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{"sheet":"Contents","index":0,"n_rows":85,"n_cols":13,"rows_kept":85,"cut":false,"hidden":false,"merged":[]}
[]
[null,null,"Contents"]
[null,null,null,"Contents",null," Colour Codes ",null,null,null,null," File Name: ",null,{"$f":"IFERROR(File_name(),\"\")","v":""}]
[null,null,null,null,null,null," Inputs ",null,"1234567890"]
[null,null,"Annual Time Series",null,null,null," Section Titles ",null,"TITLE ROW",null," Last Save Date ",null,{"$f":"IFERROR(lastsaved(),\"\")","v":""}]
[null,null,null,"Volatility",null,null," Sum Column ",null,"1000000000"]
[null,null,null,"Mean Reversion",null,null," True or 1 ",null,{"$f":"1=1","v":true},null," Last Save By",null,{"$f":"IFERROR(last_save_by(),\"\")","v":""}]
[null,null,null,"Base Valule",null,null," False or 0 ",null,{"$f":"1=2","v":false}]
[null,null,null,"Random Number",null,null," Other Sheet Links ",null,"|||||||||||||||||||"]
[null,null,null,"Std Dev Away form Mean"]
[null,null,null,"Multiplied by Volatility - % Change in Price"]
[null,null,null,"Time Series - Discrete, No Mean Reversion"]
[null,null,null,"Continual - No Mean Reversion"]
[null,null,null,"Mean Reversion - Discrete"]
[null,null,null,"Mean Reversion - Continual"]
[null,null,null,"Percent Change Continual - LN"]
[null,null,null,"Percent Change Continual - Discrete"]
[null,null,null,"Volatility Output - LN"]
[null,null,null,"Volatiity Output - Discrete"]
[null,null,null,"Percent Change Discrete - LN"]
[null,null,null,"Percent Change Discrete - Discrete"]
[null,null,null,"Volatility Output - LN"]
[null,null,null,"Volatiity Output - Discrete"]
[null,null,null,"Continuous - No Mean Reversion"]
[null,null,null,"Continuous - Mean Reversion"]
[null,null,null,"Standard Deviation - No Mean Reversion"]
[null,null,null,"Standard Deviation - Mean Reversion"]
[null,null,null,"Continual Rate of Change - No Mean Reversion"]
[null,null,null,"Continual Rate of Change - Mean Reversion"]
[null,null,null,"Volatilty - No Mean Reversion"]
[null,null,null,"Volatilty - Mean Reversion"]
[]
[null,null,"Simulation"]
[null,null,null,"Simulations"]
[null,null,null,"Row Start"]
[null,null,null,"Column Start"]
[null,null,null,"Time Series"]
[null,null,null,"Median Variance"]
[null,null,null,"Average Variance"]
[null,null,null,"Median Std Dev"]
[null,null,null,"Average Std Dev"]
[null,null,null,"Monte Carlo Scenarios"]
[]
[null,null,"Normal Distn of Return"]
[null,null,null,"Annual Volatility (Stdev of Return, Stdev of Growth)"]
[null,null,null,"Standard Deviation of Returns"]
[null,null,null,"Expected Return "]
[null,null,null,"Range - 4 Standard Deviation"]
[]
[null,null,"No MR Variance with Time"]
[null,null,null,"Row Start1"]
[null,null,null,"Time Period"]
[null,null,null,"Median of Growth ^ 2 (Variance)"]
[null,null,null,"Square Root of Growth  - Std Dev"]
[null,null,null,"Time Period ^ .5"]
[null,null,null,"Square Root Relative to First"]
[null,null,null,"Average of Growth ^ 2 (Variance)"]
[null,null,null,"Square Root of Growth  - Std Dev"]
[null,null,null,"Square Root Relative to First"]
[null,null,null,"Variance Relative to First"]
[]
[null,null,"MR Variance with Time"]
[null,null,null,"Row Start4"]
[null,null,null,"Time Period"]
[null,null,null,"Median of Growth ^ 2 (Variance)"]
[null,null,null,"Square Root of Growth  - Std Dev"]
[null,null,null,"Time Period ^ .5"]
[null,null,null,"Square Root Relative to First"]
[null,null,null,"Average of Growth ^ 2 (Variance)"]
[null,null,null,"Square Root of Growth  - Std Dev"]
[null,null,null,"Square Root Relative to First"]
[null,null,null,"Variance Relative to First"]
[]
[null,null,"20% MR Variance with Time"]
[null,null,null,"Row Start1"]
[null,null,null,"Mean Reversion"]
[null,null,null,"Time Period"]
[null,null,null,"Median of Growth ^ 2 (Variance)"]
[null,null,null,"Square Root of Growth  - Std Dev"]
[null,null,null,"Time Period ^ .5"]
[null,null,null,"Square Root Relative to First"]
[null,null,null,"Average of Growth ^ 2 (Variance)"]
[null,null,null,"Square Root of Growth  - Std Dev"]
[null,null,null,"Square Root Relative to First"]
[null,null,null,"Variance Relative to First"]

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["          "]
[null,"Assumptions"]
[null,null,"Volatility",0.2]
[null,null,"Mean Reversion",0.2,null,null,null,null,"Value","EXP","LN",null,"Value","LN","EXP"]
[null,null,"Base Valule",100,null,null,null,null,0.05,{"$f":"EXP(I5)","v":1.0512710963760241},{"$f":"LN(J5)","v":5.0000000000000072E-2},null,1.05,{"$f":"LN(M5)","v":4.8790164169432049E-2},{"$f":"EXP(N5)","v":1.05}]
[]
[null,"Time Series Factors and Equations"]
[null,null,null,null,null,null,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
[null,null,"Random Number",null,null,{"$f":"_xlfn.FORMULATEXT(G9)","v":"=RAND()"},{"$f":"RAND()","v":0.33436577903762676},{"$f":"RAND()","v":1.1534078924187896E-2},0.15208718458540427,0.26053833255925152,0.13896902252219079,8.757583508595812E-2,0.58165887826955842,0.78741870742062836,0.28436606303113399,0.6650415726495168,0.41923053439133895,0.19285047884672935,0.81629356280613019,0.21020017131983992,0.4660103497094914,0.8781082605601287,0.17334553151021115,0.82110337859165672,0.50214362417908243,0.78887677196040007]
[null,null,"Std Dev Away form Mean",null,null,{"$f":"_xlfn.FORMULATEXT(G10)","v":"=NORM.S.INV(G9)"},{"$f":"_xlfn.NORM.S.INV(G9)","v":-0.42788951911529388},{"$f":"_xlfn.NORM.S.INV(H9)","v":-2.2723039592019165},-1.0275227700061358,-0.64168664055727287,-1.0849629954255879,-1.3558350073288055,0.20613911759949799,0.79749675765847161,-0.56991975402117301,0.42626212280569159,-0.20386234838995332,-0.86744002842001866,0.90133002481676061,-0.80572688751659771,-8.5302757422906175E-2,1.1655820248259527,-0.94102692175988589,0.9195781623215914,5.373294833919749E-3,0.80252997547783189]
[null,null,"Multiplied by Volatility - % Change in Price",{"$f":"D3","v":0.2},null,{"$f":"_xlfn.FORMULATEXT(G11)","v":"=$D$11*G10"},{"$f":"$D$11*G10","v":-8.5577903823058785E-2},{"$f":"$D$11*H10","v":-0.45446079184038335},-0.20550455400122716,-0.12833732811145457,-0.21699259908511759,-0.27116700146576111,4.1227823519899599E-2,0.15949935153169434,-0.11398395080423461,8.5252424561138324E-2,-4.0772469677990669E-2,-0.17348800568400374,0.18026600496335213,-0.16114537750331956,-1.7060551484581236E-2,0.23311640496519057,-0.1882053843519772,0.1839156324643183,1.0746589667839498E-3,0.1605059950955664]
[]
[null,null,"Time Series - Discrete, No Mean Reversion",{"$f":"D5","v":100},null,{"$f":"_xlfn.FORMULATEXT(G13)","v":"=D13*(1+G11)"},{"$f":"D13*(1+G11)","v":91.442209617694132},{"$f":"G13*(1+H11)","v":49.885310627202536},{"$f":"H13*(1+I11)","v":39.633652115546603},34.547175099738453,27.050693783797549,19.715438262876663,20.528262872196017,23.802507488383437,21.089403645810112,22.887326439163935,21.954153615912851,18.145371288607869,21.416364879381923,17.965216676145086,17.658720172110058,21.775257534918648,17.677036821195998,20.928120228261303,20.950610820322538,24.313309457898349]
[null,null,"Continual - No Mean Reversion",{"$f":"D5","v":100},null,{"$f":"_xlfn.FORMULATEXT(G14)","v":"=D14*EXP(G11)"},{"$f":"D14*EXP(G11)","v":91.798162599030633},{"$f":"G14*EXP(H11)","v":58.272570298002904},{"$f":"H14*EXP(I11)","v":47.447647072981994},41.732892557128601,33.592304537885056,25.613767698907161,26.691838143929701,31.307484260365982,27.934800237454844,30.420771754190866,29.205387240404001,24.553764463175686,29.40401371870707,25.027764998983056,24.60439922127004,31.063753651617329,25.734597111216956,30.930783264646493,30.96404117548677,36.355029742797669]
[]
[null,null,"Mean Reversion - Discrete",{"$f":"D13","v":100},null,{"$f":"_xlfn.FORMULATEXT(G16)","v":"=D16+D16*G$11+$D$4*($D$5-D16)"},{"$f":"D16+D16*G$11+$D$4*($D$5-D16)","v":91.442209617694118},{"$f":"G16+G16*H11+$D$4*($D$5-G16)","v":51.596868703663702},{"$f":"H16+H16*I11+$D$4*($D$5-H16)","v":50.674103472124671},54.035903733643877,51.503331791838505,47.236661385981755,59.736793848075912,77.317414959811344,73.040987544759346,84.659711316338118,84.275983540477654,72.79991452088673,91.363281369063159,78.367854629090843,81.357284884636897,104.05154567774491,83.658175395498645,102.31258655507293,101.96002038261462,117.93321083756749]
[null,null,"Mean Reversion - Continual",{"$f":"D5","v":100},null,{"$f":"_xlfn.FORMULATEXT(G17)","v":"=D17*EXP(G11)+($D$5-D17)*$D$4"},{"$f":"D17*EXP(G11)+($D$5-D17)*$D$4","v":91.798162599030633},{"$f":"G17*EXP(H11)+($D$5-G17)*$D$4","v":59.912937778196778},{"$f":"H17*EXP(I11)+($D$5-H17)*$D$4","v":56.800706406989157},{"$f":"I17*EXP(J11)+($D$5-I17)*$D$4","v":58.599296622988561},55.448819797526646,51.189359459093858,63.106021651491005,81.397331558272072,76.349115979793766,87.873747229199438,86.788225853778997,75.607579986145979,95.421273174062833,82.135310277335151,84.318860095733939,109.59118648822309,88.871982804034133,109.04212077308273,107.35094269980453,124.57106985554984]
[]
[null,"Standard Deviation and Volatility"]
[null,null,"Percent Change Continual - LN",null,null,{"$f":"_xlfn.FORMULATEXT(H20)","v":"=LN(H14/G14)"},null,{"$f":"LN(H14/G14)","v":-0.45446079184038329},-0.20550455400122719,-0.12833732811145457,-0.21699259908511764,-0.27116700146576117,4.1227823519899683E-2,0.15949935153169442,-0.11398395080423462,8.525242456113831E-2,-4.0772469677990725E-2,-0.17348800568400374,0.1802660049633521,-0.16114537750331967,-1.7060551484581389E-2,0.23311640496519062,-0.18820538435197723,0.1839156324643183,1.0746589667838559E-3,0.16050599509556632]
[null,null,"Percent Change Continual - Discrete",null,null,{"$f":"_xlfn.FORMULATEXT(H21)","v":"=H14/G14-1"},null,{"$f":"H14/G14-1","v":-0.36520984028259573},-0.18576361347479298,-0.12044337008035821,-0.19506407345476495,-0.23751085103374747,4.2089490999347889E-2,0.17292350161676584,-0.10772772398007147,8.8991920314606121E-2,-3.9952454974105933E-2,-0.15927276495046971,0.19753587124310434,-0.14883167861331159,-1.6915844372448752E-2,0.26252843535245929,-0.17155545978658349,0.20191441626123896,1.0752366196393748E-3,0.17410481199006966]
[]
[null,"Continual",null,"Var S","Var P",null,"Change in the Continious Case"]
[null,null,"Volatility Output - LN",{"$f":"IFERROR(_xlfn.VAR.S(G20:Z20),FALSE)","v":3.4887056461079716E-2},{"$f":"IFERROR(_xlfn.VAR.P(H20:Z20),FALSE)","v":3.30508955947071E-2},null,"Chg 1","Chg 2","Chg 3","Chg 4","Chg 5","Chg 6","Chg 7","Chg 8","Chg 9","Chg 10","Chg 11","Chg 12","Chg 13","Chg 14","Chg 15","Chg 16","Chg 17","Chg 18","Chg 19","Chg 20"]
[null,null,"Volatiity Output - Discrete",{"$f":"IFERROR(_xlfn.VAR.S(G21:Z21),FALSE)","v":3.1472932942503043E-2},{"$f":"IFERROR(_xlfn.VAR.P(H21:Z21),FALSE)","v":2.981646278763446E-2},null,{"$f":"(LN(G17/$D$17)^2)","v":7.3235776227487089E-3},{"$f":"(LN(H17/$D$17)^2)","v":0.26242845684483246},{"$f":"(LN(I17/$D$17)^2)","v":0.31992759483026179},0.28563412223722262,0.3477575969142439,{"$f":"(LN(L17/$D$17)^2)","v":0.44841571881450504},0.21192579675439324,4.2365040175703333E-2,7.2821037167165176E-2,1.6710498208840498E-2,2.0078669053045374E-2,7.8183789609943155E-2,2.1966697103766547E-3,3.8731095435844541E-2,2.9092289621381266E-2,8.3881364461592493E-3,1.39176870549284E-2,7.4933348748739172E-3,5.031507491935267E-3,4.8270818388051431E-2]
[]
[null,null,"Percent Change Discrete - LN",null,null,null,null,{"$f":"LN(H13/G13)","v":-0.60598060065561388},-0.23004802493019802,-0.13735277408117585,-0.24461313103743113,-0.31631065616041532,4.040061633203855E-2,0.1479883184478287,-0.12102021432467706,8.1812609298860514E-2,-4.1626974344167844E-2,-0.19054084964729506,0.16573984100755862,-0.17571786226451261,-1.7207759394078207E-2,0.20954462764592266,-0.20850790720832432,0.16882727755836255,1.0740819342084226E-3,0.14885611267813784]
[null,null,"Percent Change Discrete - Discrete",null,null,null,null,{"$f":"H13/G13-1","v":-0.45446079184038335},-0.20550455400122714,-0.1283373281114546,-0.21699259908511759,-0.27116700146576111,4.1227823519899509E-2,0.15949935153169426,-0.11398395080423462,8.5252424561138351E-2,-4.0772469677990641E-2,-0.1734880056840038,0.18026600496335221,-0.1611453775033197,-1.7060551484581077E-2,0.23311640496519059,-0.18820538435197709,0.1839156324643183,1.0746589667840478E-3,0.16050599509556651]
[null,null,null,"Var S","Var P"]
[null,null,"Volatility Output - LN",{"$f":"IFERROR(_xlfn.VAR.S(G27:Z27),FALSE)","v":4.3673934285210034E-2},{"$f":"IFERROR(_xlfn.VAR.P(H27:Z27),FALSE)","v":4.1375306164935823E-2}]
[null,null,"Volatiity Output - Discrete",{"$f":"IFERROR(_xlfn.VAR.S(G28:Z28),FALSE)","v":3.4887056461079716E-2},{"$f":"IFERROR(_xlfn.VAR.P(H28:Z28),FALSE)","v":3.3050895594707093E-2}]
[]
[]
[]
[]
[]
[]
[null,"Graphs"]
[null,null,null,null,null,null,{"$f":"G8","v":1},2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
[null,null,"Continuous - No Mean Reversion",null,null,null,{"$f":"G14","v":91.798162599030633},58.272570298002904,47.447647072981994,41.732892557128601,33.592304537885056,25.613767698907161,26.691838143929701,31.307484260365982,27.934800237454844,30.420771754190866,29.205387240404001,24.553764463175686,29.40401371870707,25.027764998983056,24.60439922127004,31.063753651617329,25.734597111216956,30.930783264646493,30.96404117548677,36.355029742797669]
[null,null,"Continuous - Mean Reversion",null,null,null,{"$f":"G17","v":91.798162599030633},59.912937778196778,56.800706406989157,58.599296622988561,55.448819797526646,51.189359459093858,63.106021651491005,81.397331558272072,76.349115979793766,87.873747229199438,86.788225853778997,75.607579986145979,95.421273174062833,82.135310277335151,84.318860095733939,109.59118648822309,88.871982804034133,109.04212077308273,107.35094269980453,124.57106985554984]
[]
[null,null,"Standard Deviation - No Mean Reversion",{"$f":"_xlfn.STDEV.S(G40:Z40)","v":15.775984775692752},{"$f":"D43/D5","v":0.15775984775692753}]
[null,null,"Standard Deviation - Mean Reversion",{"$f":"_xlfn.STDEV.S(G41:Z41)","v":20.630368364286447},{"$f":"D44/D5","v":0.20630368364286447}]
[]
[null,null,"Continual Rate of Change - No Mean Reversion",null,null,null,null,{"$f":"LN(H40/G40)","v":-0.45446079184038329},{"$f":"LN(I40/H40)","v":-0.20550455400122719},-0.12833732811145457,-0.21699259908511764,-0.27116700146576117,4.1227823519899683E-2,0.15949935153169442,-0.11398395080423462,8.525242456113831E-2,-4.0772469677990725E-2,-0.17348800568400374,0.1802660049633521,-0.16114537750331967,-1.7060551484581389E-2,0.23311640496519062,-0.18820538435197723,0.1839156324643183,1.0746589667838559E-3,0.16050599509556632]
[null,null,"Continual Rate of Change - Mean Reversion",null,null,null,null,{"$f":"LN(H41/G41)","v":-0.4266998107467167},{"$f":"LN(I41/H41)","v":-5.3343709025779014E-2},3.1173931097720244E-2,-5.5262264004670873E-2,-7.9928742102902683E-2,0.20928450790434605,0.25452629534471938,-6.4026037556814117E-2,0.14058464067204685,-1.2430128127406771E-2,-0.13791442309321306,0.23274500031541395,-0.1499335302051101,2.6237553276272665E-2,0.26215139011405786,-0.20956001723897316,0.20453729790747158,-1.5630930855424198E-2,0.14877308940950557]
[]
[null,null,"Volatilty - No Mean Reversion",{"$f":"_xlfn.STDEV.S(H46:Z46)","v":0.1867807711224036}]
[null,null,"Volatilty - Mean Reversion",{"$f":"_xlfn.STDEV.S(H47:Z47)","v":0.18200123206412752}]

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["          "]
[null,null,null,null,null,null,"vol --> LN(Pt/Pt-1)",null,null,null,"vol --> Pt/Pt-1-1"]
[null,null,"Simulations",null,10000]
[null,null,null,null,"s"]
[null,null,"Row Start",null,15]
[null,null,"Column Start",null,{"$f":"COLUMN()","v":5}]
[]
[null,null,"Time Series",null,"Continual","Continual","Continual","Continual","Discrete","Discrete","Discrete","Discrete"]
[null,null,null,null,"LN S","LN P","Discrete S","Discrete P","LN S","LN P","Discrete S","Discrete P"]
[null,null,"Median Variance",null,{"$f":"MEDIAN(E18:E200011)","v":3.8575895855686548E-2},{"$f":"MEDIAN(F18:F200011)","v":3.6545585547492529E-2},4.0058637087153084E-2,3.7950287766776614E-2,4.1668110273593996E-2,3.9475051838141678E-2,3.8575895855686548E-2,3.6545585547492522E-2,null,null,null,"Average",{"$f":"AVERAGE(E13:E7683)","v":3.9901896171941745E-2}]
[null,null,"Average Variance",null,{"$f":"AVERAGE(E18:E200011)","v":4.0035005168142825E-2},{"$f":"AVERAGE(F18:F200011)","v":3.7927899632977415E-2},4.2561629740492067E-2,4.0321543964676791E-2,4.4833624714446157E-2,4.2473960255791011E-2,4.0035005168142825E-2,3.7927899632977415E-2]
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{"sheet":"20% MR Variance with Time","index":6,"n_rows":10017,"n_cols":44,"rows_kept":4500,"cut":true,"hidden":false,"merged":[],"bounds":{"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0}}
["          ",null,"Simulations3",null,10000,null,null,null,null,null,null,null,"Mean Reverting Series with 50% Mean Reverision"]
[]
[null,null,"Row Start1",null,17]
[null,null,"Mean Reversion",null,{"$f":"'Annual Time Series'!D4","v":0.2}]
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