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[null,"In today's class I am going to start by buying 100 shares of AAPL on 1/31/1990, and we'll evaluate the position over time."]
[null,"-- Objective is to link this issue to the stock returns."]
[{"$nulls":5},"Reinvest cash dividends",null,null,"Reinvest cash dividends"]
[{"$nulls":5},"My Position",null,null,"log rate of return (monthly)"]
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[20180531,0.73,0,186.87,null,3360.939549924141,628058.7736943242,null,0.12679210580979827,null,0.11093341562345235,0.012306222701885623,null,null,4915138,{"$nulls":10},0.026169]
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[20180731,null,null,190.28999,null,3360.939549924141,639553.1533456693,null,0.02759892879095105,null,0.01174023860460513,1.3783320249306062E-4,null,null,4829926,{"$nulls":10},0.031603]
[20180831,0.73,0,227.63,null,3371.717944122817,767504.1556206768,null,0.18237415933351286,null,0.16651546914716694,0.027727401465301105,null,null,4829926,{"$nulls":10},0.030221]
[20180928,null,null,225.74001,null,3371.717944122817,761131.6424234641,null,-0.008337564933067476,null,-0.024196255119413396,0.000585458761803739,null,null,4754986,{"$nulls":10},4.46E-4]
[20181031,null,null,218.86,null,3371.717944122817,737934.1892507197,null,-0.030951682835932637,null,-0.046810373022278556,2.191211022484864E-3,null,null,4745398,{"$nulls":10},-0.074032]
[20181130,0.73,0,178.58,null,3385.5008654981652,604582.7445606624,null,-0.19931610448602477,null,-0.2151747946723707,0.04630019226229688,null,null,4745398,{"$nulls":10},0.018535]
[20181231,null,null,157.74001,null,3385.5008654981652,534028.9403786893,null,-0.12408850872376664,null,-0.13994719891011256,0.01958521848278661,null,null,4729803,{"$nulls":10},-0.089807]
[20190131,null,null,166.44,null,3385.5008654981652,563482.7640535146,null,0.05368671274943626,null,0.03782802256309034,1.4309592910336719E-3,null,null,4715280,{"$nulls":10},0.088276]
[20190228,0.73,0,173.14999,null,3399.7741301504684,588670.8566378123,null,0.04373046449492257,null,0.027871774308576652,7.7683580310823348E-4,null,null,4715280,{"$nulls":10},0.032716]
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[20190430,null,null,200.67,null,3399.7741301504684,682232.6746972945,null,0.05490088816479144,null,0.03904219797844552,1.5242932229881355E-3,null,null,4601075,{"$nulls":10},0.037882]
[20190531,0.77,0,175.07001,null,3414.7271542590283,597816.3170433997,null,-0.1320872202732346,null,-0.14794591045958053,0.021887992421714218,null,null,4601075,{"$nulls":10},-0.061653]
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[20190731,null,null,213.03999,null,3414.7271542590283,727473.4387960718,null,0.07361698592195687,null,0.05775829573561095,3.3360207262822937E-3,null,null,4519180,{"$nulls":10},0.011882]
[20190830,0.77,0,208.74001,null,3427.323397350036,715419.5202360805,null,-0.01670837591579577,null,-0.03256706610214169,1.0606137945012664E-3,null,null,4519180,{"$nulls":10},-0.020271]
[20190930,null,null,223.97,null,3427.323397350036,767617.6213044876,null,0.07042260801598843,null,0.05456391782964251,0.00297722112891998,null,null,4443236,{"$nulls":10},0.016024]
[20191031,null,null,248.75999,null,3427.323397350036,852580.9340515609,null,0.10497642172191934,null,0.08911773153557342,0.007941970074046538,null,null,4443265,{"$nulls":10},0.019265]
[20191129,0.77,0,267.25,null,3437.1981925453942,918591.2169577567,null,0.07457306855578327,null,0.05871437836943735,3.447378227309453E-3,null,null,4443265,{"$nulls":10},0.034971]
[20191231,null,null,293.64999,null,3437.1981925453942,{"v":1009333.2148689731,"d":"1,009,333.21"},null,0.09420399800922752,null,0.0783453078228816,6.137987257862073E-3,null,null,4443265,{"$nulls":10},0.028448]
[]
[{"$nulls":10},{"$f":"SUM(K7:K365)","v":-4.718447854656915e-15},{"$f":"SUM(L7:L365)/359","v":0.016594250367349583},"= variance of monthly returns"]
[{"$nulls":6},"Sum of monthly log returns:",null,{"$f":"SUM(I7:I365)","v":5.693269776898186},{"$nulls":3},"(i.e., the average distance between the return each month and the mean return)"]
[{"$nulls":6}," = Total holding period return",null,null,"(359 months = ",{"$f":"359/12","v":29.916666666666668}," years)"]
[]
[{"$nulls":6},"So if we started with:",null,{"$f":"G6","v":{"v":3400,"d":"3,400.00"}}]
[]
[{"$nulls":6},"ending value:",null,{"$f":"I371*EXP(I368)","v":{"v":1009333.2148689687,"d":"1,009,333.21"}}]
[]
[{"$nulls":5},"Monthly holding period return:",null,null,{"$f":"I368/359","v":0.01585869018634592},"  also average monthly period rate of return."]
[{"$nulls":6},"Annualized rate of return:",null,{"$f":"I375*12","v":0.19030428223615103}]
[]
[]
["We assume that the montly returns are normally distributed."]
[null,"Mean monthly return:",null,{"$f":"I375","v":0.01585869018634592}]
["standard deviation of monthly returns:",null,null,{"$f":"SQRT(L367)","v":0.12881867243280215}]
["2 pictures of the distribution:"]
[null,"1. Cumulative distribution function - probability that the return in a month will be less than x."]
[null,"2. Probability density function - derivative of the CDF."]
[{"$nulls":5},"Start","End","Size"]
["In order to plot these pictures we need a grid for x:",{"$nulls":4},-0.35,0.38,{"$f":"(G386-F386)/1000","v":0.00073}]
[]
[{"$nulls":5},"x Grid","CDF(x)"]
[{"$nulls":5},{"$f":"F386","v":-0.35},{"$f":"_xlfn.NORM.DIST(F389,$D$380,$D$381,TRUE)","v":2.2549269545597333E-3},{"$nulls":25},"x Grid","pdf"]
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[{"$nulls":5},{"$f":"F390+$H$386","v":-0.34853999999999996},2.3363466860737694E-3,{"$nulls":25},{"$f":"AG390+$H$386","v":-0.34926999999999997},{"$f":"_xlfn.NORM.DIST(AG391,$D$380,$D$381,FALSE)","v":0.055764839948787975}]
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