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{"sheet":"Exercise 1","index":0,"n_rows":48,"n_cols":20,"rows_kept":48,"cut":false,"hidden":false,"merged":[[0,0,0,8],[12,3,14,7]]}
["DATA FOR 6 FURNITURE COMPANIES"]
["Variance-covariance matrix","La-Z-Boy","Kimball","Flexsteel","Leggett","Miller","Shaw",null,"Means"]
["La-Z-Boy",0.11520281553233175,3.9801910047161576E-2,0.1792077038938214,4.9177062475832138E-2,5.684513533227873E-2,9.8872079520042455E-2,null,0.29243448293814894]
["Kimball",3.9801910047161576E-2,6.485515464860532E-2,4.469186658014862E-2,6.2216470563204148E-3,3.4910581659125202E-2,2.6865064021170025E-2,null,0.20680399718955364]
["Flexsteel",0.1792077038938214,4.469186658014862E-2,0.33335505813088623,7.7543593069800229E-2,8.8642612198107595E-2,0.14873703591290333,null,0.25022036930790836]
["Leggett",4.9177062475832138E-2,6.2216470563204148E-3,7.7543593069800229E-2,0.10326334402494085,1.9067401683178917E-2,5.9726651940702029E-2,null,0.31641518883395475]
["Miller",5.684513533227873E-2,3.4910581659125202E-2,8.8642612198107595E-2,1.9067401683178917E-2,5.9417132484788082E-2,2.4308886678029388E-2,null,0.15338921429495214]
["Shaw",9.8872079520042455E-2,2.6865064021170025E-2,0.14873703591290333,5.9726651940702029E-2,2.4308886678029388E-2,0.16533364187811664,null,0.43872095634370767]
[]
["Constant",0,0.18]
[]
["Envelope portfolio for above constants"]
[null,{"$f":"MMULT(MINVERSE($B$3:$G$8),$I$3:$I$8-B10)/SUM(MMULT(MINVERSE($B$3:$G$8),$I$3:$I$8-B10))","v":0.4201897131641919},{"$f":"MMULT(MINVERSE($B$3:$G$8),$I$3:$I$8-C10)/SUM(MMULT(MINVERSE($B$3:$G$8),$I$3:$I$8-C10))","v":1.7337263819206683},{"$f":"getformula(C13)","v":"<--  {=MMULT(MINVERSE($B$3:$G$8),$I$3:$I$8-C10)/SUM(MMULT(MINVERSE($B$3:$G$8),$I$3:$I$8-C10))}"}]
[null,0.15789631158133774,-4.9941514034099063E-2]
[null,-0.41859645802345785,-1.0129562958947163]
[null,0.28086746851103928,0.39709909789768921]
[null,0.25118309700494335,-0.78728883250461168]
[null,0.30845986776194562,0.71936116261506944]
[]
[]
["Mean",{"$f":"MMULT(TRANSPOSE(B13:B18),$I$3:$I$8)","v":0.31351750872216622},{"$f":"MMULT(TRANSPOSE(C13:C18),$I$3:$I$8)","v":0.56369636269872414},{"$f":"getformula(C21)","v":"<--  {=MMULT(TRANSPOSE(C13:C18),$I$3:$I$8)}"}]
["Variance",{"$f":"MMULT(MMULT(TRANSPOSE(B13:B18),$B$3:$G$8),B13:B18)","v":4.1023437284749192E-2},{"$f":"MMULT(MMULT(TRANSPOSE(C13:C18),$B$3:$G$8),C13:C18)","v":0.21196538355651109},{"$f":"getformula(C22)","v":"<--  {=MMULT(MMULT(TRANSPOSE(C13:C18),$B$3:$G$8),C13:C18)}"}]
["Covariance",{"$f":"MMULT(MMULT(TRANSPOSE(B13:B18),B3:G8),C13:C18)","v":7.3759078008319823E-2},{"$f":"getformula(B23)","v":"<--  {=MMULT(MMULT(TRANSPOSE(B13:B18),B3:G8),C13:C18)}"}]
[]
["Sample portfolio calculation"]
["Proportion",0.3]
["Mean",{"$f":"B26*B21+(1-B26)*C21","v":0.48864270650575675},{"$f":"getformula(B27)","v":"<--  =B26*B21+(1-B26)*C21"}]
["Variance",{"$f":"B26^2*B22+(1-B26)^2*C22+2*B26*(1-B26)*B23","v":0.13853396006181218},{"$f":"getformula(B28)","v":"<--  =B26^2*B22+(1-B26)^2*C22+2*B26*(1-B26)*B23"}]
["Sigma",{"$f":"SQRT(B28)","v":0.37220150464743179}]
[null,null,null,null,"Sigma","Mean"]
[null,null,null,null,{"$f":"B29","v":0.37220150464743179},{"$f":"B27","v":0.48864270650575675},{"$f":"getformula(F31)&\", data table header\"","v":"<--  =B27, data table header"}]
[null,null,null,-1,0.77061576643455354,0.81387521667528206,null,null,null,null,null,null,null,null,null,null,null,null,null,1]
[null,null,null,-0.8,0.70752858452600642,0.76383944587997066,null,null,null,null,null,null,null,null,null,null,null,null,null,0.1]
[null,null,null,-0.6,0.64481190245776654,0.71380367508465892]
[null,null,null,-0.4,0.58258538804796955,0.66376790428934729]
[null,null,null,-0.2,0.52102469458632428,0.61373213349403566]
[null,null,null,0,0.46039698473872642,0.56369636269872414]
[null,null,null,0.2,0.40112552640067606,0.51366059190341262]
[null,null,null,0.4,0.34391226423304155,0.46362482110810099]
[null,null,null,0.6,0.28997802715989535,0.41358905031278936]
[null,null,null,0.8,0.24152954305252652,0.36355327951747779]
[null,null,null,1,0.20254243329423391,0.31351750872216622]
[null,null,null,1.2,0.17929865473088685,0.26348173792685464]
[null,null,null,1.4,0.17807366755877185,0.21344596713154307]
[null,null,null,1.6,0.19927395151732175,0.16341019633623144]
[null,null,null,1.8,0.23695492739082971,0.11337442554091992]
[null,null,null,2,0.28464507840858333,6.3338654745608292E-2]
[null,null,null,2.2000000000000002,0.33813555993955069,1.3302883950296662E-2]

{"sheet":"Exercise 3","index":1,"n_rows":46,"n_cols":9,"rows_kept":46,"cut":false,"hidden":false,"merged":[[0,0,0,3]]}
["Variance-covariance matrix",null,null,null,null,"Mean returns","Mean minus constant"]
[0.4,0.03,0.02,0,null,0.06,{"$f":"F2-$E$7","v":-5.0000000000000044E-3}]
[{"$f":"B2","v":0.03},0.2,1E-3,-0.06,null,0.05,{"$f":"F3-$E$7","v":-1.4999999999999999E-2}]
[{"$f":"C2","v":0.02},{"$f":"C3","v":1E-3},0.3,0.03,null,7.0000000000000007E-2,{"$f":"F4-$E$7","v":5.0000000000000044E-3}]
[{"$f":"D2","v":0},{"$f":"D3","v":-0.06},{"$f":"D4","v":0.03},0.1,null,0.08,{"$f":"F5-$E$7","v":1.4999999999999999E-2}]
[null,null,null,null,null,null,null,null,{"$f":"getformula(E9)","v":"<--  {=MMULT(MINVERSE(A2:D5),G2:G5)}"}]
[null,null,null,"Constant",6.5000000000000002E-2]
[null,"z","x",null,"z","y"]
[null,{"$f":"MMULT(MINVERSE(A2:D5),F2:F5)","v":0.10186529331294758},{"$f":"B9/SUM($B$9:$B$12)","v":5.3985865109542834E-2},{"$f":"getformula(C9)","v":"<--  =B9/SUM($B$9:$B$12)"},{"$f":"MMULT(MINVERSE(A2:D5),G2:G5)","v":-1.0089321638368079E-2},{"$f":"E9/SUM($E$9:$E$12)","v":-0.11629826823363552}]
[null,0.56570370966444017,{"$f":"B10/SUM($B$9:$B$12)","v":0.29980774774866981},null,-3.5286070652611266E-2,{"$f":"E10/SUM($E$9:$E$12)","v":-0.40673784192414386}]
[null,0.11413856924438728,6.0490371181609333E-2,null,4.715538746278284E-3,5.4355387769110405E-2]
[null,1.1051806550253478,0.58571601596017797,null,0.12741369598454977,1.4686807223886689]
[null,"Sum",{"$f":"SUM(C9:C12)","v":1},null,"Sum",{"$f":"SUM(F9:F12)","v":0.99999999999999989}]
[]
[]
[null,"Portfolio X","Portfolio Y"]
["Mean",{"$f":"MMULT(TRANSPOSE(C9:C12),F2:F5)","v":6.9321146553532956E-2},{"$f":"MMULT(TRANSPOSE(F9:F12),F2:F5)","v":9.398454674470591E-2},{"$f":"getformula(C17)","v":"<--  {=MMULT(TRANSPOSE(F9:F12),F2:F5)}"}]
["Variance",{"$f":"MMULT(MMULT(TRANSPOSE(C9:C12),A2:D5),C9:C12)","v":3.6738342818890282E-2},{"$f":"MMULT(MMULT(TRANSPOSE(F9:F12),A2:D5),F9:F12)","v":0.33410101419775762},{"$f":"getformula(C18)","v":"<--  {=MMULT(MMULT(TRANSPOSE(F9:F12),A2:D5),F9:F12)}"}]
["Sigma",{"$f":"SQRT(B18)","v":0.19167248842463094},{"$f":"SQRT(C18)","v":0.57801471797676363},"<--  =SQRT(C18)"]
["Covariance",{"$f":"MMULT(MMULT(TRANSPOSE(C9:C12),A2:D5),F9:F12)","v":4.9809281433603907E-2},"<--  {=MMULT(MMULT(TRANSPOSE(C9:C12),A2:D5),F9:F12)}"]
["Correlation",{"$f":"B20/(B19*C19)","v":0.44958477778430439},"<--  =B20/(B19*C19)"]
[]
["One Portfolio"]
["W in Port X",0.6]
["Mean",{"$f":"B24*B17+(1-B24)*C17","v":7.9186506630002138E-2},{"$f":"getformula(B25)","v":"<--  =B24*B17+(1-B24)*C17"}]
["Sigma",{"$f":"SQRT(B24^2*B18+(1-B24)^2*C18+2*B24*(1-B24)*B20)","v":0.30098242602280223},{"$f":"getformula(B26)","v":"<--  =SQRT(B24^2*B18+(1-B24)^2*C18+2*B24*(1-B24)*B20)"}]
[]
["W in Port 1","Sigma","Mean"]
[null,{"$f":"B26","v":0.30098242602280223},{"$f":"B25","v":7.9186506630002138E-2}]
[-1,1.0834690922566759,0.11864794693587886]
[{"$f":"A30+0.4","v":-0.6},0.87914195634638026,0.10878258685940968]
[{"$f":"A31+0.4","v":-0.19999999999999996},0.67724924442142909,9.8917226782940501E-2]
[0.20000000000000007,0.48086708439866593,8.9051866706471319E-2]
[0.60000000000000009,0.30098242602280212,7.9186506630002138E-2]
[1,0.19167248842463094,6.9321146553532956E-2]
[1.4,0.26396385925165922,5.9455786477063781E-2]
[1.7999999999999998,0.43520816776686305,4.9590426400594592E-2]
[2.1999999999999997,0.62922653608916645,3.9725066324125424E-2]
[2.5999999999999996,0.83020272962353781,2.9859706247656242E-2]
[2.9999999999999996,1.0340878903448176,1.9994346171187061E-2]
[3.3999999999999995,1.2394473009245044,1.0128986094717879E-2]
[3.7999999999999994,1.4456528327050389,2.6362601824869714E-4]
["Asset1",{"$f":"SQRT(A2)","v":0.63245553203367588},null,0.06]
["Asset2",{"$f":"SQRT(B3)","v":0.44721359549995793},null,0.05]
["Asset3",{"$f":"SQRT(C4)","v":0.54772255750516607},null,7.0000000000000007E-2]
["Asset4",{"$f":"SQRT(D5)","v":0.31622776601683794},null,0.08]

{"sheet":"Exercise 4","index":2,"n_rows":52,"n_cols":11,"rows_kept":52,"cut":false,"hidden":false,"merged":[[0,0,0,5],[1,0,1,3],[1,8,1,9]]}
["A FOUR-ASSET PORTFOLIO PROBLEM"]
["Variance-covariance",null,null,null,null,"Mean returns","St. dev.",null,"Excess return"]
[0.1,0.01,0.03,0.05,null,0.06,{"$f":"SQRT(A3)","v":0.31622776601683794},null,{"$f":"$F3-B$8","v":0.06},{"$f":"$F3-C$8","v":9.999999999999995E-3},{"$f":"getformula(J3)","v":"<--  =$F3-C$8"}]
[{"$f":"B3","v":0.01},0.3,0.06,-0.04,null,0.08,{"$f":"SQRT(B4)","v":0.54772255750516607},null,{"$f":"$F4-B$8","v":0.08},0.03]
[{"$f":"C3","v":0.03},{"$f":"C4","v":0.06},0.4,0.02,null,0.1,{"$f":"SQRT(C5)","v":0.63245553203367588},null,0.1,0.05]
[{"$f":"D3","v":0.05},{"$f":"D4","v":-0.04},{"$f":"D5","v":0.02},0.5,null,0.15,{"$f":"SQRT(D6)","v":0.70710678118654757},null,0.15,9.9999999999999992E-2]
[]
["Constant",0,0.05]
[]
["Portfolio 1",null,null,"Portfolio 2",null,"Both these portfolios are efficient"]
["z","x",null,"z","y"]
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[0.25673204974832409,{"$f":"A13/SUM($A$12:$A$15)","v":0.23622995763063889},null,0.10911224973478097,{"$f":"D13/SUM($D$12:$D$15)","v":0.2917672621921778}]
[0.16877337125401595,0.15529547783223951,null,0.10162216253225893,{"$f":"D14/SUM($D$12:$D$15)","v":0.27173869306293263}]
[0.27517700080506213,0.25320193292902443,null,0.2092672430008502,0.55958272976018031]
[]
["Mean",{"$f":"MMULT(TRANSPOSE(B12:B15),F3:F6)","v":9.3724592229514556E-2},null,null,{"$f":"MMULT(TRANSPOSE(E12:E15),F3:F6)","v":0.12706733864477709},{"$f":"getformula(E17)","v":"<--  {=MMULT(TRANSPOSE(E12:E15),F3:F6)}"}]
["Variance",{"$f":"MMULT(MMULT(TRANSPOSE(B12:B15),A3:D6),B12:B15)","v":8.6239939551885511E-2},null,null,{"$f":"MMULT(MMULT(TRANSPOSE(E12:E15),A3:D6),E12:E15)","v":0.20607884500118057},{"$f":"getformula(E18)","v":"<--  {=MMULT(MMULT(TRANSPOSE(E12:E15),A3:D6),E12:E15)}"}]
["Covariance",{"$f":"MMULT(MMULT(TRANSPOSE(B12:B15),A3:D6),E12:E15)","v":0.11692000299035391},null,null,null,{"$f":"getformula(B19)","v":"<--  {=MMULT(MMULT(TRANSPOSE(B12:B15),A3:D6),E12:E15)}"}]
[]
[]
[]
["Proportion of 1",0.6]
["Portfolio mean",{"$f":"B23*B17+(1-B23)*E17","v":0.10706169079561957},{"$f":"getformula(B24)","v":"<--  =B23*B17+(1-B23)*E17"}]
["Portfolio var.",{"$f":"B23^2*B18+(1-B23)^2*E18+2*B23*(1-B23)*B19","v":0.12014059487423756},{"$f":"getformula(B25)","v":"<--  =B23^2*B18+(1-B23)^2*E18+2*B23*(1-B23)*B19"}]
["Portfolio st. dev.",{"$f":"SQRT(B25)","v":0.34661303333002003},"<--  =SQRT(B25)"]
[]
[]
["Data table of portfolios"]
["Proportion of 1",{"$f":"B26","v":0.34661303333002003},{"$f":"B24","v":0.10706169079561957}]
[-1.4,0.75520991031190621,0.17374718362614466]
[{"$f":"A31+0.25","v":-1.1499999999999999},0.6989151352546501,0.16541149702232899]
[{"$f":"A32+0.25","v":-0.89999999999999991},0.64337591753521428,0.15707581041851337]
[-0.64999999999999991,0.58880610014000079,0.14874012381469776]
[-0.39999999999999991,0.535502122480779,0.14040443721088211]
[-0.14999999999999991,0.48388249619334917,0.13206875060706647]
[0.10000000000000009,0.434547885030797,0.12373306400325083]
[0.35000000000000009,0.38837006317263406,0.1153973773994352]
[0.60000000000000009,0.34661303333001997,0.10706169079561956]
[0.85000000000000009,0.31106226241912421,9.8726004191803926E-2]
[1.1000000000000001,0.28405759037546491,9.0390317587988295E-2]
[1.35,0.26819311236508575,8.205463098417265E-2]
[1.6,0.26547358383043013,7.3718944380357018E-2]
[1.85,0.27628743949918916,6.5383257776541387E-2]
[2.1,0.29917072393502758,5.7047571172725769E-2]
[2.35,0.33163435017522497,4.8711884568910124E-2]
[2.6,0.37117301854259838,4.0376197965094507E-2]
[2.85,0.41577316471057679,3.2040511361278834E-2]
["Stock A",{"$f":"G3","v":0.31622776601683794},null,{"$f":"F3","v":0.06}]
["Stock B",{"$f":"G4","v":0.54772255750516607},null,{"$f":"F4","v":0.08}]
["Stock C",{"$f":"G5","v":0.63245553203367588},null,{"$f":"F5","v":0.1}]
["Stock D",{"$f":"G6","v":0.70710678118654757},null,{"$f":"F6","v":0.15}]