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{"sheet":"TwoAssets","index":0,"n_rows":46,"n_cols":21,"rows_kept":46,"cut":false,"hidden":false,"merged":[[8,1,8,2]]}
["2 Asset Portfolio"]
["Corelation",-0.8]
[null,"StDev of Return","Mean Expected Return","Portfolio Weight"]
["Stock A",0.08,0.04,0.4]
["Stock B",0.24,0.15,{"$f":"1-D4","v":0.6}]
["Portfolio",{"$f":"(D4^2*B4^2+2*D4*D5*B2*B4*B5+D5^2*B5^2)^0.5","v":0.11994665480954439},{"$f":"C4*D4+C5*D5","v":0.106}]
[]
[]
[null,"Portfolio"]
["Weight A","StDev","Expected",null,null,null,null,null,null,null,null,"Important Formulas:"]
[null,{"$f":"B6","v":0.11994665480954439},{"$f":"C6","v":0.106},null,null,null,null,null,null,null,null,"ρ(i,j) = CORR(i,j) = Correlation of returns between assets i and j"]
[0,0.24,0.15,null,null,null,null,null,null,null,null,"σ(i) = Stdev(i) = Standard deviation of returns of asset i"]
[{"$f":"A12+0.1","v":0.1},0.20965495462783607,0.13900000000000001,null,null,null,null,null,null,null,null,"σ(i,j) = COV(i,j) = Covariance of returns of assets i and j"]
[{"$f":"A13+0.1","v":0.2},0.1794569586279674,0.128,null,null,null,null,null,null,null,null,"σ(i,j) = ρ(i,j) * σ(i) * σ(j) <-- COV(i,j) = CORR(i,j) * Stdev(i) * Stdev(j)"]
[0.30000000000000004,0.14949515042301537,0.11699999999999999,null,null,null,null,null,null,null,null,"ρ(i,j) = σ(i,j) / [σ(i) * σ(j)]"]
[0.4,0.11994665480954439,0.106,null,null,null,null,null,null,null,null,"Same two assets: COV(i,i) = VAR(i) = Stdev(i)^2"]
[0.5,9.121403400793103E-2,9.5000000000000001E-2]
[0.6,6.4398757751993954E-2,8.3999999999999991E-2,null,null,null,null,null,null,null,null,"Variance-Covariance Matrix [σ(i,j)]"]
[0.7,4.3229619475540139E-2,7.3000000000000009E-2,null,null,null,null,null,null,null,null,null,"Stock A","Stock B",null,null,"WA * WA * σ(A,A) =",{"$f":"D4*D4*M20","v":1.0240000000000002E-3}]
[0.79999999999999993,3.8533102652135359E-2,6.2000000000000013E-2,null,null,null,null,null,null,null,null,"Stock A",{"$f":"B4^2","v":6.4000000000000003E-3},{"$f":"M21","v":-1.536E-2},null,null,"WA * WB * σ(A,B) =",{"$f":"D4*D5*N20","v":-3.6863999999999998E-3}]
[0.89999999999999991,5.4728420404758608E-2,5.1000000000000011E-2,null,null,null,null,null,null,null,null,"Stock B",{"$f":"B2*B4*B5","v":-1.536E-2},{"$f":"B5^2","v":5.7599999999999998E-2},null,null,"WB * WA * σ(B,A) =",{"$f":"D5*D4*M21","v":-3.6863999999999998E-3}]
[0.99999999999999989,7.9999999999999988E-2,3.9999999999999994E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,"WB * WB * σ(B,B) =",{"$f":"D5*D5*N21","v":2.0735999999999997E-2}]
[null,null,null,null,null,null,null,null,null,null,null,"Current Wts -->",{"$f":"D4","v":0.4},{"$f":"1-M23","v":0.6},null,null,"Portfolio Variance =",{"$f":"SUM(R19:R22)","v":1.4387199999999998E-2},{"$f":"R23^0.5","v":0.11994665480954439},"<-- Portfolio Stdev"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Portfolio Variance",{"$f":"MMULT(MMULT(TRANSPOSE(D4:D5),M20:N21),D4:D5)","v":1.4387199999999998E-2},{"$f":"getformula(N25)","v":"<--  =MMULT(MMULT(TRANSPOSE(D4:D5),M20:N21),D4:D5)"}]
[null,null,null,null,null,null,null,null,null,null,null,null,"Portfolio Stdev",{"$f":"N25^0.5","v":0.11994665480954439},{"$f":"getformula(N26)","v":"<--  =N25^0.5"}]
[null,null,null,null,null,null,null,null,"Blending Portfolios:"]
[null,null,null,null,null,null,null,null,null,null,null,"4 Portfolios from 2 Stocks",null,null,null,"Var/Covar Matrix for All 4 Portfolios"]
[null,null,null,null,null,null,null,null,"S=Var/Covar Matrix",null,null,"Portfolio","Wt A","Wt B","E(Return)",null,1,2,3,4,"<-- Portfolio"]
[null,null,null,null,null,null,null,null,null,null,null,1,0.2,{"$f":"1-M30","v":0.8},{"$f":"MMULT(M30:N33,C4:C5)","v":0.128},1,{"$f":"MMULT(MMULT(M30:N33,M20:N21),TRANSPOSE(M30:N33))","v":3.2204800000000006E-2},2.1401600000000003E-2,1.0598400000000001E-2,-2.0480000000000151E-4]
[null,null,null,null,null,null,null,null,null,null,null,2,0.4,{"$f":"1-M31","v":0.6},0.106,2,2.14016E-2,1.4387199999999998E-2,7.3728000000000005E-3,3.5839999999999744E-4]
[null,null,null,null,null,null,null,null,null,null,null,3,0.6,0.4,8.3999999999999991E-2,3,1.0598400000000001E-2,7.3728000000000005E-3,4.1472000000000011E-3,9.2159999999999942E-4]
[null,null,null,null,null,null,null,null,null,null,null,4,0.8,0.19999999999999996,6.1999999999999993E-2,4,-2.0480000000000221E-4,3.5839999999999868E-4,9.2159999999999942E-4,1.4848000000000005E-3]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,"W=Weight Matrix",null,null,{"$f":"_xlfn.FORMULATEXT(Q30)","v":"=MMULT(MMULT(M30:N33,M20:N21),TRANSPOSE(M30:N33))"},null,null,null,null,null,"  <-- W S W'"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Weight Matrix * E(Returns)"]
[null,null,null,null,null,null,null,null,null,null,null,null,"X","Y"]
[null,null,null,null,null,null,null,null,{"$f":"_xlfn.FORMULATEXT(M40)","v":"=INDEX($Q$30#,L40,L40)^0.5"},null,null,1,{"$f":"INDEX(_xlfn.ANCHORARRAY($Q$30),L40,L40)^0.5","v":0.1794569586279674},{"$f":"O30","v":0.128}]
[null,null,null,null,null,null,null,null,null,null,null,2,{"$f":"INDEX(_xlfn.ANCHORARRAY($Q$30),L41,L41)^0.5","v":0.11994665480954439},{"$f":"O31","v":0.106}]
[null,null,null,null,null,null,null,null,null,null,null,3,{"$f":"INDEX(_xlfn.ANCHORARRAY($Q$30),L42,L42)^0.5","v":6.4398757751993954E-2},8.3999999999999991E-2]
[null,null,null,null,null,null,null,null,null,null,null,4,{"$f":"INDEX(_xlfn.ANCHORARRAY($Q$30),L43,L43)^0.5","v":3.8533102652135352E-2},6.1999999999999993E-2]
[]
[null,null,null,null,null,null,null,null,null,null,null,"MIN",{"$f":"MIN(M40:M43)","v":3.8533102652135352E-2},{"$f":"MIN(N40:N43)","v":6.1999999999999993E-2}]
[null,null,null,null,null,null,null,null,null,null,null,"MAX",{"$f":"MAX(M40:M43)","v":0.1794569586279674},{"$f":"MAX(N40:N43)","v":0.128}]

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["PRICES AND RETURNS FOR APPLE AND GOOGLE\nJune 2007 - June 2012",null,null,null,null,null,null,null,null,null,"STOCKHISTORY FUNCTION",null,null,null,null,null,null,"Number of Prices",{"$f":"COUNT(K11:K71)","v":61}]
["Monthly mean",{"$f":"AVERAGE(E11:E71)","v":2.6092535382995975E-2},{"$f":"AVERAGE(F11:F71)","v":-2.4269022221436731E-3},{"$f":"getformula(C2)","v":"<--  =AVERAGE(F11:F71)"},null,null,null,null,null,null,null,{"$f":"CORREL(M12:M71,P12:P71)","v":0.49874485196926593},{"$f":"_xlfn.FORMULATEXT(L2)","v":"=CORREL(M12:M71,P12:P71)"},null,null,null,null,"Start",42856]
["Monthly variance",{"$f":"_xlfn.VAR.S(E11:E71)","v":1.2477690692371124E-2},{"$f":"_xlfn.VAR.S(F11:F71)","v":1.0175180168436861E-2},{"$f":"getformula(C3)","v":"<--  =VAR.S(F11:F71)"},null,null,null,null,null,null,{"$f":"K9","v":"AAPL"},{"$f":"_xlfn.STDEV.S(M12:M71)","v":8.5812104520882615E-2},{"$f":"_xlfn.FORMULATEXT(L3)","v":"=STDEV.S(M12:M71)"},null,null,null,null,"End",44682]
["Monthly standard deviation",{"$f":"_xlfn.STDEV.S(E11:E71)","v":0.11170358406233492},{"$f":"_xlfn.STDEV.S(F11:F71)","v":0.10087209806699204},{"$f":"getformula(C4)","v":"<--  =STDEV.S(F11:F71)"},null,null,null,null,null,null,{"$f":"N10","v":"Close"},{"$f":"_xlfn.STDEV.S(P12:P71)","v":6.915453921965134E-2},"=STDEV.S(P12:P71)"]
[null,"AAPL","Google",null,null,null,"Continuously Compounded Returns",null,null,null,null,{"$f":"L2*L3*L4","v":2.9596998531795735E-3},"=L2*L3*L4",null,null,{"$f":"_xlfn.COVARIANCE.S(M12:M71,P12:P71)","v":2.9596998531795748E-3},{"$f":"_xlfn.FORMULATEXT(P5)","v":"=COVARIANCE.S(M12:M71,P12:P71)"}]
["Annual mean",{"$f":"12*B2","v":0.31311042459595173},{"$f":"12*C2","v":-2.9122826665724078E-2},{"$f":"getformula(C6)","v":"<--  =12*C2"},null,null,"for Both AAPL & Google",null,null,null,{"$f":"_xlfn.FORMULATEXT(K10)","v":"=STOCKHISTORY(K9,S2,S3,2,1,1,0)"}]
["Annual variance",{"$f":"12*B3","v":0.14973228830845348},{"$f":"12*C3","v":0.12210216202124233},{"$f":"getformula(C7)","v":"<--  =12*C3"},null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.FORMULATEXT(N10)","v":"=STOCKHISTORY(N9,S2,S3,2,1,1,0)"}]
["Annual standard deviation",{"$f":"SQRT(12)*B4","v":0.38695256596701033},{"$f":"SQRT(12)*C4","v":0.34943119783620108},{"$f":"getformula(C8)","v":"<--  =SQRT(12)*C4"},null,null,{"$f":"12^0.5*C4","v":0.34943119783620108}]
[null,"PRICES",null,null,"RETURNS",null,null,null,null,null,"AAPL",{"$f":"K9","v":"AAPL"},{"$f":"L9","v":"AAPL"},"GOOGL",{"$f":"N9","v":"GOOGL"},"GOOGL"]
["Date","AAPL","Google",null,"AAPL","Google",null,null,null,null,{"$f":"_xlfn.STOCKHISTORY(K9,S2,S3,2,1,1,0)","v":"Close"},"Date","Return",{"$f":"_xlfn.STOCKHISTORY(N9,S2,S3,2,1,1,0)","v":"Close"},"Date","Return"]
["2007-06-01",122.04,580.11,null,null,null,null,null,null,null,38.19,42856,null,49.354500000000002,42856]
["2007-07-02",131.76,645.9,null,{"$f":"LN(B12/B11)","v":7.6633226020915893E-2},{"$f":"LN(C12/C11)","v":0.10742695230781683},{"$f":"getformula(F12)","v":"<--  =LN(C12/C11)"},null,null,null,36.005000000000003,42887,{"$f":"LN(K12/K11)","v":-5.8915883536594611E-2},46.484000000000002,42887,{"$f":"LN(N12/N11)","v":-5.9920779772060832E-2}]
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["2007-10-01",189.95,515.04,null,0.21325577144663097,-0.14034256446726184,"<--  =LN(C15/C14)",null,null,null,38.53,42979,-6.2134908066241522E-2,48.686,42979,1.9161170172757896E-2]
["2007-11-01",182.22,540.96,null,-4.1546131347922108E-2,4.9100771409077877E-2,"<--  =LN(C16/C15)",null,null,null,42.26,43009,9.2403853549844414E-2,51.652000000000001,43009,5.9137402557176658E-2]
["2007-12-03",198.08,603.69000000000005,null,8.3456241210519033E-2,0.10971548218681069,"<--  =LN(C17/C16)",null,null,null,42.962499999999999,43040,1.6486629988041575E-2,51.808500000000002,43040,3.0253114833963088E-3]
["2008-01-02",135.36000000000001,506.38,null,-0.38073309363831809,-0.17577344556712143,"<--  =LN(C18/C17)",null,null,null,42.307499999999997,43070,-1.536326687584849E-2,52.67,43070,1.6491805027496587E-2]
["2008-02-01",125.02,529.02,null,-7.9464171354247048E-2,4.3738862747725364E-2,"<--  =LN(C19/C18)",null,null,null,41.857500000000002,43101,-1.0693382951542386E-2,59.110999999999997,43101,0.11537099880911227]
["2008-03-03",143.5,544.1,null,0.13786131069600946,2.8106815164888964E-2,"<--  =LN(C20/C19)",null,null,null,44.53,43132,6.1892126985049735E-2,55.195999999999998,43132,-6.8526545415102211E-2]
["2008-04-01",173.95,586.76,null,0.1924328663982752,7.5482824127682258E-2,"<--  =LN(C21/C20)",null,null,null,41.945,43160,-5.9803883035353091E-2,51.856999999999999,43160,-6.2400556504501686E-2]
["2008-05-01",188.75,613.4,null,8.1655486531183152E-2,4.440137406058902E-2,"<--  =LN(C22/C21)",null,null,null,41.314999999999998,43191,-1.5133606145110265E-2,50.929000000000002,43191,-1.8057424473910989E-2]
["2008-06-02",167.44,600.36,null,-0.1197983099913898,-2.148777639203717E-2,"<--  =LN(C23/C22)",null,null,null,46.717500000000001,43221,0.12289319666112564,55,43221,7.6900679321575655E-2]
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["2008-08-01",169.53,555.71,null,6.4440214953050093E-2,-6.6582237591538612E-2,"<--  =LN(C25/C24)",null,null,null,47.572499999999998,43282,2.7598981342321541E-2,61.360999999999997,43282,8.3250887229265741E-2]
["2008-09-02",113.66,613.70000000000005,null,-0.39981836644088625,9.9259633949873111E-2,"<--  =LN(C26/C25)",null,null,null,56.907499999999999,43313,0.17917227944538186,61.59,43313,3.7250655106901513E-3]
["2008-10-01",107.59,525.79,null,-5.4883829263157574E-2,-0.15460431591839269,"<--  =LN(C27/C26)",null,null,null,56.435000000000002,43344,-8.3376092318169122E-3,60.353999999999999,43344,-2.0272294318695757E-2]
["2008-11-03",92.67,450.02,null,-0.1492829110072178,-0.15560986725547385,"<--  =LN(C28/C27)",null,null,null,54.715000000000003,43374,-3.0951638537183281E-2,54.529000000000003,43374,-0.10149455513968871]
["2008-12-01",85.35,484.85,null,-8.2284346358150504E-2,7.4547538529370433E-2,"<--  =LN(C29/C28)",null,null,null,44.645000000000003,43405,-0.20339557590122662,55.482500000000002,43405,1.7334985474179766E-2]
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["2009-04-01",125.83,567.12,null,0.17982923486757607,7.5840213721359739E-2,"<--  =LN(C33/C32)",null,null,null,47.487499999999997,43525,9.2602608785203558E-2,58.844499999999996,43525,4.371550079749098E-2]
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["2009-07-01",163.38999999999999,619.98,null,0.1372893300962372,0.15692342686377875,"<--  =LN(C36/C35)",null,null,null,49.48,43617,0.12267701469933667,54.14,43617,-2.1651601750958271E-2]
["2009-08-03",168.21,583,null,2.9073217760958888E-2,-6.15000331038262E-2,"<--  =LN(C37/C36)",null,null,null,53.26,43647,7.3617032861498941E-2,60.91,43647,0.11782408066223812]
["2009-09-01",185.35,536.12,null,9.7032730793050262E-2,-8.3829169740196469E-2,"<--  =LN(C38/C37)",null,null,null,52.185000000000002,43678,-2.0390483113771035E-2,59.526499999999999,43678,-2.2975773296958622E-2]
["2009-10-01",188.5,495.85,null,1.6852077291324211E-2,-7.8084554978161788E-2,"<--  =LN(C39/C38)",null,null,null,55.9925,43709,7.042265592247357E-2,61.057000000000002,43709,2.5386262546970812E-2]
["2009-11-02",199.91,461.67,null,5.8769258379585923E-2,-7.1423111488264107E-2,"<--  =LN(C40/C39)",null,null,null,62.19,43739,0.10497646192130912,62.94,43739,3.0374037537855513E-2]
["2009-12-01",210.73,443.05,null,5.2710427941470024E-2,-4.1167719650558612E-2,"<--  =LN(C41/C40)",null,null,null,66.8125,43770,7.1695973669466145E-2,65.204499999999996,43770,3.5346593319593785E-2]
["2010-01-04",192.06,421.59,null,-9.276986999929468E-2,-4.9649352712548125E-2,"<--  =LN(C42/C41)",null,null,null,73.412499999999994,43800,9.4204032063373785E-2,66.969499999999996,43800,2.6708806908667681E-2]
["2010-02-01",204.62,417.23,null,6.3346777240967267E-2,-1.0395649281585149E-2,"<--  =LN(C43/C42)",null,null,null,77.377499999999998,43831,5.2601819811865784E-2,71.638999999999996,43831,6.7402326548264918E-2]
["2010-03-01",235,395.97,null,0.13843091369336494,-5.2299177690205201E-2,"<--  =LN(C44/C43)",null,null,null,68.34,43862,-0.12420079397335779,66.962500000000006,43862,-6.7506857205708398E-2]
["2010-04-01",261.08999999999997,348.06,null,0.10527966132537296,-0.12896357210294498,"<--  =LN(C45/C44)",null,null,null,63.572499999999998,43891,-7.2314259785660584E-2,58.097499999999997,43891,-0.14201012753489525]
["2010-05-03",256.88,337.99,null,-1.6256125688273504E-2,-2.9358569459494093E-2,"<--  =LN(C46/C45)",null,null,null,73.45,43922,0.14442391571840119,67.334999999999994,43922,0.14755752722982143]
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["2012-04-02",583.98,458.16,null,-2.6312638158984922E-2,-2.8446094702639788E-2,null,null,null,null,174.61,44621,5.5882433240838261E-2,139.0675,44621,2.926251522044027E-2]
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[]
["Note: Dates here run oldest (top) to most recent (bottom)!"]
[null,null,null,null,null,null,null,null,null,null,"DATA/STOCKS:"]
[null,null,null,null,null,null,null,null,null,null,null,"Beta","Ticker","High"]
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["2011-09-01",{"$f":"'Pages 198, 199'!E62","v":-9.1627607052127934E-3},{"$f":"'Pages 198, 199'!F62","v":2.0000666706669435E-2},null,-3.5255296088208765E-2,2.2427568928813108E-2,-7.9069058312401721E-4]
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[]
["Average",{"$f":"AVERAGE(B4:B63)","v":2.6092535382995975E-2},{"$f":"AVERAGE(C4:C63)","v":-2.4269022221436731E-3}]
["Variance",{"$f":"_xlfn.VAR.S(B4:B63)","v":1.2477690692371124E-2},{"$f":"_xlfn.VAR.S(C4:C63)","v":1.0175180168436861E-2},{"$f":"getformula(C66)","v":"<--  =VAR.S(C4:C63)"},null,"Covariance computation"]
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[null,{"$f":"_xlfn.VAR.P(B4:B63)","v":1.2269729180831605E-2},{"$f":"_xlfn.VAR.P(C4:C63)","v":1.0005593832296248E-2},{"$f":"getformula(C70)","v":"<--  =VAR.P(C4:C63)"},null,null,{"$f":"AVERAGE(G4:G63)*60/59","v":1.98912626457544E-3},{"$f":"getformula(G70)","v":"<--  =AVERAGE(G4:G63)*60/59"}]
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[null,{"$f":"SQRT(B70)","v":0.11076880960284625},{"$f":"SQRT(C70)","v":0.10002796525120486},"<--  =SQRT(C70)"]
[null,null,null,null,null,"Correlation computation"]
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[null,null,null,null,null,null,{"$f":"G71/(B67*C67)","v":0.1765323042664021},{"$f":"getformula(G76)","v":"<--  =G71/(B67*C67)"}]

{"sheet":"Page 202","index":3,"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"]
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["2010-10-01",{"$f":"'Pages 198, 199'!E51","v":5.8950248562960224E-2},{"$f":"'Pages 198, 199'!F51","v":0.10843903128952363}]
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["2012-03-01",{"$f":"'Pages 198, 199'!E68","v":0.1001018936056976},{"$f":"'Pages 198, 199'!F68","v":-5.4754775012495489E-2}]
["2012-04-02",{"$f":"'Pages 198, 199'!E69","v":-2.6312638158984922E-2},{"$f":"'Pages 198, 199'!F69","v":-2.8446094702639788E-2}]
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["2012-06-01",{"$f":"'Pages 198, 199'!E71","v":1.0794351321817304E-2},{"$f":"'Pages 198, 199'!F71","v":0.10957899438258194}]

{"sheet":"Page 203","index":4,"n_rows":65,"n_cols":10,"rows_kept":65,"cut":false,"hidden":false,"merged":[[0,0,0,4]]}
["CALCULATING THE MEAN AND STANDARD DEVIATION OF A PORTFOLIO"]
["Proportion of AAPL",0.5,null,"<-- Weight based on $ value in portfolio"]
["Proportion of GOOG",{"$f":"1-B2","v":0.5},{"$f":"getformula(B3)","v":"<--  =1-B2"},"<-- Weight based on $ value in portfolio"]
[]
[null,"AAPL\nreturn","GOOG\nreturn","Portfolio \nreturn",null,null,"Asset returns","AAPL","GOOG"]
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["Asset returns","AAPL","GOOG"]
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["Proportion of AAPL",0.5]
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["Portfolio Variance with 3 Assets"]
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[]
[]
[]
[]
[]
[]
[]
[null,null,null,1,2,3]
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[null,3,"W3","σ31","σ32","σ33"]

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["A FOUR-ASSET PORTFOLIO PROBLEM"]
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[{"$f":"D3","v":0.05},{"$f":"D4","v":-0.04},{"$f":"D5","v":0.02},0.5,null,0.15,null,null,"Portfolios x & y:"]
[null,"Asset Weights",null,null,null,null,null,null,"Means","Var/Covar"]
["Portfolio x",0.2,0.3,0.4,{"$f":"1-SUM(B8:D8)","v":9.9999999999999978E-2},{"$f":"getformula(E8)","v":"<--  =1-SUM(B8:D8)"},null,null,{"$f":"MMULT(B8:E9,F3:F6)","v":9.1000000000000011E-2},{"$f":"MMULT(MMULT(B8:E9,A3:D6),TRANSPOSE(B8:E9))","v":0.1216},7.1399999999999991E-2]
["Portfolio y",0.2,0.1,0.1,{"$f":"1-SUM(B9:D9)","v":0.6},"<--  =1-SUM(B9:D9)",null,null,0.12,7.1399999999999991E-2,0.2034]
[]
["Portfolio x and y statistics:  Mean, variance, covariance, correlation",null,null,null,null,null,null,null,"Combining Portfolios x & y:",null,null,"Weights"]
["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},{"$f":"getformula(E12)","v":"<--  =MMULT(B9:E9,F3:F6)"},null,null,"Mean",{"$f":"MMULT(TRANSPOSE(I8:I9),L12:L13)","v":0.1113},null,{"$f":"B18","v":0.3}]
["Variance sx2",{"$f":"MMULT(MMULT(B8:E8,A3:D6),TRANSPOSE(B8:E8))","v":0.1216},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))"},null,null,"Variance",{"$f":"MMULT(MMULT(TRANSPOSE(L12:L13),J8:K9),L12:L13)","v":0.14059799999999997},null,{"$f":"1-L12","v":0.7}]
["Covariance(x,y)",{"$f":"MMULT(MMULT(B8:E8,A3:D6),TRANSPOSE(B9:E9))","v":7.1399999999999991E-2},null,null,null,null,null,null,"StDev",{"$f":"SQRT(J13)","v":0.37496399827183408}]
["Correlation rxy",{"$f":"B14/SQRT(B13*E13)","v":0.45400010156574272},{"$f":"getformula(B15)","v":"<--  =B14/SQRT(B13*E13)"}]
[null,null,null,null,null,null,null,"Matrix Notation for X-Y Variance-Covariance Matrix"]
["Calculating returns of combinations of Portfolio x and Portfolio y",null,null,null,null,null,null,null,"Sxy = WSW'"]
["Proportion of x",0.3,null,null,null,null,null,null,null,"x","y"]
["Mean portfolio return, E(rp)",{"$f":"B18*B12+(1-B18)*E12","v":0.1113},{"$f":"getformula(B19)","v":"<--  =B18*B12+(1-B18)*E12"},null,null,null,null,null,"x",{"$f":"MMULT(MMULT(B8:E9,A3:D6),TRANSPOSE(B8:E9))","v":0.1216},7.1399999999999991E-2]
["Portfolio variance sp2",{"$f":"B18^2*B13+(1-B18)^2*E13+2*B18*(1-B18)*B14","v":0.14059799999999997},{"$f":"getformula(B20)","v":"<--  =B18^2*B13+(1-B18)^2*E13+2*B18*(1-B18)*B14"},null,null,null,null,null,"y",7.1399999999999991E-2,0.2034]
["Portfolio standard deviation sp",{"$f":"SQRT(B20)","v":0.37496399827183408},{"$f":"getformula(B21)","v":"<--  =SQRT(B20)"}]
[]
["Table of returns (using Data Table)"]
["Proportion of x","Standard deviation","Mean"]
[null,{"$f":"B21","v":0.37496399827183408},{"$f":"B19","v":0.1113}]
[-0.5,0.6172114710534794,0.13449999999999998]
[-0.4,0.58150838343054012,0.13159999999999997]
[-0.3,0.54680709578424458,0.12870000000000001,null,null,null,null,null,null,null,null,"Note on Array Functions: If you have a current version of Microsoft 365, then"]
[-0.2,0.51331082201722567,0.1258,null,null,null,null,null,null,null,null,"you can simply enter the formula in the top-left-cell of the output range, then press"]
[-0.1,0.48127123329781518,0.12290000000000001,null,null,null,null,null,null,null,null,"ENTER to confirm the formula as a dynamic array formula. Otherwise, the formula"]
[0,0.45099889135118726,0.12,null,null,null,null,null,null,null,null,"must be entered as a legacy array formula by first selecting the output range, entering"]
[0.1,0.42287350354449971,0.1171,null,null,null,null,null,null,null,null,"the formula in the top-left-cell of the output range, and then pressing"]
[0.2,0.39735123002200462,0.11420000000000001,null,null,null,null,null,null,null,null,"CTRL+SHIFT+ENTER to confirm it. Excel inserts curly brackets at the beginning and"]
[0.3,0.37496399827183408,0.1113,null,null,null,null,null,null,null,null,"end of the formula for you."]
[0.4,0.35630324163554844,0.1084]
[0.5,0.3419795315512319,0.10550000000000001]
[0.6,0.33255375505322443,0.1026]
[0.7,0.3284478649648982,9.9700000000000011E-2]
[0.8,0.32986057660775409,9.6800000000000011E-2]
[0.9,0.33672243762481879,9.3900000000000011E-2]
[1,0.34871191548325386,9.1000000000000011E-2]
[1.1000000000000001,0.36532451327552606,8.8100000000000012E-2]
[1.2,0.38596372886580932,8.5200000000000012E-2]
[1.3,0.41002195063191438,8.2300000000000012E-2]
[1.4,0.43693477774148393,7.9400000000000026E-2]

{"sheet":"Page 212 CML","index":7,"n_rows":62,"n_cols":12,"rows_kept":62,"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)","This sheet is similar to previous. Individual stocks are added to chart below."]
[0.1,0.01,0.03,0.05,"Stock1",0.06]
[0.01,0.3,0.06,-0.04,"Stock2",0.08,null,"The Sharpe Ratio measures excess return per unit of risk for an asset"]
[0.03,0.06,0.4,0.02,"Stock3",0.1,null,"(stock) or portfolio. It equals (Ri-Rf)/σi, where σi is the standard deviation"]
[0.05,-0.04,0.02,0.5,"Stock4",0.15,null,"of the rate of return on asset i (assuming Rf is constant). σi is a total risk"]
[null,null,null,null,null,null,null,"measure (also called volatility) and may be estimated from historical data."]
["Portfolio x",0.19242066451854326,0.25513683772569656,0.1949369828628989,{"$f":"1-SUM(B8:D8)","v":0.3575055148928612},"<-- Weights Must Maximize X-Sharpe Ratio",null,"Riskfree",0.03]
["Portfolio y",0.60623791345993727,0.20709300788180007,9.4205469685288562E-2,{"$f":"1-SUM(B9:D9)","v":9.2463608972974121E-2},"<-- Weights Must Minimize Y-Risk",null,"Sharpe",{"$f":"(B12-I8)/B13^0.5","v":0.2224460377887516}]
[null,null,null,null,null,null,null,null,null,"X","Y"]
["Portfolio x and y statistics:  Mean, variance, covariance, correlation",null,null,null,null,null,null,null,null,0,{"$f":"I8","v":0.03},"Riskfree"]
["Mean, E(rx)",{"$f":"MMULT(B8:E8,F3:F6)","v":0.10507571240938739},null,"Mean, E(ry)",{"$f":"MMULT(B9:E9,F3:F6)","v":7.6231803752615221E-2},{"$f":"getformula(E12)","v":"<--  {=MMULT(B9:E9,F3:F6)}"},null,null,null,{"$f":"B13^0.5","v":0.33750078515978732},{"$f":"B12","v":0.10507571240938739},"M"]
["Variance sx2",{"$f":"MMULT(MMULT(B8:E8,A3:D6),TRANSPOSE(B8:E8))","v":0.11390677998347293},null,"Variance sy2",{"$f":"MMULT(MMULT(B9:E9,A3:D6),TRANSPOSE(B9:E9))","v":7.0144078530747223E-2},{"$f":"getformula(E13)","v":"<--  {=MMULT(MMULT(B9:E9,A3:D6),TRANSPOSE(B9:E9))}"},null,null,null,{"$f":"B45","v":0.62383812983841125},{"$f":"I9*J13+I8","v":0.16877032020409935},"CML"]
["Covariance(x,y)",{"$f":"MMULT(MMULT(B8:E8,A3:D6),TRANSPOSE(B9:E9))","v":7.0144095946959778E-2},null,null,null,null,null,null,null,{"$f":"E13^0.5","v":0.26484727397265623},{"$f":"E12","v":7.6231803752615221E-2},"Min Risk"]
["Correlation rxy",{"$f":"B14/SQRT(B13*E13)","v":0.78473103286773604},{"$f":"getformula(B15)","v":"<--  =B14/SQRT(B13*E13)"},null,null,null,null,null,null,{"$f":"J12","v":0.33750078515978732},{"$f":"K12","v":0.10507571240938739},"M"]
[]
["Calculating returns of combinations of Portfolio x and Portfolio y"]
["Proportion of x",0.4]
["Mean portfolio return, E(rp)",{"$f":"B18*B12+(1-B18)*E12","v":8.7769367215324093E-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":7.7146119122965373E-2},{"$f":"getformula(B20)","v":"<--  =B18^2*B13+(1-B18)^2*E13+2*B18*(1-B18)*B14"}]
["Portfolio standard deviation sp",{"$f":"SQRT(B20)","v":0.27775190210503575},{"$f":"getformula(B21)","v":"<--  =SQRT(B20)"}]
[]
["Table of returns (using Data Table)"]
["Proportion of x","Standard deviation","Mean"]
[null,{"$f":"B21","v":0.27775190210503575},{"$f":"B19","v":8.7769367215324093E-2}]
[-1,0.33750068195282612,4.7387895095843055E-2]
[-0.8,0.31329244692746672,5.3156676827197477E-2]
[-0.6,0.29308465946651047,5.8925458558551927E-2]
[-0.4,0.27775185194166624,6.4694240289906335E-2]
[-0.2,0.26813164346841689,7.0463022021260785E-2]
[0,0.26484727397265623,7.6231803752615221E-2]
[0.2,0.26813166945000044,8.2000585483969657E-2]
[0.4,0.27775190210503575,8.7769367215324093E-2]
[0.6,0.293084730775096,9.3538148946678529E-2]
[0.8,0.31329253587291178,9.9306930678032951E-2]
[1,0.33750078515978732,0.10507571240938739]
[1.2,0.36491418205228776,0.11084449414074182]
[1.4,0.39486574157798437,0.11661327587209626]
[1.6,0.42682146245309288,0.12238205760345069]
[1.8,0.46036418309734561,0.12815083933480512]
[2,0.49517150026712947,0.13391962106615957]
[2.2000000000000002,0.53099478491256147,0.13968840279751399]
[2.4,0.56764171962735344,0.14545718452886844]
[2.6,0.60496263971280462,0.15122596626022283]
[2.7,0.62383812983841125,0.15411035712590007]
["Stock1",{"$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",{"$f":"SQRT(D6)","v":0.70710678118654757},null,0.15]
[]
["Once we have the weights on the Market portfolio (x) we can show that the expected return of each"]
["asset or stock is the SML formula: Ri = Rf + Bi*(Rm-Rf)."]
[]
[null,"For the first of the 4 stocks above:"]
[null,"Portfolio x = M",{"$f":"B8","v":0.19242066451854326},{"$f":"C8","v":0.25513683772569656},{"$f":"D8","v":0.1949369828628989},{"$f":"E8","v":0.3575055148928612},"<--Market Weights"]
[null,"Portfolio A",1,0,0,0,"<--First stock 100% weight"]
[null,"Changing the weights above to show each stock as 100% gives that stock's expected return (below):"]
[null,"Covariance(M,A)",{"$f":"MMULT(MMULT(C55:F55,A3:D6),TRANSPOSE(C56:F56))","v":4.5516820059641319E-2},{"$f":"getformula(C58)","v":"<--  =MMULT(MMULT(C55:F55,A3:D6),TRANSPOSE(C56:F56))"}]
[null,"Correlation(M,A)",{"$f":"C58/(A3*B13)^0.5","v":0.42647848409704242},"<--  =C58/(A3*B13)^0.5"]
[null,"Beta A",{"$f":"C59*(A3/B13)^0.5","v":0.39959710972644025},"<--  =C59*(A3/B13)^0.5"]
[null,"Beta A",{"$f":"C58/B13","v":0.39959710972644025},"<--  =C58/B13",null,"<-- Beta = Covariance/Variance M"]
[null,"E(Return of A)",{"$f":"I8+C60*(K12-K11)","v":6.0000037689444646E-2},"<--  =I8+C60*(K12-K11)"]

{"sheet":"Page 212","index":8,"n_rows":49,"n_cols":7,"rows_kept":49,"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)","This sheet is similar to previous. Individual stocks are added to chart below."]
[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},{"$f":"getformula(B15)","v":"<--  =B14/SQRT(B13*E13)"}]
[]
["Calculating returns of combinations of Portfolio x and Portfolio y"]
["Proportion of x",0.3]
["Mean portfolio return, E(rp)",{"$f":"B18*B12+(1-B18)*E12","v":0.1113},{"$f":"getformula(B19)","v":"<--  =B18*B12+(1-B18)*E12"}]
["Portfolio variance sp2",{"$f":"B18^2*B13+(1-B18)^2*E13+2*B18*(1-B18)*B14","v":0.140598},{"$f":"getformula(B20)","v":"<--  =B18^2*B13+(1-B18)^2*E13+2*B18*(1-B18)*B14"}]
["Portfolio standard deviation sp",{"$f":"SQRT(B20)","v":0.37496399827183408},{"$f":"getformula(B21)","v":"<--  =SQRT(B20)"}]
[]
["Table of returns (using Data Table)"]
["Proportion of x","Standard deviation","Mean"]
[null,{"$f":"B21","v":0.37496399827183408},{"$f":"B19","v":0.1113}]
[-1,0.80597766718439534,0.14899999999999997]
[-0.8,0.72884017452388006,0.14319999999999999]
[-0.6,0.65375224665005938,0.13739999999999999]
[-0.4,0.58150838343054012,0.13159999999999997]
[-0.2,0.51331082201722567,0.1258]
[0,0.45099889135118726,0.12]
[0.2,0.39735123002200462,0.11420000000000001]
[0.4,0.35630324163554844,0.1084]
[0.6,0.33255375505322443,0.1026]
[0.8,0.32986057660775409,9.6800000000000011E-2]
[1,0.34871191548325392,9.1000000000000011E-2]
[1.2,0.38596372886580937,8.5200000000000012E-2]
[1.4,0.43693477774148393,7.9400000000000026E-2]
[1.6,0.49742537128699016,7.3600000000000027E-2]
[1.8,0.56438284878263267,6.7800000000000027E-2]
[2,0.6357672530100934,6.2000000000000027E-2]
[2.2000000000000002,0.7102450281416971,5.6200000000000028E-2]
[2.4,0.78693837115748777,5.0400000000000028E-2]
[2.6,0.8652583429242392,4.4600000000000029E-2]
[2.7,0.90489667918497751,4.1700000000000043E-2]
["Stock1",{"$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]

{"sheet":"Appendix 8.2","index":9,"n_rows":71,"n_cols":8,"rows_kept":71,"cut":false,"hidden":false,"merged":[[70,4,70,5],[0,0,0,7],[65,4,65,5],[66,4,66,5],[68,4,68,5],[69,4,69,5]]}
["APPLE AND GOOGLE\nCOMPARING CONTINUOUS AND DISCRETE RETURNS"]
[]
["Date","AAPL\nprice","Continuous return","Discrete return",null,"Google\nprice","Continuous return","Discrete return"]
["2007-06-01",122.04,null,null,null,580.11]
["2007-07-02",131.76,{"$f":"LN(B5/B4)","v":7.6633226020915893E-2},{"$f":"B5/B4-1","v":7.9646017699114946E-2},{"$f":"getformula(D5)","v":"<--  =B5/B4-1"},645.9,{"$f":"LN(F5/F4)","v":0.10742695230781683},{"$f":"F5/F4-1","v":0.11340952577959351}]
["2007-08-01",138.47999999999999,{"$f":"LN(B6/B5)","v":4.9743824998568914E-2},{"$f":"B6/B5-1","v":5.1001821493624755E-2},null,599.39,{"$f":"LN(F6/F5)","v":-7.4732221645049529E-2},{"$f":"F6/F5-1","v":-7.2008050781854793E-2}]
["2007-09-04",153.47,0.10277919731904972,0.10824667822068168,null,592.64,-1.1325339375617659E-2,-1.1261449139958968E-2]
["2007-10-01",189.95,0.21325577144663097,0.23770117938359281,null,515.04,-0.14034256446726184,-0.13093952483801297]
["2007-11-01",182.22,-4.1546131347922108E-2,-4.0694919715714595E-2,null,540.96,4.9100771409077877E-2,5.0326188257222793E-2]
["2007-12-03",198.08,8.3456241210519033E-2,8.7037646800570911E-2,null,603.69000000000005,0.10971548218681069,0.11596051464063883]
["2008-01-02",135.36000000000001,-0.38073309363831809,-0.31663974151857832,null,506.38,-0.17577344556712143,-0.1611920025178486]
["2008-02-01",125.02,-7.9464171354247048E-2,-7.6388888888889062E-2,null,529.02,4.3738862747725364E-2,4.4709506694577072E-2]
["2008-03-03",143.5,0.13786131069600946,0.14781634938409849,null,544.1,2.8106815164888964E-2,2.8505538542966224E-2]
["2008-04-01",173.95,0.1924328663982752,0.21219512195121948,null,586.76,7.5482824127682258E-2,7.8404705017459886E-2]
["2008-05-01",188.75,8.1655486531183152E-2,8.5081920091980567E-2,null,613.4,4.440137406058902E-2,4.5401867884654612E-2]
["2008-06-02",167.44,-0.1197983099913898,-0.11290066225165563,null,600.36,-2.148777639203717E-2,-2.1258558852298659E-2]
["2008-07-01",158.94999999999999,-5.2035390780932597E-2,-5.0704730052556157E-2,null,593.97,-1.0700662251397116E-2,-1.0643613831700982E-2]
["2008-08-01",169.53,6.4440214953050093E-2,6.6561811890531786E-2,null,555.71,-6.6582237591538612E-2,-6.4414027644493776E-2]
["2008-09-02",113.66,-0.39981836644088625,-0.32955819029080402,null,613.70000000000005,9.9259633949873111E-2,0.10435298986881647]
["2008-10-01",107.59,-5.4883829263157574E-2,-5.3404891782509178E-2,null,525.79,-0.15460431591839269,-0.14324588561186258]
["2008-11-03",92.67,-0.1492829110072178,-0.1386745980109676,null,450.02,-0.15560986725547385,-0.14410696285589297]
["2008-12-01",85.35,-8.2284346358150504E-2,-7.898996438977024E-2,null,484.85,7.4547538529370433E-2,7.7396560152882099E-2]
["2009-01-02",90.13,5.4492623327868875E-2,5.600468658465152E-2,null,444.95,-8.5877648447684057E-2,-8.2293492832834936E-2]
["2009-02-02",89.31,-9.1396088725236701E-3,-9.0979695994674037E-3,null,485.63,8.7485100776333188E-2,9.1426002921676686E-2]
["2009-03-02",105.12,0.16298909104050577,0.1770238495129326,null,525.70000000000005,7.9283690746198177E-2,8.2511376974239825E-2]
["2009-04-01",125.83,0.17982923486757607,0.19701293759512928,null,567.12,7.5840213721359739E-2,7.8790184515883599E-2]
["2009-05-01",135.81,7.6325060512100487E-2,7.9313359294286068E-2,null,526.79999999999995,-7.3749951677636247E-2,-7.1096064325010699E-2]
["2009-06-01",142.43,4.7593800830517959E-2,4.8744569619321165E-2,null,529.94000000000005,5.9428227214138622E-3,5.9605163249811799E-3]
["2009-07-01",163.38999999999999,0.1372893300962372,0.14716000842519117,null,619.98,0.15692342686377875,0.1699060270974071]
["2009-08-03",168.21,2.9073217760958888E-2,2.9499969398372183E-2,null,583,-6.15000331038262E-2,-5.9647085389851306E-2]
["2009-09-01",185.35,9.7032730793050262E-2,0.10189643897509049,null,536.12,-8.3829169740196469E-2,-8.0411663807890221E-2]
["2009-10-01",188.5,1.6852077291324211E-2,1.6994874561640172E-2,null,495.85,-7.8084554978161788E-2,-7.5113780496903648E-2]
["2009-11-02",199.91,5.8769258379585923E-2,6.0530503978779793E-2,null,461.67,-7.1423111488264107E-2,-6.8932136734899729E-2]
["2009-12-01",210.73,5.2710427941470024E-2,5.4124355960182058E-2,null,443.05,-4.1167719650558612E-2,-4.033183875928692E-2]
["2010-01-04",192.06,-9.276986999929468E-2,-8.8596782612822E-2,null,421.59,-4.9649352712548125E-2,-4.8436970996501572E-2]
["2010-02-01",204.62,6.3346777240967267E-2,6.5396230344684003E-2,null,417.23,-1.0395649281585149E-2,-1.0341801276121276E-2]
["2010-03-01",235,0.13843091369336494,0.14847033525559561,null,395.97,-5.2299177690205201E-2,-5.095510869304698E-2]
["2010-04-01",261.08999999999997,0.10527966132537296,0.11102127659574457,null,348.06,-0.12896357210294498,-0.12099401469808324]
["2010-05-03",256.88,-1.6256125688273504E-2,-1.6124707955111228E-2,null,337.99,-2.9358569459494093E-2,-2.8931793368959347E-2]
["2010-06-01",251.53,-2.1046783061035752E-2,-2.0826845219557799E-2,null,338.53,1.596405471184585E-3,1.5976804047455051E-3]
["2010-07-01",257.25,2.2486107993936241E-2,2.2740826143998749E-2,null,307.64999999999998,-9.5649941531219279E-2,-9.1217912740377494E-2]
["2010-08-02",243.1,-5.6575493392081351E-2,-5.5004859086491775E-2,null,292.95999999999998,-4.8926692260298776E-2,-4.7749065496505816E-2]
["2010-09-01",283.75,0.15462068747353472,0.16721513780337305,null,359.36,0.20428859062387794,0.22665210267613345]
["2010-10-01",300.98,5.8950248562960224E-2,6.072246696035255E-2,null,400.52,0.10843903128952363,0.11453695458593049]
["2010-11-01",311.14999999999998,3.3231293656654268E-2,3.3789620572795442E-2,null,463.29,0.14558950506341742,0.15672126235893358]
["2010-12-01",322.56,3.6014054427722354E-2,3.6670416197975397E-2,null,473.75,2.232654849361675E-2,2.2577651147229538E-2]
["2011-01-03",339.32,5.0654449496584847E-2,5.1959325396825351E-2,null,526.41999999999996,0.10541961681369323,0.1111767810026385]
["2011-02-01",353.21,4.01191659602591E-2,4.0934810798066712E-2,null,585.79999999999995,0.10687906118330369,0.11279966566619803]
["2011-03-01",348.51,-1.3395856706299903E-2,-1.330653152515493E-2,null,574.29,-1.9843939177158147E-2,-1.9648344144759244E-2]
["2011-04-01",350.13,4.6375898988789757E-3,4.6483601618318993E-3,null,440.47,-0.26529215658624006,-0.23301816155600819]
["2011-05-02",347.83,-6.5906594228294924E-3,-6.568988661354358E-3,null,471.18,6.7397847984603548E-2,6.9720979862419652E-2]
["2011-06-01",335.67,-3.5585320181802882E-2,-3.495960670442444E-2,null,564.29999999999995,0.18034583836025603,0.1976314784158919]
["2011-07-01",390.48,0.15124821709115263,0.16328536955938877,null,691.48,0.20324820307949171,0.2253765727449939]
["2011-08-01",384.83,-1.4575073248301941E-2,-1.446937103052659E-2,null,693,2.1957711353171334E-3,2.1981836061779614E-3]
["2011-09-01",381.32,-9.1627607052127934E-3,-9.1209105319232098E-3,null,707,2.0000666706669435E-2,2.020202020202011E-2]
["2011-10-03",404.78,5.9704792012682126E-2,6.1523130179376828E-2,null,567.27,-0.22019528503533467,-0.19763790664780767]
["2011-11-01",382.2,-5.7399677831886937E-2,-5.5783388507337328E-2,null,515.25,-9.6183161090669669E-2,-9.1702363953672816E-2]
["2011-12-01",405,5.794303530036643E-2,5.9654631083202458E-2,null,510,-1.0241494052196907E-2,-1.0189228529839833E-2]
["2012-01-03",456.48,0.11965782035865079,0.12711111111111117,null,522.70000000000005,2.4596960000504701E-2,2.4901960784313726E-2]
["2012-02-01",542.44000000000005,0.17253259275455476,0.18831055029793209,null,497.91,-4.8588347918139083E-2,-4.7426822268987978E-2]
["2012-03-01",599.54999999999995,0.1001018936056976,0.10528353366270915,null,471.38,-5.4754775012495489E-2,-5.3282721777028086E-2]
["2012-04-02",583.98,-2.6312638158984922E-2,-2.5969477107830818E-2,null,458.16,-2.8446094702639788E-2,-2.80453137595994E-2]
["2012-05-01",577.73,-1.0760104160047555E-2,-1.070242131579846E-2,null,449.45,-1.9193855066193692E-2,-1.9010825912345153E-2]
["2012-06-01",584,1.0794351321817304E-2,1.0852820521696893E-2,null,501.5,0.10957899438258194,0.1158082100344866]
[]
["Monthly average",null,{"$f":"AVERAGE(C5:C64)","v":2.6092535382995975E-2},{"$f":"AVERAGE(D5:D64)","v":3.2411593445140129E-2},{"$f":"ggetformula(G66)&\" -->\"","v":"=AVERAGE(G5:G64) -->"},null,{"$f":"AVERAGE(G5:G64)","v":-2.4269022221436731E-3},{"$f":"AVERAGE(H5:H64)","v":2.5579752320811166E-3}]
["Monthly standard deviation",null,{"$f":"_xlfn.STDEV.S(C5:C64)","v":0.11170358406233492},{"$f":"_xlfn.STDEV.S(D5:D64)","v":0.10686671328971845},{"$f":"ggetformula(G67)&\" -->\"","v":"=STDEV.S(G5:G64) -->"},null,{"$f":"_xlfn.STDEV.S(G5:G64)","v":0.10087209806699204},{"$f":"_xlfn.STDEV.S(H5:H64)","v":0.10070642608124224}]
[]
["Annual average",null,{"$f":"12*C66","v":0.31311042459595173},null,{"$f":"ggetformula(G69)&\" -->\"","v":"=12*G66 -->"},null,{"$f":"12*G66","v":-2.9122826665724078E-2}]
["Annual variance",null,{"$f":"12*C67","v":1.340443008748019},null,{"$f":"ggetformula(G70)&\" -->\"","v":"=12*G67 -->"},null,{"$f":"12*G67","v":1.2104651768039045}]
["Annual standard deviation",null,{"$f":"SQRT(C70)","v":1.1577750251011718},null,{"$f":"ggetformula(G71)&\" -->\"","v":"=SQRT(G70) -->"},null,{"$f":"SQRT(G70)","v":1.1002114236836047}]