057E-2,"<--  =LN(C30/C29)"]
["2009-02-02",89.31,485.63,null,-9.1396088725236701E-3,8.7485100776333188E-2,"<--  =LN(C31/C30)"]
["2009-03-02",105.12,525.70000000000005,null,0.16298909104050577,7.9283690746198177E-2,"<--  =LN(C32/C31)"]
["2009-04-01",125.83,567.12,null,0.17982923486757607,7.5840213721359739E-2,"<--  =LN(C33/C32)"]
["2009-05-01",135.81,526.79999999999995,null,7.6325060512100487E-2,-7.3749951677636247E-2,"<--  =LN(C34/C33)"]
["2009-06-01",142.43,529.94000000000005,null,4.7593800830517959E-2,5.9428227214138622E-3,"<--  =LN(C35/C34)"]
["2009-07-01",163.38999999999999,619.98,null,0.1372893300962372,0.15692342686377875,"<--  =LN(C36/C35)"]
["2009-08-03",168.21,583,null,2.9073217760958888E-2,-6.15000331038262E-2,"<--  =LN(C37/C36)"]
["2009-09-01",185.35,536.12,null,9.7032730793050262E-2,-8.3829169740196469E-2,"<--  =LN(C38/C37)"]
["2009-10-01",188.5,495.85,null,1.6852077291324211E-2,-7.8084554978161788E-2,"<--  =LN(C39/C38)"]
["2009-11-02",199.91,461.67,null,5.8769258379585923E-2,-7.1423111488264107E-2,"<--  =LN(C40/C39)"]
["2009-12-01",210.73,443.05,null,5.2710427941470024E-2,-4.1167719650558612E-2,"<--  =LN(C41/C40)"]
["2010-01-04",192.06,421.59,null,-9.276986999929468E-2,-4.9649352712548125E-2,"<--  =LN(C42/C41)"]
["2010-02-01",204.62,417.23,null,6.3346777240967267E-2,-1.0395649281585149E-2,"<--  =LN(C43/C42)"]
["2010-03-01",235,395.97,null,0.13843091369336494,-5.2299177690205201E-2,"<--  =LN(C44/C43)"]
["2010-04-01",261.08999999999997,348.06,null,0.10527966132537296,-0.12896357210294498,"<--  =LN(C45/C44)"]
["2010-05-03",256.88,337.99,null,-1.6256125688273504E-2,-2.9358569459494093E-2,"<--  =LN(C46/C45)"]
["2010-06-01",251.53,338.53,null,-2.1046783061035752E-2,1.596405471184585E-3,"<--  =LN(C47/C46)"]
["2010-07-01",257.25,307.64999999999998,null,2.2486107993936241E-2,-9.5649941531219279E-2,"<--  =LN(C48/C47)"]
["2010-08-02",243.1,292.95999999999998,null,-5.6575493392081351E-2,-4.8926692260298776E-2,"<--  =LN(C49/C48)"]
["2010-09-01",283.75,359.36,null,0.15462068747353472,0.20428859062387794,"<--  =LN(C50/C49)"]
["2010-10-01",300.98,400.52,null,5.8950248562960224E-2,0.10843903128952363,"<--  =LN(C51/C50)"]
["2010-11-01",311.14999999999998,463.29,null,3.3231293656654268E-2,0.14558950506341742,"<--  =LN(C52/C51)"]
["2010-12-01",322.56,473.75,null,3.6014054427722354E-2,2.232654849361675E-2,"<--  =LN(C53/C52)"]
["2011-01-03",339.32,526.41999999999996,null,5.0654449496584847E-2,0.10541961681369323,"<--  =LN(C54/C53)"]
["2011-02-01",353.21,585.79999999999995,null,4.01191659602591E-2,0.10687906118330369,"<--  =LN(C55/C54)"]
["2011-03-01",348.51,574.29,null,-1.3395856706299903E-2,-1.9843939177158147E-2,"<--  =LN(C56/C55)"]
["2011-04-01",350.13,440.47,null,4.6375898988789757E-3,-0.26529215658624006,"<--  =LN(C57/C56)"]
["2011-05-02",347.83,471.18,null,-6.5906594228294924E-3,6.7397847984603548E-2,"<--  =LN(C58/C57)"]
["2011-06-01",335.67,564.29999999999995,null,-3.5585320181802882E-2,0.18034583836025603,"<--  =LN(C59/C58)"]
["2011-07-01",390.48,691.48,null,0.15124821709115263,0.20324820307949171,"<--  =LN(C60/C59)"]
["2011-08-01",384.83,693,null,-1.4575073248301941E-2,2.1957711353171334E-3,"<--  =LN(C61/C60)"]
["2011-09-01",381.32,707,null,-9.1627607052127934E-3,2.0000666706669435E-2,"<--  =LN(C62/C61)"]
["2011-10-03",404.78,567.27,null,5.9704792012682126E-2,-0.22019528503533467,"<--  =LN(C63/C62)"]
["2011-11-01",382.2,515.25,null,-5.7399677831886937E-2,-9.6183161090669669E-2,"<--  =LN(C64/C63)"]
["2011-12-01",405,510,null,5.794303530036643E-2,-1.0241494052196907E-2,"<--  =LN(C65/C64)"]
["2012-01-03",456.48,522.70000000000005,null,0.11965782035865079,2.4596960000504701E-2,"<--  =LN(C66/C65)"]
["2012-02-01",542.44000000000005,497.91,null,0.17253259275455476,-4.8588347918139083E-2,"<--  =LN(C67/C66)"]
["2012-03-01",599.54999999999995,471.38,null,0.1001018936056976,-5.4754775012495489E-2]
["2012-04-02",583.98,458.16,null,-2.6312638158984922E-2,-2.8446094702639788E-2]
["2012-05-01",577.73,449.45,null,-1.0760104160047555E-2,-1.9193855066193692E-2]
["2012-06-01",584,501.5,null,1.0794351321817304E-2,0.10957899438258194]

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["COMPUTING COVARIANCE AND CORRELATION"]
[null,"Stock returns",null,null,"Return minus average"]
["Date","AAPL","Google",null,"AAPL","Google","Product"]
["2007-07-02",{"$f":"'AAPL and Google'!E12","v":7.6633226020915893E-2},{"$f":"'AAPL and Google'!F12","v":0.10742695230781683},{"$f":"ggetformula(E4)&\" -->\"","v":"=B4-$B$65 -->"},{"$f":"B4-$B$65","v":5.0540690637919918E-2},{"$f":"C4-$C$65","v":0.10985385452996051},{"$f":"E4*F4","v":5.5520896771817912E-3},{"$f":"getformula(G4)","v":"<--  =E4*F4"}]
["2007-08-01",{"$f":"'AAPL and Google'!E13","v":4.9743824998568914E-2},{"$f":"'AAPL and Google'!F13","v":-7.4732221645049529E-2},{"$f":"ggetformula(E5)&\" -->\"","v":"=B5-$B$65 -->"},{"$f":"B5-$B$65","v":2.3651289615572939E-2},{"$f":"C5-$C$65","v":-7.2305319422905856E-2},{"$f":"E5*F5","v":-1.7101140504176577E-3},{"$f":"getformula(G5)","v":"<--  =E5*F5"}]
["2007-09-04",{"$f":"'AAPL and Google'!E14","v":0.10277919731904972},{"$f":"'AAPL and Google'!F14","v":-1.1325339375617659E-2},null,7.6686661936053752E-2,-8.8984371534739856E-3,-6.8239144174767996E-4]
["2007-10-01",{"$f":"'AAPL and Google'!E15","v":0.21325577144663097},{"$f":"'AAPL and Google'!F15","v":-0.14034256446726184},null,0.187163236063635,-0.13791566224511817,-2.5812741649655604E-2]
["2007-11-01",{"$f":"'AAPL and Google'!E16","v":-4.1546131347922108E-2},{"$f":"'AAPL and Google'!F16","v":4.9100771409077877E-2},null,-6.763866673091809E-2,5.152767363122155E-2,-3.4852631441617105E-3]
["2007-12-03",{"$f":"'AAPL and Google'!E17","v":8.3456241210519033E-2},{"$f":"'AAPL and Google'!F17","v":0.10971548218681069},null,5.7363705827523058E-2,0.11214238440895437,6.4329027500322662E-3]
["2008-01-02",{"$f":"'AAPL and Google'!E18","v":-0.38073309363831809},{"$f":"'AAPL and Google'!F18","v":-0.17577344556712143},null,-0.40682562902131408,-0.17334654334497776,7.0521816534991066E-2]
["2008-02-01",{"$f":"'AAPL and Google'!E19","v":-7.9464171354247048E-2},{"$f":"'AAPL and Google'!F19","v":4.3738862747725364E-2},null,-0.10555670673724302,4.6165764969869037E-2,-4.8731061142249527E-3]
["2008-03-03",{"$f":"'AAPL and Google'!E20","v":0.13786131069600946},{"$f":"'AAPL and Google'!F20","v":2.8106815164888964E-2},null,0.11176877531301349,3.0533717387032637E-2,3.4127161981023042E-3]
["2008-04-01",{"$f":"'AAPL and Google'!E21","v":0.1924328663982752},{"$f":"'AAPL and Google'!F21","v":7.5482824127682258E-2},null,0.16634033101527923,7.7909726349825931E-2,1.2959529670339868E-2]
["2008-05-01",{"$f":"'AAPL and Google'!E22","v":8.1655486531183152E-2},{"$f":"'AAPL and Google'!F22","v":4.440137406058902E-2},null,5.5562951148187177E-2,4.6828276282732693E-2,2.6019172274512887E-3]
["2008-06-02",{"$f":"'AAPL and Google'!E23","v":-0.1197983099913898},{"$f":"'AAPL and Google'!F23","v":-2.148777639203717E-2},null,-0.14589084537438576,-1.9060874169893497E-2,2.7808070462205558E-3]
["2008-07-01",{"$f":"'AAPL and Google'!E24","v":-5.2035390780932597E-2},{"$f":"'AAPL and Google'!F24","v":-1.0700662251397116E-2},null,-7.8127926163928579E-2,-8.2737600292534432E-3,6.4641171266357654E-4]
["2008-08-01",{"$f":"'AAPL and Google'!E25","v":6.4440214953050093E-2},{"$f":"'AAPL and Google'!F25","v":-6.6582237591538612E-2},null,3.8347679570054118E-2,-6.4155335369394939E-2,-2.4602082434549166E-3]
["2008-09-02",{"$f":"'AAPL and Google'!E26","v":-0.39981836644088625},{"$f":"'AAPL and Google'!F26","v":9.9259633949873111E-2},null,-0.42591090182388225,0.10168653617201678,-4.3309404324370492E-2]
["2008-10-01",{"$f":"'AAPL and Google'!E27","v":-5.4883829263157574E-2},{"$f":"'AAPL and Google'!F27","v":-0.15460431591839269},null,-8.0976364646153542E-2,-0.15217741369624901,1.232277374237602E-2]
["2008-11-03",{"$f":"'AAPL and Google'!E28","v":-0.1492829110072178},{"$f":"'AAPL and Google'!F28","v":-0.15560986725547385},null,-0.17537544639021377,-0.15318296503333018,2.6864530872096788E-2]
["2008-12-01",{"$f":"'AAPL and Google'!E29","v":-8.2284346358150504E-2},{"$f":"'AAPL and Google'!F29","v":7.4547538529370433E-2},null,-0.10837688174114649,7.6974440751514106E-2,-8.3422498624177305E-3]
["2009-01-02",{"$f":"'AAPL and Google'!E30","v":5.4492623327868875E-2},{"$f":"'AAPL and Google'!F30","v":-8.5877648447684057E-2},null,2.84000879448729E-2,-8.3450746225540384E-2,-2.3700085318706173E-3]
["2009-02-02",{"$f":"'AAPL and Google'!E31","v":-9.1396088725236701E-3},{"$f":"'AAPL and Google'!F31","v":8.7485100776333188E-2},null,-3.5232144255519647E-2,8.9912002998476862E-2,-3.1677926599450517E-3]
["2009-03-02",{"$f":"'AAPL and Google'!E32","v":0.16298909104050577},{"$f":"'AAPL and Google'!F32","v":7.9283690746198177E-2},null,0.1368965556575098,8.171059296834185E-2,1.1185898738098738E-2]
["2009-04-01",{"$f":"'AAPL and Google'!E33","v":0.17982923486757607},{"$f":"'AAPL and Google'!F33","v":7.5840213721359739E-2},null,0.1537366994845801,7.8267115943503413E-2,1.2032528083331172E-2]
["2009-05-01",{"$f":"'AAPL and Google'!E34","v":7.6325060512100487E-2},{"$f":"'AAPL and Google'!F34","v":-7.3749951677636247E-2},null,5.0232525129104512E-2,-7.1323049455492574E-2,-3.5827368740573946E-3]
["2009-06-01",{"$f":"'AAPL and Google'!E35","v":4.7593800830517959E-2},{"$f":"'AAPL and Google'!F35","v":5.9428227214138622E-3},null,2.1501265447521983E-2,8.3697249435575362E-3,1.7995967773417652E-4]
["2009-07-01",{"$f":"'AAPL and Google'!E36","v":0.1372893300962372},{"$f":"'AAPL and Google'!F36","v":0.15692342686377875},null,0.11119679471324123,0.15935032908592242,1.7719245830854748E-2]
["2009-08-03",{"$f":"'AAPL and Google'!E37","v":2.9073217760958888E-2},{"$f":"'AAPL and Google'!F37","v":-6.15000331038262E-2},null,2.9806823779629128E-3,-5.9073130881682527E-2,-1.7607824023012787E-4]
["2009-09-01",{"$f":"'AAPL and Google'!E38","v":9.7032730793050262E-2},{"$f":"'AAPL and Google'!F38","v":-8.3829169740196469E-2},null,7.094019541005428E-2,-8.1402267518052795E-2,-5.7746927645521799E-3]
["2009-10-01",{"$f":"'AAPL and Google'!E39","v":1.6852077291324211E-2},{"$f":"'AAPL and Google'!F39","v":-7.8084554978161788E-2},null,-9.2404580916717639E-3,-7.5657652756018115E-2,6.9911136960624013E-4]
["2009-11-02",{"$f":"'AAPL and Google'!E40","v":5.8769258379585923E-2},{"$f":"'AAPL and Google'!F40","v":-7.1423111488264107E-2},null,3.2676722996589948E-2,-6.8996209266120434E-2,-2.2545700180037699E-3]
["2009-12-01",{"$f":"'AAPL and Google'!E41","v":5.2710427941470024E-2},{"$f":"'AAPL and Google'!F41","v":-4.1167719650558612E-2},null,2.6617892558474049E-2,-3.8740817428414939E-2,-1.0311989159370078E-3]
["2010-01-04",{"$f":"'AAPL and Google'!E42","v":-9.276986999929468E-2},{"$f":"'AAPL and Google'!F42","v":-4.9649352712548125E-2},null,-0.11886240538229065,-4.7222450490404452E-2,5.6129740533356039E-3]
["2010-02-01",{"$f":"'AAPL and Google'!E43","v":6.3346777240967267E-2},{"$f":"'AAPL and Google'!F43","v":-1.0395649281585149E-2},null,3.7254241857971292E-2,-7.968747059441476E-3,-2.9686963025743029E-4]
["2010-03-01",{"$f":"'AAPL and Google'!E44","v":0.13843091369336494},{"$f":"'AAPL and Google'!F44","v":-5.2299177690205201E-2},null,0.11233837831036897,-4.9872275468061528E-2,-5.6025705487300296E-3]
["2010-04-01",{"$f":"'AAPL and Google'!E45","v":0.10527966132537296},{"$f":"'AAPL and Google'!F45","v":-0.12896357210294498},null,7.9187125942376979E-2,-0.12653666988080131,-1.0020075214179993E-2]
["2010-05-03",{"$f":"'AAPL and Google'!E46","v":-1.6256125688273504E-2},{"$f":"'AAPL and Google'!F46","v":-2.9358569459494093E-2},null,-4.2348661071269479E-2,-2.693166723735042E-2,1.1405200479187654E-3]
["2010-06-01",{"$f":"'AAPL and Google'!E47","v":-2.1046783061035752E-2},{"$f":"'AAPL and Google'!F47","v":1.596405471184585E-3},null,-4.7139318444031728E-2,4.0233076933282579E-3,-1.8965598255412348E-4]
["2010-07-01",{"$f":"'AAPL and Google'!E48","v":2.2486107993936241E-2},{"$f":"'AAPL and Google'!F48","v":-9.5649941531219279E-2},null,-3.6064273890597347E-3,-9.3223039309075606E-2,3.3620212225564253E-4]
["2010-08-02",{"$f":"'AAPL and Google'!E49","v":-5.6575493392081351E-2},{"$f":"'AAPL and Google'!F49","v":-4.8926692260298776E-2},null,-8.2668028775077326E-2,-4.6499790038155103E-2,3.84404598090926E-3]
["2010-09-01",{"$f":"'AAPL and Google'!E50","v":0.15462068747353472},{"$f":"'AAPL and Google'!F50","v":0.20428859062387794},null,0.12852815209053875,0.20671549284602161,2.656876030398414E-2]
["2010-10-01",{"$f":"'AAPL and Google'!E51","v":5.8950248562960224E-2},{"$f":"'AAPL and Google'!F51","v":0.10843903128952363},null,3.2857713179964249E-2,0.11086593351166731,3.6428010447553511E-3]
["2010-11-01",{"$f":"'AAPL and Google'!E52","v":3.3231293656654268E-2},{"$f":"'AAPL and Google'!F52","v":0.14558950506341742},null,7.1387582736582925E-3,0.14801640728556109,1.0566533521469748E-3]
["2010-12-01",{"$f":"'AAPL and Google'!E53","v":3.6014054427722354E-2},{"$f":"'AAPL and Google'!F53","v":2.232654849361675E-2},null,9.921519044726379E-3,2.4753450715760423E-2,2.4559183269911287E-4]
["2011-01-03",{"$f":"'AAPL and Google'!E54","v":5.0654449496584847E-2},{"$f":"'AAPL and Google'!F54","v":0.10541961681369323},null,2.4561914113588872E-2,0.1078465190358369,2.6489169380077534E-3]
["2011-02-01",{"$f":"'AAPL and Google'!E55","v":4.01191659602591E-2},{"$f":"'AAPL and Google'!F55","v":0.10687906118330369},null,1.4026630577263124E-2,0.10930596340544736,1.533194368580052E-3]
["2011-03-01",{"$f":"'AAPL and Google'!E56","v":-1.3395856706299903E-2},{"$f":"'AAPL and Google'!F56","v":-1.9843939177158147E-2},null,-3.948839208929588E-2,-1.7417036955014474E-2,6.877707843133676E-4]
["2011-04-01",{"$f":"'AAPL and Google'!E57","v":4.6375898988789757E-3},{"$f":"'AAPL and Google'!F57","v":-0.26529215658624006},null,-2.1454945484117E-2,-0.26286525436409636,5.6397597020502359E-3]
["2011-05-02",{"$f":"'AAPL and Google'!E58","v":-6.5906594228294924E-3},{"$f":"'AAPL and Google'!F58","v":6.7397847984603548E-2},null,-3.2683194805825468E-2,6.9824750206747221E-2,-2.2820959132752216E-3]
["2011-06-01",{"$f":"'AAPL and Google'!E59","v":-3.5585320181802882E-2},{"$f":"'AAPL and Google'!F59","v":0.18034583836025603},null,-6.1677855564798857E-2,0.1827727405823997,-1.12730306948237E-2]
["2011-07-01",{"$f":"'AAPL and Google'!E60","v":0.15124821709115263},{"$f":"'AAPL and Google'!F60","v":0.20324820307949171},null,0.12515568170815666,0.20567510530163538,2.5741408014423081E-2]
["2011-08-01",{"$f":"'AAPL and Google'!E61","v":-1.4575073248301941E-2},{"$f":"'AAPL and Google'!F61","v":2.1957711353171334E-3},null,-4.0667608631297918E-2,4.6226733574608065E-3,-1.8799307093154402E-4]
["2011-09-01",{"$f":"'AAPL and Google'!E62","v":-9.1627607052127934E-3},{"$f":"'AAPL and Google'!F62","v":2.0000666706669435E-2},null,-3.5255296088208765E-2,2.2427568928813108E-2,-7.9069058312401721E-4]
["2011-10-03",{"$f":"'AAPL and Google'!E63","v":5.9704792012682126E-2},{"$f":"'AAPL and Google'!F63","v":-0.22019528503533467},null,3.3612256629686151E-2,-0.217768382813191,-7.3196867689487109E-3]
["2011-11-01",{"$f":"'AAPL and Google'!E64","v":-5.7399677831886937E-2},{"$f":"'AAPL and Google'!F64","v":-9.6183161090669669E-2},null,-8.3492213214882913E-2,-9.3756258868525996E-2,7.8279175556807291E-3]
["2011-12-01",{"$f":"'AAPL and Google'!E65","v":5.794303530036643E-2},{"$f":"'AAPL and Google'!F65","v":-1.0241494052196907E-2},null,3.1850499917370455E-2,-7.8145918300532337E-3,-2.4889865643739435E-4]
["2012-01-03",{"$f":"'AAPL and Google'!E66","v":0.11965782035865079},{"$f":"'AAPL and Google'!F66","v":2.4596960000504701E-2},null,9.3565284975654806E-2,2.7023862222648375E-2,2.5284953700049273E-3]
["2012-02-01",{"$f":"'AAPL and Google'!E67","v":0.17253259275455476},{"$f":"'AAPL and Google'!F67","v":-4.8588347918139083E-2},null,0.1464400573715588,-4.6161445695995409E-2,-6.7598847560756637E-3]
["2012-03-01",{"$f":"'AAPL and Google'!E68","v":0.1001018936056976},{"$f":"'AAPL and Google'!F68","v":-5.4754775012495489E-2},null,7.4009358222701632E-2,-5.2327872790351816E-2,-3.8727522823731094E-3]
["2012-04-02",{"$f":"'AAPL and Google'!E69","v":-2.6312638158984922E-2},{"$f":"'AAPL and Google'!F69","v":-2.8446094702639788E-2},null,-5.2405173541980897E-2,-2.6019192480496115E-2,1.3635402973626034E-3]
["2012-05-01",{"$f":"'AAPL and Google'!E70","v":-1.0760104160047555E-2},{"$f":"'AAPL and Google'!F70","v":-1.9193855066193692E-2},null,-3.6852639543043533E-2,-1.6766952844050019E-2,6.1790646939698394E-4]
["2012-06-01",{"$f":"'AAPL and Google'!E71","v":1.0794351321817304E-2},{"$f":"'AAPL and Google'!F71","v":0.10957899438258194},null,-1.5298184061178671E-2,0.11200589660472561,-1.7134868221964396E-3]
[]
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[null,null,null,null,null,"Correlation computation"]
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{"sheet":"AAPL, GOOG trendline","index":2,"n_rows":63,"n_cols":3,"rows_kept":63,"cut":false,"hidden":false,"merged":[[0,0,0,5]]}
["USING TRENDLINE ON APPLE, GOOGLE RETURNS"]
[]
["Date","AAPL","Google"]
["2007-07-02",{"$f":"'AAPL and Google'!E12","v":7.6633226020915893E-2},{"$f":"'AAPL and Google'!F12","v":0.10742695230781683}]
["2007-08-01",{"$f":"'AAPL and Google'!E13","v":4.9743824998568914E-2},{"$f":"'AAPL and Google'!F13","v":-7.4732221645049529E-2}]
["2007-09-04",{"$f":"'AAPL and Google'!E14","v":0.10277919731904972},{"$f":"'AAPL and Google'!F14","v":-1.1325339375617659E-2}]
["2007-10-01",{"$f":"'AAPL and Google'!E15","v":0.21325577144663097},{"$f":"'AAPL and Google'!F15","v":-0.14034256446726184}]
["2007-11-01",{"$f":"'AAPL and Google'!E16","v":-4.1546131347922108E-2},{"$f":"'AAPL and Google'!F16","v":4.9100771409077877E-2}]
["2007-12-03",{"$f":"'AAPL and Google'!E17","v":8.3456241210519033E-2},{"$f":"'AAPL and Google'!F17","v":0.10971548218681069}]
["2008-01-02",{"$f":"'AAPL and Google'!E18","v":-0.38073309363831809},{"$f":"'AAPL and Google'!F18","v":-0.17577344556712143}]
["2008-02-01",{"$f":"'AAPL and Google'!E19","v":-7.9464171354247048E-2},{"$f":"'AAPL and Google'!F19","v":4.3738862747725364E-2}]
["2008-03-03",{"$f":"'AAPL and Google'!E20","v":0.13786131069600946},{"$f":"'AAPL and Google'!F20","v":2.8106815164888964E-2}]
["2008-04-01",{"$f":"'AAPL and Google'!E21","v":0.1924328663982752},{"$f":"'AAPL and Google'!F21","v":7.5482824127682258E-2}]
["2008-05-01",{"$f":"'AAPL and Google'!E22","v":8.1655486531183152E-2},{"$f":"'AAPL and Google'!F22","v":4.440137406058902E-2}]
["2008-06-02",{"$f":"'AAPL and Google'!E23","v":-0.1197983099913898},{"$f":"'AAPL and Google'!F23","v":-2.148777639203717E-2}]
["2008-07-01",{"$f":"'AAPL and Google'!E24","v":-5.2035390780932597E-2},{"$f":"'AAPL and Google'!F24","v":-1.0700662251397116E-2}]
["2008-08-01",{"$f":"'AAPL and Google'!E25","v":6.4440214953050093E-2},{"$f":"'AAPL and Google'!F25","v":-6.6582237591538612E-2}]
["2008-09-02",{"$f":"'AAPL and Google'!E26","v":-0.39981836644088625},{"$f":"'AAPL and Google'!F26","v":9.9259633949873111E-2}]
["2008-10-01",{"$f":"'AAPL and Google'!E27","v":-5.4883829263157574E-2},{"$f":"'AAPL and Google'!F27","v":-0.15460431591839269}]
["2008-11-03",{"$f":"'AAPL and Google'!E28","v":-0.1492829110072178},{"$f":"'AAPL and Google'!F28","v":-0.15560986725547385}]
["2008-12-01",{"$f":"'AAPL and Google'!E29","v":-8.2284346358150504E-2},{"$f":"'AAPL and Google'!F29","v":7.4547538529370433E-2}]
["2009-01-02",{"$f":"'AAPL and Google'!E30","v":5.4492623327868875E-2},{"$f":"'AAPL and Google'!F30","v":-8.5877648447684057E-2}]
["2009-02-02",{"$f":"'AAPL and Google'!E31","v":-9.1396088725236701E-3},{"$f":"'AAPL and Google'!F31","v":8.7485100776333188E-2}]
["2009-03-02",{"$f":"'AAPL and Google'!E32","v":0.16298909104050577},{"$f":"'AAPL and Google'!F32","v":7.9283690746198177E-2}]
["2009-04-01",{"$f":"'AAPL and Google'!E33","v":0.17982923486757607},{"$f":"'AAPL and Google'!F33","v":7.5840213721359739E-2}]
["2009-05-01",{"$f":"'AAPL and Google'!E34","v":7.6325060512100487E-2},{"$f":"'AAPL and Google'!F34","v":-7.3749951677636247E-2}]
["2009-06-01",{"$f":"'AAPL and Google'!E35","v":4.7593800830517959E-2},{"$f":"'AAPL and Google'!F35","v":5.9428227214138622E-3}]
["2009-07-01",{"$f":"'AAPL and Google'!E36","v":0.1372893300962372},{"$f":"'AAPL and Google'!F36","v":0.15692342686377875}]
["2009-08-03",{"$f":"'AAPL and Google'!E37","v":2.9073217760958888E-2},{"$f":"'AAPL and Google'!F37","v":-6.15000331038262E-2}]
["2009-09-01",{"$f":"'AAPL and Google'!E38","v":9.7032730793050262E-2},{"$f":"'AAPL and Google'!F38","v":-8.3829169740196469E-2}]
["2009-10-01",{"$f":"'AAPL and Google'!E39","v":1.6852077291324211E-2},{"$f":"'AAPL and Google'!F39","v":-7.8084554978161788E-2}]
["2009-11-02",{"$f":"'AAPL and Google'!E40","v":5.8769258379585923E-2},{"$f":"'AAPL and Google'!F40","v":-7.1423111488264107E-2}]
["2009-12-01",{"$f":"'AAPL and Google'!E41","v":5.2710427941470024E-2},{"$f":"'AAPL and Google'!F41","v":-4.1167719650558612E-2}]
["2010-01-04",{"$f":"'AAPL and Google'!E42","v":-9.276986999929468E-2},{"$f":"'AAPL and Google'!F42","v":-4.9649352712548125E-2}]
["2010-02-01",{"$f":"'AAPL and Google'!E43","v":6.3346777240967267E-2},{"$f":"'AAPL and Google'!F43","v":-1.0395649281585149E-2}]
["2010-03-01",{"$f":"'AAPL and Google'!E44","v":0.13843091369336494},{"$f":"'AAPL and Google'!F44","v":-5.2299177690205201E-2}]
["2010-04-01",{"$f":"'AAPL and Google'!E45","v":0.10527966132537296},{"$f":"'AAPL and Google'!F45","v":-0.12896357210294498}]
["2010-05-03",{"$f":"'AAPL and Google'!E46","v":-1.6256125688273504E-2},{"$f":"'AAPL and Google'!F46","v":-2.9358569459494093E-2}]
["2010-06-01",{"$f":"'AAPL and Google'!E47","v":-2.1046783061035752E-2},{"$f":"'AAPL and Google'!F47","v":1.596405471184585E-3}]
["2010-07-01",{"$f":"'AAPL and Google'!E48","v":2.2486107993936241E-2},{"$f":"'AAPL and Google'!F48","v":-9.5649941531219279E-2}]
["2010-08-02",{"$f":"'AAPL and Google'!E49","v":-5.6575493392081351E-2},{"$f":"'AAPL and Google'!F49","v":-4.8926692260298776E-2}]
["2010-09-01",{"$f":"'AAPL and Google'!E50","v":0.15462068747353472},{"$f":"'AAPL and Google'!F50","v":0.20428859062387794}]
["2010-10-01",{"$f":"'AAPL and Google'!E51","v":5.8950248562960224E-2},{"$f":"'AAPL and Google'!F51","v":0.10843903128952363}]
["2010-11-01",{"$f":"'AAPL and Google'!E52","v":3.3231293656654268E-2},{"$f":"'AAPL and Google'!F52","v":0.14558950506341742}]
["2010-12-01",{"$f":"'AAPL and Google'!E53","v":3.6014054427722354E-2},{"$f":"'AAPL and Google'!F53","v":2.232654849361675E-2}]
["2011-01-03",{"$f":"'AAPL and Google'!E54","v":5.0654449496584847E-2},{"$f":"'AAPL and Google'!F54","v":0.10541961681369323}]
["2011-02-01",{"$f":"'AAPL and Google'!E55","v":4.01191659602591E-2},{"$f":"'AAPL and Google'!F55","v":0.10687906118330369}]
["2011-03-01",{"$f":"'AAPL and Google'!E56","v":-1.3395856706299903E-2},{"$f":"'AAPL and Google'!F56","v":-1.9843939177158147E-2}]
["2011-04-01",{"$f":"'AAPL and Google'!E57","v":4.6375898988789757E-3},{"$f":"'AAPL and Google'!F57","v":-0.26529215658624006}]
["2011-05-02",{"$f":"'AAPL and Google'!E58","v":-6.5906594228294924E-3},{"$f":"'AAPL and Google'!F58","v":6.7397847984603548E-2}]
["2011-06-01",{"$f":"'AAPL and Google'!E59","v":-3.5585320181802882E-2},{"$f":"'AAPL and Google'!F59","v":0.18034583836025603}]
["2011-07-01",{"$f":"'AAPL and Google'!E60","v":0.15124821709115263},{"$f":"'AAPL and Google'!F60","v":0.20324820307949171}]
["2011-08-01",{"$f":"'AAPL and Google'!E61","v":-1.4575073248301941E-2},{"$f":"'AAPL and Google'!F61","v":2.1957711353171334E-3}]
["2011-09-01",{"$f":"'AAPL and Google'!E62","v":-9.1627607052127934E-3},{"$f":"'AAPL and Google'!F62","v":2.0000666706669435E-2}]
["2011-10-03",{"$f":"'AAPL and Google'!E63","v":5.9704792012682126E-2},{"$f":"'AAPL and Google'!F63","v":-0.22019528503533467}]
["2011-11-01",{"$f":"'AAPL and Google'!E64","v":-5.7399677831886937E-2},{"$f":"'AAPL and Google'!F64","v":-9.6183161090669669E-2}]
["2011-12-01",{"$f":"'AAPL and Google'!E65","v":5.794303530036643E-2},{"$f":"'AAPL and Google'!F65","v":-1.0241494052196907E-2}]
["2012-01-03",{"$f":"'AAPL and Google'!E66","v":0.11965782035865079},{"$f":"'AAPL and Google'!F66","v":2.4596960000504701E-2}]
["2012-02-01",{"$f":"'AAPL and Google'!E67","v":0.17253259275455476},{"$f":"'AAPL and Google'!F67","v":-4.8588347918139083E-2}]
["2012-03-01",{"$f":"'AAPL and Google'!E68","v":0.1001018936056976},{"$f":"'AAPL and Google'!F68","v":-5.4754775012495489E-2}]
["2012-04-02",{"$f":"'AAPL and Google'!E69","v":-2.6312638158984922E-2},{"$f":"'AAPL and Google'!F69","v":-2.8446094702639788E-2}]
["2012-05-01",{"$f":"'AAPL and Google'!E70","v":-1.0760104160047555E-2},{"$f":"'AAPL and Google'!F70","v":-1.9193855066193692E-2}]
["2012-06-01",{"$f":"'AAPL and Google'!E71","v":1.0794351321817304E-2},{"$f":"'AAPL and Google'!F71","v":0.10957899438258194}]

{"sheet":"Not efficient","index":4,"n_rows":54,"n_cols":6,"rows_kept":54,"cut":false,"hidden":false,"merged":[[0,0,0,6],[1,0,1,3],[12,5,14,6]]}
["A FOUR-ASSET PORTFOLIO PROBLEM"]
["Variance-covariance, S",null,null,null,null,"Mean returns E(r)"]
[0.1,0.01,0.03,0.05,null,0.06]
[0.01,0.3,0.06,-0.04,null,0.08]
[0.03,0.06,0.4,0.02,null,0.1]
[0.05,-0.04,0.02,0.5,null,0.15]
[]
["Portfolio x",0.2,0.3,0.4,0.1]
["Portfolio y",0.2,0.1,0.1,0.6]
[]
["Portfolio x and y statistics:  Mean, variance, covariance, correlation"]
["Mean, E(rx)",{"$f":"MMULT(B8:E8,F3:F6)","v":9.1000000000000011E-2},null,"Mean, E(ry)",{"$f":"MMULT(B9:E9,F3:F6)","v":0.12},{"$f":"getformula(E12)","v":"<--  {=MMULT(B9:E9,F3:F6)}"}]
["Variance sx2",{"$f":"MMULT(MMULT(B8:E8,A3:D6),TRANSPOSE(B8:E8))","v":0.12160000000000001},null,"Variance sy2",{"$f":"MMULT(MMULT(B9:E9,A3:D6),TRANSPOSE(B9:E9))","v":0.2034},{"$f":"getformula(E13)","v":"<--  {=MMULT(MMULT(B9:E9,A3:D6),TRANSPOSE(B9:E9))}"}]
["Covariance(x,y)",{"$f":"MMULT(MMULT(B8:E8,A3:D6),TRANSPOSE(B9:E9))","v":7.1400000000000005E-2}]
["Correlation rxy",{"$f":"B14/SQRT(B13*E13)","v":0.45400010156574272},{"$f":"getformula(B15)","v":"<--  =B14/SQRT(B13*E13)"}]
[]
["Calculating returns of combinations of Portfolio x and Portfolio y"]
["Proportion of x",0.72447847356743444]
["Mean portfolio return, E(rp)",{"$f":"B18*B12+(1-B18)*E12","v":9.899012426654441E-2},{"$f":"getformula(B19)","v":"<--  =B18*B12+(1-B18)*E12"}]
["Portfolio variance sp2",{"$f":"B18^2*B13+(1-B18)^2*E13+2*B18*(1-B18)*B14","v":0.107768825466523},{"$f":"getformula(B20)","v":"<--  =B18^2*B13+(1-B18)^2*E13+2*B18*(1-B18)*B14"}]
["Portfolio standard deviation sp",{"$f":"SQRT(B20)","v":0.32828162523437554},{"$f":"getformula(B21)","v":"<--  =SQRT(B20)"}]
[]
["Table of returns (using Data Table)"]
["Proportion of x","Standard deviation","Mean"]
[null,{"$f":"B21","v":0.32828162523437554},{"$f":"B19","v":9.899012426654441E-2}]
[-1,0.80597766718439534,0.14899999999999997,{"$f":"C26","v":0.14899999999999997}]
[-0.8,0.72884017452388006,0.14319999999999999,{"$f":"C27","v":0.14319999999999999}]
[-0.6,0.65375224665005938,0.13739999999999999,0.13739999999999999]
[-0.4,0.58150838343054012,0.13159999999999997,0.13159999999999997]
[-0.2,0.51331082201722567,0.1258,0.1258]
[0,0.45099889135118726,0.12,0.12]
[0.2,0.39735123002200462,0.11420000000000001,0.11420000000000001]
[0.4,0.35630324163554844,0.1084,0.1084]
[0.6,0.33255375505322443,0.1026,0.1026]
[0.724478473567434,0.32828162523437554,9.899012426654441E-2,9.899012426654441E-2]
[1,0.34871191548325392,9.1000000000000011E-2]
[1.2,0.38596372886580937,8.5200000000000012E-2]
[1.4,0.43693477774148393,7.9400000000000026E-2]
[1.6,0.49742537128699016,7.3600000000000027E-2]
[1.8,0.56438284878263267,6.7800000000000027E-2]
[2,0.6357672530100934,6.2000000000000027E-2]
[2.2000000000000002,0.7102450281416971,5.6200000000000028E-2]
[2.4,0.78693837115748777,5.0400000000000028E-2]
[2.6,0.8652583429242392,4.4600000000000029E-2]
[2.7,0.90489667918497751,4.1700000000000043E-2]
["Stock1",{"$f":"SQRT(A3)","v":0.31622776601683794},null,{"$f":"F3","v":0.06}]
["Stock2",{"$f":"SQRT(B4)","v":0.54772255750516607},null,{"$f":"F4","v":0.08}]
["Stock3",{"$f":"SQRT(C5)","v":0.63245553203367588},null,0.1]
["Stock4",{"$f":"SQRT(D6)","v":0.70710678118654757},null,0.15]
[]
[]
[]
[]
["Minimum variance portfolio"]