Getting parameters from real data
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1
Data downloaded from http://finance.yahoo.com/q/hp?s=SPY&a=00&b=1&c=2007&d=03&e=5&f=2015&g=d and http://finance.yahoo.com/q/hp?s=SSO&a=00&b=1&c=2007&d=03&e=5&f=2015&g=d
Avg % error3.305289221
2
yearly interest rate + extra expense ratio for leveraged fund
0.0226SPY sigma (daily)0.0138452663
SPY sigma (annual)
0.2197867887Max % error8.948913459
3
dummy test for 3X column
-0.0085
Avg SPY return (daily)
0.0003604530284
Avg SPY return (annual)
0.09083416315
Dummy avg % error
26.53718465
4
Dummy max % error
63.51821001
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DateSPY Adj CloseSPY daily returnPredicted SSO valueDate
SSO Adj Close
SSO Adj Close made proportional to SPY
% error
Dummy 3X column
Dummy % error
6
4/2/2015206.440.003597472047199.24478324/2/2015129.21199.25797330.006619627147199.45524930.0990052974
7
4/1/2015205.7-0.003536307707197.83908484/1/2015128.45198.08595830.1246295131197.31904440.3871621632
8
3/31/2015206.43-0.008739495798199.26628933/31/2015129.3199.39676460.06543501005199.42803440.01568220072
9
3/30/2015208.250.01219986391202.82973893/30/2015131.64203.00533710.08649932344204.79042190.879328972
10
3/27/2015205.740.002289667268198.01596193/27/2015128.48198.13222210.05867808322197.55338510.2921468017
11
3/26/2015205.27-0.002381415241197.13091273/26/2015127.97197.34573830.1088574951196.19907550.5810426061
12
3/25/2015205.76-0.0146537688198.09215753/25/2015128.56198.25559210.08243631951197.60414280.3285906039
13
3/24/2015208.82-0.005619047619204.09189173/24/2015132.34204.08482460.003462821888206.68323651.273201876
14
3/23/2015210-0.001948576589206.43028823/23/2015133.97206.59848840.08141407652210.21985181.752850852
15
3/20/2015210.410.008821978233207.25658613/20/2015134.4207.26160220.002420153197211.44879212.020243914
16
3/19/2015208.57-0.004534173349203.68111213/19/2015132.06203.65302960.01378936246205.99012291.147585786
17
3/18/2015209.520.01197836167205.56367023/18/2015133.3205.56526470.000775648542208.82360651.585064406
18
3/17/2015207.04-0.002937635444200.77184053/17/2015130.2200.78467710.006393227862201.57325530.3927482115
19
3/16/2015207.650.01332227211201.97662163/16/2015131.05202.09548340.05881464648203.35857610.6249980007
20
3/13/2015204.92-0.006111165001196.75190213/13/2015127.67196.88310080.06663788436195.53698970.683710868
21
3/12/2015206.180.01272164645199.20451053/12/2015129.19199.22713080.01135403875199.18197290.02266654949
22
3/11/2015203.59-0.002352134072194.27884053/11/2015126.04194.3694370.04661048965191.85342731.294447221
23
3/10/2015204.07-0.01619823555195.21469013/10/2015126.58195.20218450.006406455865193.21027971.020431639
24
3/9/2015207.430.004114628715201.76940193/9/2015130.87201.81790090.02403106387203.07163670.6212213076
25
3/6/2015206.58-0.01403207331200.14034463/6/2015129.8200.16782710.01372975115200.58882520.2103225395
26
3/5/2015209.520.00105112279205.93829623/5/2015133.53205.91995340.008907710305209.39656611.688332096
27
3/4/2015209.3-0.00418688743205.52466483/4/2015133.29205.54984340.01224938301208.73131881.547787796
28
3/3/2015210.18-0.004122245913207.27896153/3/2015134.37207.21533840.0307038348211.37925232.009462211
29
3/2/2015211.050.006341789052209.02097883/2/2015135.52208.98878220.01540588421214.01874722.406810993
30
2/27/2015209.72-0.003421402775206.42133012/27/2015133.9206.49053970.03351706937210.01603121.707338041
31
2/26/2015210.44-0.001186577436207.86233322/26/2015134.74207.78592470.0367727307212.18680372.117987053
32
2/25/2015210.69-0.0008536064874208.37552832/25/2015135.03208.23314090.06837881326212.93762222.259237516
33
2/24/2015210.870.002853474105208.75063142/24/2015135.35208.72662090.01150328522213.47709792.275932464
34
2/23/2015210.27-0.0001426533524207.58457372/23/2015134.56207.50834220.03673658675211.65807611.999791366
35
2/20/2015210.30.005979430758207.66244482/20/2015134.6207.57002720.04452360778211.74155092.009694664
36
2/19/2015209.05-0.0007170172084205.22657392/19/2015133.07205.21057590.007795895991208.00331081.360911764
37
2/18/2015209.20.00009561143513205.53975832/18/2015133.22205.44189470.04763569076208.44465511.461610575
38
2/17/2015209.180.001580081398205.51888992/17/2015133.25205.48815840.0149553431208.37785661.406260193
39
2/13/2015208.850.004134814174204.88977982/13/2015132.74204.70167460.09189235697207.38779261.312211017
40
2/12/2015207.990.009611183923203.22739082/12/2015131.67203.05160090.0865740121204.83995780.8807401272
41
2/11/2015206.010.0005828354947199.41210182/11/2015129.21199.25797330.07735121688199.09269290.08294796225
42
2/10/2015205.890.01065187512199.19776732/10/2015129198.93412710.1325263933198.73849390.09834069403
43
2/9/2015203.72-0.004495699765195.05975642/9/2015126.37194.87833830.09309302318192.57804631.180373364
44
2/6/2015204.64-0.002729044834196.84734332/6/2015127.52196.65178210.09944544919195.20420050.7361141535
45
2/5/2015205.20.01009106571197.94549992/5/2015128.33197.90090330.02253477726196.80886270.551811846
46
2/4/2015203.15-0.003824841858194.04662792/4/2015125.68193.8142720.1198858396191.01964421.441910225
47
2/3/2015203.930.01447617153195.56013942/3/2015126.63195.27929080.1438189604193.23035321.049234471
48
2/2/2015201.020.01238920226190.07409542/2/2015123.05189.75848320.1663230608185.18193082.411777536
49
1/30/2015198.56-0.0125814312185.49447391/30/2015120.2185.36342690.07069729074178.54000393.681105344
50
1/29/2015201.090.009234629862190.3000341/29/2015123.31190.15943570.07393705249185.53669732.4309803
51
1/28/2015199.25-0.0128319461186.86552471/28/2015121186.5971270.1438380855180.52924583.251862075
52
1/27/2015201.84-0.01320035201191.80519411/27/2015124.23191.57819080.1184912186187.75052681.997964345
53
1/26/2015204.540.002352249338197.02444791/26/2015127.58196.74430960.1423869971195.48535970.6398913488
54
1/23/2015204.06-0.005458621698196.11939291/23/2015126.96195.78819210.1691628497194.10903390.8576401655
55
1/22/2015205.180.01483826293198.30208931/22/2015128.41198.02427330.1402939232197.3338910.3486352268
56
1/21/2015202.180.005070590575192.60355811/21/2015124.7192.30298950.1562994606188.91787921.760300398
57
1/20/2015201.160.002142181039190.68686931/20/2015123.48190.4215970.1393078611186.08098132.279476587
58
1/16/2015200.730.01307156556189.89034011/16/2015122.91189.54258570.1834703201184.88656362.456451762
59
1/15/2015198.14-0.009151372706185.06866321/15/2015119.85184.82368320.1325479684177.90410723.743879493
60
1/14/2015199.97-0.006014514365188.53630361/14/2015122.06188.23177950.1617814657182.91984022.822020431
61
1/13/2015201.18-0.00282527881190.84914931/13/2015123.6190.6066520.1272239669186.27461112.272764803
62
1/12/2015201.75-0.007819415757191.95099411/12/2015124.24191.5936120.1865313437187.86054981.94842727
63
1/9/2015203.34-0.008000780564195.01834291/9/2015126.19194.60075580.2145865789192.36664561.148048051
64
1/8/2015204.980.01772503848198.20775211/8/2015128.4198.00885210.1004500824197.09063450.4637255381
65
1/7/2015201.410.01246669683191.43841431/7/2015124.04191.2851870.08010410618187.13347812.170428851
66
1/6/2015198.93-0.009411413206186.7976671/6/2015121.03186.64339070.08265833083180.38112353.355204376
67
1/5/2015200.82-0.01809114023190.39858191/5/2015123.24190.0514870.1826320413185.61557732.334056799
68
1/2/2015204.52-0.0005375555881197.56463921/2/2015127.9197.23778960.1657134865196.26069680.4953882181
69
12/31/2014204.63-0.009918714922197.795029612/31/2014128.07197.49995080.1494070106196.57107010.4703194922
70
12/30/2014206.68-0.005341931758201.816652712/30/2014130.7201.55573960.1294496003202.59261170.5144343909
71
12/29/2014207.790.001349332562204.014613512/29/2014132.04203.62218710.1927228159205.88514021.111348974
72
12/26/2014207.510.003190717912203.48372812/26/2014131.81203.26749840.1063769001205.04818930.8760332824
73
12/24/2014206.850.00009669777112202.211463412/24/2014130.92201.89500710.1567429991203.09726060.5954845121
74
12/23/2014206.830.00135560397202.190493612/23/2014130.93201.91042840.1387076726203.03151420.5552392152
75
12/22/2014206.550.004620622568201.66183212/22/2014130.5201.24731460.2059741263202.20237490.4745704518
76
12/19/2014205.60.004249499341199.833047412/19/2014129.36199.48929210.1723176573199.43115970.02914060564
77
12/18/2014204.730.02472596226198.166601812/18/2014128.31197.87006080.149866502196.9141580.4830962383
78
12/17/2014199.790.01959683593188.844799112/17/2014122.3188.60188950.1287949006183.3103972.805641266
79
12/16/2014195.95-0.007998784995181.738113812/16/2014117.55181.27679570.2544827537173.12637024.496121735
80
12/15/2014197.53-0.006887883358184.709583512/15/2014119.43184.17599070.289719015177.37678363.691690267
81
12/12/2014198.9-0.0161745066187.306674712/12/2014121.24186.9672370.181549338181.1131333.131085461
82
12/11/2014202.170.005070842655193.586363912/11/2014125.17193.02778830.2893757586190.34281611.390977017
83
12/10/2014201.15-0.01599647784191.659799112/10/2014124.05191.30060830.1877625047187.48438081.994885146
84
12/9/2014204.42-0.0006843957763198.012564512/9/2014128.11197.56163580.2282471073196.92821170.3206209927
85
12/8/2014204.56-0.006700980868198.301782612/8/2014128.34197.91632460.1947580516197.32670460.2979137798
86
12/5/2014205.940.001653696498201.013789112/5/2014130.1200.63046460.1910599603201.36800180.3676097632
87
12/4/2014205.6-0.001117427003200.369059512/4/2014129.59199.84398080.2627442789200.36720370.2618156848
88
12/3/2014205.830.00385290675200.835909912/3/2014129.95200.39914590.2179470531201.03434640.3169677095
89
12/2/2014205.040.006479481641199.317878812/2/2014128.89198.76449330.2784126445198.73057210.01706602721
90
12/1/2014203.72-0.006970509383196.785392412/1/2014127.34196.37419960.2093924751194.93476820.7330043187
91
11/28/2014205.15-0.002091643156199.5857211/28/2014129.16199.18086710.2032589251199.09135730.04493893113
92
11/26/2014205.580.002535843168200.442203311/26/2014129.69199.99819330.2220069665200.341730.1717698795
93
11/25/2014205.06-0.0007309585303199.448549811/25/2014129.12199.11918210.1654123653198.82247580.1490093755
94
11/24/2014205.210.00283438401199.75849511/24/2014129.25199.31965830.2201672938199.25269140.03359777153
95
11/21/2014204.630.005355212735198.650208511/21/2014128.42198.03969460.3082785844197.56609290.2391448143
96
11/20/2014203.540.001722525715196.56256811/20/2014127.14196.06577460.253381032194.43579940.8313410128
97
11/19/2014203.19-0.001572404304195.905233711/19/2014126.66195.32555450.2967758958193.4297120.970606517
98
11/18/2014203.510.005732641463196.540943711/18/2014127.1196.00408960.2738994379194.33989960.8490588153
99
11/17/2014202.350.0006428642073194.330319611/17/2014125.67193.79885080.2742373404191.04782941.419524117
100
11/14/2014202.220.0002473166147194.098169311/14/2014125.51193.55211080.2821247983190.67366611.487167817
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SPY and SSO
EEM and EDC
MID and UMDD
EEM and EET
ACWI