1 Introdução

Este relatório apresenta uma análise quantitativa de carteiras baseada na Teoria Moderna de Portfólios de Markowitz, utilizando dados diários do Yahoo Finance no período de 2021 a 2025.

Objetivos do Presente Relatorio:

Coletar preços históricos
Calcular retornos logarítmicos
Avaliar risco, retorno e correlações
Estimar Betas (CAPM)
Simular carteiras de 3 ativos
Determinar fronteira eficiente
Identificar a melhor relação risco/retorno

2 Carregamento das Bibliotecas de Pacote

pkgs <- c("quantmod","tidyverse","PerformanceAnalytics",
          "plotly","moments","PortfolioAnalytics",
          "combinat","GGally","kableExtra")

lapply(pkgs, require, character.only = TRUE)

require(quantmod)
library(PerformanceAnalytics)
library(PortfolioAnalytics)
library(knitr)
library(xts)
library(tidyverse)

3 Tickers das Empresas Análisadas

start_date <- "2021-01-01"
end_date   <- "2025-12-31"

tickers_acoes <- c(
  "PETR4.SA","VALE3.SA","WEGE3.SA","AMER3.SA","BBAS3.SA","ITUB4.SA",
  "SUZB3.SA","KLBN11.SA","ALPA4.SA","EQTL3.SA","PRIO3.SA","BBDC4.SA",
  "PSSA3.SA","MGLU3.SA","GOAU4.SA","JBSS32.SA","GMAT3.SA","BNBR3.SA",
  "MELI34.SA","GUAR3.SA"
)



# baixar ações
getSymbols(tickers_acoes, src="yahoo", from=start_date, to=end_date)

# baixar IBOV separado
getSymbols("^BVSP", src="yahoo", from=start_date, to=end_date)

4 Coleta de Dados na Base de Dados do Yahoo Finance

# baixar ações
getSymbols(tickers_acoes, src="yahoo", from=start_date, to=end_date)

##  [1] "PETR4.SA"  "VALE3.SA"  "WEGE3.SA"  "AMER3.SA"  "BBAS3.SA"  "ITUB4.SA" 
##  [7] "SUZB3.SA"  "KLBN11.SA" "ALPA4.SA"  "EQTL3.SA"  "PRIO3.SA"  "BBDC4.SA" 
## [13] "PSSA3.SA"  "MGLU3.SA"  "GOAU4.SA"  "JBSS32.SA" "GMAT3.SA"  "BNBR3.SA" 
## [19] "MELI34.SA" "GUAR3.SA"

# baixar IBOV separado
getSymbols("^BVSP", src="yahoo", from=start_date, to=end_date)

## [1] "BVSP"

get_adj <- function(x) Ad(get(x))

prices_acoes <- do.call(merge, lapply(tickers_acoes, get_adj))

ibov <- Ad(BVSP)
colnames(ibov) <- "IBOV"


prices <- merge(prices_acoes, ibov)
prices <- na.omit(prices)

kable(prices, caption = "Empresas da Amostra Financeira")

Empresas da Amostra Financeira
PETR4.SA.Adjusted	VALE3.SA.Adjusted	WEGE3.SA.Adjusted	AMER3.SA.Adjusted	BBAS3.SA.Adjusted	ITUB4.SA.Adjusted	SUZB3.SA.Adjusted	KLBN11.SA.Adjusted	ALPA4.SA.Adjusted	EQTL3.SA.Adjusted	PRIO3.SA.Adjusted	BBDC4.SA.Adjusted	PSSA3.SA.Adjusted	MGLU3.SA.Adjusted	GOAU4.SA.Adjusted	JBSS32.SA.Adjusted	GMAT3.SA.Adjusted	BNBR3.SA.Adjusted	MELI34.SA.Adjusted	GUAR3.SA.Adjusted	IBOV
28.49225	49.25279	40.42318	5.66	21.42678	32.62405	52.15984	17.04288	7.789287	34.91918	42.57	14.84493	50.68995	9.047619	7.081171	76.30	7.618500	91.95474	110.80	5.855272	136436
29.44042	48.82131	40.41363	5.42	21.28752	32.92310	51.85641	16.69431	7.729238	34.90959	43.31	15.30444	50.85478	9.085714	6.803478	76.65	7.676805	91.95474	109.96	5.840833	137128
30.10413	48.50000	40.38496	5.42	21.30741	33.17684	51.82705	16.85025	7.746394	35.03426	43.22	15.45448	51.76619	9.161904	6.759632	76.10	7.725391	91.95474	109.23	5.876932	137800
30.84369	47.85737	40.50919	5.34	21.47652	32.77811	52.96245	16.86860	7.849336	34.90959	43.98	15.27631	51.37836	8.514285	6.715786	76.68	7.560195	92.68446	109.30	5.783074	137213
30.54028	49.41804	40.65254	5.44	21.86447	33.37621	53.09948	16.98784	7.892229	35.40829	43.18	15.60453	52.05707	9.085714	6.766939	78.15	7.696239	92.43150	111.95	5.920250	139256
31.23244	47.19638	39.57267	5.70	21.78489	33.57558	51.52362	16.51086	7.815022	35.13976	44.03	15.83897	52.27037	8.885714	6.715786	76.00	7.773979	91.94501	109.99	5.898591	138840
31.20400	47.04032	40.00270	5.85	21.69536	33.37621	51.69002	16.54755	7.857914	35.06304	43.70	15.71706	52.00859	8.904761	6.701169	74.85	7.725391	92.43150	110.00	5.934690	138717
31.11866	45.82850	39.79247	5.83	21.23778	33.20403	50.76995	16.14395	7.772130	34.45883	43.56	15.58577	51.87284	8.428571	6.511170	75.18	7.511608	87.56668	109.73	5.790294	137116
30.34117	46.40687	39.84424	6.65	20.97915	33.13154	50.65250	16.19899	7.883650	34.14234	43.25	15.46386	51.79528	8.485714	6.540400	73.06	7.511608	87.56668	112.81	5.840833	136551
29.74383	46.39769	39.69099	6.06	21.32730	33.75682	50.75038	16.24485	7.952279	34.52596	41.56	15.51075	52.34794	8.666666	6.525785	75.00	7.705957	87.56668	116.30	6.035767	137165
29.59212	46.34261	40.05495	5.90	21.14825	33.14965	50.39801	16.14395	7.875072	33.74913	41.03	15.37946	52.26068	8.695238	6.401554	75.92	7.637935	87.56668	117.79	6.028548	135767
29.82916	47.73803	41.25220	5.86	21.48647	32.90498	50.51547	16.40996	8.055222	34.02726	41.85	15.52013	52.87151	8.971428	6.518477	80.11	7.783697	87.56668	117.25	6.064647	137114
29.59212	48.53672	40.56258	5.93	21.61578	32.86873	50.06522	16.40996	7.917964	33.83545	41.87	15.53888	53.00183	8.857142	6.445400	80.15	7.741605	91.12772	117.00	6.122405	136866
29.75331	48.33475	40.97444	5.67	21.97389	33.48496	50.12395	16.92363	7.935121	34.48760	42.40	15.78270	53.99965	9.380952	6.525785	78.21	8.006191	90.49530	118.49	6.172944	138855
29.85761	48.98656	40.70626	5.42	21.79483	33.63696	49.76180	16.93280	8.089535	34.65064	41.80	15.92319	53.57900	9.247619	6.525785	76.12	8.055189	90.49530	113.41	6.288461	139549
30.38858	50.76755	40.63921	5.34	21.87441	33.36496	50.61335	17.41896	7.420411	33.94094	42.16	15.63549	53.41270	8.638095	6.737709	74.85	7.751404	88.74397	111.26	5.970789	139051
30.49288	50.52887	40.90739	5.40	22.18278	34.19002	50.95592	17.92345	7.617716	34.58351	42.58	16.00822	55.37899	8.752380	6.840016	74.51	7.878798	93.39472	112.81	6.324561	140928
30.45495	50.67575	41.18515	5.36	22.31210	34.20815	50.84826	17.84090	7.669187	34.59310	42.58	15.93177	55.42790	8.809523	6.847324	75.30	7.917995	93.39472	111.09	6.375099	141478
30.39806	49.93214	40.54343	5.34	21.94405	33.75482	49.92819	17.30888	7.523353	33.87381	41.76	15.77885	54.04856	8.676190	6.891170	75.17	7.859199	93.16122	113.70	6.158504	139490
30.83421	50.10657	38.89603	5.32	21.88436	33.67323	49.84989	17.09791	7.557667	33.78749	43.08	15.81708	53.15835	8.476190	6.891170	72.44	7.957194	97.05307	112.23	6.086307	139303
30.64458	49.61083	38.41713	5.17	21.33725	32.97510	48.93961	16.97867	7.514775	33.27919	42.57	15.63549	51.73010	8.142857	6.876555	71.92	7.790602	97.05307	113.83	6.035767	137481
30.56873	50.74919	38.21599	5.19	21.09851	31.95965	48.79279	17.18047	7.386096	33.02984	41.80	15.42524	51.90619	7.942857	6.913094	73.77	7.849400	97.05307	111.86	5.985229	136743
30.93851	51.41018	38.07232	5.16	21.02888	31.69671	48.84174	17.02453	7.343204	32.94352	42.72	15.33922	51.21162	7.657142	6.810785	74.09	7.790602	89.32774	110.60	5.739755	136187
30.53080	50.82264	37.86161	5.18	20.57130	31.64232	48.89067	17.42813	7.231684	32.75171	42.90	15.39656	51.66162	7.571428	6.810785	72.87	7.594613	89.57098	111.12	5.768634	135299
30.29376	49.49148	37.99570	5.12	20.79014	31.75111	49.42901	17.51068	7.403254	33.05861	42.12	15.38701	51.43662	7.666666	6.730401	71.90	7.643610	89.57098	111.00	5.941909	135250
30.14206	49.94132	39.38450	5.07	20.77025	31.90524	49.44859	17.48317	7.437568	32.95312	42.39	15.34878	50.39967	7.723809	6.752324	74.10	7.741605	89.57098	111.60	5.775854	135511
29.83864	49.84951	40.31356	5.10	20.63099	32.38577	49.42901	17.51068	7.497617	33.11615	43.30	15.32011	50.86923	7.809523	6.628093	74.73	7.761204	89.60990	109.07	5.876932	135565
29.38353	50.08821	40.58175	5.10	20.15351	31.79644	49.53667	17.21716	7.317469	32.81885	43.29	14.97605	50.68337	7.504761	6.576938	73.71	7.555414	89.60990	112.53	5.552040	133382
29.44042	51.45609	40.19863	5.00	19.75561	32.16818	49.91840	17.19881	7.343204	32.93393	42.76	14.98561	50.91814	7.238095	6.803478	72.50	7.457419	89.60990	110.30	5.494281	134167
29.72486	52.78724	39.57606	4.94	19.78545	31.73299	50.17289	17.07957	7.231684	32.54072	42.58	14.93782	50.47793	7.142857	6.869247	73.70	7.359424	89.60990	111.17	5.725315	134036
30.33169	52.71380	36.40576	5.06	20.10377	32.08658	50.65250	17.14377	7.377519	33.18329	42.47	15.17675	50.96706	7.428571	7.037325	73.24	7.457419	89.60990	110.44	5.797513	135368
30.28428	51.89674	34.70089	5.07	19.96451	31.78737	50.40780	17.13460	7.283154	32.75171	42.30	14.98561	50.50728	7.180952	7.037325	74.21	7.281028	89.60990	110.30	5.725315	133808
30.32221	51.13477	34.64342	5.24	20.13361	31.92338	51.45511	17.40979	7.283154	32.49277	41.90	14.87092	50.18445	7.142857	6.971555	74.17	7.428021	89.60990	109.39	5.694315	133524
30.36013	50.63903	35.34734	5.16	19.83519	31.25245	51.04402	17.12543	7.163056	32.12833	41.48	14.75624	49.63663	6.838095	6.840016	75.79	7.212432	89.60990	109.78	5.437815	132129
30.75836	50.32690	35.20298	5.30	19.84514	31.43379	50.75038	17.01536	7.223105	32.38727	41.97	14.72757	49.99859	6.647619	6.803478	75.15	7.183033	93.39472	110.68	5.540415	132726
31.07125	49.42722	35.46281	5.26	19.79540	31.79644	51.07338	17.13460	7.334626	33.11615	42.72	14.96649	50.58554	6.990476	6.927709	74.88	7.281028	94.86390	111.43	5.686987	133990
30.94799	49.07836	35.71303	5.18	19.59645	31.87804	51.04402	17.06122	7.343204	32.67499	42.19	14.84225	50.76163	6.723809	6.847324	76.89	7.183033	96.80983	111.35	5.665001	133071
30.54028	49.34459	35.78040	5.15	18.25355	31.68542	50.64271	16.88694	7.411833	32.92435	40.99	14.87092	51.13336	6.876190	6.569631	75.35	7.222231	97.05307	109.70	5.621030	132437
30.49288	49.73935	35.67453	5.17	18.62160	32.02105	49.69328	16.83191	7.386096	32.84762	40.48	14.98477	52.12140	6.838095	6.613477	76.38	7.222231	88.59801	107.00	5.811573	132971
30.63510	49.67509	35.73228	5.16	18.52213	32.37483	49.88904	16.40079	7.411833	32.81885	40.62	15.01347	51.80836	6.857142	6.584246	76.30	7.222231	92.43150	111.10	5.708972	133151
30.67302	49.36296	36.72350	5.17	18.60171	32.78302	50.52525	16.71266	7.617716	32.89557	39.79	14.99434	51.87683	6.990476	6.503862	75.75	7.418221	92.43150	106.00	5.936159	134538
30.84369	49.72099	37.53188	5.39	18.81060	33.36358	52.99181	17.04288	7.737816	33.70118	39.65	15.10916	51.69097	7.066666	6.598862	76.75	7.506417	92.43150	105.06	6.742304	136528
28.94737	50.85018	36.66576	5.57	18.83050	33.59035	53.42248	17.37309	8.364046	34.14234	39.54	15.27183	52.34640	6.704761	6.671939	76.93	7.428021	92.43150	105.78	6.595732	135913
29.12752	50.79510	35.81889	5.76	18.99961	33.79899	52.93309	17.14158	8.115270	33.61486	39.13	15.21442	52.23879	6.685714	6.664632	77.49	7.339825	92.78176	103.50	6.441832	135623
29.20337	51.32756	35.23185	5.67	19.13887	34.49747	52.94287	17.10439	8.458410	34.85204	39.27	15.56847	53.81378	6.695238	6.745728	76.70	7.486818	92.78176	105.28	6.566418	137914
28.98530	51.39920	35.24147	5.27	19.17866	34.17091	52.71775	16.82552	8.201056	34.21907	38.87	15.43450	53.81378	6.409523	6.753100	78.46	6.967444	93.40446	104.60	6.053417	136687
28.61552	50.76252	35.11637	5.14	19.74566	34.12555	52.76669	17.04861	8.132426	34.04644	38.80	15.31968	52.17031	6.361904	6.686749	74.99	6.898848	95.35038	104.93	5.965474	136356
28.60603	50.66750	34.61594	4.94	20.54146	34.00763	52.19899	16.75115	8.063799	34.43006	38.81	15.33881	51.22141	6.304761	6.701494	76.79	6.898848	96.32335	107.80	5.980130	136341
28.78619	50.55347	35.03938	4.97	20.95925	34.25254	51.48447	16.74185	8.166741	34.46842	37.59	15.64502	51.95510	6.580952	6.767846	80.90	6.928246	96.80983	106.84	6.229302	137322
28.48277	50.59148	34.25987	4.93	19.69592	33.25730	51.88578	16.71396	7.969436	33.59568	36.85	15.10916	50.68337	6.533333	6.657259	83.33	6.634261	96.80983	106.70	5.980130	134432
28.65344	50.36342	34.71218	4.98	19.75561	33.27561	51.37681	16.71396	7.926543	33.84504	37.30	15.15700	51.48553	6.361904	6.627770	81.95	6.702858	100.15682	106.83	6.068073	134667
28.71981	50.79103	34.55820	4.93	19.58650	33.31226	51.19083	16.66749	7.737816	33.28878	37.50	15.10916	49.69533	6.361904	6.568791	83.50	6.644061	96.00000	106.73	5.906845	134511
29.54590	52.06437	36.08835	5.10	20.39225	34.24650	52.61987	17.08580	8.106691	34.28620	38.05	15.60674	49.92033	6.571428	6.789962	82.86	6.800853	96.00000	109.90	6.251288	137968
29.72044	52.18790	36.30969	5.26	19.94461	34.07248	52.27729	17.05791	8.123849	34.19030	38.18	15.64502	50.42902	6.780952	6.893176	84.08	6.771454	97.00000	108.15	6.295260	138025
29.50711	52.65353	36.17496	5.38	20.27288	33.84350	51.49426	16.99284	8.226790	34.17112	37.73	15.60674	49.88120	6.666666	6.915292	86.00	6.791053	97.99000	108.60	6.309917	137771
29.73014	52.62502	36.31932	5.60	20.52156	34.41137	51.85641	17.07650	8.278262	34.76573	38.35	15.72157	50.36054	6.838095	6.959527	89.60	6.859650	94.00000	108.38	6.537104	139206
29.99195	52.64403	36.39630	6.02	20.93935	35.12579	51.70959	17.12298	8.123849	35.13976	38.58	16.06605	51.65184	7.466666	6.966900	88.05	7.104637	94.00000	111.22	6.925519	141049
30.15679	52.79607	36.24232	6.58	21.27757	35.25402	51.33765	17.20665	8.149585	35.07262	37.87	16.10432	50.62467	7.800000	6.974272	87.26	7.153635	96.50000	112.25	6.940176	141422
30.22467	52.83408	36.38668	6.14	20.97915	35.53593	51.43553	17.04861	8.389782	34.81368	37.97	15.99906	50.69315	7.885714	7.003762	88.15	7.016441	96.75000	111.20	6.859561	141125
30.37982	52.63453	36.26157	6.84	20.31267	34.93114	51.15168	16.97425	8.364046	34.42047	37.99	15.81607	50.34097	7.761904	7.011134	88.10	6.918447	96.75000	109.00	6.749633	140335
30.11801	52.83408	36.42517	6.20	20.17340	34.62875	50.86784	16.93707	8.321154	34.12316	37.51	15.80649	49.63663	7.828571	6.915292	87.17	6.889049	96.75000	107.65	6.888875	139864
30.11801	52.93860	35.84776	6.40	20.31267	34.76620	50.57419	17.15087	8.655717	34.37251	37.32	16.12262	50.32141	8.238095	7.025878	86.73	7.036041	96.01000	109.61	6.844904	140993
29.66226	53.42324	36.42517	6.17	21.03883	35.15107	50.88741	17.21594	8.964542	35.09181	36.55	16.51538	49.84207	8.828571	7.188071	87.24	7.134036	96.01000	108.53	6.998805	142640
29.77862	53.55627	36.03061	6.58	20.83988	34.98612	50.50568	17.32749	8.818707	34.92876	36.59	16.42916	48.96164	8.485714	7.247050	84.98	6.996842	96.00000	106.33	6.830247	141792
30.01134	53.39473	35.58792	6.50	21.28752	34.68373	50.80910	17.48552	8.792973	34.72737	37.09	16.27589	48.95185	8.495238	7.143836	84.88	6.918447	96.00000	107.15	6.830247	141618
30.55436	53.76533	35.87663	6.63	21.93410	34.71123	49.72264	17.16946	8.681452	34.95754	37.63	16.16094	49.47033	8.809523	7.033251	84.77	6.869450	99.99000	105.77	6.859561	142349
30.43800	54.18344	35.44357	6.73	22.10320	34.77537	50.45674	17.36468	8.732923	34.93836	37.91	16.31421	49.32359	9.523809	7.077486	84.84	6.918447	99.99000	104.98	6.910862	143151
30.23437	54.16443	35.55906	6.83	22.19273	34.25305	49.36049	17.24383	8.552773	34.68900	38.15	16.12262	48.99099	9.380952	6.819452	84.37	6.898848	99.99000	104.39	6.778947	142272
30.49618	54.63956	35.13562	6.83	21.75504	34.82119	49.42901	17.10439	8.604245	35.06304	37.97	16.31421	49.20620	10.076190	6.996389	83.78	6.859650	99.00000	103.29	7.328591	143547
30.57375	54.82961	35.38583	7.42	21.82468	34.72955	49.60519	17.03002	8.612823	34.76573	38.47	16.27589	49.46055	10.228571	7.011134	83.49	6.889049	99.00000	105.08	7.475163	144062
30.75799	54.92463	35.32809	7.99	21.75504	35.22438	49.82053	17.15087	8.612823	35.15894	38.24	16.84109	49.79316	10.771428	7.055368	82.45	6.938046	98.50000	107.99	7.379891	145594
30.45739	54.82011	35.34734	8.07	21.98384	35.27020	49.65413	16.99284	8.518460	35.11099	38.89	16.66865	50.06707	10.695238	7.062741	82.58	6.889049	98.50000	109.96	7.255305	145500
30.11801	55.03866	34.98164	7.45	21.50636	35.73753	49.42901	17.03002	8.372626	35.66724	38.06	16.96563	50.56597	10.580952	7.018507	82.42	6.977243	97.00000	107.97	7.101405	145865
30.41860	55.11469	35.71303	7.10	21.39694	35.22438	49.28219	16.91847	8.432675	35.08222	38.18	16.99437	50.10619	10.323809	7.040624	81.01	6.898848	97.00000	108.85	7.218663	145109
30.93253	54.80110	35.31847	7.05	22.01368	35.78335	49.06686	16.82552	8.338312	35.71519	38.58	17.09974	49.93989	10.476190	7.136464	80.50	6.987043	97.00000	109.78	6.940176	146425
31.63069	55.01015	35.50131	7.13	21.99378	35.54510	48.89067	16.89059	8.295419	35.40829	38.91	16.96563	50.07685	10.361904	7.077486	80.21	6.918447	98.02000	111.06	7.064762	146492
31.37858	55.31424	34.98164	6.56	21.67547	35.26103	49.17452	16.91847	8.158163	35.13017	39.15	16.83151	49.01055	10.495238	7.018507	79.15	6.781254	98.02000	111.29	6.866890	145306
31.27192	54.24995	34.95277	6.76	21.99378	35.43514	48.40128	16.91847	8.166741	35.22607	39.24	16.91773	48.31227	10.657142	7.018507	77.89	6.793708	100.55000	110.43	7.028119	145447
30.84526	54.43050	35.10744	6.54	22.00373	35.63673	48.12721	16.64890	8.149585	35.49461	38.91	17.09016	49.07364	10.114285	7.092230	80.35	6.922452	101.00000	110.50	6.896204	146337
30.50587	54.71558	35.31981	6.11	21.97389	35.80168	48.84174	16.76974	8.080956	35.43707	38.13	17.23353	49.30106	9.142857	7.018507	79.59	6.882838	102.00000	104.10	6.940176	146237
30.42830	55.40926	34.54758	6.11	21.81473	35.15779	48.83194	16.95566	8.209634	35.21649	38.39	16.94127	48.54958	9.142857	7.188071	78.69	6.823418	101.00000	97.09	6.984148	145517
30.13740	55.77986	34.87577	6.17	21.64562	34.77274	49.03749	16.83481	8.106691	34.76573	38.30	16.66720	48.31227	8.723809	7.261795	78.12	6.773901	103.00000	100.28	6.778947	143950
30.05983	55.67533	35.13640	5.89	21.46657	35.02944	49.62477	16.96495	8.149585	34.76573	38.24	16.67695	47.47180	8.714285	7.379753	76.42	6.773901	103.00000	96.67	6.918190	144201
29.78832	56.62559	34.44139	6.01	21.29746	34.62607	48.45022	16.52805	8.149585	34.63146	37.91	16.57942	46.48301	8.533333	7.409242	71.74	6.595641	100.55000	95.42	6.734975	143608
29.89498	55.82737	34.48966	5.58	21.09851	34.07601	47.85315	16.36072	7.995170	33.77790	37.73	16.30635	45.58321	8.552380	7.261795	70.52	6.387670	99.50000	97.15	6.581075	141356
29.72044	56.25499	34.26764	5.76	21.00899	34.14018	46.81564	16.27706	8.141006	33.84504	37.64	16.56967	45.06904	8.657142	7.431360	68.46	6.397573	99.50000	97.30	6.610390	142145
29.29378	56.16947	35.90863	5.79	21.07862	34.08517	46.67860	16.28636	8.020906	33.88340	37.28	16.65745	45.85018	8.542857	7.446105	67.57	6.318347	98.56000	101.38	6.485804	141708
29.03197	55.94140	35.41633	5.48	20.50167	34.04850	47.16800	16.14692	8.149585	33.80667	36.02	16.43313	45.82052	8.390476	7.401870	69.52	6.278733	98.56000	97.08	6.456489	140680
29.31318	56.77763	36.52641	5.35	20.77025	34.18602	47.18757	16.28636	8.115270	33.94094	36.30	16.50140	46.14682	8.190476	7.556691	68.35	6.249023	98.56000	98.30	6.830247	141783
29.10955	56.77763	36.03412	5.35	20.59120	34.33270	46.97224	16.22128	8.080956	33.81627	35.32	16.73546	46.08749	8.361904	7.549318	69.71	6.140086	97.52000	98.58	6.852233	141683
28.84774	57.83241	36.12099	5.30	20.21319	34.33270	46.61988	16.26777	8.132426	34.22866	34.60	16.93052	46.15671	8.485714	7.667276	69.19	6.189603	97.52000	93.70	6.852233	142604
28.55684	57.30027	37.09593	5.09	20.26293	34.25019	46.78627	16.41650	8.252526	34.41088	34.20	17.12557	45.84029	7.809523	7.534573	69.24	6.110376	97.52000	92.35	7.050105	142200
28.82834	57.13873	38.75622	5.06	20.79014	34.36938	46.61988	16.08185	8.458410	34.84246	36.12	17.24260	45.81063	8.000000	7.630414	70.51	6.149990	97.52000	91.50	6.984148	143399
28.84774	57.87042	38.16740	5.20	20.66083	34.98361	46.69818	16.23058	8.681452	35.00549	35.41	17.56444	46.66099	7.942857	7.733627	69.89	6.209410	100.55000	94.31	7.035448	144509
28.61502	57.77539	38.29288	5.23	20.43204	34.65357	46.47306	16.10044	8.844444	34.77532	35.15	17.33037	46.50278	7.961904	7.755744	68.71	6.159893	100.55000	96.36	7.086748	144085
28.94470	58.80167	38.63073	5.33	20.58125	34.93777	47.19736	16.37002	8.861600	35.07262	36.21	17.34988	46.69065	7.942857	7.682021	70.25	6.179699	100.55000	95.00	6.984148	144873
29.27439	58.68763	40.00144	5.27	20.54146	34.91026	47.63782	16.54664	9.058907	35.17812	36.86	17.53518	46.84886	7.495238	7.718883	68.86	6.219313	100.55000	96.30	7.350577	145721
28.93501	58.65913	39.93387	5.38	20.41214	34.86443	48.05870	16.69537	9.076063	35.58092	37.05	17.63271	46.55223	7.695238	7.740999	68.65	6.249023	100.00000	97.00	7.262634	146172
29.09015	58.59261	40.22345	5.43	20.74041	35.15779	48.06849	16.51875	9.144691	35.75355	37.00	17.77899	47.05651	8.114285	7.711510	69.11	6.298540	100.00000	102.54	7.299277	146969
29.08046	59.10575	40.85089	5.42	20.84983	35.27697	48.42085	16.83481	9.101798	34.61228	36.43	17.78874	47.46191	8.247619	7.836841	70.60	6.229217	100.00000	102.00	7.130719	147429
29.10955	60.17953	40.59026	5.50	21.10846	36.06538	48.05870	16.70467	9.084641	35.19730	36.00	18.36415	47.38280	8.123809	8.153853	69.75	6.229217	100.00000	101.84	7.350577	148633
28.98349	60.63566	40.01110	5.78	21.51631	36.01954	47.65739	16.71396	9.076063	35.30280	35.77	17.65221	48.01563	8.095238	7.999033	70.63	6.288637	102.58000	106.44	7.335920	148780
28.84774	62.01353	40.63853	5.50	21.78489	36.15706	47.85315	16.76974	9.076063	35.14935	36.03	17.71073	47.51135	8.066666	8.175970	71.49	6.377767	102.58000	104.48	7.423863	149540
29.18712	62.09904	41.31423	5.27	21.96394	36.76023	47.52036	16.71396	8.732923	36.06045	36.44	17.90578	47.49157	7.942857	8.058012	71.85	6.239120	105.00000	103.43	7.116062	150454
29.33257	61.40536	41.26596	5.10	22.15294	36.65017	48.36213	17.20665	9.050327	36.21390	36.75	17.96335	48.23317	7.980952	8.013778	72.26	6.179699	105.00000	104.45	7.284619	150704
29.91438	62.46014	41.99958	5.29	22.49116	36.80610	47.86294	17.34608	9.076063	36.97155	37.81	18.34410	48.38148	8.323809	8.227577	72.00	6.338153	104.75000	104.00	7.621735	153294
30.06952	62.24158	42.38570	5.10	22.73984	36.80610	47.61824	17.08580	9.016013	37.46982	38.46	18.26600	49.06375	7.609523	8.175970	71.85	6.357960	103.00000	94.65	7.892893	153339
31.20404	61.55740	43.43786	5.17	22.76968	36.84278	46.61008	16.98354	10.002542	37.65917	38.85	18.28552	49.03408	7.752380	8.183343	69.00	6.348057	103.00000	94.48	8.383908	154064
31.37858	61.96601	43.79501	5.32	22.66026	37.09042	45.70960	16.88999	10.285633	37.95813	39.23	18.62721	49.33072	8.019047	8.220205	69.61	6.268830	105.00000	92.50	7.658378	155257
32.19310	61.80447	44.43210	5.57	23.34663	37.80581	45.56278	16.85226	10.225584	38.98456	40.30	19.02748	45.56343	8.657142	8.205205	69.61	6.506511	105.04000	93.60	7.717007	157749
31.36888	62.48865	43.33168	5.55	22.68015	36.94367	47.05054	17.30493	10.354260	39.36325	40.01	18.97867	45.28657	8.714285	8.242706	69.78	6.367863	105.04000	93.50	7.738993	157633
31.50464	62.40313	43.26411	5.20	22.38173	37.09042	46.64924	16.99372	10.414311	39.14400	39.83	19.01772	45.97873	8.628571	8.130203	69.83	6.179699	105.04000	90.62	7.489820	157162
31.70827	62.02302	42.89730	5.13	22.32205	37.23717	46.35560	16.89942	10.560146	39.32338	39.79	19.00796	45.99850	9.133333	8.115202	70.22	5.545884	106.77000	90.10	7.599749	157739
31.88281	61.97551	42.44361	5.21	22.38173	36.96201	47.47142	17.05030	10.431468	39.12407	39.85	18.86152	45.58321	8.695238	8.055201	73.86	5.436947	106.77000	91.30	7.673035	156993
31.98947	61.78546	41.93201	5.49	21.76499	36.77858	47.50079	16.82397	10.500095	39.04435	40.04	18.63698	45.39534	9.019047	8.025200	73.33	5.268590	106.77000	92.29	7.709679	156522
31.82463	61.71894	42.13472	5.62	21.46657	36.54929	47.30503	16.77682	10.532555	38.77529	39.41	18.45148	44.75262	8.885714	7.942698	72.16	5.080426	106.77000	92.42	7.834264	155381
31.58221	61.91850	41.71965	5.61	21.88436	36.65935	47.28545	16.56935	10.427420	38.70553	38.80	18.34410	45.18769	9.171428	7.980199	73.80	4.980000	106.77000	87.84	7.746321	154770
31.55312	61.85198	41.69069	5.65	21.72520	36.52177	46.96245	16.34302	10.800169	38.61584	38.54	18.35386	45.97873	9.428571	8.077701	77.23	5.070000	107.10000	90.50	7.914879	155278
31.30100	62.33661	41.46867	6.13	21.85452	36.60432	46.78627	16.56935	10.675920	39.01446	37.52	18.50030	46.06772	9.771428	8.115202	78.00	5.030000	107.60000	92.33	7.973507	155910
31.25252	63.26786	42.85869	5.98	22.10320	37.46646	46.84500	16.71081	10.828842	39.56255	37.99	19.05677	46.97740	9.628571	8.302707	78.90	5.170000	107.60000	90.71	7.936864	158555
31.41737	63.03030	42.52084	6.02	22.04352	37.33805	47.17779	16.73910	11.067783	39.52269	37.71	19.01772	46.96751	9.638095	8.265206	78.50	5.100000	105.00000	91.48	7.966179	158292
30.82587	64.04707	42.71389	5.94	22.35189	38.19102	46.57094	16.72967	10.867072	39.62234	37.21	19.18369	46.66099	9.790476	8.250206	78.60	5.100000	105.00000	92.23	8.295965	159072
30.88405	64.54119	43.61161	6.15	22.14300	37.89525	46.47306	16.73910	10.800169	39.16394	37.56	18.89081	47.20483	9.847619	8.295207	79.65	5.030000	106.00000	92.70	8.281308	158611
31.09737	65.07334	44.02668	6.66	22.51417	38.73940	47.17779	16.84283	10.847958	40.06082	37.58	19.09502	47.51135	10.085714	8.295207	78.76	5.230000	107.50000	93.83	8.618423	161092
31.33010	67.17340	43.48612	6.95	22.38000	38.73940	47.91188	17.06916	10.819283	40.02096	39.33	18.56732	47.53112	10.704761	8.542713	78.58	5.160000	108.50000	94.29	8.545137	161755
31.53373	68.34221	44.36662	7.12	22.77000	39.69366	48.48937	17.33322	11.325841	41.10719	39.59	18.83117	48.04530	11.095238	8.587714	79.59	5.240000	107.50000	95.15	8.574451	164456
30.41860	66.72678	45.53673	6.72	21.16000	37.85854	49.42901	17.58784	10.628131	39.10415	39.26	17.70736	46.75987	10.009523	8.340208	78.20	4.920000	108.93000	93.92	7.438520	157369
30.69981	66.27065	46.58008	6.75	21.60000	38.04206	49.32134	17.63499	10.933976	38.79522	39.35	17.83440	47.51135	10.038095	8.302707	75.51	4.900000	108.93000	93.76	7.570435	158187
30.89374	66.30867	46.47282	6.33	21.49000	37.95947	49.38007	17.76702	10.914861	38.41653	39.80	17.59986	48.04530	9.542857	8.362709	75.28	4.770000	108.93000	93.95	7.548449	157981
30.97132	67.52499	47.26264	6.48	21.60000	38.25822	50.57419	18.13481	10.981765	38.36671	39.60	17.91258	47.68933	9.514285	8.550213	76.85	4.750000	108.93000	91.37	7.533792	159075
30.45739	68.41823	47.34065	6.17	21.57000	38.22912	48.42085	17.69158	11.402303	38.74539	38.93	18.11780	48.25294	9.123809	8.647716	75.91	4.820000	108.93000	91.03	7.717007	159189
30.63193	68.61000	48.28649	5.99	21.70000	38.56863	48.01955	17.68214	11.612571	39.69210	39.41	18.23506	48.88577	9.400000	8.647716	77.74	4.830000	108.93000	90.80	7.988164	160766
30.73860	69.03000	48.44250	5.81	22.01000	39.15065	47.67697	18.09709	11.603014	40.30996	39.50	18.48914	49.05386	9.371428	8.805220	76.62	4.750000	109.75000	88.99	7.936864	162482
29.80771	69.29000	48.69603	5.42	21.71000	38.14182	47.88251	18.04950	11.689032	38.84505	38.55	17.98098	48.62868	9.047619	8.940223	78.59	4.650000	109.90000	87.85	7.768307	158578
30.13740	70.17000	48.55951	5.35	21.55000	37.80230	48.73407	18.16832	11.810000	37.95813	38.57	17.83440	46.48301	8.761904	8.895222	78.32	4.600000	109.90000	88.49	7.526464	157327
29.96286	70.35000	48.75453	5.33	21.59000	37.99631	51.53341	18.59000	11.780000	38.41653	38.55	17.91258	46.98729	8.904761	8.992724	78.63	4.630000	109.90000	90.79	8.251994	157923
30.06952	70.85000	48.48151	5.27	21.44000	38.34552	51.32000	18.29000	11.720000	38.57598	38.21	18.07871	45.95895	8.809523	8.960000	79.32	4.430000	109.90000	92.12	8.559795	158473
30.15679	72.92000	47.66000	5.27	21.30000	38.42313	51.20000	18.51000	11.440000	37.46982	39.41	17.82463	45.97873	8.561904	9.050000	80.85	4.390000	109.90000	91.90	8.164051	158142
30.31000	72.90000	48.28000	5.36	21.75000	39.05365	51.50000	18.61000	11.900000	38.29695	40.42	17.99076	47.24438	8.847619	9.080000	80.58	4.470000	109.90000	92.01	8.510000	160456
30.41000	73.12000	48.75000	5.35	21.85000	39.06626	51.68000	18.60000	11.790000	38.36671	40.60	17.98098	47.37292	8.809523	9.110000	80.60	4.500000	109.90000	92.51	9.070000	160897
30.73000	72.12000	48.71000	5.24	21.72000	38.94637	51.55000	18.72000	11.730000	38.36671	41.14	18.06893	47.54000	8.904761	8.940000	80.71	4.480000	109.90000	93.11	8.740000	160490
30.82000	71.96000	48.51000	5.13	21.92000	39.19615	51.45000	18.76000	11.940000	38.50000	41.42	18.15508	48.36000	8.940000	9.000000	79.13	4.510000	110.02000	92.22	8.870000	161125

5 Calculo dos Retornos Logáritmos dos Ativos

Para o estudo do retorno dos ativos foi empregado o metodo de calculo logarítmo do retorno dos ativos. Metodo apropriado para a correta estimativa de séries temporais com negociação contínua¹

Os retornos foram calculados através da seguinte expressão:

\[R_{i} = \log \Bigg(\frac{P_{t}}{P_{t-1}} \Bigg)\]

Ou ainda:

\[R_{0,T} = \ln \Big( \frac{P_{T}}{P_{0}} \Big) = \sum_{t = 1}^{T} \ln \Big(\frac{P_{t}}{P_{t-1}} \Big) = \sum_{t=1}^{T} R_{t}\]

Onde:

\(R_{i}\) é o retorno logarítmo do ativo \(i\);

\(P_{t}\) é o valor do preço do ativo observado no momento \(t\)

\(P_{t-1}\) é o valor do preço do ativo observado no momento \(t-1\)

Retornos historico dos Ativos - Ajustados
PETR4.SA.Adjusted	VALE3.SA.Adjusted	WEGE3.SA.Adjusted	AMER3.SA.Adjusted	BBAS3.SA.Adjusted	ITUB4.SA.Adjusted	SUZB3.SA.Adjusted	KLBN11.SA.Adjusted	ALPA4.SA.Adjusted	EQTL3.SA.Adjusted	PRIO3.SA.Adjusted	BBDC4.SA.Adjusted	PSSA3.SA.Adjusted	MGLU3.SA.Adjusted	GOAU4.SA.Adjusted	JBSS32.SA.Adjusted	GMAT3.SA.Adjusted	BNBR3.SA.Adjusted	MELI34.SA.Adjusted	GUAR3.SA.Adjusted	IBOV
0.0327361657	-0.0087991258	-0.0002363280	-0.043328036	-0.0065207935	0.0091247747	-0.0058341977	-0.0206642336	-0.0077390551	-0.0002746762	0.0172338143	0.0304845142	0.0032465896	0.0042017129	-0.0400052398	0.0045766469	0.007623855	0.0000000000	-7.610147e-03	-0.002469047	0.0050591560
0.0222939291	-0.0066031399	-0.0007096028	0.000000000	0.0009340854	0.0076775709	-0.0005664460	0.0092973836	0.0022171801	0.0035650277	-0.0020802076	0.0097560485	0.0177630638	0.0083507266	-0.0064655204	-0.0072013804	0.006309101	0.0000000000	-6.660873e-03	0.006161426	0.0048885624
0.0242699786	-0.0133386212	0.0030714095	-0.014870148	0.0079052267	-0.0120909332	0.0216709370	0.0010882217	0.0132014967	-0.0035650277	0.0174315954	-0.0115958656	-0.0075202128	-0.0733087025	-0.0065076665	0.0075926773	-0.021615507	0.0079043328	6.406415e-04	-0.016099442	-0.0042688956
-0.0098857704	0.0320903106	0.0035324246	0.018553390	0.0179026561	0.0180824165	0.0025839928	0.0070442159	0.0054496540	0.0141844826	-0.0183575426	0.0212579581	0.0131235634	0.0649579759	0.0075880664	0.0189891542	0.017834850	-0.0027330760	2.395589e-02	0.023443309	0.0147795029
0.0224106946	-0.0459981988	-0.0269225488	0.046687070	-0.0036462620	0.0059556856	-0.0301267001	-0.0284794593	-0.0098307153	-0.0076127716	0.0194937599	0.0149122749	0.0040891047	-0.0222585563	-0.0075880664	-0.0278967361	0.010050326	-0.0052770479	-1.766288e-02	-0.003665152	-0.0029917749
-0.0009110218	-0.0033122347	0.0108082439	0.025975504	-0.0041180656	-0.0059556856	0.0032243263	0.0022196937	0.0054733949	-0.0021857027	-0.0075230725	-0.0077266179	-0.0050208433	0.0021413419	-0.0021787385	-0.0152472498	-0.006269669	0.0052770479	9.093265e-05	0.006101278	-0.0008863045
-0.0027385461	-0.0260988276	-0.0052693939	-0.003424658	-0.0213167681	-0.0051723512	-0.0179600191	-0.0246926126	-0.0109769128	-0.0173821936	-0.0032087900	-0.0083883332	-0.0026134077	-0.0549588988	-0.0287629122	0.0043991517	-0.028062976	-0.0540672121	-2.457532e-03	-0.024631779	-0.0116086036
-0.0253021847	0.0125412388	0.0013002316	0.131599882	-0.0122528017	-0.0021854614	-0.0023161455	0.0034033145	0.0142466515	-0.0092270264	-0.0071420962	-0.0078525114	-0.0014964691	0.0067568248	0.0044791802	-0.0286042542	0.000000000	0.0000000000	2.768213e-02	0.008690359	-0.0041291117
-0.0198838727	-0.0001977955	-0.0038535885	-0.092907078	0.0164593177	0.0186969539	0.0019304685	0.0028271765	0.0086675332	0.0111732832	-0.0398590341	0.0030274132	0.0106136704	0.0211001372	-0.0022370091	0.0262071256	0.025544147	0.0000000000	3.046812e-02	0.032829577	0.0044864095
-0.0051134946	-0.0011879245	0.0091281534	-0.026757424	-0.0084308918	-0.0181504283	-0.0069672885	-0.0062304910	-0.0097561173	-0.0227570532	-0.0128347226	-0.0085005689	-0.0016683370	0.0032913565	-0.0192205306	0.0121920166	-0.008866420	0.0000000000	1.273030e-02	-0.001196726	-0.0102443995
0.0079783140	0.0296665190	0.0294520040	-0.006802741	0.0158659458	-0.0074082866	0.0023278273	0.0163430008	0.0226181335	0.0082073173	0.0197882838	0.0091047812	0.0116204002	0.0312693190	0.0181000370	0.0537205677	0.018904136	0.0000000000	-4.594978e-03	0.005970066	0.0098725154
-0.0079783140	0.0165922879	-0.0168583150	0.011874558	0.0060003747	-0.0011020647	-0.0089529690	0.0000000000	-0.0171864221	-0.0056529173	0.0004777940	0.0012076988	0.0024616950	-0.0128206617	-0.0112740922	0.0004992002	-0.005422368	0.0398615089	-2.134473e-03	0.009478710	-0.0018103516
0.0054322134	-0.0041697649	0.0101023384	-0.044835053	0.0164312596	0.0185746319	0.0011723277	0.0308225138	0.0021645105	0.0190908597	0.0125788437	0.0155692657	0.0186510876	0.0574570479	0.0123945858	-0.0245023932	0.033606144	-0.0069641606	1.265462e-02	0.008220881	0.0144278782
0.0034992834	0.0133951266	-0.0065665899	-0.045093302	-0.0081818819	0.0045288652	-0.0072513584	0.0005418432	0.0192726111	0.0047164717	-0.0142520769	0.0088617466	-0.0078203033	-0.0143151599	0.0000000000	-0.0270864264	0.006101347	0.0000000000	-4.381895e-02	0.018540517	0.0049855709
0.0176271205	0.0357114853	-0.0016483602	-0.014870148	0.0036446881	-0.0081190825	0.0169677000	0.0283062700	-0.0863368243	-0.0206942844	0.0085755793	-0.0182327040	-0.0031086873	-0.0681840168	0.0319585713	-0.0168249880	-0.038442471	-0.0195424912	-1.913978e-02	-0.051837248	-0.0035750218
0.0034263193	-0.0047126257	0.0065773874	0.011173290	0.0139987896	0.0244274823	0.0067457447	0.0285510684	0.0262422312	0.0187550374	0.0099128019	0.0235589004	0.0361517280	0.0131436447	0.0150702321	-0.0045527172	0.016301270	0.0510794061	1.383514e-02	0.057561417	0.0134083493
-0.0012446561	0.0029027336	0.0067670116	-0.007434971	0.0058128257	0.0005302794	-0.0021151597	-0.0046165525	0.0067339931	0.0002771554	0.0000000000	-0.0047875515	0.0008828342	0.0065075475	0.0010677794	0.0105468021	0.004962780	0.0000000000	-1.536432e-02	0.007959006	0.0038951063
-0.0018696427	-0.0147826927	-0.0157040032	-0.003738318	-0.0166334280	-0.0133407262	-0.0182600675	-0.0302737214	-0.0191986918	-0.0210121420	-0.0194457991	-0.0096444186	-0.0252001263	-0.0152507177	0.0063829819	-0.0017279845	-0.007453376	-0.0025033282	2.322272e-02	-0.034565682	-0.0141513139
0.0142461080	0.0034873469	-0.0414817457	-0.003752346	-0.0027234793	-0.0024202514	-0.0015695693	-0.0122635353	0.0045506490	-0.0025513907	0.0311199914	0.0024198689	-0.0166076913	-0.0233215248	0.0000000000	-0.0369935241	0.012391708	0.0409264374	-1.301301e-02	-0.011792469	-0.0013414973
-0.0061690545	-0.0099430367	-0.0123885612	-0.028600632	-0.0253178326	-0.0209503630	-0.0184290893	-0.0069985960	-0.0056915225	-0.0151582474	-0.0119091221	-0.0115467992	-0.0272354382	-0.0401199589	-0.0021230907	-0.0072043020	-0.021158244	0.0000000000	1.415576e-02	-0.008338472	-0.0131656911
-0.0024782051	0.0226865581	-0.0052494745	0.003861005	-0.0112519915	-0.0312786086	-0.0030045342	0.0118152781	-0.0172717419	-0.0075210415	-0.0182534514	-0.0135386242	0.0033981650	-0.0248680442	0.0052995059	0.0253977347	0.007518878	0.0000000000	-1.745803e-02	-0.008408348	-0.0053824740
0.0120241430	0.0129405823	-0.0037664824	-0.005797158	-0.0033056747	-0.0082610828	0.0010025668	-0.0091177539	-0.0058239865	-0.0026166684	0.0217709019	-0.0055918401	-0.0134714916	-0.0366341793	-0.0149098725	0.0043284216	-0.007518878	-0.0829459109	-1.132802e-02	-0.041878133	-0.0040743104
-0.0132656461	-0.0114943507	-0.0055500035	0.003868473	-0.0219999476	-0.0017176041	0.0010014847	0.0234302520	-0.0153034372	-0.0058394235	0.0042046383	0.0037312623	0.0087487014	-0.0112571627	0.0000000000	-0.0166034516	-0.025479035	0.0027193949	4.690648e-03	0.005018813	-0.0065417971
-0.0077942442	-0.0265413445	0.0035354373	-0.011650606	0.0105820098	0.0034322631	0.0109507935	0.0047256339	0.0234477474	0.0093268722	-0.0183491996	-0.0006207148	-0.0043647462	0.0125001788	-0.0118727675	-0.0134007834	0.006430877	0.0000000000	-1.080522e-03	0.029595232	-0.0003622264
-0.0050204969	0.0090481933	0.0358993817	-0.009813565	-0.0009573369	0.0048427832	0.0003959851	-0.0015726949	0.0046242372	-0.0031962666	0.0063898091	-0.0024877753	-0.0203657250	0.0074257614	0.0032520966	0.0301392258	0.012739001	0.0000000000	5.390835e-03	-0.028344371	0.0019279001
-0.0101170568	-0.0018400155	0.0233155017	0.005899670	-0.0067275135	0.0149486836	-0.0003959851	0.0015726949	0.0080413945	0.0049353254	0.0212401464	-0.0018696681	0.0092735688	0.0110362942	-0.0185695899	0.0084661512	0.002528503	0.0004343939	-2.293116e-02	0.017348657	0.0003984123
-0.0153700960	0.0047768488	0.0066304378	0.000000000	-0.0234157551	-0.0183646968	0.0021758261	-0.0169047474	-0.0243208150	-0.0090181008	-0.0002309348	-0.0227138936	-0.0036604420	-0.0398062516	-0.0077478568	-0.0137432001	-0.026873089	0.0000000000	3.122997e-02	-0.056869440	-0.0162340383
0.0019341987	0.0269431334	-0.0094854860	-0.019802609	-0.0199407560	0.0116233227	0.0076764507	-0.0010661788	0.0035108731	0.0035004420	-0.0123186357	0.0006379970	0.0046215052	-0.0361796248	0.0338646768	-0.0165519009	-0.013054990	0.0000000000	-2.001589e-02	-0.010457574	0.0058681008
0.0096154640	0.0255407479	-0.0156085274	-0.012072570	0.0015093411	-0.0136209985	0.0050850903	-0.0069575065	-0.0153034372	-0.0120112459	-0.0042183444	-0.0031939992	-0.0086830779	-0.0132451767	0.0096205694	0.0164161959	-0.013227744	0.0000000000	7.856591e-03	0.041189800	-0.0009768721
0.0202090726	-0.0013922245	-0.0834973788	0.024001129	0.0159604104	0.0110812204	0.0095137556	0.0037523551	0.0199654661	0.0195541067	-0.0025867294	0.0158684443	0.0096432184	0.0392206952	0.0241735561	-0.0062610671	0.013227744	0.0000000000	-6.588136e-03	0.012531448	0.0098885752
-0.0015641806	-0.0156212785	-0.0479616232	0.001974379	-0.0069513206	-0.0093687597	-0.0048426146	-0.0005351735	-0.0128732792	-0.0130911331	-0.0040109051	-0.0126744451	-0.0090619396	-0.0339015672	0.0000000000	0.0131572090	-0.023937331	0.0000000000	-1.268455e-03	-0.012531448	-0.0115910591
0.0012515401	-0.0147912889	-0.0016575908	0.032980603	0.0084346369	0.0042694710	0.0205637745	0.0159325708	0.0000000000	-0.0079377389	-0.0095012047	-0.0076825116	-0.0064122703	-0.0053191280	-0.0093897806	-0.0005391686	0.019987366	0.0000000000	-8.284481e-03	-0.005429201	-0.0021246997
0.0012499757	-0.0097420535	0.0201152912	-0.015384905	-0.0149330175	-0.0212408502	-0.0080213963	-0.0164679195	-0.0166273860	-0.0112794371	-0.0100744910	-0.0077419898	-0.0109760923	-0.0436036353	-0.0190482081	0.0216066388	-0.029453274	0.0000000000	3.558879e-03	-0.046091112	-0.0105025189
0.0130315168	-0.0061829727	-0.0040921759	0.026770307	0.0005013479	0.0057855109	-0.0057692951	-0.0064480969	0.0083482843	0.0080274186	0.0117437341	-0.0019448830	0.0072656098	-0.0282505007	-0.0053561368	-0.0084802334	-0.004084475	0.0413690130	8.164806e-03	0.018692101	0.0045081347
0.0101212823	-0.0180383869	0.0073538162	-0.007575786	-0.0025094493	0.0114710835	0.0063443533	0.0069834456	0.0153214084	0.0222556886	0.0177121168	0.0160930468	0.0116709283	0.0502899591	0.0180951255	-0.0035993410	0.013550382	0.0156083909	6.753436e-03	0.026111195	0.0094783175
-0.0039749163	-0.0070830370	0.0070309939	-0.015326047	-0.0101010539	0.0025630434	-0.0005750582	-0.0042917305	0.0011689437	-0.0134111884	-0.0124840296	-0.0083361077	0.0034749945	-0.0388938955	-0.0116712093	0.0264890256	-0.013550382	0.0203053110	-7.182138e-04	-0.003873513	-0.0068823499
-0.0132616174	0.0054099613	0.0018844742	-0.005808290	-0.0709890146	-0.0060608319	-0.0078930306	-0.0102675183	0.0093024239	0.0076024095	-0.0288550181	0.0019299337	0.0072964583	0.0224099719	-0.0414002219	-0.0202319163	0.005442246	0.0025094073	-1.492904e-02	-0.007792161	-0.0047757597
-0.0015534886	0.0079682378	-0.0029630354	0.003875970	0.0199628027	0.0105368742	-0.0189255491	-0.0032644410	-0.0034784374	-0.0023331781	-0.0125201618	0.0076263164	0.0191384351	-0.0055555349	0.0066518898	0.0135769410	0.000000000	-0.0911484916	-2.492051e-02	0.033336384	0.0040239987
0.0046533692	-0.0012928182	0.0016172991	-0.001936153	-0.0053560740	0.0109878521	0.0039316028	-0.0259467549	0.0034784374	-0.0008761438	0.0034525162	0.0019138194	-0.0060241195	0.0027815211	-0.0044297215	-0.0010478676	0.000000000	0.0423583314	3.760185e-02	-0.017812227	0.0013527632
0.0012370925	-0.0063033315	0.0273625662	0.001936153	0.0042872953	0.0125294798	0.0126718991	0.0188369328	0.0273988768	0.0023349889	-0.0206448824	-0.0012754301	0.0013208025	0.0192579373	-0.0122837105	-0.0072345339	0.026775373	0.0000000000	-4.699159e-02	0.039023262	0.0103628645
0.0055487974	0.0072268778	0.0217738296	0.041672657	0.0111672806	0.0175540344	0.0476641658	0.0195658527	0.0156428921	0.0241947577	-0.0035246609	0.0076287352	-0.0035892178	0.0108401465	0.0145010240	0.0131149421	0.011818893	0.0000000000	-8.907502e-03	0.127339370	0.0146830348
-0.0634528396	0.0224564559	-0.0233474408	0.032849725	0.0010571186	0.0067741200	0.0080942176	0.0191904749	0.0778227725	0.0130054667	-0.0027781457	0.0107088428	0.0126000598	-0.0525709413	0.0110134146	0.0023425350	-0.010498763	0.0000000000	6.829862e-03	-0.021978878	-0.0045147466
0.0062040456	-0.0010837773	-0.0233679534	0.033542430	0.0089404222	0.0061920144	-0.0092030649	-0.0134158174	-0.0301948625	-0.0155700566	-0.0104233774	-0.0037665584	-0.0020577487	-0.0028448988	-0.0010958634	0.0072529468	-0.011944443	0.0037822986	-2.178984e-02	-0.023609897	-0.0021359975
0.0026007308	0.0104279328	-0.0165247953	-0.015748383	0.0073029592	0.0204551392	0.0001848332	-0.0021716824	0.0414138134	0.0361435155	0.0035714167	0.0230040348	0.0297041609	0.0014235679	0.0120947032	-0.0102471996	0.019828831	0.0000000000	1.705184e-02	0.019155524	0.0167513248
-0.0074955388	0.0013947686	0.0002730300	-0.073158772	0.0020769149	-0.0095115412	-0.0042612069	-0.0164386912	-0.0308983750	-0.0183286588	-0.0102381629	-0.0086422224	0.0000000000	-0.0436116896	0.0010922992	0.0226872605	-0.071895349	0.0066889832	-6.479919e-03	-0.081345571	-0.0089366620
-0.0128396300	-0.0124641835	-0.0035561956	-0.024977305	0.0291357798	-0.0013282317	0.0009278858	0.0131724109	-0.0084035565	-0.0050577371	-0.0018024904	-0.0074673290	-0.0310158787	-0.0074571285	-0.0098738418	-0.0452341863	-0.009894054	0.0206192522	3.149927e-03	-0.014634404	-0.0024245277
-0.0003314603	-0.0018736886	-0.0143530539	-0.039687711	0.0395112386	-0.0034614572	-0.0108168906	-0.0176021329	-0.0084745387	0.0112046923	0.0002577538	0.0012484232	-0.0183561393	-0.0090226747	0.0022025724	0.0237196924	0.000000000	0.0101524337	2.698422e-02	0.002453882	-0.0001100122
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-0.0003333973	0.0087195310	0.0154783889	-0.001843273	0.0052618618	0.0033840932	0.0073037114	0.0189527264	-0.0047014564	-0.0324410220	-0.0155252932	0.0005481630	0.0085783413	0.0162983668	0.0161217916	0.0213306760	-0.011067304	0.0000000000	-5.280162e-03	-0.023363182	0.0031250238
0.0009998585	0.0180041775	-0.0064004161	0.014652263	0.0123282411	0.0221031727	-0.0075074483	-0.0077604627	-0.0018867471	0.0167608979	-0.0118736809	0.0318345562	-0.0016681034	-0.0151253975	0.0396547943	-0.0121127022	0.000000000	0.0000000000	-1.569895e-03	0.030366700	0.0081334763
-0.0043398272	0.0075507973	-0.0143713798	0.049655627	0.0191371797	-0.0012717613	-0.0083853129	0.0005561330	-0.0009447102	0.0029927767	-0.0064093724	-0.0395393438	0.0132672412	-0.0035231613	-0.0191699712	0.0125375238	0.009493729	0.0254728138	4.417855e-02	-0.001995922	0.0009885245
-0.0046948297	0.0224693971	0.0155597160	-0.049655627	0.0124054242	0.0038106531	0.0040992141	0.0033315696	0.0000000000	-0.0043561554	0.0072423248	0.0033094312	-0.0105580346	-0.0035357361	0.0218787175	0.0121026054	0.014073746	0.0000000000	-1.858577e-02	0.011916657	0.0050952108
0.0116960036	0.0013780699	0.0164903902	-0.042717733	0.0081855156	0.0165443888	-0.0069787031	-0.0033315696	-0.0385404403	0.0255906352	0.0113151438	0.0109529644	-0.0004163112	-0.0154672108	-0.0145324966	0.0050230414	-0.021978902	0.0233173503	-1.010064e-02	-0.042345027	0.0060934741
0.0049710068	-0.0112333981	-0.0011688894	-0.032789838	0.0085683365	-0.0029985320	0.0175586634	0.0290512480	0.0357008377	0.0042463263	0.0084711910	0.0032102968	0.0154945785	0.0047846682	-0.0055046001	0.0056901640	-0.009569515	0.0000000000	9.813400e-03	0.023410679	0.0016602585
0.0196406064	0.0170314490	0.0176215711	0.036577718	0.0151518096	0.0042454097	-0.0103754281	0.0080709958	0.0028396026	0.0207057358	0.0284354286	0.0209742511	0.0030703286	0.0420622471	0.0263293091	-0.0036046363	0.025317825	-0.0023837914	-4.317560e-03	0.045238800	0.0170399981
0.0051729849	-0.0035053161	0.0091513292	-0.036577718	0.0109964518	0.0000000000	-0.0051255774	-0.0151190900	-0.0066382907	0.0133870597	0.0170450621	-0.0042668089	0.0140032211	-0.0897194574	-0.0062922124	-0.0020855277	0.003120148	-0.0168475706	-9.420501e-02	0.034958790	0.0002935105
0.0370354002	-0.0110532731	0.0245204219	0.013632182	0.0013113946	0.0009962390	-0.0213990447	-0.0060028795	0.1038370755	0.0050405766	0.0100893212	0.0010683841	-0.0006047654	0.0185994138	0.0009013651	-0.0404740867	-0.001558857	0.0000000000	-1.797686e-03	0.060351413	0.0047169438
0.0055779681	0.0066159570	0.0081885838	0.028600632	-0.0048171303	0.0066988037	-0.0195086144	-0.0055239355	0.0279087654	0.0079071695	0.0097337110	0.0185141328	0.0060314130	0.0338196805	0.0044944466	0.0088017394	-0.012559043	0.0192313619	-2.117956e-02	-0.090514021	0.0077137079
0.0256267641	-0.0026103329	0.0144422686	0.045921749	0.0298399511	0.0191042633	-0.0032171879	-0.0022358704	-0.0058552575	0.0266821130	0.0269097015	0.0212608544	-0.0794415456	0.0765650488	-0.0018264807	0.0000000000	0.037213621	0.0003808886	1.182172e-02	0.007626388	0.0159233539
-0.0259359039	0.0110092677	-0.0250783047	-0.003597123	-0.0289625115	-0.0230685936	0.0321313222	0.0265061624	0.0125052540	0.0096668420	-0.0072220691	-0.0025686834	-0.0060949683	0.0065790126	0.0045600198	0.0024391743	-0.021539365	0.0000000000	-1.068931e-03	0.002844982	-0.0007356159
0.0043184367	-0.0013695942	-0.0015605782	-0.065139373	-0.0132451718	0.0039643303	-0.0085658385	-0.0181473850	0.0057828850	-0.0055852844	-0.0045089378	0.0020555145	0.0151682452	-0.0098847665	-0.0137428014	0.0007163248	-0.029994330	0.0000000000	-3.128647e-02	-0.032726707	-0.0029924259
0.0064426478	-0.0061097326	-0.0085145331	-0.013552907	-0.0026701490	0.0039487789	-0.0063144519	-0.0055647478	0.0139061781	0.0045720605	-0.0010047957	-0.0005135328	0.0004300062	0.0568518560	-0.0018468362	0.0055694450	-0.108213578	0.0163357180	-5.754822e-03	0.014570403	0.0036646479
0.0054895096	-0.0007662710	-0.0106323265	0.015474182	0.0026701490	-0.0074166688	0.0237857788	0.0088888825	-0.0122601275	-0.0050813816	0.0015067195	-0.0077339981	-0.0090693584	-0.0491551783	-0.0074211695	0.0505382296	-0.019838389	0.0000000000	1.323067e-02	0.009597021	-0.0047405500
0.0033399388	-0.0030713398	-0.0121269757	0.052348351	-0.0279423360	-0.0049752173	0.0006183225	-0.0133631300	0.0065573318	-0.0020396872	0.0047566104	-0.0119760253	-0.0041299909	0.0365631179	-0.0037313401	-0.0072015906	-0.031454806	0.0000000000	1.078498e-02	0.004764254	-0.0030046432
-0.0051664690	-0.0010771581	0.0048226783	0.023403430	-0.0138059597	-0.0062538509	-0.0041296049	-0.0028066900	0.0030865616	-0.0069151419	-0.0158593900	-0.0100029443	-0.0142593645	-0.0148938794	-0.0103335609	-0.0160839006	-0.036367701	0.0000000000	1.407582e-03	0.016030402	-0.0073164098
-0.0076464171	0.0032281846	-0.0098999436	-0.001780900	0.0192755348	0.0030067964	-0.0004139323	-0.0124436807	-0.0100320587	-0.0018005894	-0.0155993604	-0.0058368929	0.0096747140	0.0316481986	0.0047103147	0.0224728465	-0.019965264	0.0000000000	-5.082645e-02	-0.011288923	-0.0039400214
-0.0009214801	-0.0010749657	-0.0006944267	0.007104819	-0.0072993765	-0.0037599103	-0.0068543300	-0.0137538151	0.0351229387	-0.0023199589	-0.0067235402	0.0005319044	0.0173539936	0.0276515512	0.0121439237	0.0454292531	0.017910957	0.0030860065	2.983291e-02	0.021526401	0.0032769149
-0.0080223376	0.0078047920	-0.0053395288	0.081539207	0.0059347194	0.0022577464	-0.0037586006	0.0137538151	-0.0115710870	0.0102697092	-0.0268225504	0.0079470694	0.0019336565	0.0357181074	0.0046318320	0.0099208006	-0.007920826	0.0046576703	2.001928e-02	0.007380086	0.0040618589
-0.0015501254	0.0148285900	0.0329700948	-0.024774197	0.0113148939	0.0232797819	0.0012544372	0.0085011245	0.0142224508	0.0139507621	0.0124488750	0.0296357176	0.0195542165	-0.0147278499	0.0228424856	0.0114724205	0.027452677	0.0000000000	-1.770154e-02	-0.004606189	0.0168226186
0.0052607976	-0.0037619610	-0.0079141748	0.006666685	-0.0027039283	-0.0034331260	0.0070789599	0.0016915869	0.0218253427	-0.0010081170	-0.0073977244	-0.0020512980	-0.0002104999	0.0009886865	-0.0045268762	-0.0050826224	-0.013632182	-0.0244602834	8.452811e-03	0.003686659	-0.0016601076
-0.0190066935	0.0160027103	0.0045300394	-0.013378113	0.0138922265	0.0225875981	-0.0129464831	-0.0005636204	-0.0183011785	0.0025182933	-0.0133477692	0.0086889552	-0.0065477344	0.0156865958	-0.0018165272	0.0012730552	0.000000000	0.0000000000	8.165088e-03	0.040564334	0.0049155013
0.0018855924	0.0076854265	0.0207991576	0.034742954	-0.0093896751	-0.0077748021	-0.0021039800	0.0005636204	-0.0061755280	-0.0116368870	0.0093621731	-0.0153848333	0.0115877030	0.0058196452	0.0054397120	0.0132703755	-0.013820495	0.0094787440	5.082946e-03	-0.001768328	-0.0029022662
0.0068836193	0.0082113209	0.0094724915	0.079667364	0.0166234744	0.0220315090	0.0150504631	0.0061780427	0.0044150423	0.0226424986	0.0005323518	0.0107523231	0.0064724624	0.0238902950	0.0000000000	-0.0112367746	0.038991256	0.0140517535	1.211621e-02	0.039901227	0.0155209667
0.0074558303	0.0317623863	-0.0123540445	0.042622170	-0.0059770403	0.0000000000	0.0154403167	0.0133483777	-0.0026467737	-0.0009954767	0.0455155903	-0.0280246414	0.0004161380	0.0595685530	0.0294007772	-0.0022880435	-0.013474732	0.0092593254	4.890495e-03	-0.008539778	0.0041072145
0.0064784846	0.0172502189	0.0200455951	0.024166077	0.0172762348	0.0243343503	0.0119810658	0.0153511772	0.0457568748	0.0267795717	0.0065889320	0.0141104900	0.0107594857	0.0358274292	0.0052539417	0.0127711734	0.015384905	-0.0092593254	9.079461e-03	0.003424623	0.0165602124
-0.0360033004	-0.0239211400	0.0260318400	-0.057819586	-0.0733313004	-0.0473349202	0.0191929017	0.0145829503	-0.0635825791	-0.0499543622	-0.0083704189	-0.0615330829	-0.0271188997	-0.1029790041	-0.0292444374	-0.0176188023	-0.063012909	0.0132146293	-1.301127e-02	-0.142115122	-0.0440496911
0.0092020129	-0.0068592716	0.0226536509	0.004454382	0.0205807326	0.0048356402	-0.0021805706	0.0026774395	0.0283706758	-0.0079315422	0.0022897900	0.0071486374	0.0159432760	0.0028504235	-0.0045065902	-0.0350044824	-0.004073321	0.0000000000	-1.704988e-03	0.017578574	0.0051845114
0.0062972837	0.0005735023	-0.0023053100	-0.064242281	-0.0051056323	-0.0021732303	0.0011899986	0.0074587447	-0.0017497913	-0.0098090774	0.0113709570	-0.0132379572	0.0111756237	-0.0505944681	0.0072008508	-0.0030506470	-0.026888924	0.0000000000	2.024345e-03	-0.002908356	-0.0013031049
0.0025078393	0.0181770378	0.0168525401	0.023420289	0.0051056323	0.0078393752	0.0238945115	0.0204892739	0.0061109212	-0.0012978765	-0.0050378134	0.0176119509	-0.0074365214	-0.0029985717	0.0221737555	0.0206409711	-0.004201683	0.0000000000	-2.784547e-02	-0.001943677	0.0069010165
-0.0167328754	0.0131415862	0.0016491342	-0.049021663	-0.0013898861	-0.0007609711	-0.0435108465	-0.0247445683	0.0375791788	0.0098217543	-0.0170639103	0.0113914764	0.0117490768	-0.0419070075	0.0113390114	-0.0123069739	0.014629346	0.0000000000	-3.728118e-03	0.024028114	0.0007163864
0.0057143195	0.0027990231	0.0197824553	-0.029607476	0.0060088495	0.0088417718	-0.0083223347	-0.0005332682	0.0182728679	0.0241404562	0.0122544179	0.0064516529	0.0130294693	0.0298222936	0.0000000000	0.0238214217	0.002072488	0.0000000000	-2.529790e-03	0.034534446	0.0098577161
0.0034760909	0.0061028694	0.0032257884	-0.030510813	0.0141846102	0.0149778657	-0.0071597242	0.0231956021	-0.0008233065	0.0154461908	0.0022810846	0.0138373024	0.0034326986	-0.0030442123	0.0180494978	-0.0145117228	-0.016701834	0.0074995751	-2.013534e-02	-0.006442717	0.0106173348
-0.0307519559	0.0037594338	0.0052198724	-0.069484731	-0.0137239642	-0.0261059314	0.0043019033	-0.0026327604	0.0073860408	-0.0370178973	-0.0243445917	-0.0278688716	-0.0087054454	-0.0351638220	0.0152158162	0.0253862432	-0.021277378	0.0013658233	-1.289318e-02	-0.021466004	-0.0243206406
0.0109998079	0.0126202343	-0.0028073022	-0.012999286	-0.0073971606	-0.0089411567	0.0176278874	0.0065610238	0.0102957336	-0.0230969717	0.0005186841	-0.0081855538	-0.0451267315	-0.0320884085	-0.0050462578	-0.0034414240	-0.010810957	0.0000000000	7.258730e-03	-0.031627000	-0.0079201440
-0.0058083599	0.0025619187	0.0040080346	-0.003745319	0.0018544704	0.0051189456	0.0558520992	0.0229446183	-0.0025435102	0.0120043443	-0.0005186841	0.0043739937	0.0107904355	0.0161729070	0.0109016064	0.0039502767	0.006500610	0.0000000000	2.565963e-02	0.092029606	0.0037811306
0.0035535745	0.0070821827	-0.0056157416	-0.011320865	-0.0069718905	0.0091488216	-0.0041498583	-0.0162692975	-0.0051063486	0.0041418817	-0.0088588427	0.0092317479	-0.0221286009	-0.0107528595	-0.0036456212	0.0087370287	-0.044157348	0.0000000000	1.454295e-02	0.036621401	0.0034766593
0.0028980951	0.0287979801	-0.0170899443	0.000000000	-0.0065513242	0.0020217214	-0.0023409869	0.0119566265	-0.0241808577	-0.0290939721	0.0309223498	-0.0141538920	0.0004301912	-0.0285106634	0.0099945475	0.0191052673	-0.009070349	0.0000000000	-2.391059e-03	-0.047335787	-0.0020908682
0.0050674491	-0.0002742648	0.0129249025	0.016933641	0.0209067206	0.0162769134	0.0058422607	0.0053879645	0.0394224188	0.0218344319	0.0253050793	0.0092770893	0.0271548455	0.0328257998	0.0033094054	-0.0033450647	0.018059165	0.0000000000	1.196244e-03	0.041501471	0.0145263981
0.0032938232	0.0030133048	0.0096878265	-0.001867457	0.0045871815	0.0003226773	0.0034890577	-0.0005375022	-0.0092866567	0.0018197820	0.0044433623	-0.0005433851	0.0027170533	-0.0043151364	0.0032984894	0.0002481281	0.006689035	0.0000000000	5.419480e-03	0.063730261	0.0027446470
0.0104678646	-0.0137705283	-0.0008208684	-0.020775088	-0.0059674755	-0.0030736619	-0.0025186697	0.0064308331	-0.0051020877	0.0000000000	0.0132128404	0.0048793414	0.0035207834	0.0107528595	-0.0188371313	0.0013638414	-0.004454346	0.0000000000	6.464827e-03	-0.037062067	-0.0025327734
0.0029244587	-0.0022210401	-0.0041144014	-0.021215773	0.0091660021	0.0063930222	-0.0019417186	0.0021345214	0.0177444492	0.0034681669	0.0067829424	0.0047562684	0.0171015572	0.0039494294	0.0066890351	-0.0197704371	0.006674154	0.0010912616	-9.604556e-03	0.014764620	0.0039488259

6 Desempenho Histórico Normalizado

Interpretação: O gráfico mostra que a maioria das ações seguiu a tendência do IBOVESPA, porém com diferentes magnitudes de retorno. Alguns ativos, como Americanas e Magazine Luiza, apresentaram desempenho significativamente inferior, enquanto outros como PRIO e Petrobras superaram o mercado.

7 Retorno Acumulado

ativos <- colnames(returns)

cores <- rep("gray70", length(ativos))
cores[ativos == "IBOV"] <- "black"

larg <- rep(1, length(ativos))
larg[ativos == "IBOV"] <- 3

chart.CumReturns(
  returns,
  main = "Retorno Acumulado – Ativos vs Ibovespa",
  legend.loc = "right",
  colorset = cores,
  lwd = larg
)

8 Desempenho historico do retorno das ações

8.1 Top 5 Ativos com melhor desempenho historico

vol <- apply(returns,2,sd)

top5 <- names(sort(vol, decreasing=TRUE))[1:5]

sel <- c(top5,"IBOV")

chart.CumReturns(
  returns[,sel],
  main="Top 5 Volatilidade w IBOV",
  legend.loc="topleft")

cores <- rep("gray70", length(sel))
cores[length(sel)] <- "black"

 chart.CumReturns(
  returns[, sel],
  colorset = cores,
  lwd = c(rep(1, length(sel)-1), 3),
  main = "Top Ativos X IBOV ",
  legend.loc = "topleft"
)

9 Correlação entre os Ativos

cor_mat <- cor(returns, use="complete.obs")

heatmap(
  cor_mat,
  Rowv = NA,
  Colv = NA,
  col = colorRampPalette(c("darkgrey","white","black"))(100),
  scale = "none",
  margins = c(7,7),
  main = "Mapa de Calor – Correlação dos Retornos"
)

Interpretação: A matriz de correlação revela que bancos (Itaú, Bradesco, BB) têm alta correlação entre si (>0.8), indicando que se movem de forma similar. Ativos de setores diferentes (ex: Equatorial e Magazine Luiza) têm baixa correlação, o que é benéfico para diversificação.

a <- cor(returns)
kable(a, caption = "Correlação entre os Ativos")

Correlação entre os Ativos
	PETR4.SA.Adjusted	VALE3.SA.Adjusted	WEGE3.SA.Adjusted	AMER3.SA.Adjusted	BBAS3.SA.Adjusted	ITUB4.SA.Adjusted	SUZB3.SA.Adjusted	KLBN11.SA.Adjusted	ALPA4.SA.Adjusted	EQTL3.SA.Adjusted	PRIO3.SA.Adjusted	BBDC4.SA.Adjusted	PSSA3.SA.Adjusted	MGLU3.SA.Adjusted	GOAU4.SA.Adjusted	JBSS32.SA.Adjusted	GMAT3.SA.Adjusted	BNBR3.SA.Adjusted	MELI34.SA.Adjusted	GUAR3.SA.Adjusted	IBOV
PETR4.SA.Adjusted	1.0000000	-0.0967427	0.0743128	0.1576026	0.3239307	0.2721494	-0.0325864	-0.0629308	0.0474522	0.2195284	0.5054831	0.2713966	0.0341586	0.2253170	0.0679095	-0.0686136	0.1857183	0.0174229	-0.0084664	0.2308782	0.4331673
VALE3.SA.Adjusted	-0.0967427	1.0000000	0.0416399	0.0880261	0.1321779	0.1467514	0.1617399	0.2621462	0.0222569	0.1533244	0.0300913	0.1292062	0.0776599	0.1058870	0.5088841	0.1578953	0.1326039	-0.0635771	-0.0421373	0.0753031	0.3207158
WEGE3.SA.Adjusted	0.0743128	0.0416399	1.0000000	-0.0828506	0.1790566	0.1375681	0.1099248	0.1515041	0.1300758	0.1263897	0.1759467	0.1348105	0.1136775	0.0085810	-0.0057858	0.0866622	0.1704609	0.0117765	0.0420823	0.1607876	0.2138512
AMER3.SA.Adjusted	0.1576026	0.0880261	-0.0828506	1.0000000	0.1316073	0.1487434	0.0044033	0.1061886	0.1111968	0.1670858	0.1634812	0.1104010	0.0518963	0.3366718	0.1579803	-0.0966162	0.2276518	0.0762620	0.2538018	0.1707118	0.2544713
BBAS3.SA.Adjusted	0.3239307	0.1321779	0.1790566	0.1316073	1.0000000	0.5694184	0.0071472	0.1624060	0.2258410	0.5064494	0.2694358	0.4694035	0.1915518	0.3233369	0.3079012	0.0928930	0.4648608	0.0616512	0.1424078	0.3978594	0.6541962
ITUB4.SA.Adjusted	0.2721494	0.1467514	0.1375681	0.1487434	0.5694184	1.0000000	0.0755485	0.1743697	0.3456651	0.7362282	0.1369635	0.7626922	0.3982393	0.4611089	0.3321721	-0.0134767	0.5450913	0.0520501	0.0613327	0.4771272	0.8450195
SUZB3.SA.Adjusted	-0.0325864	0.1617399	0.1099248	0.0044033	0.0071472	0.0755485	1.0000000	0.6299613	0.0360333	0.0967728	0.0737305	-0.0540470	0.0056917	0.0095244	0.1727123	0.1597744	0.0479921	0.0225209	0.0477944	0.1927192	0.1046948
KLBN11.SA.Adjusted	-0.0629308	0.2621462	0.1515041	0.1061886	0.1624060	0.1743697	0.6299613	1.0000000	0.1179192	0.1906165	0.0719198	0.1276955	0.1736373	0.1351404	0.3028811	-0.0072631	0.1913500	0.0524621	-0.0034214	0.2093206	0.2799744
ALPA4.SA.Adjusted	0.0474522	0.0222569	0.1300758	0.1111968	0.2258410	0.3456651	0.0360333	0.1179192	1.0000000	0.4700603	0.0406946	0.4070650	0.2957201	0.2975484	0.2407468	-0.0524344	0.3645991	0.0546299	0.0481435	0.4370394	0.4524292
EQTL3.SA.Adjusted	0.2195284	0.1533244	0.1263897	0.1670858	0.5064494	0.7362282	0.0967728	0.1906165	0.4700603	1.0000000	0.1985770	0.7180674	0.3692871	0.4522104	0.3016968	-0.0341981	0.5668901	0.0779936	0.0502447	0.5257970	0.8332379
PRIO3.SA.Adjusted	0.5054831	0.0300913	0.1759467	0.1634812	0.2694358	0.1369635	0.0737305	0.0719198	0.0406946	0.1985770	1.0000000	0.0520750	0.0431278	0.0885061	0.0980459	-0.0980102	0.1388505	0.0414739	0.0304248	0.0038073	0.2737770
BBDC4.SA.Adjusted	0.2713966	0.1292062	0.1348105	0.1104010	0.4694035	0.7626922	-0.0540470	0.1276955	0.4070650	0.7180674	0.0520750	1.0000000	0.3335868	0.4281725	0.3497237	-0.0412366	0.5465943	-0.0129958	0.0389837	0.4523493	0.7982733
PSSA3.SA.Adjusted	0.0341586	0.0776599	0.1136775	0.0518963	0.1915518	0.3982393	0.0056917	0.1736373	0.2957201	0.3692871	0.0431278	0.3335868	1.0000000	0.1456582	0.1778780	0.1178767	0.2729581	0.0679508	0.0384598	0.2989638	0.4100646
MGLU3.SA.Adjusted	0.2253170	0.1058870	0.0085810	0.3366718	0.3233369	0.4611089	0.0095244	0.1351404	0.2975484	0.4522104	0.0885061	0.4281725	0.1456582	1.0000000	0.2391624	0.0702643	0.3823719	0.0517220	0.2398497	0.3559728	0.5794445
GOAU4.SA.Adjusted	0.0679095	0.5088841	-0.0057858	0.1579803	0.3079012	0.3321721	0.1727123	0.3028811	0.2407468	0.3016968	0.0980459	0.3497237	0.1778780	0.2391624	1.0000000	0.0102291	0.2403868	-0.0032444	-0.0083933	0.2773868	0.4673894
JBSS32.SA.Adjusted	-0.0686136	0.1578953	0.0866622	-0.0966162	0.0928930	-0.0134767	0.1597744	-0.0072631	-0.0524344	-0.0341981	-0.0980102	-0.0412366	0.1178767	0.0702643	0.0102291	1.0000000	0.0000651	-0.0973081	0.0225468	-0.0327023	0.0195743
GMAT3.SA.Adjusted	0.1857183	0.1326039	0.1704609	0.2276518	0.4648608	0.5450913	0.0479921	0.1913500	0.3645991	0.5668901	0.1388505	0.5465943	0.2729581	0.3823719	0.2403868	0.0000651	1.0000000	0.0314845	0.0962197	0.4562226	0.6473867
BNBR3.SA.Adjusted	0.0174229	-0.0635771	0.0117765	0.0762620	0.0616512	0.0520501	0.0225209	0.0524621	0.0546299	0.0779936	0.0414739	-0.0129958	0.0679508	0.0517220	-0.0032444	-0.0973081	0.0314845	1.0000000	0.1694613	0.0178654	0.0493863
MELI34.SA.Adjusted	-0.0084664	-0.0421373	0.0420823	0.2538018	0.1424078	0.0613327	0.0477944	-0.0034214	0.0481435	0.0502447	0.0304248	0.0389837	0.0384598	0.2398497	-0.0083933	0.0225468	0.0962197	0.1694613	1.0000000	0.0633358	0.0655431
GUAR3.SA.Adjusted	0.2308782	0.0753031	0.1607876	0.1707118	0.3978594	0.4771272	0.1927192	0.2093206	0.4370394	0.5257970	0.0038073	0.4523493	0.2989638	0.3559728	0.2773868	-0.0327023	0.4562226	0.0178654	0.0633358	1.0000000	0.5931772
IBOV	0.4331673	0.3207158	0.2138512	0.2544713	0.6541962	0.8450195	0.1046948	0.2799744	0.4524292	0.8332379	0.2737770	0.7982733	0.4100646	0.5794445	0.4673894	0.0195743	0.6473867	0.0493863	0.0655431	0.5931772	1.0000000

10 Distribuição dos Retornos dos Ativos

ativos <- setdiff(colnames(returns), "IBOV")

chart.Histogram(
  returns[, ativos],
  methods = c("add.density", "add.normal"),
  layout = c(5, 4),
  main = "Distribuição dos Retornos Log"
)

Interpretação Os ativos apresentam uma certa normalidade de retornos frente o IBOVESPA, com uma certa tendência de assimetria a direita da distribuição dos retornos.

11 Boxplot para verificação de retornos Outliers

library(xts)
library(tidyverse)

ativos <- setdiff(colnames(returns), "IBOV")

# xts -> formato longo
df_long <- returns[, ativos] |>
  fortify.zoo() |>
  pivot_longer(-Index, names_to = "Ativo", values_to = "Retorno") |>
  drop_na()

# ordenar por risco (desvio padrão)
ordem <- df_long |>
  group_by(Ativo) |>
  summarise(risco = sd(Retorno)) |>
  arrange(risco) |>
  pull(Ativo)

df_long$Ativo <- factor(df_long$Ativo, levels = ordem)

# gráfico
ggplot(df_long, aes(x = Ativo, y = Retorno, fill = Ativo)) +
  geom_boxplot(
    alpha = 0.85,
    outlier.color = "darkgrey",
    outlier.alpha = 0.4,
    width = 0.65
  ) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  coord_flip() +
  scale_y_continuous(labels = scales::percent_format()) +
  labs(
    title = "Distribuição dos Retornos Logarítmicos por Ativo",
    subtitle = "Boxplot ordenado por volatilidade (risco)",
    x = "",
    y = "Retorno diário"
  ) +
  theme_minimal(base_size = 12) +
  theme(
    legend.position = "none",
    plot.title = element_text(face = "bold")
  )

12 Exposição das Empresas ao Risco Sistématico - Beta

Realizar o calculo do beta das empresas permite identificar a exposição da empresa frente as variáções sistematicas de mercado se comparado com o índice de referência, nesse caso, o Ibovespa (IBOV).

O metodo de calculo foi desenvolvido por meio de uma regressão linear OLS (Simple Ordinare Squareds) - Mínimos quadrados Ordinarios - para o retorno de cada uma das empresas versus as variações no retorno do Ibovespa. O modelo aplicado para o cálculo se expressa da seguinte maneira:

\[R_{i}= \chi_{i}\;\alpha_{}\;+\;\beta_{0}\;+\epsilon_{i}\]

Onde:

\(R_{i}\) é o retorno do ativo \(i\);

\(\chi_{i}\) é o valor da variável explicativa - O Ibovespa;

\(\alpha\) é o coeficiênte angular da reta de regressão - Alfa de Jensen;

\(\beta_{0}\) é o valor do intercepto - coeficiênte linear - Exepressa o risco sistemático;

\(\epsilon_{i}\) é o resíduo- sendo uma constante o valor de beta tmabém expressa o erro;

13 Resultado do Betas das Empresas - CAPM

library(tidyverse)
library(broom)
library(knitr)

# separar benchmark
ibov <- returns[, "IBOV"]

ativos <- setdiff(colnames(returns), "IBOV")

# regressões CAPM
beta_tbl <- map_dfr(ativos, function(tk){

  model <- lm(returns[, tk] ~ ibov)

  tibble(
    Ativo = tk,
    Alpha = coef(model)[1],
    Beta  = coef(model)[2],
    R2    = summary(model)$r.squared
  )
})

beta_tbl <- beta_tbl |>
  mutate(across(where(is.numeric), round, 4)) |>
  arrange(desc(Beta))

kable(beta_tbl, caption = "Betas estimados pelo CAPM (Retornos log diários)")

Betas estimados pelo CAPM (Retornos log diários)
Ativo	Alpha	Beta	R2
MGLU3.SA.Adjusted	-0.0028	2.3126	0.3358
GUAR3.SA.Adjusted	0.0003	2.2170	0.3519
GMAT3.SA.Adjusted	-0.0055	1.4788	0.4191
BBAS3.SA.Adjusted	-0.0014	1.2979	0.4280
EQTL3.SA.Adjusted	-0.0008	1.2918	0.6943
BBDC4.SA.Adjusted	-0.0001	1.2754	0.6372
ITUB4.SA.Adjusted	-0.0001	1.1734	0.7141
AMER3.SA.Adjusted	-0.0020	1.1220	0.0648
ALPA4.SA.Adjusted	0.0017	1.1120	0.2047
GOAU4.SA.Adjusted	0.0008	0.7540	0.2185
PSSA3.SA.Adjusted	-0.0011	0.6892	0.1682
PETR4.SA.Adjusted	-0.0002	0.6250	0.1876
PRIO3.SA.Adjusted	-0.0008	0.4721	0.0750
VALE3.SA.Adjusted	0.0022	0.4429	0.1029
WEGE3.SA.Adjusted	0.0008	0.4144	0.0457
KLBN11.SA.Adjusted	0.0002	0.3983	0.0784
MELI34.SA.Adjusted	-0.0015	0.1590	0.0043
SUZB3.SA.Adjusted	-0.0003	0.1523	0.0110
BNBR3.SA.Adjusted	0.0012	0.0983	0.0024
JBSS32.SA.Adjusted	0.0002	0.0419	0.0004

14 Estatística descritiva das ações das empresas

library(tidyverse)
library(moments)
library(knitr)

stats_tbl <- map_dfr(colnames(returns), function(tk){

  x <- returns[, tk]

  tibble(
    Ativo     = tk,
    Media     = mean(x),
    Mediana   = median(x),
    SD        = sd(x),
    Variancia = var(x),
    Max       = max(x),
    Min       = min(x),
    Amplitude = max(x) - min(x),
    Q1        = quantile(x, 0.25),
    Q3        = quantile(x, 0.75),
    Skewness  = skewness(x),
    Kurtosis  = kurtosis(x)
  )
})

stats_tbl <- stats_tbl |>
  mutate(across(where(is.numeric), round, 5)) |>
  arrange(desc(SD))

kable(stats_tbl, caption = "Estatísticas Descritivas dos Retornos Logarítmicos")

Estatísticas Descritivas dos Retornos Logarítmicos
Ativo	Media	Mediana	SD	Variancia	Max	Min	Amplitude	Q1	Q3	Skewness	Kurtosis
AMER3.SA.Adjusted	-0.00070	0.00000	0.03903	0.00152	0.13160	-0.09824	0.22984	-0.02078	0.02066	0.21529	3.87134
MGLU3.SA.Adjusted	-0.00008	0.00112	0.03533	0.00125	0.08794	-0.10298	0.19092	-0.01700	0.02071	-0.22628	3.48047
GUAR3.SA.Adjusted	0.00295	0.00369	0.03309	0.00109	0.12734	-0.14212	0.26945	-0.01463	0.01980	-0.21180	6.36064
ALPA4.SA.Adjusted	0.00303	0.00194	0.02176	0.00047	0.10384	-0.08634	0.19017	-0.00847	0.01391	0.45833	8.01663
MELI34.SA.Adjusted	-0.00130	-0.00094	0.02147	0.00046	0.05554	-0.09421	0.14975	-0.01246	0.01078	-0.84899	5.68288
GMAT3.SA.Adjusted	-0.00372	-0.00407	0.02022	0.00041	0.03899	-0.10821	0.14720	-0.01305	0.00789	-1.30706	7.89566
JBSS32.SA.Adjusted	0.00026	-0.00130	0.01895	0.00036	0.05372	-0.06320	0.11692	-0.01211	0.01219	0.14586	3.86023
BNBR3.SA.Adjusted	0.00127	0.00000	0.01761	0.00031	0.05108	-0.09115	0.14223	0.00000	0.00309	-1.55697	12.22792
BBAS3.SA.Adjusted	0.00016	0.00093	0.01756	0.00031	0.04031	-0.07333	0.11365	-0.00791	0.01131	-1.07227	6.63754
WEGE3.SA.Adjusted	0.00129	0.00140	0.01715	0.00029	0.04678	-0.08350	0.13027	-0.00791	0.00915	-0.62021	6.97381
PRIO3.SA.Adjusted	-0.00019	-0.00023	0.01527	0.00023	0.05462	-0.03986	0.09448	-0.01024	0.00936	0.34330	3.82292
PSSA3.SA.Adjusted	-0.00033	0.00088	0.01488	0.00022	0.03615	-0.07944	0.11559	-0.00744	0.00992	-1.29457	7.99421
GOAU4.SA.Adjusted	0.00170	0.00109	0.01428	0.00020	0.03965	-0.04140	0.08106	-0.00647	0.01045	-0.17427	3.65142
BBDC4.SA.Adjusted	0.00143	0.00169	0.01414	0.00020	0.03414	-0.06153	0.09567	-0.00773	0.00976	-0.61677	5.36095
EQTL3.SA.Adjusted	0.00069	0.00000	0.01372	0.00019	0.03614	-0.04995	0.08610	-0.00716	0.00967	-0.36111	3.96051
SUZB3.SA.Adjusted	-0.00010	-0.00157	0.01287	0.00017	0.05585	-0.04351	0.09936	-0.00685	0.00584	0.73648	6.55141
PETR4.SA.Adjusted	0.00056	0.00225	0.01277	0.00016	0.03704	-0.06345	0.10049	-0.00720	0.00644	-0.78769	7.29998
KLBN11.SA.Adjusted	0.00068	0.00054	0.01260	0.00016	0.03082	-0.03027	0.06110	-0.00696	0.00850	0.03379	2.96893
ITUB4.SA.Adjusted	0.00130	0.00188	0.01229	0.00015	0.02766	-0.04733	0.07499	-0.00596	0.00817	-0.55790	4.17328
VALE3.SA.Adjusted	0.00269	0.00173	0.01222	0.00015	0.03571	-0.04600	0.08171	-0.00307	0.00872	-0.13598	4.61967
IBOV	0.00118	0.00135	0.00885	0.00008	0.02538	-0.04405	0.06943	-0.00308	0.00587	-0.97855	7.31801

15 Simulação de Uma carteira de Três Ativos

library(tidyverse)
library(knitr)

# remover benchmark
assets <- setdiff(colnames(returns), "IBOV")

# combinações de 3 ativos
comb <- combn(assets, 3)

# estatísticas
mu    <- colMeans(returns[, assets])
Sigma <- cov(returns[, assets])

w <- rep(1/3, 3)

# anualização (252 dias úteis)
annual_factor <- 252

# cálculo vetorizado
portfolios <- map_dfr(1:ncol(comb), function(i){

  a <- comb[, i]

  ret  <- sum(mu[a] * w) * annual_factor
  risk <- sqrt(t(w) %*% Sigma[a,a] %*% w) * sqrt(annual_factor)

  tibble(
    Ativos  = paste(a, collapse = ", "),
    Retorno = as.numeric(ret),
    Risco   = as.numeric(risk),
    Sharpe  = as.numeric(ret/risk)
  )
})

# ordenar
portfolios <- portfolios |> arrange(desc(Sharpe))

best_port <- portfolios |> slice(1)

kable(head(portfolios, 10), digits = 4,
      caption = "Top 10 carteiras por Sharpe Ratio")

Top 10 carteiras por Sharpe Ratio
Ativos	Retorno	Risco	Sharpe
VALE3.SA.Adjusted, ALPA4.SA.Adjusted, BNBR3.SA.Adjusted	0.5872	0.1639	3.5827
PETR4.SA.Adjusted, VALE3.SA.Adjusted, ALPA4.SA.Adjusted	0.5271	0.1491	3.5353
VALE3.SA.Adjusted, ITUB4.SA.Adjusted, ALPA4.SA.Adjusted	0.5897	0.1686	3.4982
VALE3.SA.Adjusted, ALPA4.SA.Adjusted, GOAU4.SA.Adjusted	0.6232	0.1807	3.4491
VALE3.SA.Adjusted, WEGE3.SA.Adjusted, ALPA4.SA.Adjusted	0.5890	0.1709	3.4457
VALE3.SA.Adjusted, ALPA4.SA.Adjusted, BBDC4.SA.Adjusted	0.6003	0.1779	3.3746
VALE3.SA.Adjusted, KLBN11.SA.Adjusted, ALPA4.SA.Adjusted	0.5375	0.1621	3.3156
VALE3.SA.Adjusted, BBDC4.SA.Adjusted, BNBR3.SA.Adjusted	0.4526	0.1370	3.3035
VALE3.SA.Adjusted, ITUB4.SA.Adjusted, BNBR3.SA.Adjusted	0.4421	0.1349	3.2768
VALE3.SA.Adjusted, GOAU4.SA.Adjusted, BNBR3.SA.Adjusted	0.4756	0.1508	3.1536

kable(best_port, digits = 4,
      caption = "Carteira Ótima (Maior Sharpe)")

Carteira Ótima (Maior Sharpe)
Ativos	Retorno	Risco	Sharpe
VALE3.SA.Adjusted, ALPA4.SA.Adjusted, BNBR3.SA.Adjusted	0.5872	0.1639	3.5827

15.1 Metodologia do Calculo do Risco de carteiras - MW

O retono esperado de uma carteira é calculado através da média ponderada do retorno de cada um dos ativos pelo respectivo peso ou participação na carteira. No entanto, o risco de uma carteira não é calculado através da media ponderada dos desvios individuais dos ativos.

Para o calculo do risco de uma carteira formada por 2 ou n ativos devemos considerar a correlação ou covariância entre sí, de modo que ao considerarmos a correlação entre os ativos podemos esperar uma diminuição do risco se comparado a média ponderada dos desvios individuais conforme a moderna teoria de Markowitzs.

Desse modo, o calculo do risco da carteiras foram calculados da seguinte maneira:

\[\sigma_p^2 = \sum_{i=1}^{n} w_i^2 \sigma_i^2 + 2 \sum_{i=1}^{n-1} \sum_{j=i+1}^{n} w_i \, w_j \, \rho_{ij} \, \sigma_i \, \sigma_j\]

onde:

\(w_i\) é o peso do ativo \(i\) na carteira, com \(\sum_{i=1}^{n} w_i = 1\);

\(\sigma_i^2\) é a variância do retorno do ativo \(i\);

\(\rho_{ij}\) é o coeficiente de correlação entre os retornos dos ativos \(i\) e \(j\);

\(\sigma_p^2\) é a variância do retorno da carteira.

16 Risco e Retorno das Carteiras

plot(portfolios$Risco, portfolios$Retorno,
     pch = 19,
     col = rgb(0,0,0,0.3),
     xlab = "Risco (vol anual)",
     ylab = "Retorno anual",
     main = "Carteiras Simuladas")

points(best_port$Risco, best_port$Retorno,
       col = "red", pch = 19, cex = 2)

text(best_port$Risco, best_port$Retorno,
     labels = "Ótima", pos = 4)

17 Fronteira Efieciente de Markowitz

library(PortfolioAnalytics)
library(PerformanceAnalytics)
library(ROI)
library(ROI.plugin.quadprog)

# remover benchmark corretamente
assets <- setdiff(colnames(returns), "IBOV")

R <- returns[, assets]

# especificação do portfólio
port <- portfolio.spec(assets = assets)

port <- add.constraint(port, type = "full_investment")
port <- add.constraint(port, type = "long_only")

port <- add.objective(port, type = "return", name = "mean")
port <- add.objective(port, type = "risk", name = "StdDev")

# otimização (mais pontos = fronteira suave)
opt <- optimize.portfolio(
  R,
  port,
  optimize_method = "random",
  search_size = 20000,
  trace = TRUE
)

# gráfico base (rápido)
chart.EfficientFrontier(opt,
                        match.col="StdDev",
                        type="l",
                        main="Fronteira Eficiente de Markowitz")

# pesos ótimos
weights_tbl <- data.frame(
  Ativo = names(opt$weights),
  Peso  = round(opt$weights,4)
)

knitr::kable(weights_tbl, caption="Pesos ótimos do portfólio")

Pesos ótimos do portfólio
	Ativo	Peso
PETR4.SA.Adjusted	PETR4.SA.Adjusted	0.076
VALE3.SA.Adjusted	VALE3.SA.Adjusted	0.242
WEGE3.SA.Adjusted	WEGE3.SA.Adjusted	0.052
AMER3.SA.Adjusted	AMER3.SA.Adjusted	0.010
BBAS3.SA.Adjusted	BBAS3.SA.Adjusted	0.022
ITUB4.SA.Adjusted	ITUB4.SA.Adjusted	0.018
SUZB3.SA.Adjusted	SUZB3.SA.Adjusted	0.112
KLBN11.SA.Adjusted	KLBN11.SA.Adjusted	0.010
ALPA4.SA.Adjusted	ALPA4.SA.Adjusted	0.000
EQTL3.SA.Adjusted	EQTL3.SA.Adjusted	0.038
PRIO3.SA.Adjusted	PRIO3.SA.Adjusted	0.016
BBDC4.SA.Adjusted	BBDC4.SA.Adjusted	0.042
PSSA3.SA.Adjusted	PSSA3.SA.Adjusted	0.098
MGLU3.SA.Adjusted	MGLU3.SA.Adjusted	0.000
GOAU4.SA.Adjusted	GOAU4.SA.Adjusted	0.002
JBSS32.SA.Adjusted	JBSS32.SA.Adjusted	0.108
GMAT3.SA.Adjusted	GMAT3.SA.Adjusted	0.000
BNBR3.SA.Adjusted	BNBR3.SA.Adjusted	0.128
MELI34.SA.Adjusted	MELI34.SA.Adjusted	0.018
GUAR3.SA.Adjusted	GUAR3.SA.Adjusted	0.008

18 Conclusões

Diversificação reduz volatilidade total
Betas evidenciam exposição ao mercado
Carteiras com utilities + bancos + commodities tendem melhor Sharpe
Fronteira eficiente demonstra alocação ótima de capital

19 Resultados das carteiras x perfis de investidores

# classificação
q <- quantile(portfolios$Risco, probs=c(.33,.66))

portfolios$Perfil <- cut(
  portfolios$Risco,
  breaks=c(-Inf,q[1],q[2],Inf),
  labels=c("Conservador","Moderado","Agressivo")
)

cols <- c("blue","orange","red")

plot(portfolios$Risco, portfolios$Retorno,
     col=cols[portfolios$Perfil],
     pch=19,
     xlab="Risco",
     ylab="Retorno",
     main="Perfis de Investidor")

points(best_port$Risco, best_port$Retorno,
       col="black", pch=19, cex=2)

legend("topleft",
       legend=levels(portfolios$Perfil),
       col=cols,
       pch=19)

20 Referências

NETO, Alexandre Assaf; LIMA, Fabiano Guasti. Curso de administração financeira. Atlas, 2009.
ASSAF NETO, Alexandre. Mercado financeiro. 2000.

Assaf e Lima (2009) recomendam o metodo do calculo do Retorno logarítmo para análise de desempenho dessas séries temporais. O metodo permite uma suavização exponencial.↩︎

Análise Quantitativa de Carteiras de Ações Brasileiras

Daniel Marques

2026-02-07