111-2 _ Midterm Portfolio

Problem 1

1. Loading packages and data

#Loading all the necessary packages
library(pacman)
p_load(readxl,tidyquant, lubridate, timetk, tidyverse, fPortfolio,
       quadprog,PerformanceAnalytics,IntroCompFinR,matlib,dplyr, kableExtra)
#Loading data of 8 stocks from Yahoo
symbols <- c("SPY", "QQQ", "EEM", "IWM", "EFA", "TLT", "IYR", "GLD")
asset_Prices <- NULL
for (symbol in symbols)
{
  asset_Prices <- cbind(asset_Prices,
                        getSymbols.yahoo(symbol, 
                        from  = '2018-01-01', to = '2022-12-31', auto.assign = FALSE)[, 6])
}
colnames(asset_Prices) <- c("SPY", "QQQ", "EEM", "IWM", "EFA", "TLT", "IYR", "GLD")
asset.names <- names(asset_Prices)
asset_Prices %>%  kbl(caption="ETF daily data from yahoo with ticker names of SPY, QQQ, EEM, 
                      IWM, EFA, TLT, IYR and GLD from 2018 to 2022")%>% 
             row_spec(row =0, bold= TRUE, color = "black", background = "#F9EBEA") %>%
             kable_styling(bootstrap_options = "striped", full_width = F, position = "center") %>%
             kable_paper() %>%
             scroll_box(width = "100%", height = "400px")

ETF daily data from yahoo with ticker names of SPY, QQQ, EEM, IWM, EFA, TLT, IYR and GLD from 2018 to 2022

SPY	QQQ	EEM	IWM	EFA	TLT	IYR	GLD
245.8284	152.8868	43.05478	143.94115	61.24226	112.31089	69.33669	125.15
247.3833	154.3723	43.46730	144.09082	61.53624	112.84785	69.22486	124.82
248.4260	154.6424	43.68253	144.47426	62.21065	112.82996	68.14092	125.46
250.0815	156.1956	44.05919	144.77357	62.55652	112.50781	68.20976	125.33
250.5389	156.8033	44.05919	144.99802	62.53921	112.43618	68.59687	125.31
251.1059	156.8129	43.98745	144.80164	62.60841	110.93261	67.80544	124.73
250.7218	156.4463	43.70944	144.82034	62.48735	110.79836	66.97958	125.03
252.5510	157.5171	43.97848	147.30823	62.91967	111.25482	66.74730	125.44
254.1974	158.6747	44.39996	147.92552	63.55084	111.44274	66.20536	126.96
253.3285	158.2213	44.22957	146.03622	63.49033	111.90814	66.38600	127.17
255.7431	159.9287	44.81249	147.42042	63.81889	111.75603	66.85916	126.14
255.3133	159.9577	44.86629	146.41034	63.74107	110.71782	66.20536	125.86
256.4748	160.4593	45.23397	148.33704	64.09557	110.13607	66.63547	126.42
258.5602	162.1763	45.49404	149.13199	64.42413	110.24348	67.17746	126.65
259.1090	163.5172	45.70927	149.60902	64.63165	110.71782	68.10652	127.28
259.0085	162.4561	46.09490	148.68311	64.74405	110.11820	67.86563	128.83
259.1182	162.3982	46.06799	148.73915	64.49330	111.02213	67.73661	127.97
262.1183	164.8870	46.70471	149.27232	65.06397	110.61043	67.76241	128.07
260.3803	164.0863	45.99625	148.43057	64.46736	109.84075	66.89358	127.35
257.7097	162.7358	45.36849	147.00891	63.93128	109.19639	66.53226	126.80
257.8377	163.4111	45.76308	146.24197	63.84483	109.84075	67.58176	127.65
257.5450	162.0220	45.14429	146.70030	64.02640	108.24889	66.45484	128.07
251.9382	158.7904	43.98745	143.87569	62.72944	107.24439	65.77525	126.39
241.4016	152.5299	42.44497	138.34813	60.10095	108.25783	63.65901	126.71
246.1577	156.5717	43.82602	140.00362	61.28550	107.58518	63.88266	125.38
244.8223	154.5460	42.44497	140.14384	60.63702	106.56280	63.63318	124.79
235.6393	148.0250	40.97424	136.02863	59.05474	106.44620	61.75782	124.98
239.1790	150.5813	41.62889	137.27252	59.30548	105.77357	63.03961	124.77
242.6912	153.2534	42.28355	138.57256	60.21335	106.23990	63.22887	125.37
243.2949	154.0444	42.60639	138.87187	60.03178	106.71525	63.71061	126.08
246.5784	156.9286	43.67357	141.36909	61.09527	105.53140	63.40091	128.23
249.7248	159.8419	44.57035	142.91232	61.47572	105.89020	64.02891	128.38
249.7980	159.1281	44.42687	143.41737	61.75240	106.46413	64.57088	127.96
248.2340	159.4464	43.81705	142.23894	61.17310	105.99780	63.77081	126.24
246.9992	158.9930	43.78119	142.38861	60.87912	104.69737	62.71271	125.66
247.3193	158.9737	43.80808	142.16414	61.19905	105.01125	63.29766	126.30
251.2614	162.2246	44.58829	144.01599	61.68323	105.94392	64.37299	126.14
254.1791	164.3757	45.00082	144.96060	62.26254	105.97987	64.59668	126.45
251.0053	162.3403	43.69150	142.87492	61.33739	105.82738	63.23748	125.13
248.4626	161.2985	43.06375	140.62085	60.75806	106.49998	63.08262	125.00
244.8498	158.6650	42.98304	140.24677	59.73779	107.22704	62.88476	124.72
246.1120	160.1216	43.16240	142.49147	60.02313	106.35532	62.77294	125.39
248.9565	161.8966	43.22517	143.76346	60.34304	106.06776	63.47833	125.18
249.5877	162.5815	43.62872	145.31599	60.69754	106.16663	63.88266	126.53
249.4962	162.9577	43.67357	146.59740	60.68026	106.04977	64.20957	125.72
250.7034	163.8548	43.68253	146.29808	60.80996	106.66087	64.53645	125.42
255.0663	167.0382	44.61519	148.63634	61.19905	105.95994	64.94078	125.54
254.7462	167.9256	44.72280	148.89821	61.26821	106.57101	65.26769	125.54
253.0998	165.6394	44.31924	148.20610	60.86182	107.11018	65.37092	125.78
251.8010	165.6105	44.39099	147.50464	61.00882	108.05380	65.42253	125.70
251.5267	165.4658	44.22957	146.76575	60.97424	108.05380	65.40532	124.90
251.7994	164.9738	44.13092	147.58878	60.93100	107.66736	65.79242	124.60
248.3924	161.4539	43.65563	146.16716	60.43816	107.32587	65.18165	124.87
248.8150	161.9853	44.13990	146.12973	60.42951	106.89449	65.13006	124.31
248.3374	161.2800	44.39996	146.98084	60.52462	107.01135	64.63107	126.48
242.1296	157.2992	42.92026	143.75790	59.40058	108.07177	64.25638	125.98
236.9688	153.1541	42.05038	140.66434	58.74347	107.99090	63.23284	127.61
243.4520	158.8451	43.41350	143.73915	59.79833	107.57749	64.03084	128.28
239.3104	153.7049	42.62432	140.95493	59.35736	108.72777	64.20432	127.49
238.6033	151.9367	42.40909	140.90807	59.70322	109.01533	65.44470	125.73
241.6522	154.7194	43.29691	142.33299	60.24793	109.54552	65.46207	125.79
236.4361	150.2555	42.51671	138.86441	59.41787	109.76167	64.55996	127.26
239.4665	151.9464	42.93820	140.85179	59.79833	108.91513	64.98498	126.30
242.0287	154.3426	42.95614	142.64233	60.00584	108.68996	65.71360	126.45
243.9388	155.2219	43.06375	143.82349	60.40357	107.87948	65.77431	125.80
238.5023	151.3377	42.22077	140.95493	60.00584	109.05924	65.18448	126.39
239.6777	152.4005	42.26561	141.12364	60.49868	109.23938	65.07170	126.82
243.4887	155.7629	43.09065	143.78604	61.14716	109.04120	64.82018	127.12
242.2123	154.8644	43.10859	144.09538	60.91371	109.42847	64.96764	128.11
244.2050	156.7291	43.09065	145.07973	61.14716	108.62695	64.35179	126.62
243.4887	155.9175	42.66020	144.32036	61.20768	108.87912	64.57732	127.45
245.4906	157.1060	42.71400	145.65152	61.30281	108.91513	64.88956	127.63
248.1171	160.4877	42.80368	147.23584	61.57947	109.21233	65.73093	127.75
248.3007	160.8162	43.17136	147.62955	61.89940	108.33880	65.61820	127.85
246.9232	159.3379	42.92026	146.60776	61.66594	107.45622	64.68141	127.60
244.8295	156.8161	42.38220	145.82030	61.43250	106.68170	64.12627	126.63
244.7928	156.4200	42.04141	145.60467	61.35467	106.70872	64.16964	125.62
241.4961	153.1058	41.84412	144.77035	61.10394	106.22242	64.32577	126.23
242.0929	153.2894	41.52128	144.55475	61.00017	105.51096	64.18700	125.41
244.5539	156.5166	42.12212	145.22032	61.30281	106.24946	64.96764	124.97
244.7836	156.6132	42.38220	145.01410	61.36333	107.06898	65.80902	125.50
242.9010	155.5021	42.07729	143.72978	61.16445	107.25809	65.60950	124.59
243.3327	157.2798	41.87102	144.43288	60.94829	106.87178	66.06921	123.71
241.6980	156.3523	41.53921	144.97653	60.92236	106.75447	65.84373	123.65
241.1654	156.3330	41.44953	144.18913	61.11258	107.23280	65.86973	124.28
244.2876	159.2992	41.63786	145.98903	61.32873	107.39530	66.56364	124.54
245.1142	160.6230	41.39572	147.22644	61.33739	107.22381	66.92796	124.57
245.1142	160.4587	41.62889	147.95766	61.34602	107.12453	66.59834	124.59
247.4834	162.2075	41.70960	148.75450	61.49302	106.48370	67.00600	124.33
249.7975	163.8887	42.57949	149.55136	61.89075	107.34113	67.62184	125.18
250.5597	163.7342	42.50774	149.84193	62.05502	107.61190	67.34429	125.00
250.6791	164.0144	42.56155	149.27013	62.16742	107.04327	66.84988	124.49
248.9527	162.1979	41.68270	149.29823	61.71782	105.82484	65.86105	122.48
249.9995	163.2703	42.31045	150.85440	61.80428	105.41868	65.67022	122.29
249.7883	162.6424	41.66476	151.54816	61.89940	104.88614	65.33195	122.36
249.1638	161.8018	41.31501	151.74498	61.67459	105.78873	65.47938	122.41
251.0372	162.7100	41.56611	152.74805	62.06368	105.84290	66.18198	122.48
250.3393	162.4974	41.70960	151.64186	61.98586	105.68040	66.26871	122.41
251.0280	163.8694	41.69167	151.83872	61.30281	106.44759	66.83253	122.54
250.5138	163.8211	41.46747	151.89496	61.11258	107.29598	66.66772	123.59
249.9168	163.9854	41.63786	151.62309	60.71485	107.96390	66.89325	123.21
247.0425	163.2607	40.66933	151.41685	59.47841	110.32858	67.09274	123.19
250.3393	164.4298	40.99217	153.81674	60.38628	109.58848	67.94280	123.37
248.8058	164.3236	40.97424	152.58868	60.00584	109.40798	67.82134	123.10
251.2484	166.9034	41.54818	153.59172	60.52462	108.82991	68.05555	122.49
252.4423	168.4106	41.96967	154.40733	60.70619	108.04286	68.65404	122.37
252.6259	168.9324	41.64682	155.36353	60.61108	108.29618	68.56732	122.85
254.7380	169.9179	42.27457	156.48843	61.15581	107.41865	68.64537	122.92
254.7105	168.5362	41.62889	155.63539	60.80996	108.45897	68.68876	122.86
255.4634	168.5459	41.54818	156.10416	60.87912	108.13333	68.88824	123.01
255.8033	169.0000	41.54818	156.33847	61.26821	107.93430	68.90559	123.23
256.1338	169.8889	41.44056	157.05098	60.87912	107.96141	69.25253	122.82
255.3165	169.8793	41.16256	156.43221	60.96558	107.90714	67.85606	123.19
255.9593	171.5991	40.88456	157.26654	60.83588	108.80280	68.53261	123.38
255.6327	171.0001	40.56171	157.31345	60.52462	108.90224	68.60201	121.34
255.1070	170.9013	40.06848	158.05400	60.09230	108.80280	68.54130	121.11
254.1293	170.4171	39.62618	158.06340	59.54028	109.43600	68.53261	120.80
254.5627	171.6275	39.79769	159.33832	59.58437	108.47711	69.20051	120.26
252.9670	170.1364	39.23804	157.84773	59.16110	109.04703	69.55615	120.05
253.4282	169.7587	39.64423	157.32277	59.78719	109.03798	69.99850	120.34
249.9783	165.9340	39.11167	154.75420	58.95827	109.28223	69.75563	119.89
250.5318	166.6118	38.95822	155.65416	59.06411	109.43600	70.03153	119.26
248.4563	164.3461	38.20903	153.16052	58.50855	110.46733	69.65492	118.58
249.8768	165.7597	38.53397	153.62926	58.72901	110.49444	70.39937	118.22
250.2366	166.2052	39.11167	153.52614	59.05528	110.11450	70.57454	118.65
250.7716	167.3186	38.72354	154.58540	58.51738	110.02834	70.15416	117.46
249.8861	165.3821	38.75061	155.20167	58.69374	110.61771	70.67963	118.65
251.9246	167.4349	38.65132	156.97049	59.27573	110.93507	71.59927	119.05
254.0555	170.0396	39.18388	158.29706	59.59319	111.29775	71.89703	118.86
256.3430	171.5694	39.88795	159.29439	60.16637	110.58148	71.25768	119.15
257.2655	171.6953	39.79769	158.56988	60.13993	110.57239	71.47665	118.93
255.3837	170.8238	39.02141	157.22453	59.13465	110.99855	71.25768	117.64
257.6990	173.7674	39.55397	157.98659	59.59319	110.98948	71.46789	118.13
257.9020	173.9127	39.58105	157.51616	59.77838	111.27055	71.22264	117.61
257.6713	173.4963	39.36441	156.90462	59.75193	110.80814	70.89859	117.55
258.7137	174.5517	39.65326	157.60083	59.85774	110.59962	70.52197	116.28
259.2580	174.2225	39.60813	158.04306	59.86655	110.15529	70.18914	116.31
258.2802	173.3510	39.12070	159.16266	59.74310	110.85345	70.89859	115.81
257.9849	173.3123	39.68034	158.51344	60.02528	109.49342	70.30302	116.56
258.4647	173.8642	39.41857	158.71104	60.02528	108.14243	70.12785	116.00
259.7653	174.5807	39.99627	157.01750	60.37802	108.51421	69.78630	116.04
261.9792	177.0208	40.64617	157.59146	60.82773	108.34193	70.35558	116.68
261.3611	174.3387	40.19485	158.43819	60.55437	108.13336	70.54826	115.77
259.5901	171.9858	40.33928	155.48393	60.66901	108.31469	69.86510	115.83
258.2341	169.5554	40.27609	154.48663	60.66019	107.94293	69.96146	115.65
259.5070	170.8529	40.49273	156.05789	60.73956	108.53232	71.16134	115.99
259.0735	171.5016	40.13166	155.95436	60.43091	107.64811	71.39782	115.14
260.4848	173.8352	39.59910	157.09277	60.03410	107.80260	71.16134	114.52
261.6009	174.3678	39.90599	156.54710	60.06937	108.33878	72.00214	114.92
262.5602	175.3941	39.59910	157.42210	59.81365	108.40236	71.95836	114.33
263.4273	176.0332	40.00529	157.79846	60.28100	107.83895	71.70437	114.59
263.3166	176.2462	39.95113	157.65730	60.22810	107.94800	71.27519	114.91
262.9568	176.1397	39.83379	158.06184	60.05172	108.85675	71.36279	114.74
261.1951	174.7938	38.98529	157.61971	58.85246	109.64732	70.72342	114.69
260.2173	174.6001	38.34442	156.69763	58.64083	109.42016	70.68840	112.96
261.8775	175.6942	38.57911	158.25005	58.63202	109.17482	71.07375	113.07
259.9220	173.5447	37.46886	156.26482	57.78547	109.81087	71.60802	111.19
262.0252	174.1160	37.70354	157.71374	58.19110	109.80180	72.18606	111.10
262.9476	174.1547	38.10071	158.39114	58.53501	109.93809	72.83419	112.13
263.5103	173.9998	38.27221	158.83336	58.85246	110.67419	72.94804	112.69
264.1283	174.6389	38.75964	160.65858	59.21401	110.30162	72.45758	113.02
263.9716	175.3167	39.06654	161.05374	59.44329	110.73780	72.05469	113.27
263.6210	175.0649	38.43469	160.56450	59.02002	110.91045	71.89703	112.20
265.2076	176.6916	39.14777	161.43953	59.36392	111.12859	72.26490	114.16
267.3015	178.4926	39.70742	161.67468	60.15756	110.49246	72.13352	114.59
267.4307	178.7541	39.56300	161.82524	60.10465	109.82909	72.90424	113.68
268.8697	180.8165	39.80671	162.29568	60.43091	109.97448	72.83419	114.20
267.7812	180.4969	38.76867	162.16396	59.85774	110.21072	72.58019	113.64
267.7904	180.7293	38.96725	162.78488	59.38155	109.95630	72.85169	113.51
267.3292	179.9547	38.20903	162.06044	58.87893	109.32057	72.08096	112.93
266.6097	177.6308	37.65842	161.62764	58.34100	109.02914	72.41377	113.32
265.8072	176.0429	37.69452	160.53627	58.16465	109.42986	72.69405	113.54
265.2906	175.3651	37.50496	160.45158	57.69728	108.50088	71.80946	113.23
265.7519	175.9557	37.13487	160.64920	58.05001	108.90160	72.26490	113.15
266.6282	177.3113	37.21612	160.91263	58.10292	108.07280	72.11601	113.22
266.6927	176.7884	37.40567	160.52683	58.34983	108.32782	72.17731	114.17
268.2701	178.6766	37.91115	160.56450	58.78192	108.49176	72.60647	113.76
268.3162	178.1537	37.87505	161.24191	58.87011	107.97263	72.01966	113.02
266.8956	175.5877	37.53204	159.52959	58.92301	107.97263	72.27364	113.61
268.3439	177.0402	37.89310	160.19756	59.54028	106.84327	72.01966	113.44
268.6298	176.9046	38.41663	159.61424	59.75193	106.20569	71.06500	113.88
270.8067	178.8606	38.84088	161.09139	60.49265	106.69753	71.77444	114.27
270.5594	177.8826	39.02141	160.31985	60.51909	106.65201	71.73939	113.49
269.6606	178.3773	38.57911	159.72716	60.24574	106.37879	70.47820	113.47
269.4104	178.6198	38.73255	159.97180	60.54555	106.26947	70.36434	113.65
268.6042	178.7459	38.81380	158.50958	60.57201	107.01628	69.72047	113.05
269.3548	180.2591	39.00336	158.51904	60.44856	107.08919	69.90619	112.05
269.3826	180.2203	38.74158	159.00012	59.95473	106.80680	70.77293	112.76
270.3185	180.5889	38.75061	156.90587	60.02528	106.02273	70.18920	112.57
270.1609	180.1815	38.26319	155.20793	59.71665	106.67084	70.09190	113.87
270.3091	180.3755	37.94725	156.56632	59.61082	104.81781	69.60550	113.42
268.1965	176.9126	36.99948	154.36833	58.91419	104.07844	68.90678	113.48
266.6954	174.7494	36.86409	152.97220	58.56148	103.18389	68.81834	113.80
266.6954	173.6824	36.91824	152.65144	58.27929	102.83704	69.72932	112.54
266.3062	174.2450	36.78285	152.05718	58.12937	103.87766	69.87966	112.60
257.8741	166.5818	35.69065	147.68947	56.89483	103.59466	68.82718	112.88
252.1941	164.5157	35.32958	144.86890	56.10120	104.85433	66.95218	115.78
255.6966	169.0942	36.36762	144.89717	56.30401	104.48922	66.81950	115.23
254.2603	167.0475	35.97949	145.43488	56.17174	104.44359	67.18212	116.00
259.8200	171.9073	36.88214	149.65160	57.13292	104.68090	68.64144	115.80
259.8663	171.9752	36.43081	149.01018	56.80665	104.06016	68.30536	115.79
256.1135	167.9884	35.47401	146.21788	55.88956	104.02367	68.22577	115.92
255.9746	167.8331	35.80798	144.67076	56.20702	103.79549	68.74759	116.01
254.8256	168.6965	36.19613	144.35948	55.96011	103.65854	67.84546	115.71
253.5283	168.0757	35.79896	143.06711	55.43101	103.98719	68.27882	116.39
245.8468	160.3834	34.64357	137.68059	53.86138	104.77216	68.77412	116.66
250.2574	165.9319	35.31152	140.66154	54.54038	104.33400	69.62319	116.40
245.8561	161.6638	34.90533	139.12393	54.17002	104.96386	67.98695	116.77
244.4939	158.3366	34.30056	138.35985	54.02010	104.72652	68.77412	116.31
248.1170	160.9460	34.96853	141.24646	54.67265	104.20624	69.80891	115.80
250.7670	164.7291	35.34763	141.52943	55.07829	103.67680	69.08366	115.15
253.4356	166.9020	36.61134	144.79343	55.78374	103.77287	69.34015	116.63
251.9346	164.3023	36.84602	145.27451	55.86310	102.48269	68.74759	116.65
253.3245	163.8949	36.94533	145.16130	55.86310	102.88532	69.75582	116.37
254.9275	165.1365	36.88214	145.87825	56.09238	102.82128	70.05655	116.04
260.3853	170.3164	37.57717	148.49132	56.84193	102.95848	70.94100	116.03
259.9126	169.2300	36.60232	148.09512	56.28638	102.94936	70.96753	115.78
257.3738	166.3782	35.92533	145.34996	55.91601	103.71800	71.06482	114.48
252.5647	161.3437	35.41985	142.47279	54.99892	104.39510	70.98521	113.66
252.0921	161.4795	35.82604	142.01999	55.23702	104.33104	71.04711	113.70
250.3687	160.2476	36.04268	140.98230	55.28110	104.39510	70.92331	114.64
252.9816	163.0510	36.84602	142.99165	55.45747	104.34939	70.48108	114.77
253.6396	162.4786	36.91824	143.33121	55.51920	104.95325	71.33013	115.62
249.3493	157.2017	36.42178	140.42575	55.03420	105.24606	71.33013	115.67
244.7349	154.3887	35.63648	137.71838	54.08184	105.28263	70.56952	115.67
245.5688	155.5624	36.29542	139.64276	54.84020	105.24606	70.66682	115.86
243.9287	154.4372	35.87118	139.51070	54.47865	105.35586	70.42801	115.77
247.8668	158.0068	36.31347	141.32190	55.29874	105.11798	70.67565	115.64
248.7008	158.5404	36.56621	140.15216	55.08711	105.23691	70.89678	114.95
254.4272	163.6427	37.44177	143.61426	55.87193	104.72451	71.52473	115.38
253.8712	163.1092	37.11682	143.22748	55.58975	105.13629	71.62202	115.74
255.4186	164.2926	37.08072	143.97267	55.35165	105.52973	72.32957	115.54
258.8007	167.1638	37.82992	145.34996	56.08356	106.27902	72.66564	116.41
250.4150	160.7520	37.02656	139.16170	54.62856	108.05831	71.54241	117.12
250.0350	161.8869	36.68355	138.85982	54.11711	108.39764	73.33782	117.14
244.2252	156.5421	35.99755	135.85997	53.57038	108.59941	72.30304	118.09
244.6886	158.1815	35.61843	135.46379	53.15593	109.04881	71.89620	117.68
244.7442	158.7053	35.88923	135.32230	53.32347	109.03046	71.94925	117.54
245.9765	160.1021	36.47595	136.61465	54.10829	108.54439	70.76411	117.79
245.8931	160.1506	36.46692	134.68076	54.01129	108.28762	71.18863	117.53
241.3528	156.2511	35.95241	132.64317	53.31466	108.66362	71.04711	117.06
236.6178	152.7105	35.61843	129.68915	52.89138	109.29647	68.42439	117.87
236.3584	153.6708	35.86030	129.52826	52.93417	109.95101	69.03824	118.15
232.8187	149.8975	35.26478	126.83075	52.42613	111.40355	68.28204	117.43
229.0289	147.7246	35.53963	124.73897	52.21222	110.99904	67.28561	119.24
224.3362	143.1461	35.29227	121.50195	51.30309	110.98062	66.44931	118.72
218.4086	139.5964	34.96243	119.14517	50.70592	111.53224	64.05611	120.02
229.4437	148.3126	35.65874	124.87148	51.88243	110.33714	66.15574	119.66
231.2052	148.8866	35.61293	125.39204	52.03396	110.35551	66.26250	120.57
230.9070	148.8088	35.95193	125.75173	52.31025	111.28404	66.46710	121.06
232.9294	150.0637	35.78701	126.73608	52.39047	111.70691	66.67173	121.25
233.1717	150.6668	35.87864	127.45545	52.28352	112.29530	65.23048	121.33
227.6076	145.7444	35.22812	125.17436	51.81113	113.57312	65.64862	122.43
235.2315	151.9800	36.36422	129.85005	53.39764	112.25850	66.35145	121.44
237.0862	153.7895	36.44668	132.12166	53.60263	111.92757	67.01872	121.86
239.3137	155.1806	36.58411	134.14719	53.95024	111.63337	68.23754	121.53
240.4321	156.4453	37.23461	135.25456	54.55633	111.45867	68.14860	122.31
241.2803	156.8927	37.50032	135.95497	54.77023	110.74161	69.09163	121.59
241.3734	156.3188	37.31708	135.99281	54.39589	111.17374	69.33182	121.80
239.9008	154.9374	37.00557	134.63934	54.14632	110.76006	69.10944	122.09
242.6503	157.9628	37.26210	135.77515	54.43154	110.35551	69.79447	121.88
243.2375	157.9336	37.72021	136.78789	54.58307	110.46584	70.23041	122.27
245.0829	159.1788	37.88512	138.02782	54.77915	110.49342	70.60406	122.11
248.3449	160.7547	38.06837	139.44759	55.33176	109.91422	70.87097	121.02
244.9897	157.5348	37.40870	137.24222	54.47611	110.65888	70.66634	121.45
245.5022	157.7390	37.79350	136.86362	54.72567	110.61290	70.66634	121.28
245.6327	158.7605	38.15999	137.68709	54.78806	111.33917	70.91545	121.09
247.7112	160.6575	38.66390	139.45703	55.41197	110.80598	71.74283	122.86
245.8285	158.6729	38.26077	138.70931	55.10893	110.69566	72.39231	123.29
245.5022	157.1748	38.32490	138.37802	55.23371	111.25645	72.97059	123.98
249.3888	161.1730	39.15865	139.89243	55.83980	111.17374	73.54887	124.69
251.5790	163.5855	39.48849	141.08496	55.86653	112.12980	74.32288	124.75
251.7002	162.8949	39.17697	141.19856	55.84871	111.45258	73.81577	124.50
253.4711	164.9183	39.24111	142.88338	56.05371	110.95506	74.31400	123.96
254.5335	166.3775	39.78167	143.03477	56.49044	111.46182	74.76771	124.28
254.1980	165.8813	39.24111	142.85495	56.20522	111.51707	74.25172	123.44
251.7748	163.6536	38.84714	141.68131	55.45654	112.25420	74.82112	123.74
252.0823	163.9747	38.62725	141.83276	55.27828	112.73333	74.83889	124.21
252.2221	163.8190	38.49898	143.01585	55.22480	112.29105	75.05240	123.60
255.4656	166.2413	38.81965	144.80473	55.86653	112.00541	74.61649	123.86
256.2950	166.3580	38.54479	145.21173	55.87544	111.58159	74.96344	123.37
255.7265	166.5623	38.61809	145.54300	55.89327	112.21735	75.20365	124.06
258.5133	167.2627	38.56312	147.86192	56.70436	112.39240	75.66628	124.80
258.9606	167.5935	38.86546	148.26894	56.91827	112.67805	75.68407	126.70
259.4825	167.5643	39.08535	148.96933	57.07870	112.35558	75.15027	126.48
258.5599	166.9514	39.00290	148.40144	56.96283	111.35123	75.21255	125.05
260.1630	168.1869	39.43352	149.68866	57.15000	112.01464	75.61289	125.50
260.5171	168.7998	39.87329	149.72652	57.31935	111.68291	75.06132	125.37
260.3307	168.9749	39.73586	148.69485	57.59565	112.23576	74.85671	125.58
260.2189	168.8678	39.39687	148.90309	57.36391	110.96422	74.64317	124.69
259.7343	168.4787	38.88379	148.39195	57.28369	110.58646	74.86559	123.99
261.3559	169.6461	38.92960	149.77387	57.59565	109.56430	74.70544	121.88
260.4052	169.6752	38.98457	148.42033	57.38174	110.42306	75.01684	121.56
260.0510	169.8017	39.36938	147.72942	57.43522	110.65385	75.24813	121.72
258.4760	168.8386	39.14949	144.83315	57.29261	111.06014	74.88338	121.61
256.3137	166.7666	38.42568	143.56483	56.56175	111.78035	74.74992	121.51
255.8010	166.5137	38.15083	143.52696	56.57066	112.25127	74.82112	122.84
259.5104	169.9768	38.86546	146.03516	57.06087	111.91882	75.92428	122.24
260.4891	170.9107	39.06703	146.11090	57.02522	112.70369	76.23567	122.98
262.2133	172.1948	39.11283	146.68826	57.51544	112.49135	76.58264	123.84
262.0455	171.9030	38.90212	146.09193	57.50652	111.67877	76.69830	122.41
263.3402	173.4984	39.47016	146.48003	58.13043	112.41746	76.52036	122.97
264.2951	173.9115	39.90994	147.41704	58.33543	112.35284	76.09332	123.04
264.3606	174.4963	39.92827	146.66933	58.45130	112.10352	75.87090	123.38
263.5648	175.1882	39.99240	145.44696	58.47804	113.27618	76.12448	124.18
266.5418	177.9268	40.04737	147.35457	58.44238	113.52549	77.41472	123.68
261.4118	174.0188	38.87463	141.99257	57.31935	115.28906	76.94879	123.97
261.2152	173.6874	38.96624	142.61890	57.39956	115.47372	76.96671	124.92
263.1624	174.4963	39.08535	144.11836	57.68479	115.39063	77.54016	124.30
261.7862	173.3755	38.66390	143.55844	57.71152	116.45251	77.37889	123.65
262.7786	173.7751	38.92044	144.83960	57.56891	116.85877	78.05090	121.90
264.4355	175.0908	39.32356	145.28566	57.80956	116.74797	77.98817	122.01
267.5715	177.4102	39.97407	146.87051	58.54934	115.08967	77.96129	121.53
267.7025	178.0827	39.84581	146.49089	58.56716	115.30253	78.46305	121.98
268.1239	179.1060	40.12067	147.25015	59.02172	114.30308	78.38242	121.80
268.8353	179.0378	40.36804	147.97137	58.89695	114.62701	78.26593	122.11
270.1365	179.9636	40.67955	149.35698	59.04847	114.77504	78.80352	121.98
270.3425	180.4217	40.67955	149.11021	59.08412	114.36789	78.33761	122.51
268.9570	179.7882	40.59709	147.28810	58.70977	114.72880	77.96129	123.15
269.8744	180.7530	40.78950	149.29051	58.93260	115.00639	78.66913	123.53
269.7994	180.3242	40.34971	149.10075	58.80781	114.33089	78.58849	121.95
271.6249	181.1038	40.64291	149.64168	59.21781	113.51652	79.00064	121.83
271.4471	181.1331	40.43218	149.15767	59.24456	113.80340	78.59745	121.60
271.6249	181.7569	40.73453	149.50884	59.28911	113.09082	76.91295	120.51
270.9603	182.3903	40.85363	148.14221	59.45847	113.13712	76.21406	120.28
271.4938	182.6242	40.82614	147.70563	59.42282	113.72935	76.73376	120.37
271.7278	183.1407	40.56045	147.31661	59.32477	113.18340	75.98111	120.37
274.1712	185.4699	40.65207	149.53731	59.44064	113.42397	76.88607	120.12
273.5627	184.8852	40.10234	150.00229	59.03064	114.34939	77.38785	120.47
273.3942	185.6356	40.04737	148.75909	58.98607	114.18282	77.23551	120.57
274.6673	185.8013	40.20312	150.20161	59.22673	114.57146	77.81792	121.37
275.0979	186.1619	40.28559	150.92287	59.46738	113.84040	77.07423	120.83
275.2383	184.7195	40.24894	150.22058	59.50304	114.42341	77.95232	121.20
273.1695	184.1250	39.94658	148.79706	59.16433	114.89542	77.89856	120.40
272.5798	183.3259	40.03820	149.48981	59.07520	114.34830	77.92542	119.94
275.2477	186.2496	40.51464	152.34637	59.70803	114.67285	78.54368	120.65
274.1150	185.1093	39.68089	152.51720	59.03064	114.98815	78.28385	120.81
269.5373	181.5034	38.90212	149.49928	57.99674	115.86912	76.85919	121.21
269.1630	181.0454	38.84714	148.76857	58.06804	115.36834	76.85023	120.91
268.3485	180.0708	38.23328	148.22763	57.80065	115.84127	77.02943	121.20
269.6965	180.2950	38.46234	148.63573	58.22847	115.68364	77.84481	121.43
262.9190	174.0382	37.17965	143.90008	56.87371	116.59242	77.75520	122.67
265.2967	175.9484	37.70188	145.71271	57.44413	116.24928	78.07777	122.46
266.8507	178.4336	37.77519	146.18720	57.64914	116.96334	78.58849	122.39
269.3220	180.2267	37.59194	147.09830	58.11261	116.57386	79.05441	121.51
267.5809	178.3848	36.91394	145.04843	57.72934	116.83350	78.83041	120.65
265.8115	175.3734	36.75819	144.04245	57.49761	116.59242	77.66560	120.64
268.2080	177.2056	37.22545	145.97842	57.88086	116.40698	78.31971	120.36
267.3842	176.4162	37.04222	144.75420	57.64914	117.07463	78.59745	120.24
264.1172	173.7166	36.56579	141.77428	57.12326	118.39144	78.70497	121.17
264.7163	173.6289	36.60243	143.10292	57.73826	118.49341	78.96482	121.30
262.2543	172.9760	36.73071	141.96407	57.17674	119.34652	78.13153	120.83
260.4944	171.5531	36.96891	140.77780	56.81131	119.70818	77.19968	120.87
261.2059	172.2743	37.17049	140.38870	57.02522	120.73753	77.51327	121.69
257.6861	169.5260	37.29875	138.42424	56.50827	122.24909	77.83584	123.33
257.0308	165.7934	37.63775	138.90825	56.83805	123.06684	78.14047	125.11
262.6101	170.4616	37.72021	142.50503	57.48870	121.66366	77.88960	125.15
264.8848	171.7285	37.41786	142.53349	57.47087	120.97605	79.52032	125.47
266.6073	173.0929	37.43619	142.16341	57.70260	121.36631	79.63682	125.88
269.2753	176.4357	37.72937	143.16934	58.43347	122.41634	79.87875	126.59
270.5110	178.4920	38.12333	144.01399	58.59390	121.26410	79.63682	125.33
270.4454	178.7356	38.55396	143.58691	58.88803	121.33846	79.77121	125.18
269.9680	177.7026	38.14167	143.74824	58.45130	121.43134	80.03106	125.83
271.0820	178.7552	38.07753	145.26666	58.50478	121.84952	80.32674	126.60
270.7824	177.9950	37.65608	143.99501	58.07695	122.15615	80.46114	126.56
270.8854	179.0670	37.80471	144.98831	58.11884	122.36988	81.32340	126.48
273.7218	181.6691	38.71866	146.67398	58.89279	122.98320	81.17893	127.12
274.3397	182.3513	39.04178	147.19780	59.25699	123.15974	81.68455	127.89
276.9608	184.0470	39.61416	147.89302	59.77599	123.48499	82.04571	131.11
276.5582	183.7742	39.48492	146.61685	59.52104	122.12826	81.00738	131.98
276.2196	183.7800	39.42953	144.83591	59.64852	123.03890	80.50178	133.94
273.5104	180.6252	39.02332	143.95024	59.29342	123.41985	79.47247	134.20
273.2376	181.4652	39.39260	143.61688	59.36626	122.63007	77.97368	132.97
274.2065	182.1587	39.66956	146.31210	59.51194	123.49426	78.87656	132.84
275.6175	182.3931	39.61416	148.09300	59.84885	123.41061	78.83141	133.20
278.1197	184.8544	40.08499	148.66443	60.13110	123.12200	79.10228	130.62
278.8441	185.5870	39.98344	147.75969	60.30410	124.07166	80.33926	133.41
281.0733	186.9837	39.90959	148.81680	60.71383	124.95615	81.40467	133.63
280.7536	186.6028	39.63263	149.21681	60.24947	123.29890	81.03446	132.14
279.2108	185.2940	39.39260	147.79782	59.90347	123.46652	81.29631	131.29
279.5589	186.2219	39.27258	147.99780	59.64852	123.41987	81.69359	131.75
280.8947	188.0776	39.60494	148.25491	59.85794	122.74030	82.12698	133.83
281.5532	187.9409	39.53108	147.53113	59.83972	121.10162	81.20603	132.70
282.8137	189.0250	39.55877	148.67398	59.91257	121.24130	81.06156	133.53
282.9077	189.6306	39.70648	147.89302	59.96720	121.93961	81.06156	133.53
281.9952	188.6539	39.65110	147.84543	59.72136	121.57645	80.87196	132.40
280.0763	187.7260	39.53108	146.78828	59.63941	122.88921	80.54691	134.58
281.1016	187.9409	39.77111	147.34064	59.82152	122.89853	80.56498	136.48
279.5401	186.5637	39.56800	146.49304	59.64852	122.60991	79.38217	134.47
280.2267	188.0483	39.57724	146.35969	59.71226	122.84267	79.23772	134.45
282.2305	189.2790	39.62339	147.33113	60.08557	122.17230	80.04131	133.69
283.5568	190.6073	39.68803	149.76918	60.13110	122.70300	80.26703	134.37
282.2022	188.8004	39.33721	147.95967	59.52104	122.11643	79.89682	133.42
284.0930	190.7441	39.42030	149.71204	59.63941	122.40507	80.16769	133.64
283.5756	190.0896	39.34644	148.71205	59.76689	122.44235	80.40245	134.53
282.8795	189.2692	39.04178	150.32155	59.07489	122.74030	80.98030	134.98
279.7847	186.6516	38.56173	149.10249	58.68336	123.72719	80.70943	133.21
277.3484	185.7237	37.80471	146.94064	58.51946	126.18443	80.62817	136.41
275.2600	182.9889	37.43543	145.31210	58.00047	127.35052	80.98933	135.89
266.9822	176.5230	36.05064	140.95027	56.55274	129.55223	79.53568	137.79
270.7260	178.9941	36.56764	142.24550	56.93515	130.58777	80.37535	138.91
270.8859	179.9611	36.73380	142.20743	57.15368	130.63435	81.21504	141.02
276.2007	183.8777	37.18617	145.27402	57.70910	130.91429	82.57842	141.73
274.3193	182.1489	36.80766	143.44545	57.30847	130.65308	82.56941	141.26
270.9800	180.0587	36.36453	141.58836	56.85320	133.37714	82.25337	142.63
275.1941	184.0047	36.82613	143.11212	57.39041	132.92001	82.34366	141.78
267.0573	178.5058	35.76446	139.11221	55.81521	135.91463	81.00738	142.75
267.7628	178.3006	36.00448	138.55981	56.00642	137.42586	81.90124	143.70
271.7138	181.1624	36.50301	141.55028	56.68020	136.32507	82.61453	142.78
274.9872	184.0438	36.65071	142.97879	57.02620	134.37529	83.23753	141.11
272.8802	182.6177	36.72457	142.04547	56.83499	135.76532	82.61453	142.21
275.1002	184.2391	37.07538	143.21692	57.23562	134.86044	82.92151	141.76
275.0155	183.6433	36.59533	142.88354	57.12637	133.96481	83.38198	141.40
267.9510	177.8318	36.05064	138.50269	56.41616	136.16655	82.23532	144.17
270.9141	180.5178	36.24451	140.02650	56.88052	135.61610	82.84026	144.19
269.8511	180.1369	36.30913	137.95032	56.83499	137.70575	82.52425	145.57
271.7513	180.7815	36.41069	139.55980	56.83499	137.88307	82.71384	145.16
275.2224	183.5456	36.81690	142.00743	57.32668	137.36066	83.37296	144.12
275.1002	183.1061	37.10308	141.75026	57.55431	137.39796	83.48130	143.75
273.4916	181.3285	36.87228	139.67410	57.44505	137.57548	84.29390	145.75
276.5958	183.9461	37.49083	140.79790	58.25542	137.78107	84.95301	146.66
280.1516	187.3158	37.91549	143.41689	58.56500	135.28587	84.42031	143.14
280.3680	187.1302	38.08166	142.75981	58.75621	136.24841	84.58282	141.92
280.5091	186.7395	38.20168	144.67403	58.92921	133.82794	84.03207	141.39
280.4432	186.2023	38.22937	146.52162	59.02936	131.48221	83.13821	140.18
282.4374	187.9506	38.49710	149.52159	59.35715	131.24861	83.21946	141.03
283.4156	188.7320	38.77406	149.55968	59.70315	130.38875	83.62577	141.32
283.2276	188.0581	38.99562	149.81683	60.04005	127.60384	82.65065	140.15
282.3528	187.2181	38.69097	150.37872	59.50283	129.22994	83.49937	141.32
283.0676	188.1167	38.69097	149.98822	59.70315	129.93088	84.41127	141.60
283.2370	188.0385	38.53403	149.06442	59.63031	130.48219	84.11333	140.71
283.2181	188.3511	38.37708	148.34064	59.83062	130.87474	84.51964	141.28
281.8800	186.3586	38.41401	148.02634	59.69405	132.60361	84.48351	142.95
281.8138	186.4408	38.45094	147.91209	59.53925	132.57565	84.60992	143.75
279.6025	183.9647	38.04474	145.67952	59.31163	134.17368	84.50442	144.51
281.2563	186.0298	38.01704	147.27557	59.13862	132.21121	84.56808	141.83
280.6704	185.3447	38.00780	145.63173	59.35715	133.06161	85.25918	141.79
279.1583	183.0447	37.51852	144.46574	59.15684	133.38875	84.74088	141.06
280.4530	184.7868	37.73085	144.63779	59.37536	133.71582	85.05914	138.87
277.1171	183.2796	37.46313	141.79932	58.79262	134.11835	84.15889	139.63
272.2219	180.1282	37.17694	140.72890	57.59073	134.44604	83.83154	141.26
274.4521	182.1052	37.65700	141.19724	57.97315	135.67242	84.64992	141.90
278.1661	184.7868	37.82317	142.53525	58.42842	136.67418	85.10458	141.90
276.9659	184.2290	37.50928	142.28673	58.35558	135.54132	84.86817	140.69
272.6661	181.4690	37.24156	139.97389	57.80926	135.90646	84.43169	141.92
275.2555	183.2405	37.52775	140.61424	58.22810	135.13881	84.70450	142.05
277.1171	184.6596	37.91549	141.17813	58.63784	133.12599	84.86817	140.81
279.9900	187.0378	38.52480	143.56737	59.68495	131.47830	84.80451	140.03
279.6781	187.0182	38.35863	143.04176	59.43910	132.43323	84.82272	140.59
282.4470	189.3965	38.70020	144.68561	60.13110	130.83232	84.86817	139.61
281.9934	188.9267	38.81099	144.83855	60.22216	130.99149	84.93182	140.41
282.8251	189.4259	38.95869	146.54925	60.36784	130.67319	85.40467	140.61
281.5870	187.6054	38.75560	145.85155	60.34051	130.67319	86.08667	140.46
283.4960	189.2692	39.10640	147.21822	60.66831	129.69020	86.71412	139.79
282.5699	187.7620	39.13410	147.38068	60.52262	130.44853	86.43223	140.20
283.3921	188.1241	39.14333	147.56226	60.85041	130.57958	86.55044	140.53
283.8551	189.9543	39.14333	147.35202	60.95967	130.31737	86.44132	141.53
285.0175	191.4713	39.42030	148.13570	61.02342	129.68089	85.55924	141.86
286.6240	193.3602	39.65110	149.41637	61.29657	128.50125	85.09550	140.64
286.5389	191.8628	39.44799	149.90376	61.27836	128.58551	85.38650	140.25
287.4178	192.7925	39.62339	149.40681	61.53331	130.46718	85.85934	141.02
286.6524	192.8806	39.30951	148.56578	61.38762	132.22723	85.71385	142.43
289.3079	194.6324	39.90036	151.09843	61.93393	131.82025	85.65022	142.56
290.4702	195.8362	40.29733	151.91077	62.25263	130.08531	84.98640	142.15
290.1489	195.9439	40.52812	152.10191	62.13425	128.62224	83.60419	139.85
290.2150	195.5035	40.39888	151.22267	62.10693	129.40068	83.84972	140.45
291.2357	196.1592	40.69430	151.62407	62.29814	127.05609	83.04951	138.27
291.9539	196.9422	40.32502	152.03503	62.26172	126.52153	82.89492	137.39
291.3963	196.6779	40.03883	151.74832	62.17978	126.60596	83.08588	137.06
292.0107	197.2455	39.78033	151.79611	62.20710	127.18741	82.50391	137.43
292.1051	197.2945	39.47568	151.14619	61.98857	128.01270	83.17681	137.98
292.5304	197.1379	39.50338	151.09843	61.81557	129.33505	83.84061	138.56
294.6472	198.5864	39.81728	151.88214	62.20710	129.19440	84.28619	138.21
294.8645	198.7430	39.75264	151.49982	62.27994	129.42879	84.72268	138.62
294.7794	199.0365	39.83573	152.06366	62.19799	130.50725	84.83180	138.69
293.6833	197.8426	39.66032	151.49026	61.80646	131.85779	84.81362	138.76
293.2108	197.4021	39.57724	150.74481	61.72452	131.03250	83.64967	138.00
293.8628	197.5294	39.57724	151.21310	61.89752	131.20126	83.37688	137.74
296.1404	199.8684	39.97421	154.42432	62.38920	131.58577	83.70422	137.08
296.8112	200.2502	39.85419	154.52943	62.35278	132.35483	84.71359	137.74
298.1343	201.6496	39.90036	155.61897	62.51667	131.97029	84.98640	137.01
297.0287	200.7297	39.27258	154.60591	62.07963	131.68890	84.74994	137.86
294.5055	198.6744	39.26335	153.09584	61.76094	129.93312	83.49509	137.79
292.5304	197.1184	39.06025	152.60843	61.53331	132.65755	84.00429	139.11
294.3354	198.1166	39.35567	153.65973	62.09784	131.33295	84.33165	138.92
294.8645	198.5080	39.53108	153.81264	61.97946	130.69412	84.40441	139.00
297.5578	200.6318	39.76188	155.60941	62.54399	129.97069	84.54990	137.62
296.6223	199.7217	39.60494	155.31310	62.21620	130.25258	84.72268	137.58
296.2915	199.5553	39.74340	155.40869	62.24352	130.26193	84.21345	137.97
297.1326	200.6122	40.32502	155.36090	62.57130	131.28592	83.39505	138.92
299.6935	202.1096	41.02664	156.69891	62.99014	129.12523	82.30386	138.43
299.8732	202.7752	41.00818	156.09682	63.42720	130.61893	82.38570	139.05
301.9333	204.8108	41.35612	157.19705	64.10490	129.44459	82.91465	139.04
301.9995	204.9283	41.73328	157.98361	63.73657	129.26614	82.20755	139.01
302.0183	205.0849	41.95958	158.29053	63.65370	128.20456	83.27279	139.02
303.2563	206.3670	41.97845	158.97157	63.65370	128.40968	83.96151	139.38
304.5858	207.1989	42.06331	159.20177	63.69975	128.57909	84.48495	139.52
305.0512	207.7461	42.11987	159.51833	63.80104	128.39088	84.00742	139.95
305.0606	207.8541	42.02558	159.88286	63.73657	128.75781	84.23702	141.27
306.6846	209.6881	42.32732	159.88286	64.01282	129.06839	84.68698	142.38
306.6086	209.5116	42.49704	159.09627	64.12331	129.20949	84.91658	142.33
304.9182	208.1385	42.21417	158.69344	63.64452	128.73906	84.98084	142.63
305.6590	208.5308	42.30846	158.91405	63.93916	127.47813	85.47674	142.90
308.5175	212.0127	43.16651	159.01955	64.58371	128.91775	84.53088	143.95
306.1813	210.0706	42.36503	158.39607	63.78263	130.90323	85.13696	145.86
307.3493	211.4242	42.26131	158.60710	64.03123	130.15984	85.21042	147.39
306.4852	211.3948	42.23303	158.07954	63.85627	129.52002	84.34721	147.97
308.1186	212.9837	42.47819	158.56873	64.04044	128.66374	84.54925	146.86
310.2079	214.7884	42.76105	158.76056	64.18776	129.11540	84.59516	146.03
309.3152	214.2391	42.98736	158.16583	63.94836	130.26337	85.32981	146.91
311.4424	216.7108	43.65682	159.19222	64.27984	129.86818	86.23895	145.82
310.9676	215.8575	43.41167	159.77734	64.34431	130.53624	85.90836	145.69
311.6704	215.9458	43.07222	160.54469	64.34431	131.40189	86.67054	146.54
314.2629	218.0152	43.34566	162.61662	64.61133	130.98782	87.31337	146.31
315.2411	219.0942	43.59082	162.17539	64.80468	129.86818	87.41439	146.58
314.6238	218.9961	42.48761	160.83247	64.28906	131.23250	88.30515	146.74
314.6618	219.5747	42.83649	160.72696	64.41795	131.69357	87.80007	146.79
315.0227	220.2809	42.39332	160.62144	64.26143	132.61568	88.32352	147.12
312.2211	218.4272	42.05387	158.64546	63.98519	133.68840	88.12148	147.98
307.2164	213.9155	40.60179	156.84212	62.65927	135.76785	87.69904	148.99
310.4358	217.2012	40.94123	158.14665	63.24858	134.70464	88.07556	147.66
310.1794	217.5543	41.13925	157.24501	63.25777	136.02194	87.80007	148.46
311.1861	218.3291	40.52636	157.24501	63.20253	136.04065	87.91029	148.47
305.5355	214.8669	39.70602	153.98366	62.13442	137.28271	86.84504	149.33
307.8051	218.1134	40.14919	155.70068	62.28175	137.17151	87.11133	148.36
312.4966	223.1057	41.18639	158.05075	63.32223	135.32422	88.00211	146.43
316.1053	223.8413	41.42212	160.48717	63.92995	133.84447	88.02048	146.61
317.1689	225.7735	41.45984	160.12264	64.10490	134.44772	88.35107	147.40
315.4785	224.8025	40.88466	158.15625	63.49717	136.12532	88.31432	147.79
317.8336	227.5193	41.11096	159.04833	63.62608	136.50233	89.20509	148.17
318.3845	227.5586	41.64842	160.15144	64.05885	135.81433	89.93057	147.66
320.4357	229.7752	42.21417	161.25455	64.27984	135.12634	90.64685	147.54
320.0938	229.4810	41.65785	161.67660	63.82865	135.64465	91.26211	148.38
320.6067	230.1381	41.67671	161.05309	63.71816	136.23846	92.08860	149.00
319.7804	230.2264	41.40327	160.70778	63.31303	137.17151	92.02432	150.91
321.3094	232.4333	41.70499	161.53271	63.52480	137.16211	90.86726	151.79
319.9894	230.2754	41.05438	161.92600	63.14728	138.23653	91.84985	152.41
316.6941	225.8520	40.81866	160.28574	62.85263	139.52776	92.02432	154.70
306.1908	217.1423	39.29114	155.46086	60.33890	141.61067	90.79380	156.09
296.9125	211.2379	38.97998	149.93573	59.34445	142.36472	88.36025	153.30
295.8204	212.3265	39.29114	148.19954	59.41811	141.61067	87.43276	153.97
282.5347	201.6945	38.34823	142.98138	57.65941	143.14697	82.85036	154.00
281.3475	201.8515	38.20679	140.36270	57.30952	146.37973	80.26071	148.38
293.5318	212.2677	39.03656	144.87105	58.04614	145.30278	84.12681	149.20
285.1272	205.4608	38.77254	141.91666	57.57655	147.55864	84.13599	153.89
297.1119	214.0332	39.46086	145.95499	59.29841	145.99182	87.35012	154.16
287.2354	207.5303	38.63110	141.31235	57.72387	149.62579	85.44918	157.49
282.4872	204.0289	37.83905	138.51140	56.85833	157.41295	83.99825	157.55
260.4264	189.8561	35.25548	125.04398	52.44778	161.67929	77.77208	157.81
273.9022	200.1939	37.04701	128.94797	54.38143	153.39189	80.77496	154.48
260.5499	191.4744	35.32148	120.74667	51.60987	147.74748	76.07319	153.93
235.6212	173.9179	31.78556	107.40391	45.93785	148.66306	68.66239	147.79
255.7636	188.6497	34.07684	114.59807	48.71862	145.30278	74.52124	143.28
227.7770	166.0518	29.82430	99.39441	43.69114	154.71339	61.94951	141.64
240.0752	178.6454	31.87985	103.95073	45.81815	144.39664	64.86055	143.56
227.9194	173.2117	29.12655	95.89328	43.19392	136.25087	58.47829	140.70
228.4037	174.2514	29.35285	99.63422	43.86609	139.96027	58.50583	138.04
218.5609	167.4249	29.56972	97.26494	43.32283	150.48473	55.94373	140.11
212.9727	167.5458	28.86254	95.82613	42.81639	156.68614	53.11532	146.30
232.2687	180.5201	31.03123	104.59338	46.44428	153.76950	57.36712	153.40
235.7458	179.1834	32.12501	105.89335	47.95437	153.42026	60.51674	151.30
249.5109	188.6192	33.34137	112.47977	50.09979	154.17534	65.00426	153.24
242.0791	182.1321	31.44611	108.38733	48.67257	158.29069	65.08772	152.25
249.9408	188.7568	31.96471	110.77540	49.65782	156.98816	66.38577	152.92
246.2153	187.1449	32.18159	110.21690	49.22505	155.71390	64.50359	148.05
235.1344	179.1932	30.80493	102.70606	47.04279	157.89554	60.24786	149.45
240.5603	182.8300	31.84214	103.67861	47.96357	158.89749	60.50747	151.90
237.0832	180.2351	31.23867	100.74168	46.86785	159.27563	59.56175	152.65
253.0071	193.1209	32.94534	108.45474	49.35396	158.85968	64.03073	156.88
253.2651	193.0423	33.11506	108.73400	49.63019	157.19608	64.65196	156.04
261.7668	197.1410	33.45452	113.69308	50.03534	156.05231	69.27855	154.65
265.7502	197.4261	33.33193	119.13361	51.16790	156.33594	73.13559	158.69
263.3239	199.5590	33.37909	115.90782	50.67989	154.90855	70.15935	161.41
271.0900	208.2380	34.14284	118.25736	51.58225	154.87071	72.01372	162.68
265.3299	205.8495	33.26593	113.43309	49.97088	158.97317	69.28781	161.85
266.6099	209.6042	33.44509	112.57607	49.99851	160.77864	68.50899	161.71
273.8124	211.6094	34.18999	117.53516	51.32443	158.62338	70.54877	158.57
268.9884	209.1030	33.75625	116.14854	50.56018	159.89952	67.98978	159.70
260.8211	201.3872	32.82277	113.37530	49.57494	161.91290	66.74735	158.61
266.6099	207.3632	33.71853	114.75230	50.41285	160.25868	67.81360	161.73
266.5908	206.9209	33.59596	115.87891	50.25632	161.10942	67.19239	163.34
270.3067	210.1841	33.54881	117.87219	50.83641	161.48755	67.47055	162.64
274.2041	211.8747	34.22771	122.54240	51.50859	158.48161	69.60305	161.56
272.9432	207.8842	34.29371	124.32381	51.89532	160.30598	70.23354	160.84
280.0884	215.2560	35.29319	130.43840	53.19362	159.47415	71.30906	161.73
277.4806	215.1675	34.54829	125.47932	52.08868	157.61200	70.51170	158.80
270.1347	209.1030	33.30365	120.50099	50.95612	158.96167	68.11957	159.78
270.8799	211.5406	33.66196	121.02097	50.93770	158.21394	67.91560	160.34
273.3826	213.9388	33.85054	121.95500	51.02978	157.20120	68.24010	161.02
271.5294	215.2560	33.74682	121.05948	50.69830	154.66463	67.10895	158.95
274.8059	218.0277	34.02026	122.71571	51.46254	157.24852	67.99905	161.39
279.3529	221.0157	34.73688	127.45334	52.33729	155.20412	69.62159	160.42
279.4102	222.9914	34.51057	126.81778	52.29125	153.99263	68.63880	159.42
273.8412	218.3226	34.37857	122.26314	51.62829	155.57329	65.48640	160.04
268.9980	215.5901	34.31257	118.17069	51.23235	156.66170	63.93802	161.58
272.2172	218.0376	34.44458	118.55588	50.74434	158.19502	64.23472	163.01
273.4686	219.4530	33.97312	120.44321	50.79037	157.78801	63.93802	163.93
281.7984	223.5418	35.30262	127.76145	52.84372	154.32387	67.66526	162.69
278.9039	222.9816	35.01975	125.23858	52.11631	154.90126	66.90498	164.26
283.6420	227.4341	35.48178	129.03255	53.20283	155.36505	67.55399	164.65
281.6837	224.9572	35.07633	129.26366	52.58590	155.75308	67.46128	162.25
282.2186	225.7337	34.35028	129.88954	52.43858	156.69012	68.37919	163.21
285.6957	225.1243	35.10461	133.63533	53.93945	154.58891	70.87328	160.89
289.9466	226.3530	35.21776	137.78554	54.59321	154.30501	72.23623	161.18
289.4117	226.0581	34.97261	134.52124	55.10885	153.73711	72.53293	161.72
290.7012	229.3704	35.57607	133.75087	54.91548	154.83499	71.78191	162.91
291.8762	230.0585	36.39640	135.03157	56.14012	153.79259	73.44156	163.66
294.2930	231.6016	37.26389	136.14859	56.66497	153.23337	74.09986	162.60
298.2095	232.6435	38.13136	139.43216	58.01852	151.19585	76.32507	159.60
297.4262	231.0119	37.59390	139.22998	57.76991	149.00665	75.67607	161.28
305.0491	235.5922	38.58396	144.61270	58.76435	147.94525	78.42977	158.01
308.7363	237.4204	38.81968	147.41484	59.52861	148.51384	80.49737	159.72
306.4342	239.1405	38.55567	144.68976	58.75515	150.20071	79.19933	161.26
304.7243	242.0106	38.83855	140.76103	58.62624	152.42781	77.17807	163.57
287.1573	230.0192	36.81128	130.02435	55.48637	155.30890	72.30113	162.39
290.5962	231.8474	37.59390	133.14426	56.44398	153.81148	74.88795	162.62
293.3091	234.6683	37.25248	136.22252	56.67558	153.89673	75.74942	162.33
298.9547	238.6982	37.48958	139.49786	57.37597	151.53702	77.24277	162.25
297.7128	239.4550	37.84996	136.97615	57.59075	152.16251	76.19743	162.56
297.8274	240.1037	37.86893	136.92784	57.28258	153.77359	75.38541	162.24
296.1254	240.0644	37.85945	136.22252	57.00243	153.89673	74.43343	164.03
298.0250	242.9435	38.32416	137.58484	57.68414	153.91573	74.29344	165.09
299.3971	245.0111	38.69402	138.16454	58.00165	152.86381	74.06941	166.48
291.7598	239.9601	38.18189	133.68146	56.51682	154.50333	71.95076	165.90
294.8877	242.2444	38.34313	135.70076	57.31994	154.94871	72.83742	165.80
287.8836	236.5238	37.87842	132.04858	56.48880	156.60721	71.39077	166.54
292.1148	239.1034	38.04912	136.36745	56.94640	156.11436	72.72543	166.63
295.8567	243.7903	37.92583	138.33843	56.84367	155.35623	73.55609	167.37
297.9291	246.6357	38.35261	137.02444	57.05845	155.05453	75.20809	166.62
299.5698	248.3096	39.22512	137.58484	57.68414	155.21578	74.97476	166.98
304.1943	254.4142	40.91324	138.57999	58.62733	154.58015	74.98408	167.98
301.0569	252.6615	40.23040	136.12589	57.76818	156.75293	73.55609	169.04
303.3596	255.9895	41.27363	137.14040	58.25379	156.12665	73.48142	170.09
301.6326	258.1459	41.27363	134.36745	57.59075	158.61258	73.07076	169.63
304.7124	259.9083	41.00808	136.53168	58.20710	157.81554	73.27609	169.19
302.0739	254.5619	40.73305	134.80223	57.83356	158.33740	72.37075	169.40
305.9886	256.3637	40.78995	137.03412	58.68336	158.56511	72.92142	170.19
308.7997	256.8856	40.91324	142.05826	59.34640	157.82504	73.67743	170.34
307.7827	255.1330	40.33472	141.21770	58.96352	158.57459	72.87476	168.73
308.6750	255.4283	40.56235	141.63315	59.30904	158.24254	73.78941	170.12
311.1696	262.6750	41.08395	141.02449	59.59854	158.63153	72.91209	170.94
311.8316	259.9379	41.46330	143.02447	59.71994	158.72641	73.09875	173.00
313.6066	260.8535	41.28311	143.10175	59.87870	159.20081	74.21875	175.63
309.8647	254.0400	40.95118	143.24666	59.40243	161.06049	73.83608	177.18
307.8690	251.6277	40.91324	141.14040	59.07558	161.05101	73.27609	178.70
310.1142	256.1176	41.54865	142.60901	59.85068	160.45322	74.12543	182.23
308.1473	252.8585	41.20724	141.18869	59.46780	161.56334	75.45076	183.75
311.9371	255.7729	41.87111	144.29984	60.09348	161.28818	77.14010	185.13
310.8241	257.1120	41.34001	143.72977	59.20632	162.35088	76.74810	183.76
313.2803	261.7003	41.05550	142.37709	57.94561	162.24654	76.58943	185.43
315.4583	265.2351	41.34001	144.69597	59.07558	161.42964	75.59075	185.64
316.6768	266.2197	41.89007	145.69113	59.40243	162.96834	76.54277	189.59
318.6437	266.8794	42.34530	148.58964	59.59854	161.54362	76.25342	191.35
320.7737	270.4141	42.47808	148.53171	59.66391	162.44598	76.26275	193.89
321.0040	267.2929	41.60556	150.88919	59.42111	161.36308	77.29876	190.81
321.9634	266.1508	41.70988	152.45442	59.61721	160.64125	77.48542	190.15
319.3057	261.1096	41.59608	151.57521	59.83200	158.73200	76.36543	179.94
323.7575	267.6769	42.15562	152.19354	61.15807	157.28816	77.10275	179.10
323.1723	268.2874	42.03233	151.87473	60.88725	155.60690	76.22543	183.33
323.1819	267.9723	41.95646	151.77811	60.51372	154.99899	76.23476	182.54
324.2086	271.0837	42.48756	152.56070	60.97130	155.38843	76.83209	186.50
324.9089	273.6929	42.44014	151.10178	60.93395	156.49980	76.46808	188.18
323.5561	271.8517	41.91853	151.11145	60.66313	155.52144	75.09608	182.24
324.5635	275.6227	41.78575	150.49307	60.46702	156.92731	75.77743	183.50
325.7149	277.5329	41.99440	149.38197	60.15885	157.86763	75.88942	182.03
329.0154	279.2658	42.45910	150.94717	60.95262	157.61118	76.48676	181.00
330.1667	281.4615	42.88588	151.11145	60.98998	156.40483	76.67342	181.22
333.4768	287.4677	42.99968	150.16455	61.34484	155.80637	75.95475	183.36
334.2060	286.5716	42.63930	150.53172	60.71917	153.15628	77.03741	181.24
336.3647	288.0289	43.19884	151.80710	61.14874	153.04230	77.51343	184.39
335.1463	290.3427	42.24098	150.17424	60.68181	154.05862	76.76676	184.83
338.3029	295.3052	42.96175	151.89404	60.74718	155.82071	76.85076	185.05
343.1961	298.1014	42.84794	153.10178	61.55964	157.30421	78.25075	182.62
331.3852	282.9877	42.03233	148.58002	60.16819	157.75117	77.28011	181.14
328.6795	279.2166	42.05130	147.63318	60.25223	154.75568	76.92544	181.64
319.6991	265.7963	41.32105	144.79257	59.51449	155.70660	75.96409	181.29
326.0122	273.6043	41.93750	146.98583	60.62578	155.28824	76.65477	183.05
320.3515	268.1495	41.26414	145.07277	59.91605	156.07750	75.62810	182.46
320.5146	266.2887	41.66246	144.10657	60.51372	156.41032	75.20809	182.45
324.7362	270.9262	42.33582	147.90370	60.84057	156.40082	77.22409	183.89
326.3769	274.7661	42.78155	148.18390	61.23279	156.02049	78.12009	183.45
325.0816	270.3846	42.72465	149.58485	61.23279	155.55452	78.54009	183.97
322.2225	266.1606	42.55394	148.49307	61.31684	156.02997	77.06544	182.96
318.5128	262.7637	42.22201	148.10657	60.82188	155.54497	75.40409	183.20
314.9680	263.3938	41.83318	142.91818	59.28102	156.33424	73.30408	179.52
318.1757	268.2874	41.52020	144.01962	59.26235	156.21063	74.16275	178.65
310.7968	260.0954	40.87530	139.72896	58.76741	156.41988	72.03030	174.79
311.6252	261.3065	40.68563	139.72896	58.71138	157.01892	72.34955	175.44
316.6633	267.3815	40.72356	141.99843	58.90749	157.01892	73.81438	174.94
321.9229	272.9348	41.17878	145.49965	59.79465	156.57199	75.28861	176.70
320.1697	271.7040	41.15034	144.84012	59.72928	156.75262	74.72522	178.19
322.5972	273.5649	41.81421	145.27658	59.43979	155.25017	74.96935	177.12
324.6683	277.9070	42.20304	147.59456	59.78531	155.50623	76.41541	178.70
321.5857	270.0892	41.71937	148.24440	59.66391	154.92557	77.63609	178.54
327.2884	275.8493	42.27891	152.33722	60.56975	151.89848	78.06805	179.41
322.6357	270.9262	42.35478	151.90077	59.92538	152.71709	77.57976	177.30
328.2517	275.6129	42.81949	155.21771	60.43901	151.60335	77.66426	177.22
331.1609	277.0800	43.17039	156.98288	60.85924	152.42200	78.88497	177.85
334.1181	281.3138	43.46439	157.79758	61.33550	152.39345	78.54693	181.08
339.4933	289.9981	43.84375	158.85474	61.69036	152.87892	79.01643	180.56
337.2777	289.9883	43.66356	157.79758	60.99932	153.97365	77.74879	177.72
335.1585	287.5661	43.36956	156.23610	60.89660	154.32584	76.83796	178.27
334.7443	285.6363	43.05659	157.84608	60.17753	154.05936	77.15721	178.92
334.5420	284.0708	43.20833	157.45811	60.45768	153.63097	76.67832	178.30
329.4558	279.4332	43.08504	155.57660	60.23357	153.05026	75.43883	178.39
330.7755	280.0338	43.55923	155.91602	60.53238	151.59386	76.00224	179.25
330.1494	279.8172	43.68252	154.57761	60.24291	151.07030	75.70176	180.60
331.9604	279.8073	43.67303	157.24475	60.28959	149.49960	75.60786	178.83
333.0874	280.3587	43.92910	158.15642	60.68181	150.41345	76.06798	178.64
326.9320	276.1544	43.36007	154.74248	59.58920	151.81277	75.10082	178.55
325.8050	278.3108	43.54974	153.41377	59.12227	152.83134	73.99281	179.02
314.6693	267.4603	42.45910	148.69051	57.35729	152.97409	72.18053	176.13
317.8675	272.1372	42.88588	150.46538	57.62811	151.48910	73.27916	175.40
314.5537	265.2351	42.40220	148.47714	57.32927	149.99461	72.78149	176.20
318.0794	265.8258	42.94278	151.12488	58.07636	151.11812	74.61253	177.91
323.6953	270.4240	43.13246	155.41171	59.59854	150.24138	76.04919	178.92
330.9297	282.4954	44.48864	155.58630	60.25223	153.50052	76.20884	178.82
337.3837	289.8603	45.24736	159.94098	61.69971	153.76730	76.45297	182.93
337.3067	290.0769	45.45600	158.68986	61.83045	151.90907	76.02103	183.19
341.5451	284.1495	45.76896	164.44118	63.63279	148.71677	78.21827	175.08
341.0442	279.0590	45.24736	167.49623	64.20243	147.85904	79.09155	175.66
343.5777	285.3015	45.54135	167.42837	64.74407	148.39267	79.59860	174.90
340.2447	283.9624	45.19993	164.85820	63.80088	150.91798	78.64082	175.96
344.9552	286.4535	45.83535	168.27217	64.78142	150.71786	80.69722	177.16
349.2611	288.6886	46.40438	172.27769	65.45380	150.35577	81.35452	177.15
347.3827	287.7729	46.35696	173.08270	65.38843	151.33731	81.42025	176.50
343.2020	285.6461	46.19573	170.65805	65.04290	151.77568	79.95541	175.49
344.6469	287.8811	46.27161	171.96736	65.50050	152.55705	80.11504	175.16
342.2868	285.9119	46.52767	172.15167	65.69660	153.91025	79.73944	175.69
344.3387	285.9218	46.65096	175.37160	65.61256	153.20506	79.67372	172.23
349.8873	289.9391	47.27689	178.66914	66.59310	151.68037	79.89908	169.59
349.3478	291.7212	47.01134	178.05814	66.50906	151.21344	79.96481	169.51
350.3208	294.4092	47.45708	178.81462	66.96664	152.68094	79.72067	167.79
348.7698	295.0098	46.21470	175.56560	65.50983	152.49037	79.02581	166.67
352.5845	298.7907	47.12515	177.19495	67.05069	150.24200	79.92725	170.18
353.3262	299.1747	47.19153	177.37921	67.06002	149.04965	79.21362	171.46
353.2299	299.5981	47.73212	178.37817	67.17210	150.25153	79.80517	172.81
356.2739	300.8189	48.22527	182.52920	67.74174	148.04797	80.97891	172.32
355.5418	302.5224	48.22527	182.70383	67.19077	149.38348	80.34978	174.89
356.5822	303.5464	48.24424	185.05089	67.42424	150.08936	79.95541	175.50
353.3840	296.6738	47.82695	183.70277	67.51762	149.59331	79.34508	172.50
353.2684	297.8651	48.44340	185.47763	67.61101	150.91928	78.88497	172.17
352.8542	297.2055	48.10199	184.56595	67.40556	151.45348	78.92253	172.49
351.2744	299.3618	47.85190	184.78192	67.44704	151.03371	78.55463	171.54
356.0234	302.5618	48.36932	189.40315	68.13538	150.52820	80.06784	173.94
356.5822	304.2258	48.59929	188.72215	68.39939	150.12749	80.19077	174.90
358.5762	306.2147	48.91548	190.96954	68.88028	149.73025	80.97576	176.74
357.1444	305.2891	48.85799	190.04527	68.52196	149.28146	79.51928	176.44
355.8674	304.7180	48.13935	189.94801	67.64505	149.87349	79.00858	175.88
355.2676	305.5466	47.75608	192.10783	67.47533	150.64696	79.63279	174.49
355.5869	304.0078	48.24475	193.74228	68.20139	149.60619	79.09370	175.65
356.9703	305.3493	48.03395	193.61581	68.22967	150.19818	79.71791	176.35
360.0369	308.4268	48.16810	192.89589	68.78599	150.26502	80.44614	175.71
359.3501	308.7030	48.88673	189.15994	69.22916	150.07408	79.79358	176.35
359.8628	308.7130	49.53831	191.08630	69.32345	150.39870	80.15295	177.70
361.6912	309.4725	49.50956	190.74579	68.79542	150.61832	81.00414	178.36
356.7671	305.1027	49.82576	188.25516	69.15372	150.43690	78.25198	182.33
359.2243	307.6180	51.02349	191.16412	69.87035	149.31967	78.24254	182.87
361.3719	303.3567	50.59231	198.98621	70.67183	146.25442	78.20470	179.90
366.7410	310.6956	51.07141	202.52753	70.74725	144.96527	78.19523	179.48
368.8306	314.6905	52.42245	202.08972	71.40731	144.49738	78.95185	173.34
366.3444	310.1432	51.71340	201.91460	70.47381	144.25858	77.83586	173.00
366.4218	309.6500	52.22123	205.53377	70.79441	144.14403	77.80746	174.12
367.4085	311.7412	52.33621	204.06470	70.70012	145.76741	78.76269	173.37
366.1219	310.0741	52.82489	208.14116	71.26587	144.40190	79.10316	173.28
363.4519	307.6180	52.07750	205.03761	70.15322	144.97485	80.00163	171.13
366.3057	312.1061	52.93987	207.66443	70.66241	145.44272	79.78410	172.58
371.3749	319.3660	53.86932	208.57893	71.14329	145.58594	81.39190	175.39
371.7134	321.9208	53.96513	206.76936	71.19986	144.56427	81.14600	175.28
370.3978	320.9936	53.49562	209.17241	70.86041	145.03207	81.30677	173.90
371.8586	323.6469	53.89806	208.96806	70.77554	146.74138	81.91207	174.05
371.2781	324.1205	53.50520	207.51848	70.87927	146.46446	82.50790	173.62
362.2039	315.0851	52.02002	203.71448	69.25744	146.83687	81.13654	172.52
365.3189	316.9493	52.38412	203.06264	69.70062	146.02524	81.48648	172.68
358.0054	310.2813	51.08099	199.98827	68.25795	145.14671	80.65421	172.61
363.9646	318.0344	52.46078	204.90138	69.06887	145.31496	82.60246	174.23
369.1112	323.2229	53.14109	207.82008	69.76662	144.37804	83.04698	172.11
369.4014	321.9405	53.40939	208.44273	69.93635	143.09698	82.81999	171.85
373.5999	325.7480	53.42855	212.69429	70.01178	142.71457	83.29287	168.15
375.0703	326.8528	53.88848	215.64217	70.44553	141.51958	83.45364	169.81
377.7791	329.0425	53.98429	221.14873	70.93585	142.14098	83.68064	171.52
377.5275	328.9735	54.55920	222.18974	71.32245	142.24614	84.04948	172.08
377.3630	328.2239	54.75084	220.73042	71.07728	143.19260	84.58855	172.71
377.9725	330.0290	55.33534	220.47745	71.55817	142.40868	84.56964	171.21
379.8396	331.8735	55.38324	221.10008	71.95419	140.64004	84.68314	170.69
379.5107	330.9760	55.51740	219.70886	72.47280	138.49854	83.85088	168.24
379.5977	329.3878	55.53656	217.98683	72.04848	139.37811	83.73737	166.33
377.9822	327.9476	54.77001	214.61090	71.69019	138.81403	83.51040	166.32
377.3146	326.5174	55.12454	219.08623	71.89762	136.96893	83.89815	167.01
374.4125	318.0541	53.50520	217.66577	71.71846	135.92686	84.39941	169.51
374.8672	317.1072	53.74475	215.74918	71.78447	135.53488	84.87228	169.12
378.9979	319.7212	53.39980	220.84714	72.01077	134.64578	85.32625	169.00
369.8657	308.5748	52.18290	212.68455	70.78497	132.44693	83.88870	165.82
367.9599	309.8670	51.48343	212.39269	69.78548	136.82550	82.61192	161.81
376.8794	319.1885	52.86321	219.94235	71.09614	135.01836	82.81999	161.53
373.9384	314.0690	52.34580	215.71024	71.02070	135.02794	82.14850	162.41
368.9854	304.9548	52.24040	213.37534	70.58696	133.56345	81.42972	160.62
364.4193	299.9636	51.02349	207.41150	69.91750	132.70200	80.62582	159.04
371.1233	304.4813	51.57925	211.80896	70.37009	132.96046	81.64726	159.14
369.2756	295.8602	50.18988	212.81104	70.12494	131.92671	82.31875	157.49
374.5479	307.5292	51.29179	217.28635	71.06786	133.75491	82.83890	160.84
376.8794	306.6514	51.06182	221.06119	71.36959	134.02295	83.63335	161.66
380.7006	313.7140	52.67158	225.92567	71.74674	133.05618	84.53181	161.52
381.2133	311.1690	51.73256	227.25851	71.92591	130.23250	85.94099	161.49
383.4867	314.4932	51.85712	228.06601	71.98247	130.99826	87.12318	162.20
383.0030	316.2194	52.07750	224.25229	72.10506	130.47183	86.93404	162.35
384.3090	317.5215	52.14458	226.01320	72.52937	129.49551	86.97187	163.51
378.7174	307.7956	51.18639	219.13484	71.86934	128.18417	86.20580	162.56
378.0167	308.8806	51.81880	220.78877	72.06735	128.97862	85.15601	163.24
381.0351	314.6731	51.66548	219.12512	72.13335	130.42395	85.91262	163.00
378.0361	313.3003	50.67855	211.17656	71.13386	131.60127	85.92207	161.81
376.1143	308.0164	49.51914	206.29260	70.77554	132.30955	85.52485	162.37
378.2302	307.4831	49.74911	211.18379	71.30359	131.26625	86.23198	161.78
384.3254	312.0954	51.04266	215.03397	72.22764	130.80684	88.14233	162.24
384.1312	312.0065	50.68813	208.98093	71.94476	129.69649	87.80968	160.31
383.1122	310.4362	50.85102	212.49968	71.85047	130.37610	87.74314	157.57
384.6650	315.1867	51.10973	215.35562	71.53931	129.64864	87.38199	159.96
388.8191	320.5594	51.60800	218.08485	72.47280	131.80046	88.94068	161.98
394.3998	326.9594	51.80921	219.28375	73.52888	131.22536	89.29234	161.92
394.1669	326.7323	52.09667	218.64044	72.74625	132.11670	89.52994	163.22
394.6231	327.5224	51.33012	215.11195	72.89711	131.19659	89.52994	162.76
396.4963	330.9396	51.75172	216.93469	73.31200	132.27968	89.31135	164.51
399.3788	332.9445	51.31095	216.96393	73.53830	131.80046	89.30184	163.27
399.5244	332.5100	51.00433	216.11589	73.13285	131.74293	89.78657	162.28
400.7085	336.3914	51.21513	215.55057	73.55716	132.73015	90.32830	163.43
399.3400	332.3520	51.47385	217.67546	73.61374	132.30841	89.77705	162.72
403.6299	337.3889	51.94336	218.62094	74.22664	134.52251	91.36426	165.35
404.9790	337.7841	52.07750	218.97183	74.76410	133.47777	91.54485	166.35
402.9894	334.6927	51.88586	216.12566	74.63210	133.09436	91.76345	165.89
400.0389	332.2531	51.46426	211.70041	73.29315	133.70779	92.72337	166.48
403.8240	335.0976	51.78046	216.87620	74.04748	133.97618	93.15106	168.13
400.1359	331.0582	51.59841	215.97946	73.80231	134.56085	92.77089	167.04
404.4743	335.2260	52.34580	220.05380	74.55666	134.24457	93.33164	166.40
405.3187	337.4087	52.41287	222.34442	74.61324	134.05287	93.48371	166.84
405.2314	335.9470	52.38412	222.67580	74.36807	132.88354	93.51221	166.42
405.1149	334.8112	52.77698	223.05595	74.55666	132.96977	93.12255	166.91
407.6967	336.0161	52.65242	222.22745	74.58495	132.57684	93.88289	166.22
405.0179	333.8137	51.72297	219.20579	73.65145	132.88354	94.27256	165.66
405.8914	332.0359	51.72297	220.27800	74.46237	132.96318	94.12049	167.81
403.3873	326.0606	51.13848	217.64621	73.35915	133.86554	93.26510	166.58
403.5135	324.9644	51.37803	216.77872	74.35864	134.08624	91.91551	167.27
406.7358	327.4137	51.86670	216.96393	74.97154	134.30705	92.40974	170.06
409.6960	330.0705	52.40329	219.69315	75.82017	133.64468	93.70231	171.59
405.6390	321.7348	51.46426	214.10797	75.41472	132.29128	93.74033	172.11
402.0188	321.2903	51.32054	213.42567	74.42466	131.54259	92.67585	172.14
393.4778	312.9744	49.90242	206.49538	73.23656	130.16034	90.38533	170.43
398.2045	315.3941	49.83534	210.29680	73.78346	130.36189	91.48782	171.13
404.3190	322.3570	50.73605	215.43361	75.01868	131.58098	92.50478	172.69
403.2903	320.4015	50.68813	215.72603	74.87724	131.30260	92.59031	174.70
399.8156	318.2386	51.36845	214.08849	75.03754	130.96663	92.71388	175.04
398.7673	318.6039	51.21513	212.44119	74.37750	130.64989	92.45725	175.16
403.0573	324.7668	51.51217	213.85454	75.35813	131.72496	93.59776	175.96
402.7273	322.9694	50.91810	214.41014	75.46185	132.14728	93.43617	176.04
406.8328	328.4014	51.33970	215.80400	75.92388	132.63683	94.49115	176.35
405.9301	328.8557	51.84753	213.71808	75.94276	133.86554	94.57669	177.95
406.7358	330.0014	52.23081	217.70473	75.89560	133.63516	94.89033	177.64
406.9492	328.7668	52.24040	219.94658	76.03705	133.09758	94.56720	177.71
407.6772	329.8038	52.57576	219.80037	76.21619	132.88640	95.22297	178.38
407.3181	328.7076	53.65852	222.29567	76.48964	132.85658	96.72465	177.90
407.9587	329.3495	53.74475	222.55885	76.74423	133.16422	97.88417	178.77
406.4446	325.9224	53.16984	220.69713	76.36706	132.66437	97.69409	175.27
410.1619	331.4532	53.64893	221.65233	77.01768	134.48109	97.70359	177.16
409.7639	332.4408	53.38064	224.62526	77.27226	134.06779	98.66351	177.87
409.8513	332.5989	53.12193	227.00357	77.23455	135.00983	99.30031	177.32
409.2398	332.6779	52.96862	225.49277	77.02710	136.20180	99.51891	176.98
411.1421	336.1446	53.39302	223.82053	77.23930	137.01888	100.26778	177.74
411.8215	337.0235	53.21018	226.18291	77.42091	136.79778	99.77108	175.74
412.7436	340.2531	53.35453	225.51912	77.55472	135.74999	100.21047	174.71
411.9865	338.0309	52.98883	224.87483	77.65030	135.58659	99.15974	174.05
409.6862	336.7964	52.26704	224.39651	77.17239	135.47122	98.27140	171.11
409.5504	341.0728	52.55576	221.87791	76.63713	137.49950	98.42423	165.85
404.0254	338.3963	52.19005	216.84079	75.05048	140.08534	96.86726	164.93
409.8094	340.4995	52.41139	221.47771	76.03498	137.73979	98.83498	166.95
412.0003	343.6735	52.17080	222.48318	76.04452	138.07631	98.35738	166.25
411.5037	343.8416	52.48839	223.21532	75.55706	137.72060	98.09947	166.14
413.9381	345.9675	52.96958	226.36841	76.28348	137.94168	97.77470	166.04
415.4084	345.5423	53.41228	226.74911	76.44598	136.50943	98.60571	166.59
416.2459	349.7446	53.46040	224.95294	75.95850	137.91286	98.21409	166.58
416.4698	351.0103	53.42190	223.87912	75.97762	138.14355	97.92752	164.83
416.8204	350.4566	53.07544	223.90839	75.39458	138.75879	97.37352	165.63
419.1281	350.5950	52.77710	225.88029	75.57618	138.76649	97.75558	166.20
422.3318	354.6194	52.71936	223.73268	75.83424	139.60388	98.08036	167.29
421.5625	356.1520	51.79547	220.48198	75.33723	141.24014	98.82542	168.12
423.0523	356.9035	51.73773	218.43198	75.74822	142.49141	99.18840	168.76
419.6053	354.7479	50.65986	216.42102	74.77330	143.04964	99.22659	168.65
424.0845	356.9628	51.53563	220.98958	76.04452	141.03803	100.67851	169.21
425.6035	358.3570	51.58374	221.17508	76.36951	140.85510	101.41402	169.00
424.1526	358.3570	51.63187	217.00676	75.96807	139.77710	99.95256	169.22
424.7856	358.9998	51.85321	213.65840	76.14012	141.36530	100.76449	171.04
423.3347	356.4783	51.97832	212.44795	75.41370	142.92458	101.02239	171.07
420.0142	353.5910	51.57412	209.83176	74.85933	142.65505	101.04150	169.41
413.8115	350.6939	50.70798	206.68845	73.50207	145.78325	99.27438	169.61
419.7416	354.7677	50.87159	213.10200	74.03732	144.37796	101.50954	169.39
423.1400	357.5067	51.19879	216.77246	75.16518	142.54921	101.34717	168.76
424.0260	359.8699	51.29504	213.32651	75.19385	143.89671	100.59255	169.09
428.3885	364.0722	50.53475	214.32224	75.71956	142.93420	101.49044	168.56
429.4401	364.3590	49.57236	214.94698	75.82469	142.51067	101.42358	168.16
427.4829	360.3445	48.57149	212.43819	75.51883	144.03146	102.16863	168.44
427.3076	361.7288	49.88995	215.56201	75.84381	144.04109	101.68149	169.29
429.0798	362.3715	50.14017	217.22153	76.36951	143.24222	101.68149	171.17
426.9960	360.4829	49.65898	215.78654	75.97762	143.91597	101.93938	169.82
426.1001	360.5126	50.01506	214.71272	76.35994	145.19960	101.71014	169.61
429.5667	362.6978	50.22679	215.60103	76.90475	145.27666	101.91073	169.49
427.4536	363.2219	50.48663	212.91650	76.67537	145.57542	101.50954	169.53
430.1607	365.5258	50.40964	216.74319	77.04813	144.83334	102.53161	168.86
430.8715	363.9239	49.98619	218.07080	76.76138	142.41457	102.28327	164.64
430.5210	364.5963	50.14980	216.87007	76.72315	141.90375	101.72924	161.72
431.0565	362.7275	50.21717	217.29961	76.89520	141.24847	100.70717	161.77
432.1276	362.1045	50.35189	218.36366	77.42091	141.16168	101.28029	164.00
433.4226	363.4097	49.90920	217.84627	77.35400	140.93043	101.67193	164.04
434.2114	364.6852	49.78409	215.86462	77.82234	143.15654	102.25461	166.39
435.2339	364.8435	49.33177	213.85364	77.42091	143.50349	102.12089	167.22
432.3807	361.6299	48.42713	211.24724	76.69448	143.44565	102.13042	166.97
427.6484	358.1494	48.50413	209.40222	76.39818	143.92752	101.13701	167.10
428.3105	359.8797	47.67647	206.89343	75.64309	144.98758	101.69102	166.61
431.7187	363.6075	47.63798	210.38818	75.93939	145.08398	102.20684	166.70
435.5162	369.0459	48.35976	214.39058	76.64670	144.98758	101.97760	168.73
436.2076	370.1731	49.45688	216.49913	76.80918	143.86006	101.51910	168.65
437.1230	370.5982	49.51462	217.26057	76.83785	142.66507	101.50954	167.48
434.5425	368.2449	49.04306	214.95674	76.43642	143.06021	101.38537	167.67
438.4277	371.8243	49.64936	221.01889	77.13416	144.03352	102.36923	170.19
440.3557	375.9970	49.75522	220.11102	77.11504	144.40936	103.42950	169.35
439.7033	375.6905	50.43852	220.54057	77.07681	143.42642	103.91667	169.69
439.9370	376.3134	51.08331	222.02435	77.77455	143.66664	105.78886	169.70
441.2905	376.1354	50.85234	223.56674	78.08997	144.29387	106.25691	169.25
441.1834	377.2923	51.12180	222.53197	78.44362	142.98154	106.28556	171.06
439.6060	377.8263	51.42014	220.99936	78.50097	141.77539	105.10112	167.71
439.0704	376.5112	50.66948	218.58818	77.87969	142.74034	105.68379	167.29
437.1911	375.2159	50.57325	218.48079	77.74586	144.46753	103.63010	168.03
433.7440	372.3682	50.51551	216.34294	77.57383	143.19383	102.25461	167.18
434.8541	372.1111	50.65024	217.57294	78.18555	144.06226	102.66534	167.74
432.5074	371.0531	50.22679	214.80055	77.86057	145.80876	102.40743	168.82
436.1200	373.8118	50.21717	216.74319	78.08997	145.29738	102.78951	167.83
435.4286	374.0688	49.64936	216.89937	77.96572	144.63159	102.98057	164.03
431.1870	369.6391	49.43763	217.18245	76.94299	143.93683	102.00626	163.77
423.9974	362.0011	48.10955	212.01843	75.51883	145.72195	101.47133	164.94
423.5968	362.4466	48.46563	212.34058	76.26437	145.59648	101.47133	166.04
427.7289	365.8320	49.07193	215.64009	76.64670	146.46493	102.46474	165.42
432.9259	369.2076	49.45688	219.45699	77.47825	143.15524	102.11131	163.51
433.6390	369.5540	48.86982	218.39854	76.75184	141.75612	100.94280	163.30
432.3984	366.6041	49.18741	221.71785	76.70404	141.23506	99.57314	163.64
423.6848	356.2301	48.55224	216.67522	75.03137	139.03502	98.86437	162.05
424.3979	355.6461	48.09992	216.21506	74.85933	139.27629	99.62104	161.32
419.2108	354.3394	48.48488	214.18823	74.56302	139.25703	98.06939	164.22
424.1927	356.5370	48.43675	217.64458	74.74462	140.42892	99.44862	164.59
418.7223	349.0535	47.72459	215.66670	73.96085	140.07146	99.24749	165.36
423.0791	353.7653	48.06143	216.41087	74.46744	138.71886	98.68239	164.59
424.8374	356.0322	47.79196	215.28484	73.97041	139.50140	99.65935	165.03
428.5105	359.2987	48.72547	218.60414	74.54390	138.04254	99.84133	164.16
427.7289	357.5071	48.90832	216.95920	74.53435	137.07640	98.96973	164.23
424.6323	354.7651	48.81209	215.71565	74.29539	136.72861	99.23792	163.92
423.5871	353.5277	48.56186	216.90045	74.33363	139.06665	100.58842	164.66
425.1110	356.3588	49.23553	217.92853	75.06960	140.41927	101.29719	167.59
432.2616	362.9217	49.38951	221.15973	75.81514	140.94099	102.66684	168.00
435.5536	365.2083	49.98619	220.46452	76.44598	140.11974	102.64769	165.33
436.8431	368.8808	49.86108	220.33722	76.12099	140.77672	102.88713	164.92
440.2133	371.6723	50.52512	221.15973	76.57979	138.83475	103.11701	165.45
441.9423	371.1873	50.51551	222.62843	76.84741	137.89763	104.64950	166.90
443.0950	373.4541	50.18829	223.19635	76.48420	137.73338	104.81233	166.75
442.6359	370.3162	50.08243	222.66759	76.94299	139.25024	105.37743	167.77
445.0097	374.1075	50.34227	224.78256	76.79006	139.03767	105.71266	168.93
445.4102	375.2854	50.08243	223.08865	76.94299	140.18736	106.02872	167.68
443.4370	376.1565	49.67823	218.98602	76.63713	142.73798	105.06136	168.12
447.7156	380.3338	49.72635	223.35300	77.38268	142.25494	106.27776	168.08
448.6241	382.2047	49.00456	223.29428	76.93343	142.68968	105.20501	166.65
449.3958	383.5113	49.38951	229.08104	77.67896	141.66234	105.39658	167.52
451.2127	385.1150	48.94682	229.56078	77.51649	142.29112	105.80844	167.16
453.9675	389.2032	49.17778	233.66339	78.14732	140.82072	106.01916	165.77
456.1068	394.1922	49.06230	233.57532	78.09953	142.30083	105.09010	167.65
457.6894	394.5684	49.00456	236.76730	78.21423	144.42903	105.58814	169.84
458.0801	394.0338	49.45688	237.50165	78.20467	144.15816	105.37743	170.45
456.5659	391.3216	49.26440	236.12108	78.03262	146.03491	105.60730	171.29
452.8930	385.5703	49.06230	232.40031	77.08637	143.36490	105.12839	173.15
453.0395	386.6394	49.90920	234.27049	77.36356	143.15212	105.34869	174.12
456.4585	390.7078	50.04393	234.50548	77.78411	142.52333	105.39658	174.45
456.6148	390.6187	49.88033	233.57532	77.64074	140.73364	106.01916	174.18
458.4220	393.4003	49.94770	234.00613	77.46869	140.37575	105.39658	172.92
457.3084	393.6082	49.68785	230.94139	77.37310	141.48822	105.77013	174.50
458.8616	397.6866	49.08155	229.96223	77.44958	142.02023	105.72223	173.94
458.0411	399.9039	49.00456	227.86687	76.79006	143.51971	105.24333	172.61
456.7516	395.2613	48.60998	226.89751	76.34084	141.83647	104.53457	168.74
457.3572	393.4597	48.56186	226.50584	76.26437	139.78561	105.37743	167.28
458.5782	394.7268	48.49450	226.75066	75.75779	142.02992	106.65131	167.12
448.3505	387.2433	46.86807	218.20270	73.72190	145.61888	103.70128	166.85
453.8503	395.6474	47.05092	218.06564	74.09467	144.44838	104.79318	166.62
445.0195	389.8368	47.00280	213.62028	73.44472	146.64430	102.66684	165.50
440.0765	383.2045	47.17603	208.81270	73.02416	147.54892	101.08647	166.16
446.8169	385.9663	47.75346	214.63861	73.93218	147.73296	104.16102	165.24
442.9290	379.2549	47.07980	210.23247	73.62632	149.49573	103.69170	166.63
448.1747	382.2938	47.44550	214.45258	74.33363	147.44237	105.35828	166.22
457.4452	393.8061	48.19616	219.42665	75.90115	146.25108	106.93864	166.81
458.6564	395.5681	48.38863	220.92471	76.04452	143.72317	107.59952	166.90
455.5598	389.7477	48.15767	215.92129	75.41370	144.52707	106.22987	165.88
459.8482	393.9843	48.19616	215.32402	75.57618	144.17841	106.48848	166.58
455.7747	388.2925	47.43182	212.17728	74.86824	146.30917	107.65649	167.00
452.6389	384.2736	47.32444	210.35054	74.46955	145.96053	106.34042	165.44
459.7115	393.0341	47.18778	213.68977	75.48088	144.55612	107.80164	166.15
455.6575	382.9273	47.24635	209.36842	75.49060	144.61235	107.83067	168.16
450.8079	381.0169	47.01207	211.29338	74.53762	146.25104	107.61778	167.80
446.0143	377.3209	46.30923	208.32738	74.37230	145.15538	106.75653	167.09
453.9351	385.7654	47.09017	214.27904	75.19888	144.60268	107.83067	167.02
458.4739	390.4635	47.31468	216.34149	75.89903	145.27170	108.87579	168.59
461.3265	393.4072	47.55872	218.07002	76.34637	144.01120	108.77902	168.97
467.8553	399.9091	47.77348	220.11282	76.93954	144.36028	110.59829	169.37
467.4730	398.0557	47.61729	218.76733	76.96872	143.78815	110.97571	168.64
468.0710	397.9962	47.40254	219.00304	76.93954	142.21738	111.70147	168.59
466.7770	396.8069	47.94558	218.94409	76.73784	143.40999	112.20467	169.80
465.6006	394.3289	47.71117	218.47270	76.66962	143.69119	112.38854	170.96
468.2964	398.1251	48.05301	221.29137	77.16660	139.91928	111.53696	168.33
468.1396	392.9612	47.88697	220.95744	77.60510	139.33748	111.32407	169.57
459.1503	380.8890	47.10563	213.47369	76.92298	138.58121	108.02422	169.06
458.7189	380.6214	47.32050	214.69153	76.53320	138.93993	108.00486	166.99
456.9054	376.4982	47.75024	212.20676	76.75732	137.94122	107.27908	167.75
456.3369	376.7460	47.75024	211.47018	76.04598	138.28062	106.73718	168.26
460.4933	382.4055	48.85390	213.71922	76.87426	139.20172	107.00813	170.29
461.7383	383.9219	49.66455	212.12820	77.62459	138.66846	107.11458	170.74
455.3761	374.3177	48.96133	210.18358	77.05940	139.89993	106.77589	170.16
455.5624	376.6469	48.94179	210.47821	76.98144	137.78609	105.75980	169.67
447.4946	367.2706	48.07254	204.11410	75.85108	135.84683	104.81145	169.39
442.8480	363.2366	48.27765	200.79451	75.78288	136.78735	103.49538	172.08
437.9465	358.5188	48.56089	197.16067	75.41258	137.63094	102.20835	171.65
429.3493	348.5775	47.85767	193.46791	74.38940	139.26964	101.96642	171.09
431.1727	350.1732	47.18376	197.92673	73.64883	138.12543	102.13094	172.03
425.9085	342.0557	47.09586	195.28482	73.20059	137.90243	101.66643	172.58
424.8400	341.5205	46.50008	192.46614	72.91800	136.23463	100.02135	169.79
422.7421	338.0812	45.96290	188.09572	72.57694	138.73634	98.52141	167.60
433.2411	348.6865	46.18754	191.75902	72.82056	138.78484	101.58902	167.10
441.0442	359.8369	47.70140	197.64192	73.88271	138.06728	103.13733	168.09
444.0243	362.2851	47.99441	199.72401	74.58431	137.60899	102.56639	168.23
448.3376	365.2288	47.91628	197.74011	75.13974	138.07506	103.98891	168.84
437.7995	350.4211	47.40840	193.99824	73.95091	136.99721	102.68252	168.60
439.8581	354.8416	47.52560	194.83307	74.12631	134.97755	101.73417	168.86
438.4465	351.9871	47.42793	195.79553	74.25299	135.06499	101.55998	170.11
442.0540	355.9417	47.88697	199.13475	74.63303	134.16193	101.02776	170.63
448.5239	363.4844	48.63902	202.91591	75.84134	134.41441	103.34055	171.21
440.4659	355.2578	48.31672	199.80258	74.87663	132.27824	100.75681	170.56
431.7805	343.9884	47.58421	197.77942	73.74628	134.23962	99.71168	173.81
430.3688	344.4146	47.25213	197.09193	73.26880	132.56950	98.78270	174.74
437.3093	352.9782	48.27765	202.37572	74.61353	131.06450	99.53750	173.08
437.7995	352.8890	48.62926	202.79805	74.89613	131.84129	99.86652	174.86
428.4475	342.3927	48.06278	197.60261	73.68781	132.82198	98.74399	177.25
425.6732	338.4876	47.58421	195.90356	73.37599	134.22018	98.23111	177.12
421.1051	335.0880	46.91029	193.14380	72.51847	134.56976	97.72790	177.49
413.6352	326.5046	46.36335	189.52959	71.92406	132.71518	96.00540	178.29
419.8600	337.4766	45.40619	194.49911	70.95935	132.80257	97.70855	177.14
429.1239	342.7099	46.24614	198.87939	72.73285	132.89966	100.06006	176.55
428.0260	343.7308	45.64059	199.68474	71.34913	135.81262	98.40529	178.38
421.5070	338.4678	45.03505	195.92320	69.79002	137.38287	98.15369	181.62
429.2611	344.1470	45.11318	200.58829	70.66702	132.68678	99.84717	179.73
427.1240	339.2310	44.47834	198.21156	69.27355	134.03825	100.66970	180.80
423.6538	334.3148	43.57978	195.10805	67.26620	136.35226	101.16324	183.68
411.1649	321.9849	41.94871	190.25638	65.13215	135.31190	99.09235	186.41
408.0475	320.4883	42.08545	191.30722	65.69733	133.95073	98.54076	191.51
418.9876	332.0253	43.27701	196.69907	68.44527	132.63815	100.11811	185.82
417.0957	328.3382	42.46636	196.34551	67.62674	130.73248	100.36004	186.40
411.7923	321.5290	41.57758	193.21256	66.89590	131.17000	99.51814	185.09
408.7827	315.3542	40.57159	189.26445	67.50980	128.10731	98.81173	182.30
417.7721	325.2459	40.63018	192.27956	68.15294	127.88367	99.49880	178.89
427.0358	337.3081	43.90209	198.32939	70.59881	129.13796	100.74712	180.01
432.3785	341.3917	43.67745	201.44272	71.19321	128.17539	102.21802	180.89
437.1142	348.3793	44.30254	203.56412	71.88508	129.74075	102.41156	179.30
436.9864	347.4107	43.61885	201.76683	71.43683	126.73643	101.86964	180.67
442.0997	354.2382	44.40997	203.78999	72.10920	125.11271	102.15028	179.36
436.4062	349.1474	44.11696	200.25435	71.17374	127.85455	101.04710	181.81
442.9847	356.9077	44.35136	202.55705	71.83636	126.85311	101.69138	183.13
445.1481	356.6100	43.99976	202.83256	71.87534	125.09328	102.87688	182.38
448.3145	362.1276	44.14626	202.90144	71.64146	126.16275	104.04294	179.06
453.8604	368.3598	44.89831	208.33342	73.22982	127.11562	107.00672	179.14
451.0580	364.2910	44.77134	204.15120	72.92774	128.10731	106.27792	180.58
444.1156	359.7757	44.09743	201.99614	71.71943	128.41846	105.16043	180.65
445.3743	359.0910	44.82995	204.25946	72.39179	128.90732	106.91927	179.50
449.1896	366.4842	45.62106	204.59404	72.68412	128.01144	106.53056	180.37
443.5157	358.3467	44.78110	199.75249	71.69994	125.11935	106.18075	179.24
439.0809	350.5665	44.19510	196.91843	70.84242	124.10661	107.42456	179.66
441.2934	351.4001	43.84349	196.27881	70.99833	123.17179	106.61803	180.34
440.1134	346.4878	43.88256	194.71413	71.02756	121.83775	106.74434	181.47
432.5909	338.2908	43.33561	193.40536	70.27724	119.90970	105.55884	182.37
430.9880	336.8618	43.19888	194.01549	69.75104	119.74416	105.32563	183.77
435.9243	343.7091	43.76536	197.70567	70.50137	119.98759	105.94752	184.65
430.4963	335.8495	43.19888	195.78676	70.17979	117.58240	105.43252	184.04
430.6733	336.1076	43.05238	194.46814	69.77052	116.99814	105.05354	184.61
437.6255	343.6198	42.83750	198.34531	70.10184	116.12174	107.25937	181.82
437.3010	338.6083	42.58356	199.10301	70.56957	118.45879	109.20282	182.71
430.7618	331.6022	41.76315	194.64528	69.80950	117.58240	108.33798	182.06
418.9421	322.9189	41.39201	189.60693	68.66940	116.84232	106.46255	180.29
421.3709	327.0670	41.08923	190.75829	68.33808	118.01084	106.10300	177.05
409.1677	314.7219	40.19068	184.74571	66.42817	119.19885	104.37333	177.32
410.3182	314.3448	40.65949	183.97816	66.73025	117.67002	103.75142	175.98
420.6826	325.5090	41.24550	187.41249	67.67546	117.84530	105.68516	176.93
405.1360	310.8615	41.39201	182.00021	66.88616	116.31649	100.81681	176.91
407.5747	316.0517	41.33340	183.90926	66.72051	114.30029	98.32918	173.63
409.4430	316.3891	41.63618	185.48375	67.21748	115.07087	99.80621	174.09
421.9118	327.0869	42.08545	190.43355	68.39655	115.70490	100.90427	175.80
406.9158	310.6134	40.53252	182.70874	66.19430	112.53476	98.27087	175.13
404.4870	306.8920	39.97581	179.66801	65.55116	110.87655	97.00763	175.42
391.5364	294.8843	38.82332	172.11050	63.57303	111.85196	92.89722	172.88
392.4410	298.4668	39.00888	172.15971	64.05051	112.86639	91.09952	171.42
386.2067	289.6148	38.73542	167.87909	63.67047	115.04161	90.90519	172.82
385.8035	288.9301	38.48148	169.84720	63.51457	114.82700	91.55623	170.17
395.0273	299.6378	39.54607	175.22994	65.27831	113.12978	94.03413	168.79
393.4244	296.1645	39.38980	174.39351	65.33678	113.01273	93.41223	170.40
401.5173	303.8355	40.35672	179.72707	66.55485	111.64712	94.45199	169.33
385.3315	288.9201	39.38980	173.42914	64.96649	114.02717	91.72143	169.42
382.9715	287.3720	40.01488	173.71451	65.59014	114.30029	91.49794	171.91
383.1387	286.4789	40.18091	173.27168	66.03838	115.59759	92.19757	172.03
390.3072	291.2423	40.48369	175.36772	67.15900	113.69551	93.32478	172.83
387.3277	285.0498	39.78047	172.76982	67.05181	115.93899	94.21877	174.13
390.7497	289.0392	39.97581	175.87941	67.07130	116.39745	94.88927	173.08
398.5575	297.0477	40.60089	179.80577	67.81188	115.87071	94.97672	172.76
408.3417	306.7432	41.06970	184.64732	68.63042	116.15360	97.52264	172.85
406.0505	305.9294	41.64594	182.35448	68.22116	113.69551	96.33714	171.14
402.7661	303.6668	41.35294	181.32121	67.50006	113.56556	95.48202	172.23
410.4362	311.9829	42.06592	185.74945	68.90327	113.62418	96.86187	174.35
403.7003	303.8653	41.38224	184.07657	67.91907	113.37990	95.56947	172.58
404.9295	304.8775	41.60687	184.87363	68.19192	111.28878	95.23908	171.82
408.8137	307.5073	41.73385	187.85530	68.39655	112.49068	96.51205	172.94
404.3690	305.2943	41.95848	184.95236	67.44159	111.49397	94.29651	172.78
394.7519	297.1171	40.96561	181.11829	66.02528	111.86530	92.20472	172.23
383.3058	286.6377	40.51252	176.20479	64.43166	111.17152	90.17632	174.54
368.7524	273.3101	39.09414	167.92683	62.30021	107.68304	85.72942	169.93
367.6413	273.8062	39.63588	167.11781	61.71257	106.32479	85.05653	168.57
372.8824	280.6437	40.15792	169.56467	62.86793	108.30843	86.97767	170.77
360.5415	269.3207	38.92669	161.71097	61.48348	109.16833	84.79324	172.69
361.3188	272.5955	39.07444	162.97389	61.23448	109.52013	85.48563	171.27
370.4144	279.4730	39.70483	165.89436	62.16077	107.66351	86.82163	170.63
369.7429	279.0654	38.99564	165.57863	61.74245	110.62431	88.06988	171.31
373.3673	283.2215	39.11384	167.56178	61.67272	111.53306	89.79599	170.26
385.2381	292.9256	40.03973	172.75153	63.51534	109.98914	91.70737	170.09
383.7666	290.7780	40.08898	173.39285	63.24641	109.05109	91.50258	169.90
375.9252	281.9189	39.84273	170.13693	62.81813	109.55920	90.42011	169.62
375.6190	282.1774	39.68513	168.41029	62.57909	111.26923	89.87401	169.49
372.5674	278.6776	39.49798	167.09807	62.24045	112.24638	89.69847	168.46
376.5078	280.5170	39.25174	169.12068	62.38985	113.39878	91.38555	168.32
377.2189	285.3194	38.94639	170.52171	61.05520	114.28977	91.00523	164.75
378.4930	287.1488	38.70999	169.25880	61.10500	112.37073	90.99548	162.14
384.1617	293.2935	39.48814	173.26457	62.03129	111.38186	91.15151	162.23
383.8456	293.6614	39.48814	173.24484	62.10101	110.14820	90.70292	162.30
379.4608	287.3875	38.43420	169.76199	61.09504	112.04764	90.52738	161.43
376.1029	284.6035	38.28645	169.17989	61.08508	112.71343	90.06905	160.83
374.1278	284.0169	38.19780	169.03189	61.05520	114.00582	89.68871	161.60
373.2192	285.0311	37.85306	167.29538	60.19864	113.07568	88.81104	159.33
380.3496	290.2013	38.05005	170.77824	61.15480	113.71209	90.32259	159.01
377.2091	287.7455	38.31600	170.29480	61.40380	112.52739	89.59119	159.16
387.4009	296.5945	38.94639	176.30345	63.07709	111.92035	91.90240	159.54
389.8699	301.2975	38.77894	179.06606	62.65877	112.21407	91.62935	158.04
393.8400	305.6227	39.22219	179.98364	63.30618	114.15268	92.42901	160.27
390.1859	300.2635	38.82819	177.11250	63.14682	116.07172	92.98487	160.67
390.6600	298.5533	38.96609	178.03009	63.63486	114.93596	93.12140	160.23
386.0381	292.6870	38.66074	176.93491	62.74841	115.02408	93.17991	160.04
396.0621	305.0559	39.37978	180.96042	64.23246	114.37788	93.96007	161.67
401.0297	308.0388	39.54723	183.44675	64.56114	115.28843	97.08070	163.64
406.8762	313.6564	39.36008	184.74913	65.45755	114.97513	97.64630	164.10
405.6713	313.4675	39.02519	184.68005	65.54719	117.74414	96.82714	165.03
402.9950	312.5329	38.83804	184.50246	64.50139	115.25271	95.57889	164.05
409.3056	321.0440	39.14339	187.21573	64.87987	117.06734	95.88120	164.45
409.0291	322.5453	39.41919	186.82109	65.20855	117.02810	95.83244	167.17
408.3378	319.9105	39.45859	188.25171	64.75039	114.24242	96.10550	165.29
407.8638	318.8764	39.50784	190.24474	64.89979	116.08646	96.87589	166.69
406.2441	315.2672	39.36008	187.64987	64.55119	115.63525	97.45127	167.20
414.7769	324.0666	39.85258	193.00734	66.00535	114.87997	98.90431	166.78
414.7769	322.2272	40.01018	193.72760	65.98543	112.20219	98.56298	166.34
421.7986	328.5011	40.43372	197.68402	66.49340	113.34001	100.14281	167.87
423.5367	331.1558	40.24657	198.38455	66.09499	113.24192	100.63040	165.71
424.3664	330.3803	40.23672	198.30562	66.07507	113.71275	100.25983	165.42
421.3542	326.6120	40.06928	194.97076	65.54719	112.52588	99.84049	164.35
422.5788	327.3975	39.84273	196.26326	65.32806	112.69263	99.07009	163.92
416.9002	321.0141	39.30099	192.05029	64.43166	110.87801	98.16317	162.72
408.2193	312.5627	38.95624	188.09384	63.33606	110.50528	96.11525	161.64
407.2317	312.3042	39.16309	188.39969	63.36594	109.89714	94.83775	162.77
408.5353	313.2090	39.15324	189.84021	63.44562	109.09282	95.40336	163.25
414.3029	318.7472	40.00033	192.79027	64.14282	110.61317	96.87589	163.75
400.2791	305.6823	39.40933	186.45601	62.45957	111.44692	94.49642	161.76
397.6324	302.6696	39.16309	184.73927	62.32013	110.52490	93.65776	161.86
393.2672	299.2990	38.70015	182.15425	61.87192	110.79954	92.29249	160.51
390.2748	297.5590	38.83804	181.04921	61.45361	109.74020	91.92191	159.27
391.4995	297.6883	38.53270	179.07593	60.62692	107.73106	92.08769	157.87
387.3713	293.4825	38.17810	177.68475	60.22852	108.34048	90.89796	159.26
385.9097	291.3746	37.72501	175.92853	60.07911	105.65703	91.94141	158.33
392.8426	297.2607	38.05990	179.75670	60.60700	107.32806	93.73577	159.94
395.4103	298.8018	37.85306	181.25641	60.64684	106.22715	94.00883	158.98
401.5531	305.3343	38.41450	184.89711	62.19065	106.46306	94.90601	159.82
405.8689	308.9634	38.98579	187.13681	63.05718	105.58823	95.72517	160.63
388.2206	292.0209	37.78411	179.81590	60.86596	105.83396	92.18520	158.54
389.7020	294.3375	37.97125	180.51643	61.06516	106.19766	90.97598	157.93
385.2776	289.4357	37.56741	179.20418	60.52732	106.12884	89.30839	154.98
382.3384	287.6659	37.22266	176.59944	60.15880	105.24419	89.24013	155.84
385.3034	289.9060	37.34086	178.10902	60.36796	105.48994	89.12310	155.96
380.8807	287.5952	37.13401	175.68187	59.34207	104.43818	86.94843	155.07
374.2367	282.4455	36.51347	172.99820	58.56519	106.18783	85.63190	155.79
371.0931	278.9692	36.33617	169.10095	58.39587	103.47488	84.78348	155.70
364.8755	274.4271	35.43984	165.07546	56.53333	103.89755	83.67176	153.01
361.2660	273.2916	35.00644	162.81525	55.69669	101.91200	81.40817	151.23
360.3438	273.4012	34.96704	163.37062	55.31820	99.22855	80.24535	151.54
367.4340	278.8397	35.27239	168.53763	56.65286	102.55093	81.80236	154.69
359.7587	270.8015	34.48440	164.75908	55.98553	102.02013	79.46684	154.66
354.1955	266.2096	34.35635	163.55905	55.78632	100.70297	80.23548	154.67
363.5467	272.4549	34.91779	167.89299	56.89189	102.30309	81.73338	158.43
374.8118	281.0211	36.06038	174.54762	59.17275	102.01736	83.31995	160.70
373.9392	280.8717	36.08008	173.25835	58.54527	101.04192	81.65453	159.81
370.0817	278.6604	35.86338	172.28644	57.51938	100.48030	79.34858	159.63
359.7587	268.0423	35.11479	167.21860	56.60305	99.50485	77.48608	157.88
357.0118	265.3629	34.62230	166.28636	56.28433	97.95795	76.61888	155.48
354.7508	261.7173	34.07070	166.33595	55.66680	98.39147	77.46636	155.16
353.5807	261.6277	34.11011	165.87975	55.48752	98.87427	76.58932	155.99
362.9121	267.7634	34.20860	169.98558	56.63294	97.92838	77.84084	154.91
354.6418	259.7152	33.69641	165.43346	55.78632	97.12045	75.85023	152.98
363.7550	268.2914	34.62230	170.70956	57.16082	96.64751	78.64891	153.42
368.0290	270.4130	34.63215	172.73273	57.56918	96.87412	79.53581	153.75
365.4210	269.4269	34.00176	169.79717	56.86201	95.11045	77.55505	151.69
362.3568	268.0523	34.21846	167.63515	56.73253	93.48471	77.19044	151.45
371.1626	274.3375	34.74050	171.27486	57.75842	91.79985	77.72259	154.15
375.7043	277.3556	33.42061	172.00876	57.76838	91.04118	77.66345	153.65
381.7038	283.0930	33.69641	176.69972	59.04327	93.69162	80.75777	154.00
378.8279	276.8376	34.24800	177.57246	59.60103	95.04147	80.91545	154.98
376.8051	271.7975	33.98206	177.61212	59.04327	96.03663	81.06327	154.74
385.7695	280.1147	33.77521	181.64854	59.63091	95.37647	82.86664	153.16
382.9829	276.8576	33.67671	181.81714	59.07315	94.69662	82.76810	151.91
381.3071	274.0287	34.29725	182.06508	59.54127	95.58162	82.61043	153.46
371.7377	264.6358	34.01160	176.02534	58.67475	95.16678	80.39316	152.39
367.9100	259.4662	34.20860	174.84515	58.17674	94.65316	80.33403	151.81
373.2054	263.6397	35.65654	177.20549	60.50740	93.06294	81.44759	156.47
376.7753	266.5382	35.67623	178.00884	60.69664	92.13448	81.49686	155.85
378.8081	268.4806	35.93233	178.07825	61.38388	93.14195	81.87134	159.45
371.0039	262.2851	35.31179	173.18893	60.52732	93.44813	81.06327	158.65
391.3921	281.6387	36.59227	183.85023	63.92370	97.04345	86.96613	163.48
395.1802	286.8282	37.58711	185.35767	65.19859	96.68787	86.75918	164.56
391.8185	284.3181	37.36056	183.28491	64.51134	96.45081	84.76856	164.92
395.1604	288.2526	38.21750	186.00232	64.93962	98.01141	85.74416	165.50
392.1458	284.3181	37.60681	182.72955	64.79023	100.15477	84.96566	165.12
390.9459	283.6906	37.67576	181.03366	64.76035	99.09790	84.28570	163.92
392.7209	283.7006	37.45906	182.20392	64.88983	98.41637	85.33027	162.79
391.2929	280.7821	36.98627	181.25183	64.40179	98.83122	85.79343	161.88
396.5586	284.8261	37.07492	183.18574	65.29819	100.23379	86.22704	162.07
399.0575	287.6848	37.38026	183.66179	66.01531	101.98205	86.34529	163.08
398.9683	285.7923	37.20296	184.04858	66.35396	101.63635	86.91685	163.22
392.6019	281.5988	37.03551	180.33943	65.49739	101.92278	84.52220	161.93
391.9276	279.4673	37.83335	180.86505	65.68663	100.72765	85.93140	162.73
404.2736	292.2070	38.92669	185.82379	66.85196	101.46843	87.87273	164.81
403.9761	292.5656	38.79864	185.41719	67.49936	104.70993	87.76434	167.84
403.5100	291.4001	38.94639	186.49818	67.44956	106.02672	87.48841	167.26
396.2512	286.5095	38.50315	181.36093	66.56312	104.54162	85.92155	164.39
390.5393	280.5729	38.45390	178.58405	66.26431	105.88811	85.11347	164.84
389.8749	279.4274	38.22735	178.05841	66.26431	108.38309	85.28100	166.33
392.9292	282.7344	38.69029	179.34767	66.60296	108.08606	85.93140	166.47
389.9939	280.9315	38.43420	177.14600	66.64280	105.27426	85.82300	167.06
395.6165	284.4576	38.31600	179.22867	66.84200	105.61089	86.45369	165.68
398.6113	287.5155	38.59000	180.71320	67.79000	106.63066	88.06850	168.51
396.0627	285.3839	38.61000	179.52757	67.73000	107.08610	87.47189	168.10
386.3744	275.8017	37.72000	175.03413	66.00000	107.50392	86.21903	165.35
381.8128	273.1721	37.83000	173.72896	65.42000	106.30305	84.04142	166.79
378.5752	269.3330	37.86000	171.37764	65.26000	104.51660	83.04708	166.32
379.0932	269.1234	37.85000	172.28429	65.52000	102.66070	82.81839	169.08
384.7616	273.0273	38.19000	175.25333	66.20000	102.91873	83.67352	168.80
379.2725	266.3477	37.85000	172.96181	65.66000	102.89888	83.33544	166.76
381.4542	266.9467	37.80000	173.74889	65.89000	101.39033	84.05137	167.26
379.9499	263.1726	38.36000	172.58319	65.99000	99.38555	83.99171	168.67
375.2279	259.6980	37.80000	169.90308	65.29000	98.80000	82.56981	167.91
381.9822	266.0282	38.43000	174.20720	66.32000	99.92149	84.40933	168.85
380.9760	265.8684	37.90000	173.71899	65.64000	98.80993	83.71330	169.64

2. Calculate weekly and monthly returns using log returns

prices_weekly <- to.weekly(asset_Prices, indexAt = "last", OHLC = FALSE)
prices_monthly <- to.monthly(asset_Prices, indexAt = "last", OHLC = FALSE)

day_ret <- na.omit(Return.calculate(asset_Prices))
wk_ret <- na.omit(Return.calculate(prices_weekly))
mon_ret <- na.omit(Return.calculate(prices_monthly))

6 first rows of weekly return data of 8 stocks

head(wk_ret)

##                     SPY         QQQ         EEM          IWM          EFA
## 2018-01-12  0.016458320  0.01587203  0.00773430  0.021771563  0.015894794
## 2018-01-19  0.008959258  0.01124657  0.01878421  0.002781900  0.008571578
## 2018-01-26  0.022003965  0.02759413  0.03251401  0.006305155  0.015108672
## 2018-02-02 -0.038837634 -0.03697415 -0.05817970 -0.036152964 -0.035880518
## 2018-02-09 -0.050644406 -0.05169793 -0.05361891 -0.045894933 -0.054583077
## 2018-02-16  0.044397796  0.05675840  0.06721249  0.044763889  0.041259697
##                     TLT          IYR          GLD
## 2018-01-12 -0.009466649 -0.029385867  0.013005641
## 2018-01-19 -0.011725044  0.006496679 -0.004253316
## 2018-01-26  0.004307018  0.016911983  0.013051804
## 2018-02-02 -0.030431453 -0.029325505 -0.013117888
## 2018-02-09 -0.013714629 -0.041590692 -0.012817486
## 2018-02-16  0.006528653  0.024290586  0.025567060

6 first rows of monthly return data of 8 stocks

head(mon_ret)

##                     SPY          QQQ          EEM          IWM          EFA
## 2018-02-28 -0.036360550 -0.012928193 -0.058984801 -0.038437145 -0.048348047
## 2018-03-29 -0.027410381 -0.040788178  0.005414345  0.012175598 -0.008396104
## 2018-04-30  0.005167986  0.005058538 -0.028168914  0.009813529  0.015212523
## 2018-05-31  0.024309305  0.056729268 -0.026214856  0.061635813 -0.018942506
## 2018-06-29  0.005750739  0.011450432 -0.045456882  0.006143667 -0.015841140
## 2018-07-31  0.037046545  0.027963940  0.035310428  0.016490703  0.028520395
##                     TLT          IYR          GLD
## 2018-02-28 -0.030414641 -0.066573262 -0.020759906
## 2018-03-29  0.028596624  0.037719661  0.006320008
## 2018-04-30 -0.020881163  0.002252159 -0.009539749
## 2018-05-31  0.020044130  0.033712143 -0.011959211
## 2018-06-29  0.006457664  0.040594847 -0.036149440
## 2018-07-31 -0.014368534  0.008314613 -0.022418912

Question 1: Find the GMVP for these eight assets using the derived asset returns data

cov_wk <- as.matrix(cov(wk_ret))
cov_mon <- as.matrix(cov(mon_ret))

wk_meanret <- colMeans(wk_ret)
mon_meanret <- colMeans(mon_ret)

wk_gmvp = globalMin.portfolio(wk_meanret,cov_wk)
mon_gmvp = globalMin.portfolio(mon_meanret,cov_mon)

wk_gmvp_weight <- as.data.frame(wk_gmvp$weights)
mon_gmvp_weight <- as.data.frame(mon_gmvp$weights)

gmvp <- mutate(wk_gmvp_weight, mon_gmvp_weight)
gmvp %>% kbl(align = "c", caption="Weekly and monthly GMVP weights of each stock ", col.names = c("Weekly","Monthly"), booktabs = TRUE)%>%
  row_spec(row =0, bold= TRUE, color = "black", background = "#F9EBEA") %>%
  kable_styling(bootstrap_options = "striped", full_width = F, position = "center") %>%
  kable_paper()

Weekly and monthly GMVP weights of each stock

	Weekly	Monthly
SPY	0.9920172	1.1924566
QQQ	-0.4595019	-0.7673268
EEM	0.1668419	0.0189774
IWM	-0.0741904	0.1903888
EFA	-0.1213636	-0.1510413
TLT	0.4855621	0.5703828
IYR	-0.2326814	-0.3098995
GLD	0.2433162	0.2560620

The return of weekly GMVP is:

head(wk_gmvp$er)

## [1] 0.0004881287

The return of weekly GMVP is:

head(mon_gmvp$er)

## [1] 0.001731834

Question 2: Given the portfolio return is specified as 0.045 annual rate. Try to find the optimal weights for the minimum variance portfolio

We calculate the optimal weights for weekly and monthly minimum variance portfolio by using matrix algebra and the Lagrangian Function:

#First, we find solve the matrix to find the weekly optimal weights
mu <- 0.045/52 #calculate weekly rate
Ax <- rbind(2*cov_wk, wk_meanret, rep(1, 8))
Ax <- cbind(Ax, rbind(t(tail(Ax, 2)), matrix(0, 2, 2)))
b0 <- matrix(c(rep(0, 8), mu, 1),ncol=1)
out <- solve(Ax, b0)
wgt_wk <- as.data.frame(out[1:8], row.names = asset.names)
sum(wgt_wk) #checking the sum of weights 

## [1] 1

#Then apply the same calculation to find monthly optimal weights
mu <- 0.045/12
Ax <- rbind(2*cov_mon, mon_meanret, rep(1, 8))
Ax <- cbind(Ax, rbind(t(tail(Ax, 2)), matrix(0, 2, 2)))
b0 <- matrix(c(rep(0, 8), mu, 1),ncol=1)
out <- solve(Ax, b0)
wgt_mon <- as.data.frame(out[1:8], row.names = asset.names)
sum(wgt_mon)

## [1] 1

wgt <- cbind(wgt_wk, wgt_mon)
wgt %>% kbl(align = "c", caption="Weekly and monthly optimal weights of each stock in minimum variance portfolio ", col.names = c("Weekly","Monthly"), booktabs = TRUE)%>%
  row_spec(row =0, bold= TRUE, color = "black", background = "#F9EBEA") %>%
  kable_styling(bootstrap_options = "striped", full_width = F, position = "center") %>%
  kable_paper()

Weekly and monthly optimal weights of each stock in minimum variance portfolio

	Weekly	Monthly
SPY	1.0759005	1.3335744
QQQ	-0.4015915	-0.7064535
EEM	0.0884024	-0.0449001
IWM	-0.0962369	0.1495385
EFA	-0.1668206	-0.2471827
TLT	0.4265152	0.4885667
IYR	-0.2435865	-0.3155997
GLD	0.3174174	0.3424566

Question 3: Find the tangency portfolio based on Q2. Risk-free rate is assumed to be zero

The tangency portfolio is the portfolio of risky assets that maximizes Sharpe’s slope. We use Lagrangian function to compute the optimal weights of portfolio in weekly and monthly data:

#Compute the optimal weights for weekly data
ax <- inv(cov_wk)%*%wk_meanret
mt1x8 <- matrix(rep(1,8)) #matrix of 1
bx <- t(mt1x8)%*%ax
tangency_w <- ax/as.vector(bx)
sum(tangency_w) #checking the sum of 8 weights

## [1] 1

#Compute the optimal weights for monthly data
ax <- inv(cov_mon)%*%mon_meanret
bx <- t(mt1x8)%*%ax
tangency_m <- ax/as.vector(bx)
sum(tangency_w)

## [1] 1

tangency <- cbind(tangency_w,tangency_m)
row.names(tangency) <- symbols
tangency %>% kbl(align = "c", caption="Weekly and monthly optimal weights of each stock in tangency portfolio ",  col.names = c("Weekly","Monthly"), booktabs = TRUE)%>%
  row_spec(row =0, bold= TRUE, color = "black", background = "#F9EBEA") %>%
  kable_styling(bootstrap_options = "striped", full_width = F, position = "center") %>%
  kable_paper()

Weekly and monthly optimal weights of each stock in tangency portfolio

	Weekly	Monthly
SPY	2.8906406	4.2186592
QQQ	0.8512486	0.5380703
EEM	-1.6085653	-1.3508447
IWM	-0.5731913	-0.6856272
EFA	-1.1502416	-2.2127459
TLT	-0.8509115	-1.1841255
IYR	-0.4795082	-0.4321382
GLD	1.9205286	2.1087520

Problem 2: BERNDT Data

Question 4: Compute GMVP (global minimum variance portfolio) weights and its return by using the covariance derived from single index model.

At first, we load the data from excel

data <- read_excel("C:/Users/admin/Downloads/berndt.xlsx")
attach(data)
dim(data)

## [1] 120  17

We separate data into 2 data frame of stocks return data and market return data. With the market return, we compute by taking the MARKET column minus RKFREE column:

mrkret <- data %>% select(MARKET,RKFREE) %>% mutate(market=MARKET-RKFREE) %>% select(-c(MARKET,RKFREE))
stockret <- data %>% select(-c(MARKET,RKFREE))
mrkret <- as.matrix(mrkret)
stockret <- as.matrix(stockret)
TT <- dim(stockret)[1]
TT #checking the dimension of matrix stockret

## [1] 120

ones = rep(1, 120) #create a matrix 1x120 of number 1

Covariance

We use the single index model (method 2) to compute the covariance of 15 stocks

X = as.matrix(cbind(ones, mrkret))
Y = stockret
b_hat = solve(t(X)%*%X)%*%t(X) %*% Y
E_hat = Y - X %*% b_hat
# Excluding constant term
b_hat = as.matrix(b_hat[-1,])
diagD_hat = diag(t(E_hat) %*% E_hat)/(TT-2)
# Covariance matrix by single factor model 
cov = as.numeric(var(mrkret))*b_hat%*%t(b_hat) + diag(diagD_hat)
cov %>% kbl(align = "c", caption="Covariance of 15 stocks")%>% 
             row_spec(row =0, bold= TRUE, color = "black", background = "#FFE4B5") %>%
             column_spec(column = 1, bold = TRUE, color = "black") %>%
             kable_styling(bootstrap_options = "striped", full_width = F, position = "center") %>%
             kable_paper() %>%
             scroll_box(width = "100%", height = "400px")

Covariance of 15 stocks

	CITCRP	CONED	CONTIL	DATGEN	DEC	DELTA	GENMIL	GERBER	IBM	MOBIL	PANAM	PSNH	TANDY	TEXACO	WEYER
CITCRP	0.0065945	0.0002777	0.0022678	0.0032029	0.0026307	0.0015148	0.0008299	0.0019387	0.0014121	0.0022166	0.0022784	0.0006530	0.0032627	0.0019001	0.0025472
CONED	0.0002777	0.0025484	0.0003045	0.0004301	0.0003533	0.0002034	0.0001115	0.0002603	0.0001896	0.0002977	0.0003060	0.0000877	0.0004382	0.0002552	0.0003421
CONTIL	0.0022678	0.0003045	0.0228816	0.0035125	0.0028850	0.0016613	0.0009102	0.0021261	0.0015486	0.0024309	0.0024987	0.0007161	0.0035781	0.0020838	0.0027935
DATGEN	0.0032029	0.0004301	0.0035125	0.0163622	0.0040747	0.0023463	0.0012855	0.0030027	0.0021872	0.0034333	0.0035290	0.0010114	0.0050535	0.0029430	0.0039453
DEC	0.0026307	0.0003533	0.0028850	0.0040747	0.0098844	0.0019271	0.0010558	0.0024663	0.0017965	0.0028200	0.0028986	0.0008307	0.0041508	0.0024173	0.0032405
DELTA	0.0015148	0.0002034	0.0016613	0.0023463	0.0019271	0.0092715	0.0006080	0.0014202	0.0010345	0.0016238	0.0016691	0.0004783	0.0023901	0.0013919	0.0018660
GENMIL	0.0008299	0.0001115	0.0009102	0.0012855	0.0010558	0.0006080	0.0042633	0.0007781	0.0005668	0.0008897	0.0009145	0.0002621	0.0013095	0.0007626	0.0010223
GERBER	0.0019387	0.0002603	0.0021261	0.0030027	0.0024663	0.0014202	0.0007781	0.0077478	0.0013239	0.0020781	0.0021361	0.0006122	0.0030588	0.0017814	0.0023881
IBM	0.0014121	0.0001896	0.0015486	0.0021872	0.0017965	0.0010345	0.0005668	0.0013239	0.0035052	0.0015137	0.0015559	0.0004459	0.0022281	0.0012976	0.0017395
MOBIL	0.0022166	0.0002977	0.0024309	0.0034333	0.0028200	0.0016238	0.0008897	0.0020781	0.0015137	0.0064838	0.0024424	0.0007000	0.0034974	0.0020368	0.0027305
PANAM	0.0022784	0.0003060	0.0024987	0.0035290	0.0028986	0.0016691	0.0009145	0.0021361	0.0015559	0.0024424	0.0174986	0.0007195	0.0035950	0.0020936	0.0028066
PSNH	0.0006530	0.0000877	0.0007161	0.0010114	0.0008307	0.0004783	0.0002621	0.0006122	0.0004459	0.0007000	0.0007195	0.0120838	0.0010303	0.0006000	0.0008043
TANDY	0.0032627	0.0004382	0.0035781	0.0050535	0.0041508	0.0023901	0.0013095	0.0030588	0.0022281	0.0034974	0.0035950	0.0010303	0.0163674	0.0029980	0.0040190
TEXACO	0.0019001	0.0002552	0.0020838	0.0029430	0.0024173	0.0013919	0.0007626	0.0017814	0.0012976	0.0020368	0.0020936	0.0006000	0.0029980	0.0063917	0.0023405
WEYER	0.0025472	0.0003421	0.0027935	0.0039453	0.0032405	0.0018660	0.0010223	0.0023881	0.0017395	0.0027305	0.0028066	0.0008043	0.0040190	0.0023405	0.0072710

Global minimum variance portfolio

stock_mean <- colMeans(stockret,na.rm = TRUE)
stock.names <- names(stock_mean) 
cov.mat <- as.matrix(cov)
dimnames(cov.mat) = list(stock.names, stock.names)
stock.gmvp = globalMin.portfolio(stock_mean,cov.mat)
attributes(stock.gmvp)

## $names
## [1] "call"    "er"      "sd"      "weights"
## 
## $class
## [1] "portfolio"

w_gmvp <- as.data.frame(stock.gmvp$weights)
w_gmvp %>%  kbl(align = "c", caption="", col.names = "Optimal weight")%>% 
            row_spec(row =0, bold= TRUE, color = "black", background = "#FFE4B5") %>%
            kable_styling(bootstrap_options = "striped", full_width = F, position = "center") %>%
             kable_paper()

	Optimal weight
CITCRP	0.0443133
CONED	0.3755073
CONTIL	0.0057706
DATGEN	-0.0236873
DEC	-0.0050185
DELTA	0.0526752
GENMIL	0.1816517
GERBER	0.0428599
IBM	0.1859635
MOBIL	0.0338142
PANAM	0.0075571
PSNH	0.0662851
TANDY	-0.0262830
TEXACO	0.0581522
WEYER	0.0004386