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{"sheet":"Mean_Std dev","index":0,"n_rows":25,"n_cols":8,"rows_kept":25,"cut":false,"hidden":false,"merged":[[0,1,0,2]]}
[null,"RETURNS"]
[null,"Microsoft","Google",null,null,null,"Yearly Returns of portfolio"]
["Year 1",0.11,0.12,null,null,null,{"$f":"B3*$C$14+C3*$C$15","v":0.113}]
["Year 2",0.03,-0.04,null,null,null,{"$f":"B4*$C$14+C4*$C$15","v":8.9999999999999959E-3}]
["Year 3",0.15,0.21,null,null,null,{"$f":"B5*$C$14+C5*$C$15","v":0.16799999999999998}]
["Year 4",0.183,0.13,null,null,null,{"$f":"B6*$C$14+C6*$C$15","v":0.1671}]
["Year 5",0.08,0.25,null,null,null,{"$f":"B7*$C$14+C7*$C$15","v":0.13100000000000001}]
["Mean",{"$f":"AVERAGE(B3:B7)","v":0.1106},{"$f":"AVERAGE(C3:C7)","v":0.13399999999999998},null,null,null,{"$f":"AVERAGE(G3:G7)","v":0.11761999999999999}]
["Std. Dev.",{"$f":"_xlfn.STDEV.S(B3:B7)","v":5.9638913470988028E-2},{"$f":"_xlfn.STDEV.S(C3:C7)","v":0.1114899098573499},null,null,null,{"$f":"_xlfn.STDEV.S(G3:G7)","v":6.5163425324333613E-2},"Std Dev"]
[]
[]
["PORTFOLIO"]
["Stock","Exp. Returns","Fraction of wealth invested","Std dev of returns",null,"Variance"]
["Microsoft",{"$f":"AVERAGE(B3:B7)","v":0.1106},0.7,{"$f":"_xlfn.STDEV.S(B3:B7)","v":5.9638913470988028E-2},null,{"$f":"D14^2","v":3.5567999999999971E-3}]
["Google",{"$f":"AVERAGE(C3:C7)","v":0.13399999999999998},{"$f":"1-C14","v":0.30000000000000004},{"$f":"_xlfn.STDEV.S(C3:C7)","v":0.1114899098573499},null,{"$f":"D15^2","v":1.2430000000000005E-2}]
[]
[]
["Returns of portfolio",{"$f":"B14*C14+B15*C15","v":0.11762},"=B14*C14+B15*C15"]
["Variance of portfolio",{"$f":"F14*C14^2+F15*C15^2+2*C14*C15*A25*D14*D15","v":4.2462719999999997E-3},"=[F14*C14^2+F15*C15^2]+2*C14*C15*A25*D14*D15"]
["Std dev of portfolio",{"$f":"SQRT(B19)","v":6.5163425324333585E-2}]
[]
["Covariance"]
[{"$f":"_xlfn.COVARIANCE.S(B3:B7,C3:C7)","v":3.2970000000000005E-3}]
["Correlation","Cov/std X /std Y"]
[{"$f":"CORREL(B3:B7,C3:C7)","v":0.49585381635613912},{"$f":"A23/B9/C9","v":0.49585381635613907}]

{"sheet":"Normal Distribution","index":1,"n_rows":55,"n_cols":9,"rows_kept":55,"cut":false,"hidden":false,"merged":[]}
["Normal Distribution"]
["MICROSOFT"]
["Mean Returns, mu",{"$f":"B54","v":0.11280643052436179}]
["Yearly Std dev. or sigma",{"$f":"B55","v":5.7659985892917265E-2},null,null,null,null,null,null,"The returns will lie between mu - 1*sigma and mu +1*sigma for 68%"]
[null,null,null,null,null,null,null,null,"The returns will lie between mu - 2*sigma and mu +2*sigma for 95%"]
["Assuming that the returns of Microsoft are normally distributed:"]
[]
["This means: There is a 68.2% probability that the returns will lie between -1 std and +1 std dev "]
[null,"Therefore, there is a 68.2% prob that the returns will lie between 11%-6% and 11%+6% (5% and 17%)"]
[null,"Therefore, there is a 95% prob that the returns will lie between 11%-2*6% and 11%+2*6% (-1% and 23%)"]
[]
[]
["If Microsoft is trading at $100 at the start of the year, then at the end of year 1:"]
["It is expected that there is a 68.2% chance that Microsoft will be trading between: $105 and $117"]
["It is expected that there is a 95% chance that Microsoft will be trading between: $99 and $123"]
[]
[]
["Microsoft"]
["Year","Return",null,"Range","Frequency"]
[1,0.16071183533253686,null,-0.1,{"$f":"FREQUENCY(B20:B53,D20:D28)","v":0}]
[{"$f":"A20+1","v":2},0.12629246360292035,null,{"$f":"D20+5%","v":-0.05},0]
[{"$f":"A21+1","v":3},0.15405274432088012,null,{"$f":"D21+5%","v":0},1]
[4,0.13493372673280773,null,0.05,3]
[5,7.0092286726817943E-2,null,0.1,10]
[6,0.15085910095245841,null,0.15000000000000002,11]
[7,8.4443377154878804E-2,null,0.2,7]
[8,0.17177849253148103,null,0.25,2]
[9,0.11919681889820011,null,0.3,0]
[10,0.1125]
[11,0.1654863871921812]
[12,2.3E-2]
[13,0.10626645244562527]
[14,9.177203841642366E-2]
[15,-3.3625369123994553E-2]
[16,1.2E-2]
[17,1.2E-2]
[18,7.6711657106760561E-2]
[19,0.24199999999999999]
[20,5.1210168445414483E-2]
[21,8.8089728096573894E-2]
[22,9.589103034827115E-2]
[23,0.21351431618589556]
[24,0.14787430885098427]
[25,0.14563400235697171]
[26,0.10947637805878904]
[27,0.12899405078187812]
[28,6.7786317004837893E-2]
[29,0.17259389644962622]
[30,9.8064512772885498E-2]
[31,0.14265940193841328]
[32,0.18385134648137519]
[33,0.11854854445762412]
[34,9.0758623308782926E-2]
["Average Returns",{"$f":"AVERAGE(B20:B53)","v":0.11280643052436179}]
["Std Dev",{"$f":"_xlfn.STDEV.S(B20:B54)","v":5.7659985892917265E-2}]

{"sheet":"Sheet1","index":2,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"Mean_Std dev (2)","index":3,"n_rows":25,"n_cols":8,"rows_kept":25,"cut":false,"hidden":false,"merged":[[0,1,0,2]]}
[null,"RETURNS"]
[null,"Microsoft","Google",null,null,null,"Yearly Returns of portfolio"]
["Year 1",0.13,0.12,null,null,null,{"$f":"B3*$C$14+C3*$C$15","v":0.125}]
["Year 2",0.13,-0.4,null,null,null,{"$f":"B4*$C$14+C4*$C$15","v":-0.13500000000000001}]
["Year 3",0.13,0.21,null,null,null,{"$f":"B5*$C$14+C5*$C$15","v":0.16999999999999998}]
["Year 4",0.13,0.13,null,null,null,{"$f":"B6*$C$14+C6*$C$15","v":0.13}]
["Year 5",0.1295,1,null,null,null,{"$f":"B7*$C$14+C7*$C$15","v":0.56474999999999997}]
["Mean",{"$f":"AVERAGE(B3:B7)","v":0.12989999999999999},{"$f":"AVERAGE(C3:C7)","v":0.21200000000000002},null,null,null,{"$f":"AVERAGE(G3:G7)","v":0.17094999999999999}]
["Std. Dev.",{"$f":"_xlfn.STDEV.S(B3:B7)","v":2.2360679774997917E-4},{"$f":"_xlfn.STDEV.S(C3:C7)","v":0.50266290891610454},null,null,null,{"$f":"_xlfn.STDEV.S(G3:G7)","v":0.25123348204409379},"Std Dev"]
[]
[]
["PORTFOLIO"]
["Stock","Exp. Returns","Fraction of wealth invested","Std dev of returns",null,"Variance"]
["Microsoft",{"$f":"AVERAGE(B3:B7)","v":0.12989999999999999},0.5,{"$f":"_xlfn.STDEV.S(B3:B7)","v":2.2360679774997917E-4},null,{"$f":"D14^2","v":5.000000000000009E-8}]
["Google",{"$f":"AVERAGE(C3:C7)","v":0.21200000000000002},{"$f":"1-C14","v":0.5},{"$f":"_xlfn.STDEV.S(C3:C7)","v":0.50266290891610454},null,{"$f":"D15^2","v":0.25267000000000001}]
[]
[]
["Returns of portfolio",{"$f":"B14*C14+B15*C15","v":0.17094999999999999},"=B14*C14+B15*C15"]
["Variance of portfolio",{"$f":"F14*C14^2+F15*C15^2+2*C14*C15*A25*D14*D15","v":6.3118262499999994E-2},"=F14*C14^2+F15*C15^2+2*C14*C15*A25*D14*D15"]
["Std dev of portfolio",{"$f":"SQRT(B19)","v":0.25123348204409379}]
[]
["Covariance"]
[{"$f":"_xlfn.COVARIANCE.S(B3:B7,C3:C7)","v":-9.850000000000009E-5}]
["Correlation","Cov/std X /std Y"]
[{"$f":"CORREL(B3:B7,C3:C7)","v":-0.87634353709789992},{"$f":"A23/B9/C9","v":-0.87634353709790003}]