Investments Markowitz Optimization

library(tidyquant)         

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

## ── Attaching core tidyquant packages ─────────────────────── tidyquant 1.0.11 ──
## ✔ PerformanceAnalytics 2.0.8      ✔ TTR                  0.24.4
## ✔ quantmod             0.4.27     ✔ xts                  0.14.1
## ── Conflicts ────────────────────────────────────────── tidyquant_conflicts() ──
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## ✖ zoo::as.Date.numeric()         masks base::as.Date.numeric()
## ✖ PerformanceAnalytics::legend() masks graphics::legend()
## ✖ quantmod::summary()            masks base::summary()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

library(timetk)            

## 
## Attaching package: 'timetk'
## 
## The following object is masked from 'package:tidyquant':
## 
##     FANG

library(tidyverse)         

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.4     ✔ readr     2.1.5
## ✔ forcats   1.0.0     ✔ stringr   1.5.1
## ✔ ggplot2   3.5.2     ✔ tibble    3.2.1
## ✔ lubridate 1.9.4     ✔ tidyr     1.3.1
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

library(PerformanceAnalytics) 
library(quadprog)
library(tseries) 
library(zoo)     
library(xts)     
library(quantmod)
library(ggplot2) 
library(reshape2)

## 
## Attaching package: 'reshape2'
## 
## The following object is masked from 'package:tidyr':
## 
##     smiths

library(corrplot)

## corrplot 0.95 loaded

Getting data - 20 stocks from 4 industries: Technology, Automotive, Financial, Helathcare + 1 commodity (gold), 1 crypto (Bitcoin), 1 ESG ETF (ESGU) and S&P 500 index ETF (SPY)

library(tidyquant)

tickers <- c("AAPL", "MSFT", "GOOGL", "AMZN", "NVDA",       # Tech
             "TSLA", "F", "GM", "APTV", "BWA",              # Automotive
             "JPM", "BAC", "WFC", "GS", "MS",               # Financials
             "JNJ", "PFE", "MRK", "ABBV", "UNH",            # Healthcare
             "GLD", "BTC-USD", "ESGU", "SPY")               # Commodity, Crypto, ESG, Market Index

prices <- tq_get(
  tickers,
  from = "2020-01-01",
  to = "2025-01-01",
  get = "stock.prices",
  periodicity = "weekly"
)

library(tidyr)
library(dplyr)

prices_wide <- prices %>%
  select(date, symbol, adjusted) %>%
  pivot_wider(names_from = symbol, values_from = adjusted) %>%
  arrange(date)

Getting Risk free rate data

library(quantmod)

# Getting 1-month T-Bill from FRED
getSymbols("DGS1MO", src = "FRED")

## [1] "DGS1MO"

rf_weekly <- mean(DGS1MO, na.rm = TRUE) / 100 / 52  # decimal, weeklyized
rf_annual <- mean(DGS1MO, na.rm = TRUE) / 100  # Convert to decimal and annualize

library(knitr)

rf_table <- data.frame(
  Frequency = c("Weekly", "Annual"),
  Risk_Free_Rate = c(rf_weekly, rf_annual)
)

kable(rf_table, digits = 6, caption = "Risk-Free Rate (Weekly vs. Annual)")

Risk-Free Rate (Weekly vs. Annual)

Frequency	Risk_Free_Rate
Weekly	0.000307
Annual	0.015962

Calculate weekly log returns and annualized returns

library(dplyr)
library(lubridate)
library(knitr)

# Compute weekly log returns
weekly_returns <- prices_wide %>%
  mutate(date = as.Date(date)) %>%
  arrange(date) %>%
  mutate(across(-date, ~ log(. / lag(.)))) %>%
  mutate(year = year(date)) %>%
  na.omit()

# Compute annual log returns by summing weekly returns
annual_log_returns <- weekly_returns %>%
  group_by(year) %>%
  summarize(across(where(is.numeric), sum, .names = "{.col}")) %>%
  ungroup()

# Show table
kable(annual_log_returns, caption = "Annual Log Returns", digits = 4)

Annual Log Returns

year	AAPL	MSFT	GOOGL	AMZN	NVDA	TSLA	F	GM	APTV	BWA	JPM	BAC	WFC	GS	MS	JNJ	PFE	MRK	ABBV	UNH	GLD	BTC-USD	ESGU	SPY
2020	0.5718	0.3346	0.2209	0.5235	0.8058	2.0587	-0.0502	0.1820	0.3829	-0.0662	-0.0426	-0.1081	-0.5057	0.1640	0.3406	0.1150	0.0515	-0.0639	0.2346	0.1901	0.2118	1.4264	0.1932	0.1588
2021	0.3222	0.4204	0.5066	0.0402	0.7825	0.4471	1.0384	0.4562	0.2554	0.2221	0.3143	0.4802	0.5604	0.4255	0.4293	0.1023	0.4211	0.0308	0.2852	0.3672	-0.0755	0.3003	0.2477	0.2648
2022	-0.3566	-0.3079	-0.4826	-0.6689	-0.7150	-1.2655	-0.7009	-0.6602	-0.6167	-0.1573	-0.1857	-0.3361	-0.2097	-0.1369	-0.1612	0.0667	-0.0299	0.3985	0.2217	0.0677	0.0087	-1.0122	-0.2334	-0.2102
2023	0.4005	0.4458	0.4385	0.5579	1.2138	0.8321	0.1401	0.0745	-0.0304	0.0267	0.2712	0.0422	0.1967	0.1459	0.1292	-0.0780	-0.5004	0.0463	0.0237	0.0541	0.1088	0.9915	0.2263	0.2311
2024	0.3042	0.1354	0.3185	0.3807	1.0256	0.4859	-0.1380	0.4008	-0.3994	-0.1096	0.3551	0.2848	0.3795	0.4124	0.3276	-0.0697	-0.0545	-0.1026	0.1420	-0.0486	0.2387	0.7315	0.2245	0.2278

kable(weekly_returns, caption = "Weekly Log Returns", digits = 4)

Weekly Log Returns

date	AAPL	MSFT	GOOGL	AMZN	NVDA	TSLA	F	GM	APTV	BWA	JPM	BAC	WFC	GS	MS	JNJ	PFE	MRK	ABBV	UNH	GLD	BTC-USD	ESGU	SPY	year
2020-01-08	0.0468	0.0285	0.0251	-0.0198	0.0302	0.1370	0.0043	0.0000	-0.0242	-0.0169	0.0277	0.0200	-0.0659	0.0423	0.0374	0.0106	0.0335	0.0082	-0.0078	-0.0054	-0.0155	0.0782	0.0168	0.0145	2020
2020-01-15	0.0124	0.0266	0.0355	0.0120	0.0027	0.0171	-0.0086	-0.0046	0.0221	-0.0299	-0.0142	-0.0305	-0.0073	0.0002	0.0563	0.0186	0.0067	0.0004	0.0110	0.0418	0.0072	-0.0093	0.0124	0.0117	2020
2020-01-22	0.0035	-0.0063	-0.0217	-0.0207	0.0001	0.0354	-0.0264	-0.0393	-0.0151	-0.1337	-0.0178	-0.0302	-0.0326	-0.0128	-0.0346	0.0015	-0.0561	-0.0422	-0.0491	-0.0500	0.0063	0.0677	-0.0117	-0.0134	2020
2020-01-29	0.0036	0.0849	-0.0035	0.1007	-0.0034	0.4477	0.0231	0.0215	0.0097	-0.0286	0.0064	0.0114	-0.0023	-0.0026	0.0000	0.0139	-0.0119	0.0242	0.0070	-0.0178	-0.0084	-0.0192	0.0101	0.0066	2020
2020-02-05	0.0024	0.0237	0.0438	0.0482	0.0807	-0.1358	-0.1083	0.0184	0.0055	-0.0093	0.0198	0.0336	0.0153	-0.0229	0.0386	0.0026	0.0207	-0.0358	0.1293	0.0348	0.0084	0.1061	0.0170	0.0187	2020
2020-02-12	0.0005	0.0150	0.0062	0.0023	0.1017	0.1030	-0.0050	-0.0173	-0.0309	0.0067	-0.0172	-0.0145	-0.0104	-0.0138	-0.0047	-0.0189	-0.0476	-0.0333	-0.0252	0.0383	0.0218	-0.0065	0.0048	0.0044	2020
2020-02-19	-0.1020	-0.1080	-0.0917	-0.0887	-0.1237	-0.0706	-0.1087	-0.0805	-0.0818	-0.1098	-0.0717	-0.0977	-0.0406	-0.0692	-0.1449	-0.0306	-0.0681	-0.0269	-0.0485	-0.1373	0.0157	-0.0822	-0.0735	-0.0742	2020
2020-02-26	0.0043	-0.0187	-0.0357	-0.0328	0.0145	-0.0704	-0.0366	-0.0395	-0.0067	0.0152	-0.0765	-0.1133	-0.1073	-0.0674	-0.0786	-0.0583	0.0108	-0.0143	-0.0182	-0.0076	0.0038	-0.0611	-0.0401	-0.0405	2020
2020-03-04	-0.0139	-0.0221	-0.0479	-0.0090	-0.0177	-0.1443	-0.1074	-0.1181	-0.1009	-0.1115	-0.1497	-0.1616	-0.1444	-0.0924	-0.1169	0.0437	0.0084	0.0359	-0.0005	0.0687	0.0038	-0.1053	-0.0424	-0.0402	2020
2020-03-11	-0.1208	-0.0934	-0.1315	-0.0454	-0.1837	-0.4055	-0.2227	-0.2765	-0.4106	-0.2205	-0.0714	-0.0652	-0.1688	-0.1500	-0.1561	-0.0363	-0.0728	-0.0964	-0.1812	-0.1367	-0.0733	-0.4145	-0.1246	-0.1318	2020
2020-03-18	-0.0239	0.0120	0.0106	0.0706	0.1370	0.1603	-0.0120	0.0381	0.0247	0.0222	-0.0585	-0.0442	-0.0243	-0.0325	-0.0170	-0.1363	-0.0796	-0.0675	-0.0788	-0.1010	0.0663	0.2537	-0.0354	-0.0389	2020
2020-03-25	0.0296	0.0613	0.0279	0.0049	0.0563	0.0369	-0.0245	-0.0158	-0.0057	0.0670	0.0179	0.0095	-0.0076	0.0064	0.0232	0.0956	0.0944	0.1082	0.1213	0.1263	-0.0355	-0.0450	0.0475	0.0642	2020
2020-04-01	0.0200	0.0360	0.0176	0.0312	-0.0175	0.0401	-0.0252	0.0247	0.0830	0.0122	0.0068	0.0420	0.0024	0.0713	0.0829	0.0473	0.0293	0.0208	-0.0106	-0.0054	0.0526	0.1085	0.0369	0.0282	2020
2020-04-08	0.1012	0.0606	0.0676	0.1267	0.0919	0.2635	0.1161	0.0759	0.1606	0.0973	0.0626	0.0694	0.0478	0.0710	0.0761	0.0603	0.0808	0.0530	0.0856	0.0867	0.0417	-0.0477	0.0696	0.0680	2020
2020-04-15	-0.0673	-0.0344	-0.0429	0.0194	-0.0522	-0.0332	-0.1035	-0.0787	-0.0738	-0.0638	-0.0699	-0.0922	-0.1173	-0.0251	-0.0758	0.0247	-0.0228	-0.0530	-0.0070	0.0135	-0.0253	0.0055	-0.0412	-0.0386	2020
2020-04-22	0.0373	0.0118	0.0167	-0.0060	0.0780	0.1133	0.1203	0.0433	0.1334	0.1126	0.0677	0.0989	0.0729	0.0732	0.0826	0.0114	0.0623	0.0328	0.0294	0.0504	0.0140	0.1264	0.0472	0.0454	2020
2020-04-29	0.0659	0.0625	0.0903	0.0016	0.0081	-0.0012	-0.0793	-0.0424	-0.0157	-0.0573	-0.0351	-0.0529	-0.0925	-0.0477	-0.0551	-0.0126	0.0157	-0.0398	0.0310	0.0161	0.0011	0.1425	0.0031	0.0016	2020
2020-05-06	0.0455	0.0096	0.0192	0.0167	0.0606	0.0522	0.0020	0.0594	-0.0175	0.0457	-0.0555	-0.0355	-0.0906	-0.0061	0.0203	-0.0159	-0.0303	-0.0106	0.0579	-0.0184	-0.0061	-0.0223	0.0053	0.0017	2020
2020-05-13	0.0082	0.0061	-0.0006	0.0384	0.1209	-0.0017	0.0623	0.0902	0.0818	0.0235	0.0187	0.0154	0.0164	0.0035	0.0234	0.0127	0.0184	0.0047	0.0081	0.0047	0.0260	0.0999	0.0175	0.0183	2020
2020-05-20	0.0114	-0.0113	0.0336	-0.0113	-0.0100	0.0134	0.0970	0.1041	0.0780	0.0871	0.0775	0.0891	0.0921	0.0976	0.1051	-0.0304	-0.0051	-0.0037	-0.0054	0.0200	-0.0207	-0.0964	0.0252	0.0241	2020
2020-05-27	0.0207	0.0210	0.0146	0.0207	0.0123	0.0738	0.0102	0.0004	0.0513	0.0740	0.0319	0.0228	0.0425	0.0404	0.0424	0.0321	-0.0361	0.0453	0.0036	0.0380	0.0106	0.0757	0.0304	0.0296	2020
2020-06-03	0.0619	0.0261	0.0068	0.0506	0.0247	0.0649	0.2047	0.0856	-0.0482	0.0821	0.1110	0.1276	0.1747	0.0724	0.1005	-0.0156	0.0014	0.0174	0.0548	0.0094	-0.0083	0.0275	0.0391	0.0404	2020
2020-06-10	0.0232	0.0197	-0.0039	0.0055	0.0029	0.0431	-0.1002	-0.0722	0.0032	-0.0869	-0.0798	-0.0827	-0.1346	-0.0398	-0.0372	-0.0103	-0.0808	-0.0665	-0.0011	-0.0538	0.0061	-0.0267	-0.0279	-0.0247	2020
2020-06-17	0.0402	0.0422	0.0120	0.0555	0.0412	0.0198	-0.0630	-0.0567	0.0337	0.0528	-0.0413	-0.0399	-0.0463	-0.0232	-0.0139	-0.0111	-0.0190	0.0099	0.0129	0.0156	0.0257	0.0096	0.0080	-0.0029	2020
2020-06-24	-0.0047	0.0079	-0.0319	-0.0020	0.0050	0.0750	-0.0114	-0.0369	-0.0107	-0.0034	-0.0403	-0.0429	-0.0617	-0.0356	0.0085	-0.0157	-0.0021	0.0027	0.0089	-0.0046	0.0053	-0.0524	-0.0080	-0.0075	2020
2020-07-01	0.0214	0.0230	0.0494	0.0838	0.0386	0.2524	0.0066	-0.0067	-0.0104	-0.0074	-0.0187	-0.0317	-0.0456	0.0088	-0.0169	0.0157	0.0399	0.0178	0.0118	0.0057	0.0099	0.0124	0.0174	0.0174	2020
2020-07-08	0.0409	0.0005	0.0206	0.0276	0.0499	0.0874	0.0385	0.0201	0.0139	0.0348	0.0715	0.0479	-0.0086	0.0709	0.0615	0.0349	0.0347	-0.0060	-0.0048	0.0392	0.0068	-0.0010	0.0162	0.0162	2020
2020-07-15	-0.0006	0.0019	0.0228	0.0175	-0.0047	0.0334	0.0491	0.0197	0.0460	0.0384	0.0121	0.0115	0.0773	-0.0093	0.0366	0.0122	0.0406	0.0081	-0.0028	-0.0111	0.0164	0.0141	0.0187	0.0189	2020
2020-07-22	-0.0394	-0.0328	-0.0342	-0.0450	-0.0110	-0.0604	0.0482	0.0069	0.0037	0.0210	-0.0212	-0.0025	-0.0259	-0.0503	-0.0413	-0.0196	0.0616	0.0101	-0.0071	-0.0171	0.0603	0.1519	-0.0127	-0.0119	2020
2020-07-29	0.1621	0.0543	-0.0204	0.0451	0.0945	0.0071	-0.0216	-0.0203	-0.0141	-0.0354	-0.0184	0.0263	-0.0527	0.0001	-0.0201	0.0027	-0.0163	0.0245	-0.0253	0.0151	0.0313	0.0265	0.0294	0.0273	2020
2020-08-05	-0.0026	-0.0476	0.0049	-0.0187	-0.0342	-0.0788	0.0525	0.1002	0.0921	0.1162	0.0830	0.0736	0.0444	0.0457	0.0568	-0.0017	-0.0060	-0.0093	-0.0173	0.0356	-0.0522	0.0181	0.0055	0.0083	2020
2020-08-12	0.0568	0.0391	0.0496	0.0726	0.1222	0.3170	-0.0482	0.0452	-0.0182	-0.0128	-0.0544	-0.0530	-0.0478	-0.0473	-0.0167	0.0210	0.0150	0.0441	0.0317	0.0040	0.0448	0.0496	0.0214	0.0174	2020
2020-08-19	0.0771	0.0233	0.0317	0.0102	0.0391	0.0697	0.0072	-0.0050	-0.0218	-0.0051	0.0219	0.0182	0.0234	0.0230	0.0219	0.0130	0.0013	0.0132	-0.0168	-0.0146	-0.0377	-0.0535	0.0165	0.0161	2020
2020-08-26	0.0723	0.0511	0.0302	0.0446	0.0807	0.1604	-0.0160	0.0034	0.0196	0.0140	-0.0036	-0.0112	-0.0230	-0.0026	0.0101	0.0031	-0.0406	-0.0147	-0.0195	0.0020	0.0209	0.0518	0.0267	0.0243	2020
2020-09-02	-0.1734	-0.1146	-0.0828	-0.1052	-0.1483	-0.3637	0.0289	0.0834	-0.0278	0.0048	-0.0022	-0.0090	-0.0033	-0.0086	-0.0469	-0.0285	-0.0261	-0.0131	-0.0221	-0.0180	-0.0205	-0.1668	-0.0626	-0.0566	2020
2020-09-09	0.0238	0.0298	0.0075	0.0020	0.0866	0.3090	0.0014	-0.0250	0.0158	0.0157	-0.0064	-0.0009	0.0373	-0.0224	0.0044	0.0110	0.0283	0.0105	0.0076	-0.0001	0.0118	0.0636	0.0232	0.0207	2020
2020-09-16	-0.0328	-0.0065	-0.0503	-0.0086	-0.0276	-0.0584	-0.0376	-0.0702	-0.0176	-0.1221	-0.0518	-0.0545	-0.0507	-0.0328	-0.0563	-0.0319	-0.0194	-0.0079	-0.0257	-0.0390	-0.0265	-0.0242	-0.0240	-0.0294	2020
2020-09-23	0.0202	-0.0008	0.0042	0.0051	0.0455	-0.0122	-0.0269	-0.0241	0.0840	0.0164	0.0114	-0.0071	-0.0166	0.0266	-0.0082	0.0196	-0.0022	-0.0126	-0.0195	0.0331	-0.0026	0.0286	0.0024	0.0102	2020
2020-09-30	-0.0082	-0.0065	-0.0103	-0.0144	0.0379	-0.0122	0.0560	0.0562	0.0275	0.0490	0.0276	0.0249	0.0388	0.0216	0.0105	-0.0055	0.0000	-0.0281	-0.0116	0.0333	-0.0050	-0.0224	0.0130	0.0077	2020
2020-10-07	0.0678	0.0791	0.0769	0.1051	0.0366	0.0760	0.1059	0.0472	0.0167	-0.0251	0.0370	0.0235	0.0229	0.0472	0.0550	0.0143	0.0200	0.0135	0.0223	0.0526	0.0024	0.0746	0.0452	0.0444	2020
2020-10-14	-0.0301	-0.0375	-0.0103	-0.0681	-0.0432	-0.0569	-0.0026	0.1107	0.0420	0.0087	-0.0041	-0.0330	-0.0812	-0.0133	0.0202	-0.0260	0.0159	-0.0307	-0.0416	-0.0245	0.0086	0.0420	-0.0191	-0.0195	2020
2020-10-21	-0.0078	-0.0065	0.0304	0.0213	-0.0184	0.0065	0.0230	-0.0201	-0.0397	-0.0456	-0.0104	-0.0121	-0.0444	-0.0612	-0.0576	-0.0097	-0.0016	-0.0036	-0.0049	-0.0090	-0.0013	0.1361	-0.0148	-0.0151	2020
2020-10-28	-0.0543	-0.0325	0.0288	-0.0752	-0.0286	-0.0018	-0.0051	0.0131	0.0555	-0.0325	0.0403	0.0346	0.0123	0.0114	0.0519	-0.0330	-0.0337	-0.0138	0.0615	0.0026	-0.0006	0.0215	-0.0078	-0.0065	2020
2020-11-04	0.0489	0.0219	0.0544	-0.0044	-0.0193	-0.0325	0.0615	0.1502	0.0670	0.0655	0.1194	0.1136	0.0908	0.0941	0.0929	0.0682	0.0665	0.0530	0.1169	0.0959	-0.0184	0.0918	0.0514	0.0522	2020
2020-11-11	0.0308	0.0162	0.0137	0.0326	0.0498	0.0734	0.0432	0.0217	0.0502	-0.0208	-0.0035	-0.0040	0.0391	0.0325	0.0534	0.0072	-0.0079	0.0048	0.0034	-0.0045	0.0048	0.1432	0.0200	0.0184	2020
2020-11-18	-0.0360	-0.0028	0.0013	-0.0056	-0.0352	0.2292	0.0770	0.1014	0.0612	0.0630	0.0602	0.0506	0.1333	0.0556	0.0783	-0.0374	0.0154	-0.0168	0.0468	-0.0468	-0.0399	0.0796	0.0110	0.0072	2020
2020-11-25	0.0635	0.0135	0.0177	0.0322	0.0328	0.0515	-0.0225	-0.0391	0.0045	-0.0445	-0.0295	-0.0101	-0.0194	-0.0231	-0.0050	0.0315	0.0740	0.0174	0.0008	0.0153	0.0035	-0.0161	0.0091	0.0077	2020
2020-12-02	0.0134	-0.0009	0.0089	-0.0134	-0.0030	0.1056	0.0011	-0.0199	0.0070	0.0207	0.0187	0.0083	0.0309	0.0341	0.0099	0.0274	0.0769	0.0198	0.0345	0.0194	0.0308	-0.0260	0.0130	0.0113	2020
2020-12-09	0.0278	-0.0087	-0.0281	-0.0038	0.0011	-0.0259	-0.0109	-0.0501	-0.0037	-0.0428	-0.0139	-0.0039	0.0269	0.0149	0.0006	-0.0065	-0.0948	-0.0330	-0.0463	-0.0202	-0.0089	0.0581	-0.0051	-0.0016	2020
2020-12-16	0.0308	0.0448	-0.0235	0.0130	-0.0062	0.0111	-0.0401	-0.0184	0.0196	0.0367	0.0112	0.0197	-0.0262	0.0311	0.0412	0.0142	-0.0522	-0.0054	-0.0002	-0.0138	0.0032	0.2028	0.0057	-0.0064	2020
2020-12-23	0.0224	0.0009	0.0216	0.0354	-0.0256	0.0393	0.0034	0.0162	0.0239	-0.0144	0.0271	0.0270	0.0279	0.0312	0.0159	0.0093	0.0084	0.0249	0.0183	0.0362	0.0106	0.1402	0.0080	0.0157	2020
2020-12-30	-0.0290	-0.0283	-0.0101	-0.0316	0.0350	0.0987	-0.0195	0.0022	0.0407	0.0106	0.0051	0.0083	0.0249	0.0489	0.0259	0.0269	0.0038	-0.0039	0.0170	-0.0074	0.0363	0.2170	-0.0004	-0.0004	2020
2021-01-06	-0.0170	-0.0137	-0.0015	-0.0308	0.0060	0.1446	0.1228	0.1379	0.1246	0.0552	0.1169	0.1065	0.1059	0.1093	0.0869	-0.0013	-0.0003	0.0242	0.0303	0.0358	-0.0490	-0.0020	0.0221	0.0198	2021
2021-01-13	-0.0076	0.0070	0.0267	0.0000	-0.0347	-0.0058	0.0242	0.1370	-0.0580	-0.0465	-0.0157	-0.0268	-0.0394	-0.0269	-0.0107	0.0290	-0.0122	0.0012	0.0216	-0.0146	-0.0089	0.0614	-0.0001	-0.0003	2021
2021-01-20	0.1133	0.0708	0.0669	0.0637	0.0310	0.0446	0.1104	-0.0524	-0.0494	0.1121	-0.0479	-0.0575	-0.0391	-0.0432	-0.0517	0.0462	0.0157	-0.0360	-0.0190	-0.0261	0.0060	-0.1021	0.0139	0.0135	2021
2021-01-27	-0.0588	0.0304	0.0058	0.0161	0.0090	-0.0117	-0.0299	0.0130	0.0402	-0.0614	0.0153	0.0029	-0.0203	0.0183	-0.0037	-0.0557	-0.0642	-0.0314	-0.0502	-0.0129	-0.0087	0.0864	-0.0044	-0.0059	2021
2021-02-03	0.0075	0.0176	0.0783	-0.0224	0.0508	-0.0271	0.0940	0.0614	0.0485	0.0373	0.0437	0.0600	0.0785	0.0459	0.0505	0.0307	0.0102	-0.0357	0.0185	-0.0272	-0.0002	0.2692	0.0233	0.0225	2021
2021-02-10	-0.0195	-0.0003	0.0169	-0.0110	0.0721	-0.0647	-0.0332	-0.0475	0.0449	0.0201	0.0357	0.0393	0.0481	0.0376	0.0241	-0.0072	-0.0080	-0.0106	-0.0115	-0.0153	-0.0226	0.0568	0.0063	0.0052	2021
2021-02-17	-0.0566	-0.0437	-0.0243	-0.0230	-0.0807	-0.1305	0.0069	-0.0450	-0.0224	0.0248	0.0404	0.0358	0.0654	0.0230	0.0189	-0.0284	-0.0227	0.0039	0.0197	0.0150	0.0052	-0.0077	-0.0155	-0.0123	2021
2021-02-24	-0.0059	0.0049	0.0021	-0.0318	-0.0534	-0.0179	0.0770	0.0570	0.0167	0.0294	-0.0040	0.0003	0.0000	0.0361	0.0416	-0.0027	-0.0119	-0.0229	0.0148	0.0154	-0.0405	-0.0092	-0.0043	-0.0025	2021
2021-03-03	-0.0327	-0.0004	-0.0118	-0.0103	-0.0684	-0.0189	0.0016	0.0099	-0.0720	0.0603	0.0121	0.0220	0.0263	0.0029	0.0007	-0.0083	0.0277	0.0176	-0.0099	0.0505	-0.0097	0.1251	-0.0019	0.0016	2021
2021-03-10	0.0363	0.0167	0.0211	0.0094	0.0601	0.0049	-0.0064	0.0442	0.0265	-0.0029	0.0110	0.0407	0.0315	0.0331	0.0207	0.0230	0.0393	0.0354	0.0372	0.0074	0.0093	0.0355	0.0229	0.0223	2021
2021-03-17	-0.0244	-0.0005	-0.0206	0.0147	-0.0167	-0.0220	-0.0227	-0.0169	-0.0549	-0.0961	-0.0267	-0.0199	-0.0286	-0.0295	-0.0423	-0.0063	-0.0132	0.0017	-0.0557	0.0420	-0.0033	-0.0370	-0.0132	-0.0163	2021
2021-03-24	-0.0218	-0.0244	0.0025	-0.0266	-0.0153	-0.0409	0.0203	0.0410	-0.0158	0.0491	0.0330	0.0551	0.0296	0.0007	-0.0004	0.0286	0.0210	0.0090	0.0184	0.0136	-0.0266	0.0736	0.0073	0.0166	2021
2021-03-31	0.0513	0.0668	0.0765	0.0537	0.0741	0.0844	0.0363	0.0570	0.0497	0.0030	-0.0126	0.0178	0.0116	-0.0150	0.0000	-0.0099	-0.0017	-0.0153	-0.0133	-0.0249	0.0352	-0.0124	0.0328	0.0284	2021
2021-04-07	0.0631	0.0420	0.0202	0.0532	0.1232	0.0973	-0.0573	-0.0573	-0.0216	0.0109	0.0160	-0.0094	-0.0015	0.0019	0.0055	-0.0242	0.0303	0.0084	0.0266	0.0274	0.0013	0.0873	0.0179	0.0165	2021
2021-04-14	-0.0099	-0.0009	0.0108	-0.0194	-0.0330	-0.0585	-0.0634	-0.0476	-0.0446	0.0158	-0.0318	-0.0320	0.0668	0.0127	-0.0286	0.0430	0.0491	0.0276	0.0075	0.0572	0.0185	-0.1173	-0.0024	-0.0017	2021
2021-04-21	0.0096	0.0143	0.0052	0.0245	0.0138	-0.0200	0.0869	0.0558	0.0829	0.0445	0.0132	0.0462	0.0582	0.0435	0.0587	-0.0200	-0.0150	-0.0155	0.0339	-0.0051	-0.0004	-0.0258	0.0126	0.0129	2021
2021-04-28	-0.0499	-0.0556	0.0069	-0.0314	-0.0693	-0.0452	-0.0904	-0.0635	-0.0487	-0.0327	0.0276	0.0277	0.0143	0.0092	0.0083	0.0277	0.0383	-0.0179	0.0218	0.0418	0.0010	-0.0314	-0.0074	-0.0046	2021
2021-05-05	-0.0153	-0.0063	-0.0161	-0.0269	-0.0031	-0.0874	0.0148	0.0070	0.0063	0.0629	0.0195	0.0138	-0.0004	0.0284	0.0315	0.0066	-0.0151	0.0192	0.0087	0.0009	0.0328	0.0613	-0.0041	-0.0034	2021
2021-05-12	-0.0068	-0.0129	-0.0033	0.0026	-0.0205	-0.0658	0.0472	0.0029	-0.0237	-0.0101	0.0237	0.0141	0.0268	0.0128	0.0239	0.0093	0.0274	0.0245	0.0200	-0.0032	0.0167	-0.2788	-0.0070	-0.0055	2021
2021-05-19	0.0163	0.0349	0.0434	0.0082	0.1101	0.0454	0.0537	0.0154	0.0325	-0.0264	-0.0031	-0.0036	-0.0166	-0.0001	0.0215	-0.0022	-0.0181	-0.0240	-0.0229	0.0065	0.0165	-0.1110	0.0171	0.0152	2021
2021-05-26	-0.0209	-0.0150	0.0077	-0.0125	0.0387	0.0313	0.1451	0.0497	0.0880	0.0615	0.0256	0.0214	0.0251	0.0480	0.0359	-0.0209	-0.0213	-0.0304	-0.0207	-0.0154	-0.0003	-0.0457	0.0035	0.0034	2021
2021-06-02	0.0196	0.0207	0.0072	0.0140	0.0708	-0.0331	0.0539	0.0691	0.0278	0.0151	-0.0063	-0.0009	-0.0138	0.0093	0.0074	-0.0130	0.0091	0.0092	0.0012	-0.0123	-0.0033	-0.0916	0.0081	0.0062	2021
2021-06-09	0.0226	0.0227	0.0124	0.0358	0.0188	-0.0070	-0.0411	-0.0499	-0.0144	-0.0284	-0.0614	-0.0312	-0.0250	-0.0355	-0.0228	0.0067	0.0189	0.0446	0.0306	-0.0036	-0.0186	0.1883	0.0032	0.0052	2021
2021-06-16	0.0329	0.0273	0.0075	0.0355	0.0601	0.0398	-0.0060	-0.0262	-0.0347	-0.0716	-0.0326	-0.0349	-0.0432	-0.0378	-0.0567	-0.0053	0.0005	0.0150	-0.0098	-0.0040	-0.0458	-0.2176	0.0029	-0.0032	2021
2021-06-23	0.0174	0.0219	-0.0005	-0.0165	0.0586	0.0875	0.0067	-0.0069	0.0430	-0.0027	0.0258	0.0228	0.0283	0.0413	0.0560	0.0025	-0.0130	0.0133	-0.0211	0.0022	-0.0086	0.0984	0.0131	0.0141	2021
2021-06-30	0.0409	0.0228	0.0315	0.0639	0.0330	-0.0316	-0.0346	-0.0236	-0.0044	-0.0112	-0.0047	-0.0203	-0.0295	-0.0074	-0.0048	0.0237	0.0048	0.0116	0.0301	0.0301	0.0198	-0.0466	0.0107	0.0122	2021
2021-07-07	0.0252	0.0119	0.0091	0.0004	-0.0219	0.0135	-0.0055	0.0219	-0.0004	-0.0055	0.0202	-0.0053	-0.0060	0.0164	0.0327	0.0077	0.0091	-0.0064	0.0187	0.0200	0.0065	-0.0458	0.0057	0.0061	2021
2021-07-14	0.0035	-0.0059	-0.0089	-0.0287	-0.0843	-0.0121	-0.0360	-0.0449	-0.0282	-0.0112	-0.0389	-0.0560	0.0366	-0.0303	-0.0096	-0.0049	0.0347	-0.0187	-0.0159	-0.0134	0.0010	-0.0927	-0.0094	-0.0105	2021
2021-07-21	0.0042	0.0255	0.0441	0.0148	0.0315	-0.0241	-0.0087	-0.0207	0.0369	0.0072	0.0116	0.0077	0.0067	0.0273	0.0441	0.0247	0.0253	0.0218	0.0274	0.0051	-0.0056	0.2792	0.0178	0.0183	2021
2021-07-28	0.0040	0.0020	0.0279	-0.0744	0.0311	0.0960	0.0165	0.0510	0.0625	0.0412	0.0095	0.0149	0.0368	0.0146	0.0012	0.0100	0.0816	-0.0187	-0.0146	0.0162	0.0062	-0.0323	0.0039	0.0049	2021
2021-08-04	-0.0120	-0.0024	0.0086	-0.0136	0.0061	0.0004	-0.0144	-0.0646	0.0037	-0.0735	0.0408	0.0720	0.0581	0.0701	0.0621	-0.0036	0.0625	-0.0161	-0.0124	-0.0243	-0.0466	0.1780	0.0028	0.0035	2021
2021-08-11	0.0325	0.0229	-0.0011	-0.0240	-0.0243	-0.0644	-0.0619	-0.0724	-0.0702	-0.0258	-0.0142	-0.0082	-0.0144	-0.0074	0.0081	0.0323	0.0452	0.0473	0.0413	0.0240	0.0316	-0.0197	0.0023	0.0031	2021
2021-08-18	-0.0038	0.0320	0.0331	0.0195	0.1133	0.0623	0.0069	-0.0180	-0.0039	-0.0295	0.0042	0.0094	-0.0072	0.0088	0.0021	-0.0230	-0.0413	-0.0142	0.0002	0.0039	0.0100	0.0652	0.0101	0.0088	2021
2021-08-25	0.0147	-0.0005	0.0240	0.0487	0.0268	0.0377	-0.0038	-0.0114	-0.0352	-0.0165	0.0144	0.0065	-0.0566	0.0120	0.0129	-0.0070	-0.0489	-0.0186	0.0091	-0.0170	0.0061	-0.0114	0.0086	0.0080	2021
2021-09-01	0.0315	-0.0056	-0.0029	0.0110	0.0125	0.0231	-0.0062	-0.0059	-0.0104	0.0128	-0.0046	-0.0104	-0.0309	-0.0029	-0.0024	-0.0047	0.0147	-0.0041	-0.1023	0.0119	-0.0117	-0.0076	-0.0001	-0.0002	2021
2021-09-08	-0.0562	-0.0013	-0.0121	-0.0170	-0.0187	-0.0113	-0.0070	0.0406	-0.0052	-0.0026	-0.0135	-0.0314	0.0385	-0.0163	-0.0220	-0.0446	-0.0446	-0.0523	-0.0237	-0.0209	0.0066	0.0060	-0.0166	-0.0163	2021
2021-09-15	-0.0322	-0.0168	-0.0249	-0.0313	-0.0458	-0.0069	-0.0070	-0.0274	-0.0516	-0.0329	-0.0264	-0.0180	-0.0044	-0.0715	-0.0361	-0.0016	-0.0178	0.0070	0.0063	0.0030	-0.0166	-0.1460	-0.0205	-0.0240	2021
2021-09-22	-0.0107	-0.0390	-0.0233	-0.0083	-0.0261	0.0503	0.1139	0.0681	0.0804	0.0735	0.0822	0.0980	0.0015	0.0357	0.0373	-0.0105	-0.0202	0.0186	0.0018	-0.0338	-0.0243	0.0083	-0.0046	0.0034	2021
2021-09-29	-0.0057	0.0183	0.0014	-0.0291	-0.0121	0.0039	-0.0014	0.0278	0.0249	0.0133	0.0154	0.0243	0.0435	-0.0095	-0.0282	-0.0200	-0.0169	0.1070	0.0200	-0.0131	0.0156	0.2275	0.0008	-0.0014	2021
2021-10-06	0.0028	0.0142	0.0031	0.0081	0.0107	0.0317	0.0903	0.0816	0.0306	0.0430	-0.0138	-0.0155	-0.0277	0.0019	-0.0144	-0.0119	-0.0112	-0.0249	-0.0086	0.0246	0.0004	0.0842	0.0027	0.0012	2021
2021-10-13	0.0500	0.0511	0.0485	0.0588	0.0754	0.0701	-0.0142	-0.0364	0.0216	-0.0322	0.0192	0.0653	0.0761	0.0642	0.0398	0.0384	0.0057	-0.0013	-0.0104	0.0511	0.0048	0.1369	0.0399	0.0385	2021
2021-10-20	0.0038	0.0061	-0.0278	-0.0200	0.1034	0.1641	0.0332	0.0091	0.0155	-0.0396	0.0166	0.0313	0.0057	0.0131	0.0168	0.0114	0.0343	0.0341	0.0309	0.0689	0.0134	-0.0626	0.0105	0.0117	2021
2021-10-27	0.0047	0.0716	0.0430	-0.0189	0.0659	0.1404	0.1221	-0.0315	0.0316	0.0661	-0.0054	-0.0017	0.0131	0.0148	0.0114	-0.0010	0.0425	0.0791	0.0623	-0.0057	-0.0031	0.0463	0.0123	0.0129	2021
2021-11-03	0.0053	0.0084	0.0237	0.0765	0.1495	-0.1355	0.1108	0.0531	-0.0123	-0.0118	-0.0159	-0.0211	-0.0279	-0.0446	-0.0416	-0.0188	0.0399	-0.0734	-0.0079	0.0269	0.0244	0.0576	0.0115	0.0118	2021
2021-11-10	0.0027	0.0105	-0.0070	-0.0100	-0.0149	0.0301	-0.0165	0.0658	0.0124	0.0400	-0.0145	0.0043	0.0134	-0.0056	0.0098	0.0010	0.0562	0.0167	0.0070	-0.0322	0.0095	-0.1072	0.0039	0.0041	2021
2021-11-17	0.0667	-0.0054	-0.0143	0.0110	0.0498	0.0502	0.0205	0.0070	-0.0251	-0.0137	0.0175	0.0089	0.0202	0.0080	0.0116	-0.0122	0.0294	-0.0157	0.0209	-0.0056	-0.0332	-0.0440	-0.0064	-0.0023	2021
2021-11-24	0.0238	-0.0194	-0.0270	-0.0206	0.0289	0.0317	-0.0463	-0.0857	-0.0602	-0.0981	-0.0578	-0.0659	-0.0730	-0.0644	-0.0716	-0.0235	0.0506	-0.1001	-0.0308	-0.0065	-0.0107	-0.0098	-0.0265	-0.0273	2021
2021-12-01	0.0350	0.0130	0.0372	0.0046	-0.0076	-0.0847	0.0393	0.0613	0.0443	0.0549	0.0233	0.0054	0.0504	0.0490	0.0779	0.0465	-0.0381	-0.0357	0.0526	0.0451	0.0079	-0.1172	0.0250	0.0275	2021
2021-12-08	0.0182	-0.0198	-0.0231	-0.0410	-0.1347	-0.0928	0.0045	-0.0522	-0.0414	-0.0211	-0.0214	-0.0083	-0.0274	-0.0234	-0.0366	0.0415	0.0713	0.0197	0.0465	0.0345	-0.0082	-0.0841	-0.0172	-0.0106	2021
2021-12-15	-0.0077	-0.0032	-0.0030	0.0078	0.0257	-0.0211	-0.0222	-0.0638	-0.0176	-0.0396	-0.0193	0.0014	-0.0223	-0.0221	-0.0107	-0.0183	0.0596	0.0338	0.0207	0.0160	0.0095	0.0487	0.0065	-0.0006	2021
2021-12-22	0.0358	0.0418	0.0222	0.0014	0.0420	0.1482	0.0570	0.0415	0.0288	0.0465	0.0162	0.0115	0.0127	0.0190	0.0223	0.0186	-0.0161	0.0167	0.0336	0.0318	0.0097	-0.0279	0.0285	0.0329	2021
2021-12-29	0.0023	-0.0365	-0.0157	-0.0186	-0.0346	0.0546	0.1579	0.1407	0.0572	0.0651	0.0563	0.0710	0.0857	0.0500	0.0420	0.0043	-0.0619	0.0026	0.0057	-0.0242	0.0055	-0.0362	-0.0007	0.0014	2021
2022-01-05	-0.0260	-0.0436	-0.0328	-0.0130	-0.0516	-0.0770	0.0016	-0.0673	-0.0754	0.0135	-0.0020	0.0251	0.0609	-0.0109	0.0158	0.0010	0.0388	0.0588	0.0133	-0.0456	0.0042	-0.0714	-0.0180	-0.0165	2022
2022-01-12	-0.0306	-0.0399	-0.0271	-0.0398	-0.0713	-0.0324	0.0012	-0.0444	-0.0656	0.0078	-0.0959	-0.0618	0.0112	-0.1286	-0.1193	-0.0245	-0.0466	-0.0016	-0.0014	-0.0172	-0.0053	-0.0085	-0.0322	-0.0286	2022
2022-01-19	-0.0608	-0.0479	-0.0690	-0.1268	-0.1487	-0.1152	-0.1990	-0.1247	-0.0956	-0.1032	-0.0318	-0.0181	-0.0562	-0.0369	0.0521	0.0032	-0.0294	-0.0258	-0.0170	-0.0090	0.0187	-0.1369	-0.0502	-0.0494	2022
2022-01-26	0.0888	0.0679	0.0810	0.0770	0.0986	0.0139	0.0335	0.0410	0.0294	0.0124	0.0310	0.0327	0.0368	0.0638	0.0484	0.0192	0.0100	0.0305	0.0290	0.0250	-0.0255	0.0473	0.0422	0.0417	2022
2022-02-02	0.0013	-0.0137	0.0127	0.0654	0.0189	-0.0100	-0.1484	-0.0891	-0.0419	-0.0047	0.0313	0.0507	0.0551	0.0165	0.0298	0.0037	-0.0186	-0.0631	0.0464	0.0520	0.0142	0.1299	-0.0069	-0.0044	2022
2022-02-09	-0.0105	-0.0135	-0.0202	-0.0308	0.0538	0.0005	0.0201	0.0042	0.0675	0.0174	-0.0079	-0.0327	-0.0018	-0.0168	-0.0278	-0.0248	-0.0376	0.0116	0.0087	-0.0312	0.0143	0.0103	-0.0101	-0.0108	2022
2022-02-16	-0.0503	-0.0434	-0.0510	-0.0412	-0.1246	-0.1158	-0.0447	-0.0602	-0.0433	-0.0662	-0.0186	-0.0478	-0.0546	-0.0556	-0.0877	-0.0376	-0.0465	-0.0242	0.0055	-0.0334	0.0252	-0.1521	-0.0410	-0.0378	2022
2022-02-23	-0.0068	0.0269	0.0322	0.0063	0.0037	0.0508	-0.0347	-0.0493	-0.1527	-0.0875	-0.1071	-0.0702	-0.0946	-0.0478	-0.0781	0.0240	-0.0382	0.0051	0.0145	0.0293	0.0230	0.1471	0.0035	0.0010	2022
2022-03-02	-0.0359	-0.0669	-0.0533	-0.1055	-0.0873	-0.0473	-0.0409	-0.1021	-0.1645	-0.0683	-0.0616	-0.0958	-0.0792	-0.0152	-0.0506	0.0284	0.0363	0.0080	-0.0037	-0.0059	0.0530	-0.1354	-0.0355	-0.0325	2022
2022-03-09	-0.0150	0.0401	0.0163	0.0802	0.0658	-0.0277	0.0019	0.0469	0.0762	0.0110	0.0321	0.0776	0.0756	0.0240	0.0356	0.0430	0.0958	0.0217	0.0576	0.0504	-0.0682	0.0154	0.0195	0.0236	2022
2022-03-16	0.0848	0.0572	0.0794	0.1123	0.1437	0.2147	0.0622	0.0561	0.0904	0.0515	0.0738	0.0626	0.0634	0.0412	0.0875	-0.0065	0.0158	0.0172	0.0261	0.0177	0.0026	0.0740	0.0610	0.0535	2022
2022-03-23	0.0583	0.0366	0.0187	0.0265	0.0773	0.1010	0.0379	0.0374	0.0642	0.0415	-0.0101	-0.0169	-0.0341	-0.0098	-0.0256	0.0155	-0.0057	0.0282	0.0135	0.0106	-0.0012	0.1138	0.0239	0.0294	2022
2022-03-30	-0.0220	-0.0145	-0.0135	-0.0316	-0.0999	-0.0076	-0.1151	-0.1105	-0.1120	-0.0778	-0.0571	-0.0790	-0.0698	-0.0473	-0.0741	-0.0007	-0.0289	0.0260	0.0077	0.0137	0.0006	-0.0411	-0.0206	-0.0231	2022
2022-04-06	-0.0432	-0.0973	-0.0961	-0.0843	-0.1872	-0.1005	-0.0295	-0.0339	-0.0172	-0.0005	-0.0062	-0.0245	0.0062	-0.0130	-0.0160	0.0128	0.0358	0.0226	0.0235	0.0303	0.0250	-0.1269	-0.0325	-0.0287	2022
2022-04-13	-0.0016	0.0114	0.0178	0.0475	0.0318	0.0409	0.0502	0.0497	-0.0035	0.0363	-0.0032	0.0102	-0.0123	0.0493	0.0576	0.0175	-0.0567	0.0019	-0.0678	0.0074	-0.0107	0.0337	0.0156	0.0153	2022
2022-04-20	-0.0654	-0.0543	-0.0914	-0.1260	-0.1668	-0.1597	-0.0934	-0.1009	-0.0748	-0.0673	-0.0638	-0.0821	-0.0704	-0.0704	-0.0764	0.0087	-0.0232	-0.0154	0.0074	-0.0455	-0.0251	-0.0851	-0.0682	-0.0672	2022
2022-04-27	0.0169	0.0419	-0.0112	-0.1150	0.0424	0.0368	-0.0036	0.0487	0.0486	0.0597	0.0001	0.0185	-0.0095	0.0049	0.0166	-0.0352	0.0053	0.0305	-0.0430	-0.0279	-0.0184	-0.0097	0.0019	0.0007	2022
2022-05-04	-0.0317	-0.0446	-0.0254	-0.1323	-0.1080	-0.1280	-0.0868	-0.0315	-0.1152	-0.0494	-0.0342	-0.0376	-0.0248	-0.0310	-0.0340	-0.0068	0.0040	0.0081	0.0165	-0.0235	-0.0155	-0.1963	-0.0477	-0.0424	2022
2022-05-11	-0.0332	-0.0100	0.0180	0.0581	0.0325	-0.0492	0.0134	-0.0156	0.0335	0.0835	0.0273	0.0064	0.0200	0.0256	0.0327	0.0097	0.0367	0.0574	0.0175	0.0092	-0.0123	-0.0194	0.0246	0.0229	2022
2022-05-18	-0.0613	-0.0274	-0.0945	-0.1028	-0.1180	-0.1926	-0.0856	-0.0789	-0.0852	-0.0523	0.0336	-0.0095	-0.0097	0.0031	-0.0118	0.0143	0.0476	0.0175	-0.0373	0.0102	0.0280	-0.0256	-0.0377	-0.0360	2022
2022-05-25	0.0587	0.0484	0.0710	0.1439	0.1449	0.1882	0.0966	0.0940	0.1541	0.0738	0.0454	0.0426	0.0557	0.0403	0.0497	-0.0040	-0.0070	-0.0280	-0.0117	-0.0016	-0.0173	0.0696	0.0480	0.0472	2022
2022-06-01	-0.0009	0.0023	0.0293	0.0229	0.0135	-0.0564	0.0044	-0.0080	0.0317	-0.0079	-0.0165	-0.0231	-0.0066	-0.0104	-0.0094	-0.0067	0.0172	-0.0170	0.0119	0.0006	0.0105	-0.0202	0.0087	0.0068	2022
2022-06-08	-0.1135	-0.1085	-0.0933	-0.1842	-0.1783	-0.0783	-0.1189	-0.1447	-0.1444	-0.1276	-0.1313	-0.1387	-0.1946	-0.1292	-0.1296	-0.0586	-0.1187	-0.0684	-0.0804	-0.0738	-0.0256	-0.3386	-0.1126	-0.1062	2022
2022-06-15	0.0232	0.0371	0.0443	0.0604	0.0453	0.0706	-0.0626	-0.0170	-0.0456	0.0097	0.0154	0.0432	0.0408	0.0080	-0.0044	0.0283	0.0040	0.0491	0.0416	0.0394	0.0121	-0.0698	0.0102	0.0032	2022
2022-06-22	0.0115	0.0107	0.0041	-0.0118	-0.0359	-0.0186	0.0301	0.0405	0.0528	0.0182	-0.0001	-0.0181	0.0301	0.0503	0.0462	0.0225	0.0516	0.0429	0.0610	0.0605	-0.0059	-0.0210	0.0163	0.0191	2022
2022-06-29	0.0295	0.0245	0.0111	0.0552	-0.0658	0.0017	-0.0530	-0.0488	-0.0535	-0.0668	-0.0280	-0.0321	-0.0020	-0.0077	-0.0266	0.0068	0.0192	0.0081	0.0094	-0.0063	-0.0291	-0.0045	0.0029	0.0034	2022
2022-07-06	0.0299	-0.0355	0.0067	-0.0384	0.0079	0.0000	0.0316	-0.0263	-0.0080	0.0232	0.0119	0.0038	-0.0125	-0.0158	-0.0022	-0.0129	0.0077	0.0103	-0.0096	0.0180	-0.0241	-0.0438	-0.0032	-0.0030	2022
2022-07-13	0.0346	0.0228	-0.0018	0.0791	0.1192	0.0521	0.0854	0.0871	0.0770	0.0350	0.0140	0.0615	0.0800	0.0836	0.0725	-0.0239	-0.0130	-0.0133	-0.0180	0.0363	-0.0081	0.1909	0.0300	0.0296	2022
2022-07-20	0.0040	-0.0298	-0.0804	-0.0292	-0.0274	0.0529	-0.0040	-0.0313	-0.0090	0.0199	-0.0100	-0.0090	0.0000	0.0016	-0.0106	0.0115	0.0179	-0.0117	0.0168	-0.0035	0.0031	-0.0964	-0.0032	-0.0035	2022
2022-07-27	0.0540	0.0871	0.0919	0.1558	0.1138	0.1494	0.1897	0.0804	0.1194	0.0560	-0.0088	-0.0003	-0.0005	0.0289	0.0334	-0.0044	-0.0512	-0.0411	-0.0720	0.0073	0.0247	0.0787	0.0445	0.0430	2022
2022-08-03	0.0302	0.0269	0.0129	0.0270	-0.0809	-0.0591	0.0020	0.0135	-0.0867	-0.0131	0.0259	0.0263	0.0121	0.0263	0.0428	-0.0160	0.0095	0.0216	-0.0010	0.0034	0.0190	0.0081	0.0089	0.0080	2022
2022-08-10	0.0494	0.0362	0.0426	0.0492	0.0998	0.0788	0.0785	0.0627	0.0833	0.0434	0.0691	0.0771	0.0663	0.0531	0.0613	-0.0155	0.0016	0.0119	0.0163	0.0164	-0.0107	0.0306	0.0437	0.0436	2022
2022-08-17	-0.0341	-0.0572	-0.0666	-0.0802	-0.0942	-0.0335	-0.0600	-0.0111	-0.1181	-0.0679	-0.0678	-0.0628	-0.0374	-0.0426	-0.0391	-0.0086	-0.0378	-0.0043	-0.0251	-0.0191	-0.0161	-0.1038	-0.0420	-0.0412	2022
2022-08-24	-0.0510	-0.0478	-0.0442	-0.0373	-0.1050	-0.0653	0.0084	0.0147	-0.0180	0.0297	-0.0097	-0.0093	-0.0052	-0.0194	-0.0448	-0.0158	-0.0460	-0.0375	-0.0253	-0.0245	-0.0140	-0.0838	-0.0354	-0.0349	2022
2022-08-31	-0.0279	-0.0377	-0.0197	-0.0206	-0.1387	-0.0119	-0.0276	-0.0085	-0.0591	-0.0487	-0.0059	-0.0307	-0.0290	-0.0216	0.0083	0.0046	-0.0020	-0.0053	0.0149	-0.0099	-0.0137	-0.0497	-0.0206	-0.0189	2022
2022-09-07	-0.0045	-0.0050	-0.0236	0.0056	-0.0251	0.0625	-0.0195	0.0459	0.0874	0.0448	0.0230	0.0346	0.0079	0.0133	0.0223	-0.0114	0.0094	-0.0016	0.0068	-0.0072	0.0013	0.0746	0.0066	0.0060	2022
2022-09-14	0.0197	-0.0386	-0.0310	-0.0372	0.0037	0.0553	-0.1187	-0.0369	-0.0421	-0.0409	-0.0048	0.0050	0.0044	-0.0157	0.0016	0.0223	-0.0312	-0.0033	0.0231	0.0202	-0.0221	-0.0718	-0.0208	-0.0232	2022
2022-09-21	-0.0333	-0.0252	-0.0367	-0.0658	-0.0597	-0.0872	-0.0945	-0.1181	-0.1141	-0.0902	-0.0901	-0.1113	-0.0811	-0.1038	-0.0926	-0.0002	-0.0153	0.0062	-0.0004	-0.0280	-0.0230	0.0116	-0.0612	-0.0513	2022
2022-09-28	-0.0380	0.0514	0.0416	0.0567	0.0590	-0.1260	0.0371	0.0309	0.0600	0.0311	0.0633	0.0575	0.0841	0.0775	0.0550	0.0041	0.0084	0.0293	0.0019	0.0287	0.0587	0.0622	0.0455	0.0394	2022
2022-10-05	-0.0500	-0.0990	-0.0449	-0.0762	-0.1279	-0.1416	-0.0669	-0.1094	-0.0731	-0.0416	-0.1008	-0.0840	-0.0791	-0.0679	-0.0867	-0.0176	-0.0588	0.0296	-0.0034	-0.0457	-0.0351	-0.0653	-0.0569	-0.0550	2022
2022-10-12	0.0337	0.0564	0.0363	0.0363	0.0324	0.0169	0.0399	0.0651	0.0734	0.0352	0.1621	0.1584	0.1047	0.0646	0.0312	0.0200	0.0505	0.0384	0.0216	0.0438	-0.0091	0.0147	0.0371	0.0367	2022
2022-10-19	0.0580	0.0497	0.0362	0.0358	0.1027	0.0101	0.0644	0.0775	0.0240	0.0639	0.0320	0.0145	0.0155	0.0574	0.0134	0.0279	0.0335	0.0322	0.0456	0.0339	0.0016	0.0386	0.0366	0.0365	2022
2022-10-26	-0.0112	-0.0940	-0.1440	-0.2199	0.0210	0.0240	0.0435	0.0613	0.0142	0.0258	0.0435	0.0226	0.0342	0.0475	0.0391	0.0138	0.0517	0.0208	-0.0196	0.0130	-0.0035	0.0192	-0.0006	-0.0010	2022
2022-11-02	-0.0769	0.0031	-0.0175	-0.0730	0.0753	-0.1747	0.0236	-0.0077	0.0991	0.0404	0.0254	0.0248	0.0049	0.0433	0.0281	0.0043	-0.0138	0.0173	0.0110	0.0104	0.0383	-0.0997	-0.0073	-0.0066	2022
2022-11-09	0.0745	0.0557	0.1019	0.0949	0.1322	0.0162	0.0414	0.0300	0.0945	0.0966	0.0113	0.0158	-0.0036	0.0505	0.0594	-0.0084	0.0340	-0.0189	0.0299	-0.0948	0.0372	-0.0936	0.0441	0.0423	2022
2022-11-16	0.0009	0.0126	-0.0142	-0.0598	-0.0384	-0.1348	-0.0058	-0.0067	-0.0374	-0.0073	0.0157	-0.0056	0.0085	0.0026	-0.0092	0.0254	0.0104	0.0707	0.0432	0.0391	-0.0209	-0.0420	0.0019	0.0035	2022
2022-11-23	-0.0619	-0.0166	-0.0194	-0.0084	-0.0252	0.0623	-0.0230	-0.0055	-0.0497	-0.0130	0.0112	-0.0132	0.0097	-0.0004	0.0156	0.0023	0.0083	0.0180	-0.0100	0.0093	0.0041	0.0156	-0.0119	-0.0117	2022
2022-11-30	0.0123	0.0197	0.0186	-0.0462	0.0220	-0.0056	-0.0348	-0.0445	-0.0215	-0.0224	-0.0371	-0.1144	-0.0917	-0.0557	-0.0400	0.0001	0.0044	0.0008	0.0343	0.0212	0.0129	0.0384	-0.0045	-0.0035	2022
2022-12-07	0.0178	0.0470	-0.0140	0.0469	0.1228	-0.1109	0.0216	0.0218	-0.0216	0.0070	0.0187	-0.0018	-0.0181	0.0223	0.0577	0.0175	0.0654	0.0180	0.0065	0.0010	0.0220	0.0397	0.0180	0.0205	2022
2022-12-14	-0.0949	-0.0607	-0.0716	-0.0822	-0.1165	-0.1553	-0.1681	-0.0966	-0.0406	-0.0162	-0.0256	-0.0172	-0.0392	-0.0679	-0.0849	-0.0200	-0.0335	-0.0109	-0.0259	-0.0340	0.0034	-0.0505	-0.0481	-0.0548	2022
2022-12-21	-0.0173	-0.0202	-0.0185	-0.0256	-0.1302	-0.2335	-0.0238	-0.0549	-0.0238	-0.0077	0.0080	0.0105	0.0015	-0.0073	-0.0012	0.0100	-0.0037	0.0283	0.0149	0.0224	-0.0024	-0.0113	0.0009	0.0068	2022
2022-12-28	-0.0389	0.0110	0.0196	0.0329	0.0136	-0.0092	0.0420	0.0149	0.0157	0.0030	0.0253	0.0297	0.0181	0.0124	0.0077	0.0043	0.0025	-0.0088	-0.0037	-0.0254	0.0141	-0.0022	-0.0008	-0.0015	2022
2023-01-04	0.0443	-0.0458	-0.0079	0.0461	0.1056	0.0948	0.0947	0.0928	0.0695	0.0672	0.0254	0.0180	0.0135	0.0317	0.0367	-0.0172	-0.0737	-0.0030	-0.0170	-0.0650	0.0213	0.0449	0.0253	0.0253	2023
2023-01-11	0.0391	0.0490	0.0319	0.0665	0.1068	0.1011	-0.0133	-0.0136	0.0288	0.0270	0.0231	0.0117	0.0407	-0.0210	0.0878	-0.0161	-0.0329	-0.0033	-0.0436	-0.0019	0.0162	0.1931	0.0197	0.0182	2023
2023-01-18	0.0473	0.0070	0.0679	0.0028	0.0846	0.0901	0.0055	-0.0113	0.0333	0.0061	-0.0168	0.0014	0.0075	-0.0046	-0.0163	-0.0238	-0.0302	-0.0176	-0.0247	0.0134	0.0150	0.0674	0.0050	0.0061	2023
2023-01-25	0.0123	0.0236	0.0116	0.0683	0.0140	0.1855	0.0587	0.0827	0.0646	0.0601	0.0108	0.0260	0.0530	0.0490	0.0189	-0.0295	-0.0124	-0.0103	0.0004	0.0153	-0.0048	0.0220	0.0165	0.0156	2023
2023-02-01	0.0693	0.0767	0.0853	-0.0099	0.1266	0.1277	-0.0045	0.0515	0.0246	0.0006	0.0260	0.0357	0.0265	0.0232	0.0273	-0.0001	-0.0039	-0.0162	-0.0178	-0.0457	-0.0307	0.0054	0.0204	0.0212	2023
2023-02-08	-0.0094	0.0171	-0.1283	-0.0239	0.0354	0.0613	-0.0363	0.0246	0.0438	0.0491	-0.0031	-0.0318	0.0140	-0.0070	0.0134	-0.0084	0.0030	0.0285	0.0501	0.0329	-0.0079	-0.0459	-0.0064	-0.0062	2023
2023-02-15	-0.0298	-0.0743	-0.0310	-0.0527	-0.1063	-0.0584	-0.0001	-0.0311	-0.0404	-0.0073	-0.0252	-0.0314	-0.0477	-0.0291	-0.0297	-0.0252	-0.0236	0.0030	-0.0039	-0.0031	-0.0116	0.0950	-0.0340	-0.0334	2023
2023-02-22	-0.0072	-0.0104	-0.0190	-0.0037	0.1169	0.0414	-0.0107	-0.0599	-0.0002	0.0191	0.0263	-0.0064	0.0114	-0.0266	-0.0115	-0.0233	-0.0512	-0.0263	0.0124	-0.0318	-0.0049	-0.0542	-0.0066	-0.0071	2023
2023-03-01	0.0280	0.0188	0.0413	-0.0072	0.0031	-0.0916	0.0611	0.0255	0.0026	-0.0026	-0.0336	-0.0386	-0.0509	-0.0160	-0.0046	0.0054	-0.0057	0.0463	-0.0063	-0.0043	-0.0069	-0.0409	0.0043	0.0051	2023
2023-03-08	0.0065	0.0258	0.0012	0.0141	0.0329	-0.0240	-0.0727	-0.1077	-0.0312	-0.0486	-0.0293	-0.1311	-0.1012	-0.0645	-0.0655	-0.0011	-0.0110	-0.0394	0.0060	-0.0198	0.0475	0.1077	-0.0186	-0.0166	2023
2023-03-15	0.0429	0.0486	0.1102	0.0586	0.0850	0.0752	-0.0178	-0.0141	-0.0180	-0.0084	-0.0307	-0.0059	-0.0430	-0.0152	-0.0135	-0.0002	0.0189	-0.0065	0.0188	0.0364	0.0198	0.1298	0.0224	0.0182	2023
2023-03-22	-0.0103	0.0053	-0.0378	-0.0341	0.0080	-0.0434	-0.0103	-0.0254	-0.0274	0.0097	-0.0129	-0.0166	-0.0344	0.0036	-0.0447	-0.0135	-0.0166	-0.0001	0.0094	-0.0158	0.0169	-0.0327	-0.0147	-0.0045	2023
2023-03-29	0.0494	0.0425	0.0359	0.0667	0.0387	0.0178	0.0922	0.0435	-0.0071	-0.0050	-0.0036	-0.0050	-0.0100	0.0131	-0.0007	0.0430	0.0225	0.0308	0.0096	0.0428	0.0244	0.0325	0.0375	0.0325	2023
2023-04-05	-0.0296	-0.0153	0.0060	-0.0395	-0.0104	-0.0305	0.0117	-0.0093	-0.0212	0.0057	0.0008	0.0258	0.0672	0.0145	0.0032	0.0358	0.0215	0.0331	0.0100	0.0547	-0.0091	0.0708	0.0013	0.0026	2023
2023-04-12	0.0347	0.0194	-0.0081	0.0235	0.0182	-0.0134	-0.0109	-0.0023	0.0239	0.0162	0.1033	0.0624	0.0616	0.0198	0.0544	-0.0200	-0.0301	0.0206	-0.0112	-0.0322	-0.0002	0.0054	0.0108	0.0109	2023
2023-04-19	-0.0164	-0.0459	-0.0062	0.0026	-0.0529	-0.1373	-0.0784	-0.0710	-0.0495	-0.0027	-0.0267	-0.0579	-0.0320	0.0165	-0.0201	0.0256	-0.0305	0.0147	0.0419	-0.0252	-0.0027	-0.0712	-0.0213	-0.0198	2023
2023-04-26	0.0287	0.1034	0.0141	0.0103	0.0724	-0.0022	0.0150	0.0052	-0.0107	-0.0220	0.0090	-0.0239	-0.0431	-0.0182	-0.0203	-0.0009	-0.0069	0.0116	-0.0840	0.0030	0.0095	0.0131	0.0125	0.0117	2023
2023-05-03	0.0190	0.0052	0.0191	0.0284	0.0127	0.0537	0.0051	0.0060	-0.0808	-0.0608	-0.0182	-0.0179	-0.0078	-0.0261	-0.0139	-0.0244	-0.0150	-0.0039	-0.0321	-0.0061	0.0080	-0.0363	0.0002	0.0002	2023
2023-05-10	0.0017	0.0153	0.1073	0.0617	0.0222	-0.0157	-0.0528	-0.0537	-0.0268	-0.0204	-0.0154	-0.0109	0.0039	-0.0123	-0.0302	-0.0107	-0.0390	-0.0116	-0.0244	-0.0220	-0.0222	-0.0227	-0.0028	-0.0017	2023
2023-05-17	-0.0016	0.0112	0.0252	0.0139	0.0493	0.1094	0.0418	0.0579	0.0172	0.0691	0.0168	0.0436	0.0709	0.0086	0.0095	-0.0160	0.0794	-0.0245	-0.0054	-0.0006	-0.0078	0.0070	0.0100	0.0093	2023
2023-05-24	0.0329	0.0515	0.0090	0.0564	0.2678	0.0796	0.0708	-0.0018	-0.0136	-0.0004	0.0063	-0.0113	-0.0056	0.0222	0.0094	-0.0082	-0.0687	-0.0369	-0.0436	0.0009	-0.0076	0.0174	0.0144	0.0146	2023
2023-05-31	0.0107	0.0074	0.0290	0.0399	-0.0370	0.0955	0.0266	0.0548	0.0452	0.0056	0.0136	0.0337	0.0068	-0.0123	0.0288	0.0244	0.0361	0.0077	-0.0074	0.0160	0.0016	-0.0169	0.0202	0.0185	2023
2023-06-07	0.0226	0.0018	-0.0277	0.0004	0.0595	0.1561	0.0888	0.0689	0.0580	-0.0025	0.0191	0.0137	0.0331	0.0545	0.0278	0.0161	0.0486	-0.0002	0.0210	0.0076	-0.0099	-0.0497	0.0160	0.0200	2023
2023-06-14	0.0092	0.0112	-0.0059	-0.0070	0.0658	0.0591	0.0063	-0.0088	-0.0098	-0.0062	0.0036	-0.0182	-0.0180	-0.0350	-0.0177	0.0209	-0.0236	0.0022	-0.0035	-0.0456	-0.0044	0.0889	0.0073	0.0012	2023
2023-06-21	0.0164	-0.0103	-0.0395	0.0267	-0.0451	-0.0925	0.0133	0.0043	0.0038	-0.0009	-0.0236	-0.0221	-0.0237	-0.0536	-0.0269	-0.0051	-0.0771	0.0343	-0.0386	0.0318	-0.0115	0.0800	-0.0033	0.0014	2023
2023-06-28	0.0231	0.0102	0.0132	0.0080	0.0127	0.1118	0.0560	0.0387	0.0245	0.0742	0.0519	0.0334	0.0591	0.0411	0.0232	0.0004	0.0063	0.0089	0.0180	-0.0097	0.0044	0.0029	0.0177	0.0173	2023
2023-07-05	-0.0230	-0.0165	-0.0233	-0.0111	-0.0002	-0.0365	-0.0007	0.0256	0.0689	0.0363	0.0055	-0.0062	-0.0153	-0.0177	-0.0169	-0.0293	-0.0173	-0.0505	0.0041	-0.0319	0.0055	-0.0051	-0.0022	-0.0030	2023
2023-07-12	0.0296	0.0781	0.0550	0.0310	0.1133	0.0837	-0.0721	-0.0212	-0.0131	0.0018	0.0483	0.0563	0.0648	0.0498	0.0790	0.0027	0.0061	-0.0256	0.0074	0.0771	0.0231	-0.0253	0.0274	0.0262	2023
2023-07-19	-0.0006	-0.0240	-0.0126	-0.0283	-0.0390	-0.1005	-0.0425	-0.0314	0.0088	0.0076	0.0204	0.0461	-0.0026	0.0504	0.0266	0.0805	0.0224	0.0148	0.0473	0.0216	-0.0067	-0.0213	0.0029	0.0027	2023
2023-07-26	0.0102	-0.0426	0.0736	0.0196	0.0180	-0.0160	-0.0010	0.0053	-0.0037	0.0102	0.0023	-0.0166	0.0050	0.0085	-0.0376	-0.0205	-0.0399	-0.0211	0.0476	-0.0122	-0.0107	0.0152	0.0016	0.0023	2023
2023-08-02	-0.0843	-0.0311	-0.0011	0.0608	-0.0404	-0.0445	-0.0411	-0.0342	-0.0294	-0.1033	-0.0083	-0.0111	-0.0273	-0.0268	-0.0183	0.0251	0.0119	0.0107	0.0072	0.0022	-0.0101	0.0030	-0.0185	-0.0171	2023
2023-08-09	-0.0132	-0.0129	-0.0124	-0.0164	-0.0163	-0.0694	-0.0724	-0.1010	-0.0887	-0.0278	-0.0329	-0.0435	-0.0323	-0.0472	-0.0265	-0.0014	-0.0070	0.0209	0.0166	0.0016	-0.0115	-0.0202	-0.0126	-0.0131	2023
2023-08-16	0.0001	0.0019	-0.0054	-0.0252	0.0386	0.0010	-0.0092	-0.0112	-0.0121	-0.0329	-0.0299	-0.0514	-0.0292	-0.0412	-0.0376	-0.0408	0.0402	-0.0132	-0.0258	-0.0287	-0.0028	-0.1138	-0.0120	-0.0108	2023
2023-08-23	0.0381	0.0204	0.0417	0.0049	0.0660	0.0979	0.0151	0.0160	0.0476	0.0324	0.0161	0.0253	0.0120	0.0423	0.0305	-0.0104	-0.0189	0.0254	-0.0044	0.0010	0.0212	0.0631	0.0262	0.0248	2023
2023-08-30	0.0299	0.0155	0.0089	0.0173	-0.0048	-0.0027	0.0033	-0.0054	0.0229	-0.0047	-0.0242	-0.0180	-0.0110	-0.0268	-0.0083	-0.0151	-0.0215	-0.0228	-0.0101	-0.0247	-0.0069	-0.0728	0.0010	0.0002	2023
2023-09-06	-0.0733	-0.0054	-0.0032	0.0284	-0.0788	0.0420	0.0293	0.0084	-0.0048	0.0220	0.0078	0.0194	0.0238	0.0301	0.0083	0.0179	-0.0354	0.0139	0.0215	-0.0019	-0.0065	0.0021	-0.0084	-0.0073	2023
2023-09-13	0.0156	-0.0094	0.0198	-0.0258	-0.0305	-0.0037	0.0088	0.0145	-0.0010	-0.0027	0.0175	-0.0111	0.0159	0.0327	0.0340	-0.0085	-0.0047	-0.0153	0.0279	0.0055	0.0097	0.0520	-0.0057	-0.0074	2023
2023-09-20	-0.0405	-0.0515	-0.0711	-0.0884	-0.0377	-0.0877	-0.0104	-0.0514	-0.0615	-0.0338	-0.0272	-0.0530	-0.0613	-0.0543	-0.0743	-0.0198	-0.0479	-0.0117	0.0027	0.0503	-0.0165	-0.0372	-0.0433	-0.0352	2023
2023-09-27	0.0026	0.0040	0.0296	-0.0101	0.0376	0.0098	-0.0294	-0.0277	-0.0197	-0.0252	-0.0154	-0.0475	-0.0499	-0.0562	-0.0518	-0.0234	0.0453	-0.0350	-0.0430	0.0079	-0.0412	0.0452	-0.0062	-0.0101	2023
2023-10-04	0.0342	0.0468	0.0416	0.0375	0.0511	0.0670	0.0107	0.0032	0.0369	0.0226	0.0204	0.0416	0.0293	0.0279	0.0267	0.0193	-0.0218	0.0179	0.0099	0.0286	0.0197	-0.0014	0.0309	0.0303	2023
2023-10-11	-0.0070	0.0111	0.0120	0.0153	-0.0415	-0.0338	-0.0132	-0.0372	-0.0158	-0.0073	0.0202	0.0223	0.0528	-0.0173	0.0025	-0.0144	-0.0127	0.0054	0.0019	0.0234	0.0328	0.0367	0.0032	0.0034	2023
2023-10-18	-0.0212	-0.0046	-0.0065	-0.0224	-0.0063	-0.1630	-0.0555	-0.0601	-0.0618	-0.0275	-0.0441	-0.0810	-0.0665	-0.0335	-0.1156	-0.0316	-0.0735	-0.0110	-0.0095	-0.0219	0.0258	0.1765	-0.0311	-0.0288	2023
2023-10-25	-0.0155	0.0227	-0.1122	0.0346	-0.0683	-0.0752	-0.1555	-0.0127	-0.0403	-0.0398	-0.0151	0.0336	0.0124	0.0147	-0.0104	-0.0193	0.0043	-0.0032	-0.0357	0.0199	0.0062	0.0224	-0.0123	-0.0129	2023
2023-11-01	0.0627	0.0642	0.0540	0.0698	0.1195	0.1010	0.0576	0.0074	-0.1412	-0.1230	0.0350	0.0668	0.0314	0.0648	0.0763	0.0171	0.0223	0.0126	0.0069	0.0042	-0.0082	0.0221	0.0447	0.0438	2023
2023-11-08	0.0304	0.0267	0.0200	0.0214	0.0775	0.0663	0.0224	-0.0074	0.0476	0.0269	0.0303	0.0370	0.0339	0.0446	0.0364	-0.0217	-0.0658	-0.0178	-0.0293	0.0049	-0.0026	0.0027	0.0279	0.0266	2023
2023-11-15	0.0182	0.0075	0.0248	-0.0131	0.0058	0.0158	-0.0204	-0.0107	0.0177	0.0148	0.0301	0.0149	0.0123	-0.0111	0.0020	0.0232	0.0483	0.0004	0.0048	-0.0016	0.0176	0.0077	0.0107	0.0101	2023
2023-11-22	-0.0013	0.0275	0.0017	0.0215	-0.0434	0.0226	0.0175	0.0349	0.0138	-0.0100	0.0037	-0.0044	0.0179	0.0080	-0.0205	0.0113	-0.0203	-0.0201	-0.0047	0.0017	0.0209	0.0548	0.0044	0.0037	2023
2023-11-29	0.0157	-0.0270	-0.0463	-0.0010	-0.0266	-0.0330	0.0219	0.1233	-0.0135	-0.0210	0.0284	0.0349	0.0255	0.0121	0.0419	0.0446	-0.0204	0.0586	0.0459	0.0178	-0.0112	0.1529	0.0054	0.0037	2023
2023-12-06	0.0066	0.0050	0.0116	0.0041	0.0232	-0.0072	0.0515	0.0252	-0.0051	0.0020	0.0160	0.0132	0.0435	0.0395	0.0419	-0.0222	-0.0177	-0.0178	0.0582	-0.0049	-0.0198	-0.0615	0.0166	0.0163	2023
2023-12-13	0.0114	-0.0030	0.0307	0.0419	0.0400	0.0818	0.0742	0.0707	0.0993	0.0709	0.0482	0.0863	0.0750	0.0812	0.0949	0.0089	-0.0148	0.0202	0.0023	-0.0405	0.0303	0.0196	0.0273	0.0229	2023
2023-12-20	-0.0199	0.0037	0.0350	-0.0025	-0.0066	-0.0024	0.0351	0.0072	0.0067	0.0179	-0.0004	0.0104	-0.0090	-0.0022	0.0100	-0.0020	0.0088	0.0179	0.0066	-0.0077	0.0136	0.0059	-0.0010	0.0058	2023
2023-12-27	-0.0391	-0.0102	-0.0240	-0.0229	-0.0228	-0.0324	-0.0236	-0.0022	0.0081	-0.0017	0.0217	0.0012	-0.0063	0.0174	0.0114	0.0242	0.0454	0.0508	0.0331	0.0365	-0.0052	0.0557	-0.0045	-0.0063	2023
2024-01-03	-0.0027	0.0132	0.0199	0.0096	0.0982	-0.0557	-0.0267	0.0135	-0.0918	-0.0564	-0.0083	-0.0080	-0.0008	-0.0118	-0.0198	0.0103	-0.0112	0.0448	0.0155	-0.0018	-0.0147	0.0259	0.0017	0.0026	2024
2024-01-10	-0.0082	0.0378	0.0109	0.0118	0.0592	-0.0662	-0.0326	-0.0320	-0.0180	-0.0256	-0.0096	-0.0459	-0.0514	-0.0086	-0.0684	-0.0069	-0.0374	0.0005	-0.0051	-0.0364	-0.0001	-0.0669	0.0029	0.0022	2024
2024-01-17	0.0610	0.0219	0.0314	0.0185	0.0601	-0.0502	-0.0079	-0.0045	0.0105	0.0102	0.0059	0.0200	0.0480	0.0008	0.0089	-0.0044	0.0039	0.0113	0.0461	-0.0070	0.0002	-0.0798	0.0203	0.0207	2024
2024-01-24	-0.0373	0.0240	0.0296	0.0189	0.0473	-0.0876	0.0354	0.0796	0.0604	0.0286	0.0422	0.0598	0.0413	0.0159	0.0101	-0.0065	-0.0509	0.0151	-0.0155	-0.0234	0.0034	0.0751	0.0115	0.0124	2024
2024-01-31	0.0067	-0.0076	-0.0498	0.0619	0.0832	-0.0345	0.0243	-0.0032	-0.0296	-0.0102	-0.0067	-0.0516	-0.0583	-0.0049	-0.0078	-0.0045	0.0325	0.0420	0.0495	0.0139	-0.0002	0.0031	0.0059	0.0063	2024
2024-02-07	-0.0228	0.0020	0.0072	-0.0030	0.0557	-0.0059	0.0493	0.0073	-0.0625	-0.0928	-0.0048	-0.0088	0.0060	-0.0163	-0.0250	-0.0101	-0.0195	-0.0115	0.0000	0.0120	-0.0216	0.1437	0.0004	0.0002	2024
2024-02-14	-0.0177	-0.0087	-0.0281	-0.0093	-0.0378	0.0516	-0.0345	0.0181	-0.0170	-0.0291	0.0309	0.0363	0.0706	0.0151	0.0163	0.0088	0.0227	0.0153	0.0141	0.0081	0.0158	0.0498	0.0046	0.0054	2024
2024-02-21	0.0059	0.0134	-0.0160	0.0379	0.1250	0.0303	0.0060	0.0296	0.0137	0.0171	0.0205	0.0094	0.0571	0.0162	0.0016	0.0271	-0.0257	0.0129	0.0183	-0.0148	0.0028	0.0878	0.0197	0.0203	2024
2024-02-28	-0.0710	-0.0119	-0.0457	0.0033	0.0883	-0.0999	0.0472	0.0116	0.0076	0.0206	0.0274	0.0319	0.0321	0.0003	0.0417	-0.0063	-0.0306	-0.0492	0.0009	-0.0817	0.0477	0.1112	0.0005	0.0005	2024
2024-03-06	0.0181	0.0309	0.0430	0.0073	0.0670	-0.0179	-0.0381	-0.0331	-0.0091	0.0418	0.0068	0.0230	0.0177	0.0001	-0.0236	0.0172	0.0714	-0.0014	0.0098	0.0337	0.0131	0.1137	0.0186	0.0188	2024
2024-03-13	0.0163	0.0147	0.0598	0.0029	-0.0277	-0.0357	0.0156	0.0570	-0.0101	-0.0236	0.0206	0.0019	-0.0105	0.0012	0.0156	-0.0410	-0.0137	-0.0038	-0.0070	0.0120	0.0001	-0.1437	0.0010	-0.0021	2024
2024-03-20	-0.0368	0.0006	0.0245	0.0136	0.0348	0.0364	0.0113	0.0583	-0.0172	0.0572	0.0100	0.0290	-0.0058	0.0441	0.0318	-0.0028	-0.0014	0.0331	-0.0026	-0.0020	0.0092	0.1226	0.0030	0.0091	2024
2024-03-27	-0.0051	-0.0005	0.0255	0.0133	-0.0342	-0.0642	0.0653	0.0200	0.0074	0.0319	0.0159	0.0056	0.0118	0.0097	0.0155	0.0125	-0.0015	0.0378	0.0083	-0.0719	0.0449	-0.0671	0.0032	0.0001	2024
2024-04-03	0.0049	0.0114	0.0131	0.0272	-0.0469	0.0597	0.0194	-0.0036	0.0227	0.0247	-0.0086	0.0115	0.0040	0.0014	0.0147	-0.0351	-0.0283	-0.0283	-0.0602	0.0034	0.0316	0.0549	0.0018	0.0009	2024
2024-04-10	-0.0017	-0.0278	-0.0141	-0.0127	0.0239	-0.1185	-0.1133	-0.0474	-0.0927	-0.0932	-0.0808	-0.0843	-0.0205	-0.0343	-0.0539	-0.0529	-0.0416	-0.0131	-0.0457	0.0198	0.0162	-0.0802	-0.0332	-0.0309	2024
2024-04-17	-0.0148	-0.0171	0.0247	-0.0208	-0.0588	-0.0824	0.0679	0.0556	-0.0238	0.0274	0.0608	0.1011	0.0772	0.0661	0.0505	0.0348	0.0242	0.0144	0.0515	0.0362	-0.0283	0.0399	0.0044	0.0042	2024
2024-04-24	0.0203	-0.0458	0.0282	-0.0256	0.0471	0.2365	-0.0630	-0.0127	0.0106	-0.0172	-0.0021	-0.0361	-0.0269	0.0064	-0.0316	-0.0338	-0.0270	0.0183	-0.0415	-0.0051	-0.0149	-0.0909	-0.0061	-0.0073	2024
2024-05-01	0.0685	0.0501	0.0507	0.0757	0.0469	-0.0303	0.0016	0.0167	0.1562	0.1160	0.0001	0.0222	0.0157	0.0393	0.0623	0.0282	0.0806	0.0089	-0.0006	0.0351	0.0110	0.0276	0.0307	0.0298	2024
2024-05-08	0.0272	0.0175	-0.0053	-0.0090	0.0088	-0.0015	0.0340	-0.0055	-0.0019	0.0212	0.0496	0.0170	0.0267	0.0325	0.0368	0.0177	0.0217	-0.0133	-0.0059	0.0255	0.0180	-0.0126	0.0132	0.0118	2024
2024-05-15	0.0273	0.0295	0.0431	-0.0212	0.0432	0.0497	-0.0236	-0.0024	-0.0064	-0.0294	-0.0099	0.0297	-0.0012	0.0257	0.0214	-0.0009	0.0213	0.0162	0.0083	0.0186	0.0278	0.1305	0.0136	0.0153	2024
2024-05-22	-0.0123	0.0048	-0.0082	-0.0055	0.1774	-0.0542	-0.0395	-0.0416	0.0099	-0.0155	-0.0001	-0.0084	-0.0327	-0.0228	-0.0286	-0.0384	-0.0091	-0.0364	-0.0477	-0.0387	-0.0273	-0.0266	-0.0038	-0.0029	2024
2024-05-29	0.0227	-0.0337	-0.0149	-0.0155	0.0220	-0.0113	0.0295	0.0491	0.0079	-0.0345	-0.0017	0.0091	-0.0132	-0.0099	-0.0214	0.0234	0.0412	0.0206	0.0428	0.0036	-0.0135	0.0327	-0.0057	-0.0027	2024
2024-06-05	0.0638	0.0391	0.0162	0.0431	0.0377	-0.0238	0.0066	0.0631	-0.0939	-0.0261	-0.0244	-0.0209	-0.0271	-0.0185	-0.0120	-0.0071	-0.0508	0.0240	0.0337	-0.0185	-0.0052	-0.0469	0.0136	0.0161	2024
2024-06-12	0.0339	0.0311	-0.0076	-0.0239	0.1146	0.0799	-0.0276	-0.0135	-0.0771	-0.0213	0.0135	0.0347	0.0331	0.0292	0.0222	-0.0076	-0.0224	-0.0296	0.0216	-0.0310	0.0061	-0.0331	0.0239	0.0213	2024
2024-06-19	-0.0247	0.0103	0.0498	0.0191	-0.0726	0.0134	0.0260	-0.0220	0.0381	-0.0043	0.0054	-0.0154	-0.0318	-0.0001	0.0024	0.0105	0.0209	0.0438	-0.0036	0.0114	-0.0042	-0.0526	-0.0038	-0.0067	2024
2024-06-26	0.0522	0.0183	0.0066	0.0707	-0.0275	0.2106	0.0625	0.0116	-0.0549	-0.0344	0.0529	0.0386	0.0638	0.0178	0.0187	-0.0079	-0.0057	-0.0399	-0.0285	0.0280	0.0046	0.0036	0.0081	0.0109	2024
2024-07-03	0.0375	0.0006	0.0200	-0.0033	0.0686	0.1261	0.0023	-0.0148	-0.0052	-0.0032	-0.0058	0.0119	-0.0180	0.0154	0.0293	0.0070	-0.0040	-0.0132	0.0125	-0.0124	0.0138	-0.0670	0.0130	0.0123	2024
2024-07-10	0.0265	-0.0220	-0.0271	-0.0322	-0.0390	-0.0222	0.1093	0.0731	0.0608	0.0862	0.0340	0.0634	0.0060	0.0619	0.0346	0.0266	0.0622	-0.0048	0.0068	0.1092	0.0436	0.1153	0.0175	0.0161	2024
2024-07-17	-0.0427	-0.0104	-0.0116	-0.0348	-0.0303	-0.0405	-0.0397	-0.0705	-0.0679	-0.0585	-0.0155	-0.0398	-0.0095	-0.0218	-0.0259	0.0088	0.0000	-0.0085	0.0322	0.0106	-0.0253	0.0127	-0.0213	-0.0198	2024
2024-07-24	-0.0280	-0.0506	-0.0653	-0.0255	-0.1671	-0.1014	-0.2436	-0.0475	-0.0141	-0.0031	0.0228	-0.0270	0.0057	0.0271	0.0025	0.0573	0.0621	-0.0762	0.0758	0.0383	-0.0003	0.0041	-0.0201	-0.0215	2024
2024-07-31	-0.0543	-0.0567	-0.0731	-0.1152	0.0050	-0.1040	-0.1029	-0.0854	0.0208	-0.0183	-0.0715	-0.1116	-0.1364	-0.0727	-0.1098	-0.0147	-0.0542	-0.0362	-0.0057	-0.0139	-0.0082	-0.1667	-0.0378	-0.0373	2024
2024-08-07	0.0656	0.0354	0.0364	0.0500	0.1080	0.0352	0.0361	0.0646	-0.0158	0.0003	0.0372	0.0409	0.0097	0.0452	0.0484	-0.0037	-0.0162	0.0287	0.0293	0.0103	0.0328	0.0785	0.0377	0.0374	2024
2024-08-14	0.0246	0.0257	0.0182	0.0496	0.0914	0.0619	0.0673	0.0596	0.0273	0.0199	0.0312	0.0060	0.0678	0.0109	0.0412	0.0111	0.0017	0.0065	0.0254	0.0111	0.0191	-0.0267	0.0298	0.0303	2024
2024-08-21	0.0067	-0.0243	-0.0151	-0.0327	0.0082	-0.0553	0.0422	0.0687	0.0139	0.0345	0.0260	0.0250	0.0020	0.0197	0.0128	0.0173	-0.0028	0.0117	-0.0012	0.0115	0.0040	0.0083	0.0051	0.0051	2024
2024-08-28	-0.0233	-0.0107	-0.0455	0.0179	-0.1722	0.0066	-0.0145	-0.0172	-0.0102	-0.0168	0.0005	0.0256	0.0368	-0.0398	-0.0279	0.0331	-0.0182	0.0007	0.0090	0.0191	-0.0134	-0.0355	-0.0161	-0.0170	2024
2024-09-04	-0.0120	0.0116	-0.0569	0.0186	0.0009	0.0713	-0.0620	-0.0771	-0.0698	-0.0441	-0.0693	-0.0355	-0.0787	-0.0367	-0.0271	0.0013	0.0496	-0.0108	0.0084	0.0006	0.0101	0.0038	-0.0064	-0.0060	2024
2024-09-11	-0.0152	0.0493	0.0706	0.0400	0.0670	0.0075	0.0547	0.0610	0.0714	0.0416	0.0178	0.0133	0.0103	0.0383	0.0328	-0.0019	0.0030	0.0253	-0.0300	-0.0358	0.0201	0.0451	0.0280	0.0257	2024
2024-09-18	0.0476	-0.0138	0.0185	0.0372	0.0448	0.1096	-0.0028	0.0115	0.0266	0.0647	0.0111	-0.0025	-0.0064	0.0257	0.0271	-0.0260	-0.0111	-0.0219	0.0003	-0.0013	0.0361	0.0641	0.0167	0.0145	2024
2024-09-25	-0.0051	-0.0200	0.0285	-0.0466	-0.0325	0.0146	-0.0111	-0.0687	-0.0223	0.0110	-0.0217	-0.0058	0.0225	-0.0159	0.0178	-0.0049	-0.0285	-0.0019	0.0177	0.0140	-0.0019	-0.0554	-0.0084	-0.0016	2024
2024-10-02	-0.0019	-0.0143	-0.0158	-0.0131	0.1273	-0.0538	-0.0245	0.0249	-0.0131	-0.0231	0.0178	0.0179	0.0339	0.0130	0.0290	-0.0143	0.0176	-0.0557	-0.0203	-0.0030	-0.0133	0.0211	0.0117	0.0080	2024
2024-10-09	0.0352	0.0097	0.0065	0.0268	-0.0098	-0.1075	0.0328	0.0392	0.0057	0.0086	0.0599	0.0539	0.0953	0.0507	0.0431	0.0272	0.0089	0.0274	-0.0060	-0.0445	0.0145	0.0760	0.0115	0.0115	2024
2024-10-16	0.0086	0.0207	-0.0019	0.0107	0.0872	-0.0073	0.0246	0.1159	-0.0046	-0.0228	0.0077	0.0038	0.0278	-0.0078	0.0529	-0.0040	-0.0206	-0.0448	-0.0083	0.0241	0.0321	0.0048	0.0031	0.0061	2024
2024-10-23	-0.0093	0.0103	0.0271	0.0059	-0.0164	0.1745	-0.0651	-0.0416	-0.0076	0.0009	-0.0055	0.0054	0.0075	0.0115	0.0082	-0.0208	-0.0133	-0.0277	0.0036	-0.0137	0.0085	0.0766	-0.0019	-0.0027	2024
2024-10-30	-0.0447	-0.0486	0.0004	0.0444	-0.0095	-0.0316	0.0181	0.0411	-0.2246	-0.0059	-0.0063	-0.0154	-0.0190	0.0051	-0.0126	-0.0109	-0.0167	-0.0203	0.0626	0.0087	-0.0106	-0.0473	-0.0071	-0.0088	2024
2024-11-06	0.0035	0.0277	0.0676	0.0461	0.0582	0.2673	0.0461	0.0668	0.0204	0.0324	0.0784	0.0908	0.1250	0.1174	0.1239	-0.0367	-0.0665	-0.0307	-0.1645	0.0807	-0.0541	0.2375	0.0365	0.0344	2024
2024-11-13	0.0190	-0.0125	-0.0195	-0.0208	-0.0087	0.0519	0.0090	-0.0409	-0.0788	-0.0589	0.0146	0.0119	0.0171	-0.0191	-0.0005	0.0024	-0.0271	-0.0209	-0.0268	-0.0632	0.0132	0.0487	-0.0118	-0.0111	2024
2024-11-20	0.0293	0.0241	-0.0518	0.0158	-0.0711	-0.0227	0.0045	-0.0058	0.0591	0.0309	0.0279	0.0285	0.0520	0.0406	-0.0073	0.0099	0.0263	0.0513	0.0839	0.0503	-0.0012	-0.0039	0.0189	0.0174	2024
2024-11-27	0.0318	0.0095	0.0130	0.0265	0.0241	0.0383	-0.0255	-0.0208	0.0077	-0.0094	-0.0208	-0.0197	-0.0424	-0.0057	-0.0064	-0.0061	-0.0082	0.0023	0.0020	-0.0026	0.0040	0.0427	0.0050	0.0054	2024
2024-12-04	0.0209	0.0277	0.0776	0.0529	-0.0377	0.1320	-0.0243	-0.0173	0.0475	0.0254	-0.0080	-0.0231	-0.0286	-0.0238	-0.0284	-0.0208	0.0004	-0.0084	-0.0326	-0.0684	0.0189	0.0070	-0.0021	-0.0018	2024
2024-12-11	0.0228	0.0248	0.0550	0.0268	-0.0352	0.1796	-0.0575	-0.0284	-0.0096	-0.0404	-0.0187	-0.0099	-0.0174	-0.0178	0.0075	-0.0191	0.0331	-0.0094	-0.0017	-0.1481	-0.0189	0.0934	-0.0016	0.0025	2024
2024-12-18	0.0184	-0.0339	0.0035	-0.0091	0.0727	-0.0373	0.0050	0.0451	0.0355	-0.0324	0.0164	-0.0150	0.0110	0.0140	-0.0053	-0.0038	0.0117	0.0019	0.0260	0.0415	-0.0103	-0.0729	0.0004	-0.0050	2024
2024-12-25	-0.0306	-0.0414	-0.0353	-0.0431	-0.0432	-0.1352	-0.0120	-0.0045	0.0088	-0.0122	-0.0108	-0.0097	-0.0190	-0.0176	-0.0106	-0.0085	-0.0079	0.0003	-0.0129	-0.0005	0.0029	-0.0546	-0.0258	-0.0223	2024

a) Efficient frontier

library(quadprog)
library(dplyr)
library(ggplot2)

compute_efficient_frontier <- function(returns_data, n_points = 150, buffer = 0.1) {
  R <- as.matrix(returns_data[, -1])
  mu <- colMeans(R)
  cov_matrix <- cov(R)

  
  mu_annual <- mu * 52
  min_ret <- min(mu_annual) * (1 - buffer)
  max_ret <- max(mu_annual) * (1 + buffer)
  target_returns <- seq(min_ret / 52, max_ret / 52, length.out = n_points)

  eff_data <- data.frame(Return = numeric(n_points), Risk = numeric(n_points))

  for (i in seq_along(target_returns)) {
    Dmat <- 2 * cov_matrix
    dvec <- rep(0, ncol(R))
    Amat <- cbind(rep(1, ncol(R)), mu)
    bvec <- c(1, target_returns[i])

    result <- tryCatch(
      solve.QP(Dmat, dvec, Amat, bvec, meq = 2),
      error = function(e) return(NULL)
    )

    if (!is.null(result)) {
      w <- result$solution
      port_return <- sum(w * mu) * 52
      port_sd <- sqrt(t(w) %*% cov_matrix %*% w) * sqrt(52)
      eff_data[i, ] <- c(port_return, port_sd)
    } else {
      eff_data[i, ] <- c(NA, NA)
    }
  }

  return(na.omit(eff_data))
}

stock_tickers <- c("AAPL", "MSFT", "GOOGL", "AMZN", "NVDA", "TSLA", "F", "GM", "APTV", "BWA",
                   "JPM", "BAC", "WFC", "GS", "MS", "JNJ", "PFE", "MRK", "UNH", "ABBV")
gold_ticker <- "GLD"
crypto_ticker <- "BTC-USD"
esg_ticker <- "ESGU"

# Subsets
returns_20 <- weekly_returns %>% select(date, all_of(stock_tickers))
returns_gold <- weekly_returns %>% select(date, all_of(c(stock_tickers, gold_ticker)))
returns_crypto <- weekly_returns %>% select(date, all_of(c(stock_tickers, gold_ticker, crypto_ticker)))
returns_full <- weekly_returns %>% select(date, all_of(c(stock_tickers, gold_ticker, crypto_ticker, esg_ticker)))

clean_efficient_curve <- function(data) {
  data <- data[order(data$Risk), ]  # sort by risk (x-axis)
  data_clean <- data[1, , drop = FALSE]

  for (i in 2:nrow(data)) {
    if (data$Return[i] >= tail(data_clean$Return, 1)) {
      data_clean <- rbind(data_clean, data[i, ])
    }
  }

  return(data_clean)
}

eff_20 <- compute_efficient_frontier(returns_20)
eff_20$Group <- "20 Stocks"

eff_gold <- compute_efficient_frontier(returns_gold)
eff_gold$Group <- "20 Stocks + Gold"

eff_crypto <- compute_efficient_frontier(returns_crypto)
eff_crypto$Group <- "Stocks + Gold + Crypto"

eff_full <- compute_efficient_frontier(returns_full)
eff_full$Group <- "Stocks + Gold + Crypto + ESG"

# Combine
all_eff <- bind_rows(eff_20, eff_gold, eff_crypto, eff_full)

eff_20_clean <- clean_efficient_curve(eff_20)
eff_20_clean$Group <- "20 Stocks"

eff_gold_clean <- clean_efficient_curve(eff_gold)
eff_gold_clean$Group <- "20 Stocks + Gold"

eff_crypto_clean <- clean_efficient_curve(eff_crypto)
eff_crypto_clean$Group <- "Stocks + Gold + Crypto"

eff_full_clean <- clean_efficient_curve(eff_full)
eff_full_clean$Group <- "Stocks + Gold + Crypto + ESG"

all_eff_clean <- bind_rows(eff_20_clean, eff_gold_clean, eff_crypto_clean, eff_full_clean)

ggplot(all_eff_clean, aes(x = Risk, y = Return, color = Group)) +
  geom_line(size = 1.4) +
  labs(title = "Efficient Frontier",
       x = "Annualized Risk (σ)",
       y = "Annualized Return") +
  theme_minimal() +
  scale_color_manual(values = c(
    "20 Stocks" = "blue",
    "20 Stocks + Gold" = "orange",
    "Stocks + Gold + Crypto" = "green",
    "Stocks + Gold + Crypto + ESG" = "red"
  ))

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

plot_frontier <- function(data, title) {
  ggplot(data, aes(x = Risk, y = Return)) +
    geom_line(color = "steelblue", size = 1.2) +
    labs(title = title, x = "Annualized Risk", y = "Annualized Return") +
    theme_minimal()
}

plot_frontier(eff_20_clean, "Efficient Frontier: 20 Stocks")

plot_frontier(eff_gold_clean, "Efficient Frontier: Stocks + Gold")

plot_frontier(eff_crypto_clean, "Efficient Frontier: Stocks + Gold + Crypto")

plot_frontier(eff_full_clean, "Efficient Frontier: Stocks + Gold + Crypto + ESG")

# Annualized table with Sharpe ratios
create_annual_frontier_table <- function(frontier_data, rf_rate) {
  frontier_data %>%
    mutate(Portfolio = row_number(),
           Sharpe = (Return - rf_rate) / Risk) %>%
    select(Portfolio, Return, Risk, Sharpe)
}

eff_20_table <- create_annual_frontier_table(eff_20_clean, rf_annual)
eff_gold_table <- create_annual_frontier_table(eff_gold_clean, rf_annual)
eff_crypto_table <- create_annual_frontier_table(eff_crypto_clean, rf_annual)
eff_full_table <- create_annual_frontier_table(eff_full_clean, rf_annual)

kable(eff_20_table, caption = "Efficient Frontier: 20 Stocks (Annualized)", digits = 4, row.names = "False")

Efficient Frontier: 20 Stocks (Annualized)

Portfolio	Return	Risk	Sharpe
1	0.0945	0.1420	0.5529
2	0.0996	0.1420	0.5887
3	0.1047	0.1421	0.6242
4	0.1097	0.1422	0.6595
5	0.1148	0.1424	0.6945
6	0.1199	0.1426	0.7292
7	0.1250	0.1428	0.7636
8	0.1301	0.1431	0.7976
9	0.1352	0.1434	0.8312
10	0.1403	0.1438	0.8644
11	0.1454	0.1443	0.8971
12	0.1505	0.1447	0.9293
13	0.1555	0.1452	0.9611
14	0.1606	0.1458	0.9923
15	0.1657	0.1464	1.0230
16	0.1708	0.1470	1.0532
17	0.1759	0.1477	1.0828
18	0.1810	0.1484	1.1118
19	0.1861	0.1492	1.1402
20	0.1912	0.1500	1.1680
21	0.1963	0.1508	1.1952
22	0.2013	0.1517	1.2218
23	0.2064	0.1526	1.2478
24	0.2115	0.1536	1.2732
25	0.2166	0.1546	1.2979
26	0.2217	0.1556	1.3220
27	0.2268	0.1567	1.3456
28	0.2319	0.1578	1.3685
29	0.2370	0.1589	1.3908
30	0.2421	0.1601	1.4124
31	0.2471	0.1613	1.4335
32	0.2522	0.1625	1.4540
33	0.2573	0.1638	1.4739
34	0.2624	0.1650	1.4933
35	0.2675	0.1664	1.5121
36	0.2726	0.1677	1.5303
37	0.2777	0.1691	1.5480
38	0.2828	0.1705	1.5651
39	0.2879	0.1719	1.5817
40	0.2929	0.1734	1.5978
41	0.2980	0.1748	1.6134
42	0.3031	0.1763	1.6285
43	0.3082	0.1779	1.6432
44	0.3133	0.1794	1.6573
45	0.3184	0.1810	1.6711
46	0.3235	0.1826	1.6843
47	0.3286	0.1842	1.6972
48	0.3337	0.1858	1.7096
49	0.3387	0.1875	1.7216
50	0.3438	0.1892	1.7333
51	0.3489	0.1909	1.7445
52	0.3540	0.1926	1.7554
53	0.3591	0.1943	1.7659
54	0.3642	0.1961	1.7761
55	0.3693	0.1978	1.7859
56	0.3744	0.1996	1.7954
57	0.3795	0.2014	1.8046
58	0.3845	0.2032	1.8135
59	0.3896	0.2051	1.8221
60	0.3947	0.2069	1.8303
61	0.3998	0.2088	1.8384
62	0.4049	0.2107	1.8461
63	0.4100	0.2126	1.8536
64	0.4151	0.2145	1.8608
65	0.4202	0.2164	1.8678
66	0.4253	0.2183	1.8746
67	0.4304	0.2203	1.8811
68	0.4354	0.2222	1.8874
69	0.4405	0.2242	1.8935
70	0.4456	0.2262	1.8994
71	0.4507	0.2282	1.9051
72	0.4558	0.2302	1.9107
73	0.4609	0.2322	1.9160
74	0.4660	0.2342	1.9211
75	0.4711	0.2363	1.9261
76	0.4762	0.2383	1.9309
77	0.4812	0.2404	1.9356
78	0.4863	0.2424	1.9401
79	0.4914	0.2445	1.9444
80	0.4965	0.2466	1.9486
81	0.5016	0.2487	1.9527
82	0.5067	0.2508	1.9566
83	0.5118	0.2529	1.9604
84	0.5169	0.2550	1.9641
85	0.5220	0.2572	1.9676
86	0.5270	0.2593	1.9711
87	0.5321	0.2614	1.9744
88	0.5372	0.2636	1.9776
89	0.5423	0.2657	1.9807
90	0.5474	0.2679	1.9837
91	0.5525	0.2701	1.9866
92	0.5576	0.2722	1.9894
93	0.5627	0.2744	1.9921
94	0.5678	0.2766	1.9948
95	0.5728	0.2788	1.9973
96	0.5779	0.2810	1.9998
97	0.5830	0.2832	2.0022
98	0.5881	0.2854	2.0045
99	0.5932	0.2877	2.0067
100	0.5983	0.2899	2.0088
101	0.6034	0.2921	2.0109
102	0.6085	0.2943	2.0129
103	0.6136	0.2966	2.0149
104	0.6186	0.2988	2.0168
105	0.6237	0.3011	2.0186
106	0.6288	0.3033	2.0204
107	0.6339	0.3056	2.0221
108	0.6390	0.3079	2.0238
109	0.6441	0.3101	2.0254
110	0.6492	0.3124	2.0269
111	0.6543	0.3147	2.0284
112	0.6594	0.3170	2.0299
113	0.6644	0.3193	2.0313
114	0.6695	0.3215	2.0326
115	0.6746	0.3238	2.0339
116	0.6797	0.3261	2.0352
117	0.6848	0.3284	2.0364

kable(eff_gold_table, caption = "Efficient Frontier: 20 Stocks + Gold (Annualized)", digits = 4, row.names = "False")

Efficient Frontier: 20 Stocks + Gold (Annualized)

Portfolio	Return	Risk	Sharpe
1	0.0945	0.1062	0.7390
2	0.0996	0.1063	0.7866
3	0.1047	0.1064	0.8338
4	0.1097	0.1065	0.8803
5	0.1148	0.1068	0.9262
6	0.1199	0.1070	0.9713
7	0.1250	0.1074	1.0156
8	0.1301	0.1078	1.0591
9	0.1352	0.1082	1.1017
10	0.1403	0.1087	1.1432
11	0.1454	0.1093	1.1838
12	0.1505	0.1099	1.2233
13	0.1555	0.1106	1.2617
14	0.1606	0.1114	1.2991
15	0.1657	0.1122	1.3353
16	0.1708	0.1130	1.3703
17	0.1759	0.1139	1.4042
18	0.1810	0.1148	1.4370
19	0.1861	0.1158	1.4686
20	0.1912	0.1169	1.4990
21	0.1963	0.1180	1.5283
22	0.2013	0.1191	1.5565
23	0.2064	0.1203	1.5836
24	0.2115	0.1215	1.6096
25	0.2166	0.1228	1.6346
26	0.2217	0.1241	1.6585
27	0.2268	0.1254	1.6814
28	0.2319	0.1268	1.7033
29	0.2370	0.1282	1.7242
30	0.2421	0.1296	1.7442
31	0.2471	0.1311	1.7634
32	0.2522	0.1326	1.7816
33	0.2573	0.1342	1.7990
34	0.2624	0.1357	1.8157
35	0.2675	0.1373	1.8315
36	0.2726	0.1390	1.8466
37	0.2777	0.1406	1.8610
38	0.2828	0.1423	1.8747
39	0.2879	0.1440	1.8877
40	0.2929	0.1458	1.9001
41	0.2980	0.1475	1.9119
42	0.3031	0.1493	1.9232
43	0.3082	0.1511	1.9339
44	0.3133	0.1530	1.9440
45	0.3184	0.1548	1.9537
46	0.3235	0.1567	1.9629
47	0.3286	0.1586	1.9716
48	0.3337	0.1605	1.9799
49	0.3387	0.1624	1.9878
50	0.3438	0.1643	1.9953
51	0.3489	0.1663	2.0024
52	0.3540	0.1683	2.0092
53	0.3591	0.1702	2.0156
54	0.3642	0.1722	2.0217
55	0.3693	0.1743	2.0275
56	0.3744	0.1763	2.0330
57	0.3795	0.1783	2.0382
58	0.3845	0.1804	2.0432
59	0.3896	0.1825	2.0479
60	0.3947	0.1846	2.0523
61	0.3998	0.1866	2.0566
62	0.4049	0.1888	2.0606
63	0.4100	0.1909	2.0644
64	0.4151	0.1930	2.0680
65	0.4202	0.1951	2.0714
66	0.4253	0.1973	2.0747
67	0.4304	0.1994	2.0777
68	0.4354	0.2016	2.0806
69	0.4405	0.2038	2.0834
70	0.4456	0.2060	2.0860
71	0.4507	0.2082	2.0885
72	0.4558	0.2104	2.0908
73	0.4609	0.2126	2.0930
74	0.4660	0.2148	2.0951
75	0.4711	0.2170	2.0971
76	0.4762	0.2192	2.0990
77	0.4812	0.2215	2.1007
78	0.4863	0.2237	2.1024
79	0.4914	0.2260	2.1040
80	0.4965	0.2282	2.1055
81	0.5016	0.2305	2.1069
82	0.5067	0.2328	2.1082
83	0.5118	0.2350	2.1094
84	0.5169	0.2373	2.1106
85	0.5220	0.2396	2.1117
86	0.5270	0.2419	2.1127
87	0.5321	0.2442	2.1136
88	0.5372	0.2465	2.1145
89	0.5423	0.2488	2.1154
90	0.5474	0.2511	2.1162
91	0.5525	0.2534	2.1169
92	0.5576	0.2558	2.1176
93	0.5627	0.2581	2.1182
94	0.5678	0.2604	2.1188
95	0.5728	0.2628	2.1193
96	0.5779	0.2651	2.1198
97	0.5830	0.2674	2.1203
98	0.5881	0.2698	2.1207
99	0.5932	0.2721	2.1211
100	0.5983	0.2745	2.1215
101	0.6034	0.2768	2.1218
102	0.6085	0.2792	2.1221
103	0.6136	0.2816	2.1223
104	0.6186	0.2839	2.1225
105	0.6237	0.2863	2.1227
106	0.6288	0.2887	2.1229
107	0.6339	0.2911	2.1231
108	0.6390	0.2934	2.1232
109	0.6441	0.2958	2.1233
110	0.6492	0.2982	2.1234
111	0.6543	0.3006	2.1234
112	0.6594	0.3030	2.1235
113	0.6644	0.3054	2.1235
114	0.6695	0.3078	2.1235
115	0.6746	0.3102	2.1235
116	0.6797	0.3126	2.1234
117	0.6848	0.3150	2.1234

kable(eff_crypto_table, caption = "Efficient Frontier: Stocks + Gold + Crypto (Annualized)", digits = 4, row.names = "False")

Efficient Frontier: Stocks + Gold + Crypto (Annualized)

Portfolio	Return	Risk	Sharpe
1	0.0894	0.1057	0.6949
2	0.0945	0.1057	0.7428
3	0.0996	0.1058	0.7902
4	0.1047	0.1060	0.8371
5	0.1097	0.1062	0.8834
6	0.1148	0.1064	0.9290
7	0.1199	0.1068	0.9739
8	0.1250	0.1071	1.0179
9	0.1301	0.1076	1.0611
10	0.1352	0.1081	1.1033
11	0.1403	0.1086	1.1446
12	0.1454	0.1092	1.1849
13	0.1505	0.1099	1.2242
14	0.1555	0.1106	1.2624
15	0.1606	0.1113	1.2996
16	0.1657	0.1121	1.3356
17	0.1708	0.1130	1.3705
18	0.1759	0.1139	1.4043
19	0.1810	0.1148	1.4370
20	0.1861	0.1158	1.4686
21	0.1912	0.1169	1.4990
22	0.1963	0.1180	1.5284
23	0.2013	0.1191	1.5567
24	0.2064	0.1203	1.5839
25	0.2115	0.1215	1.6101
26	0.2166	0.1227	1.6352
27	0.2217	0.1240	1.6594
28	0.2268	0.1253	1.6825
29	0.2319	0.1267	1.7047
30	0.2370	0.1280	1.7260
31	0.2421	0.1295	1.7464
32	0.2471	0.1309	1.7659
33	0.2522	0.1324	1.7845
34	0.2573	0.1339	1.8024
35	0.2624	0.1355	1.8194
36	0.2675	0.1370	1.8357
37	0.2726	0.1386	1.8513
38	0.2777	0.1402	1.8662
39	0.2828	0.1419	1.8804
40	0.2879	0.1436	1.8939
41	0.2929	0.1453	1.9069
42	0.2980	0.1470	1.9192
43	0.3031	0.1487	1.9310
44	0.3082	0.1505	1.9423
45	0.3133	0.1523	1.9530
46	0.3184	0.1541	1.9632
47	0.3235	0.1559	1.9729
48	0.3286	0.1577	1.9822
49	0.3337	0.1596	1.9911
50	0.3387	0.1614	1.9995
51	0.3438	0.1633	2.0076
52	0.3489	0.1652	2.0153
53	0.3540	0.1671	2.0226
54	0.3591	0.1691	2.0296
55	0.3642	0.1710	2.0362
56	0.3693	0.1730	2.0425
57	0.3744	0.1750	2.0486
58	0.3795	0.1769	2.0543
59	0.3845	0.1789	2.0598
60	0.3896	0.1810	2.0650
61	0.3947	0.1830	2.0700
62	0.3998	0.1850	2.0747
63	0.4049	0.1871	2.0792
64	0.4100	0.1891	2.0835
65	0.4151	0.1912	2.0876
66	0.4202	0.1933	2.0915
67	0.4253	0.1953	2.0952
68	0.4304	0.1974	2.0988
69	0.4354	0.1995	2.1021
70	0.4405	0.2017	2.1053
71	0.4456	0.2038	2.1084
72	0.4507	0.2059	2.1113
73	0.4558	0.2081	2.1141
74	0.4609	0.2102	2.1167
75	0.4660	0.2123	2.1192
76	0.4711	0.2145	2.1216
77	0.4762	0.2167	2.1239
78	0.4812	0.2188	2.1260
79	0.4863	0.2210	2.1281
80	0.4914	0.2232	2.1300
81	0.4965	0.2254	2.1319
82	0.5016	0.2276	2.1336
83	0.5067	0.2298	2.1353
84	0.5118	0.2320	2.1369
85	0.5169	0.2342	2.1384
86	0.5220	0.2365	2.1398
87	0.5270	0.2387	2.1412
88	0.5321	0.2409	2.1425
89	0.5372	0.2432	2.1437
90	0.5423	0.2454	2.1449
91	0.5474	0.2476	2.1460
92	0.5525	0.2499	2.1470
93	0.5576	0.2521	2.1480
94	0.5627	0.2544	2.1489
95	0.5678	0.2567	2.1498
96	0.5728	0.2589	2.1506
97	0.5779	0.2612	2.1514
98	0.5830	0.2635	2.1521
99	0.5881	0.2658	2.1528
100	0.5932	0.2680	2.1535
101	0.5983	0.2703	2.1541
102	0.6034	0.2726	2.1547
103	0.6085	0.2749	2.1552
104	0.6136	0.2772	2.1557
105	0.6186	0.2795	2.1562
106	0.6237	0.2818	2.1566
107	0.6288	0.2841	2.1570
108	0.6339	0.2864	2.1574
109	0.6390	0.2887	2.1577
110	0.6441	0.2911	2.1580
111	0.6492	0.2934	2.1583
112	0.6543	0.2957	2.1586
113	0.6594	0.2980	2.1589
114	0.6644	0.3003	2.1591
115	0.6695	0.3027	2.1593
116	0.6746	0.3050	2.1595
117	0.6797	0.3073	2.1596
118	0.6848	0.3097	2.1598

kable(eff_full_table, caption = "Efficient Frontier: Stocks + Gold + Crypto + ESG (Annualized)", digits = 4, row.names = "False")

Efficient Frontier: Stocks + Gold + Crypto + ESG (Annualized)

Portfolio	Return	Risk	Sharpe
1	0.0741	0.1044	0.5569
2	0.0792	0.1044	0.6056
3	0.0843	0.1045	0.6539
4	0.0894	0.1046	0.7019
5	0.0945	0.1048	0.7493
6	0.0996	0.1050	0.7963
7	0.1047	0.1053	0.8427
8	0.1097	0.1056	0.8884
9	0.1148	0.1059	0.9334
10	0.1199	0.1063	0.9776
11	0.1250	0.1068	1.0211
12	0.1301	0.1073	1.0637
13	0.1352	0.1079	1.1054
14	0.1403	0.1085	1.1462
15	0.1454	0.1091	1.1861
16	0.1505	0.1098	1.2250
17	0.1555	0.1105	1.2629
18	0.1606	0.1113	1.2998
19	0.1657	0.1121	1.3356
20	0.1708	0.1130	1.3705
21	0.1759	0.1139	1.4043
22	0.1810	0.1148	1.4372
23	0.1861	0.1158	1.4689
24	0.1912	0.1168	1.4997
25	0.1963	0.1179	1.5295
26	0.2013	0.1190	1.5583
27	0.2064	0.1201	1.5861
28	0.2115	0.1212	1.6129
29	0.2166	0.1224	1.6388
30	0.2217	0.1237	1.6638
31	0.2268	0.1249	1.6879
32	0.2319	0.1262	1.7111
33	0.2370	0.1275	1.7334
34	0.2421	0.1288	1.7549
35	0.2471	0.1302	1.7755
36	0.2522	0.1316	1.7954
37	0.2573	0.1330	1.8146
38	0.2624	0.1345	1.8329
39	0.2675	0.1359	1.8506
40	0.2726	0.1374	1.8676
41	0.2777	0.1389	1.8839
42	0.2828	0.1405	1.8995
43	0.2879	0.1420	1.9146
44	0.2929	0.1436	1.9290
45	0.2980	0.1452	1.9429
46	0.3031	0.1468	1.9562
47	0.3082	0.1484	1.9690
48	0.3133	0.1501	1.9812
49	0.3184	0.1517	1.9930
50	0.3235	0.1534	2.0043
51	0.3286	0.1551	2.0152
52	0.3337	0.1568	2.0256
53	0.3387	0.1586	2.0356
54	0.3438	0.1603	2.0451
55	0.3489	0.1621	2.0543
56	0.3540	0.1639	2.0632
57	0.3591	0.1656	2.0717
58	0.3642	0.1674	2.0798
59	0.3693	0.1692	2.0876
60	0.3744	0.1711	2.0951
61	0.3795	0.1729	2.1023
62	0.3845	0.1748	2.1092
63	0.3896	0.1766	2.1159
64	0.3947	0.1785	2.1222
65	0.3998	0.1804	2.1283
66	0.4049	0.1822	2.1342
67	0.4100	0.1841	2.1399
68	0.4151	0.1860	2.1453
69	0.4202	0.1880	2.1505
70	0.4253	0.1899	2.1555
71	0.4304	0.1918	2.1603
72	0.4354	0.1938	2.1649
73	0.4405	0.1957	2.1694
74	0.4456	0.1977	2.1737
75	0.4507	0.1996	2.1778
76	0.4558	0.2016	2.1817
77	0.4609	0.2036	2.1855
78	0.4660	0.2056	2.1891
79	0.4711	0.2076	2.1926
80	0.4762	0.2096	2.1960
81	0.4812	0.2116	2.1992
82	0.4863	0.2136	2.2024
83	0.4914	0.2156	2.2054
84	0.4965	0.2176	2.2082
85	0.5016	0.2196	2.2110
86	0.5067	0.2217	2.2137
87	0.5118	0.2237	2.2162
88	0.5169	0.2258	2.2187
89	0.5220	0.2278	2.2211
90	0.5270	0.2299	2.2234
91	0.5321	0.2319	2.2256
92	0.5372	0.2340	2.2277
93	0.5423	0.2361	2.2297
94	0.5474	0.2381	2.2317
95	0.5525	0.2402	2.2336
96	0.5576	0.2423	2.2354
97	0.5627	0.2444	2.2371
98	0.5678	0.2465	2.2388
99	0.5728	0.2486	2.2404
100	0.5779	0.2507	2.2420
101	0.5830	0.2528	2.2435
102	0.5881	0.2549	2.2449
103	0.5932	0.2570	2.2463
104	0.5983	0.2591	2.2476
105	0.6034	0.2612	2.2489
106	0.6085	0.2633	2.2501
107	0.6136	0.2654	2.2513
108	0.6186	0.2676	2.2525
109	0.6237	0.2697	2.2536
110	0.6288	0.2718	2.2546
111	0.6339	0.2740	2.2556
112	0.6390	0.2761	2.2566
113	0.6441	0.2782	2.2576
114	0.6492	0.2804	2.2585
115	0.6543	0.2825	2.2593
116	0.6594	0.2847	2.2602
117	0.6644	0.2868	2.2610
118	0.6695	0.2890	2.2618
119	0.6746	0.2911	2.2625
120	0.6797	0.2933	2.2632
121	0.6848	0.2954	2.2639

b) Minimum variance porfolio

compute_mvp <- function(returns_data) {
  R <- as.matrix(returns_data[,-1])
  cov_matrix <- cov(R)
  n_assets <- ncol(R)

  Dmat <- 2 * cov_matrix
  dvec <- rep(0, n_assets)
  Amat <- matrix(1, nrow = n_assets)
  bvec <- 1

  sol <- solve.QP(Dmat, dvec, Amat, bvec, meq = 1)
  weights <- sol$solution
  mu <- colMeans(R)

  exp_return <- sum(weights * mu) * 52  # annualized
  risk <- sqrt(t(weights) %*% cov_matrix %*% weights) * sqrt(52)  # annualized

  return(list(weights = weights, return = exp_return, risk = risk))
}

mvp_20 <- compute_mvp(returns_20)
mvp_gold <- compute_mvp(returns_gold)
mvp_crypto <- compute_mvp(returns_crypto)
mvp_full <- compute_mvp(returns_full)

mvp_table <- data.frame(
  Portfolio = c("20 Stocks", "20 + Gold", "20 + Gold + Crypto", "20 + Gold + Crypto + ESG"),
  Return = c(mvp_20$return, mvp_gold$return, mvp_crypto$return, mvp_full$return),
  Risk = c(mvp_20$risk, mvp_gold$risk, mvp_crypto$risk, mvp_full$risk)
) %>%
  mutate(
    Sharpe = (Return - rf_annual) / Risk
  )

library(knitr)
kable(mvp_table, caption = "Minimum Variance Portfolios (Annualized)", digits = 4)

Minimum Variance Portfolios (Annualized)

Portfolio	Return	Risk	Sharpe
20 Stocks	0.0949	0.1420	0.5560
20 + Gold	0.0941	0.1062	0.7359
20 + Gold + Crypto	0.0889	0.1057	0.6906
20 + Gold + Crypto + ESG	0.0758	0.1044	0.5729

# Adding MVP points to efficient frontiers
mvp_points <- data.frame(
  Risk = c(mvp_20$risk, mvp_gold$risk, mvp_crypto$risk, mvp_full$risk),
  Return = c(mvp_20$return, mvp_gold$return, mvp_crypto$return, mvp_full$return),
  Group = c("20 Stocks", "20 Stocks + Gold", "Stocks + Gold + Crypto", "Stocks + Gold + Crypto + ESG")
)

# Plot all frontiers + MVP points
ggplot(all_eff_clean, aes(x = Risk, y = Return, color = Group)) +
  geom_line(size = 1.2) +
  geom_point(data = mvp_points, aes(x = Risk, y = Return, color = Group), size = 4, shape = 21, fill = "white", stroke = 1.5) +
  labs(title = "Efficient Frontier with MVP (Annualized)",
       x = "Annualized Risk (σ)", y = "Annualized Return") +
  theme_minimal()

compute_mvp <- function(returns_data) {
  R <- as.matrix(returns_data[,-1])
  cov_matrix <- cov(R)
  n_assets <- ncol(R)
  asset_names <- colnames(R)

  Dmat <- 2 * cov_matrix
  dvec <- rep(0, n_assets)
  Amat <- matrix(1, nrow = n_assets)
  bvec <- 1

  sol <- solve.QP(Dmat, dvec, Amat, bvec, meq = 1)
  weights <- sol$solution
  names(weights) <- asset_names

  mu <- colMeans(R)
  exp_return <- sum(weights * mu) * 52
  risk <- sqrt(t(weights) %*% cov_matrix %*% weights) * sqrt(52)

  return(list(weights = weights, return = exp_return, risk = risk))
}

mvp_20 <- compute_mvp(returns_20)
mvp_gold <- compute_mvp(returns_gold)
mvp_crypto <- compute_mvp(returns_crypto)
mvp_full <- compute_mvp(returns_full)

weights_20 <- data.frame(Asset = names(mvp_20$weights), Weight = round(mvp_20$weights, 4))
weights_gold <- data.frame(Asset = names(mvp_gold$weights), Weight = round(mvp_gold$weights, 4))
weights_crypto <- data.frame(Asset = names(mvp_crypto$weights), Weight = round(mvp_crypto$weights, 4))
weights_full <- data.frame(Asset = names(mvp_full$weights), Weight = round(mvp_full$weights, 4))

kable(weights_20, caption = "MVP Weights: 20 Stocks", digits = 4)

MVP Weights: 20 Stocks

	Asset	Weight
AAPL	AAPL	0.0038
MSFT	MSFT	0.1213
GOOGL	GOOGL	0.0952
AMZN	AMZN	0.0185
NVDA	NVDA	0.0129
TSLA	TSLA	-0.0111
F	F	-0.0232
GM	GM	0.0389
APTV	APTV	-0.0307
BWA	BWA	0.0453
JPM	JPM	0.2631
BAC	BAC	-0.1381
WFC	WFC	0.0111
GS	GS	0.0067
MS	MS	-0.0921
JNJ	JNJ	0.4099
PFE	PFE	0.0201
MRK	MRK	0.1962
UNH	UNH	0.0332
ABBV	ABBV	0.0189

kable(weights_gold, caption = "MVP Weights: 20 Stocks + Gold", digits = 4)

MVP Weights: 20 Stocks + Gold

	Asset	Weight
AAPL	AAPL	0.0094
MSFT	MSFT	0.0265
GOOGL	GOOGL	0.0729
AMZN	AMZN	-0.0098
NVDA	NVDA	-0.0048
TSLA	TSLA	-0.0003
F	F	-0.0072
GM	GM	0.0313
APTV	APTV	-0.0349
BWA	BWA	-0.0147
JPM	JPM	0.1898
BAC	BAC	-0.0275
WFC	WFC	0.0065
GS	GS	-0.0057
MS	MS	-0.0927
JNJ	JNJ	0.2224
PFE	PFE	0.0013
MRK	MRK	0.1073
UNH	UNH	0.0422
ABBV	ABBV	0.0031
GLD	GLD	0.4849

kable(weights_crypto, caption = "MVP Weights: Stocks + Gold + Crypto", digits = 4)

MVP Weights: Stocks + Gold + Crypto

	Asset	Weight
AAPL	AAPL	0.0034
MSFT	MSFT	0.0302
GOOGL	GOOGL	0.0769
AMZN	AMZN	-0.0072
NVDA	NVDA	-0.0014
TSLA	TSLA	0.0015
F	F	-0.0112
GM	GM	0.0341
APTV	APTV	-0.0302
BWA	BWA	-0.0174
JPM	JPM	0.1811
BAC	BAC	-0.0177
WFC	WFC	0.0086
GS	GS	-0.0023
MS	MS	-0.0932
JNJ	JNJ	0.2183
PFE	PFE	-0.0010
MRK	MRK	0.1084
UNH	UNH	0.0453
ABBV	ABBV	0.0024
GLD	GLD	0.4909
BTC-USD	BTC-USD	-0.0195

kable(weights_full, caption = "MVP Weights: Stocks + Gold + Crypto + ESG", digits = 4)

MVP Weights: Stocks + Gold + Crypto + ESG

	Asset	Weight
AAPL	AAPL	-0.0342
MSFT	MSFT	-0.0076
GOOGL	GOOGL	0.0531
AMZN	AMZN	-0.0259
NVDA	NVDA	-0.0225
TSLA	TSLA	-0.0015
F	F	-0.0192
GM	GM	0.0257
APTV	APTV	-0.0381
BWA	BWA	-0.0210
JPM	JPM	0.1670
BAC	BAC	-0.0263
WFC	WFC	-0.0037
GS	GS	-0.0235
MS	MS	-0.1080
JNJ	JNJ	0.1804
PFE	PFE	-0.0073
MRK	MRK	0.0872
UNH	UNH	0.0268
ABBV	ABBV	-0.0058
GLD	GLD	0.4598
BTC-USD	BTC-USD	-0.0214
ESGU	ESGU	0.3661

c) Optimal risky portfolio

compute_orp <- function(returns_data, rf_rate) {
  R <- as.matrix(returns_data[, -1])
  mu <- colMeans(R)
  Σ <- cov(R)
  asset_names <- colnames(R)

  # Excess returns
  excess_mu <- mu - rf_rate / 52  # convert annual rf to weekly

  invΣ <- solve(Σ)
  numer <- invΣ %*% excess_mu
  denom <- sum(numer)

  weights <- as.vector(numer / denom)
  names(weights) <- asset_names

  # Compute performance (annualized)
  port_return <- sum(weights * mu) * 52
  port_risk <- sqrt(t(weights) %*% Σ %*% weights) * sqrt(52)
  sharpe <- (port_return - rf_rate) / port_risk

  return(list(weights = weights, return = port_return, risk = port_risk, sharpe = sharpe))
}

orp_20 <- compute_orp(returns_20, rf_annual)
orp_gold <- compute_orp(returns_gold, rf_annual)
orp_crypto <- compute_orp(returns_crypto, rf_annual)
orp_full <- compute_orp(returns_full, rf_annual)

orp_table <- data.frame(
  Portfolio = c("20 Stocks", "20 + Gold", "20 + Gold + Crypto", "20 + Gold + Crypto + ESG"),
  Return = c(orp_20$return, orp_gold$return, orp_crypto$return, orp_full$return),
  Risk = c(orp_20$risk, orp_gold$risk, orp_crypto$risk, orp_full$risk),
  Sharpe = c(orp_20$sharpe, orp_gold$sharpe, orp_crypto$sharpe, orp_full$sharpe)
)

kable(orp_table, caption = "Optimal Risky Portfolios (Annualized)", digits = 4)

Optimal Risky Portfolios (Annualized)

Portfolio	Return	Risk	Sharpe
20 Stocks	1.1084	0.5282	2.0680
20 + Gold	0.6670	0.3066	2.1235
20 + Gold + Crypto	0.7301	0.3306	2.1603
20 + Gold + Crypto + ESG	0.9610	0.4151	2.2769

orp_points <- data.frame(
  Risk = c(orp_20$risk, orp_gold$risk, orp_crypto$risk, orp_full$risk),
  Return = c(orp_20$return, orp_gold$return, orp_crypto$return, orp_full$return),
  Group = c("20 Stocks", "20 Stocks + Gold", "Stocks + Gold + Crypto", "Stocks + Gold + Crypto + ESG")
)

ggplot(all_eff_clean, aes(x = Risk, y = Return, color = Group)) +
  geom_line(size = 1.2) +
  geom_point(data = mvp_points, aes(x = Risk, y = Return, fill = Group),
             shape = 21, size = 4, color = "black", stroke = 1.2, show.legend = FALSE) +
  geom_point(data = orp_points, aes(x = Risk, y = Return, fill = Group),
             shape = 24, size = 4, color = "black", stroke = 1.2, show.legend = FALSE) +
  scale_fill_manual(values = c("20 Stocks" = "blue", "20 Stocks + Gold" = "orange",
                               "Stocks + Gold + Crypto" = "green", "Stocks + Gold + Crypto + ESG" = "red")) +
  labs(title = "Efficient Frontiers with MVP (●) and ORP (▼)",
       x = "Annualized Risk", y = "Annualized Return") +
  theme_minimal()

# Data for points
mvp_points <- data.frame(
  Risk = c(mvp_20$risk, mvp_gold$risk, mvp_crypto$risk, mvp_full$risk),
  Return = c(mvp_20$return, mvp_gold$return, mvp_crypto$return, mvp_full$return),
  Group = c("20 Stocks", "20 + Gold", "20 + Gold + Crypto", "20 + Gold + Crypto + ESG")
)

orp_points <- data.frame(
  Risk = c(orp_20$risk, orp_gold$risk, orp_crypto$risk, orp_full$risk),
  Return = c(orp_20$return, orp_gold$return, orp_crypto$return, orp_full$return),
  Group = c("20 Stocks", "20 + Gold", "20 + Gold + Crypto", "20 + Gold + Crypto + ESG")
)

# CML = line from (0, rf) to (ORP risk, ORP return)
cml_data <- bind_rows(
  data.frame(Group = "20 Stocks", x = c(0, orp_20$risk), y = c(rf_annual, orp_20$return)),
  data.frame(Group = "20 + Gold", x = c(0, orp_gold$risk), y = c(rf_annual, orp_gold$return)),
  data.frame(Group = "20 + Gold + Crypto", x = c(0, orp_crypto$risk), y = c(rf_annual, orp_crypto$return)),
  data.frame(Group = "20 + Gold + Crypto + ESG", x = c(0, orp_full$risk), y = c(rf_annual, orp_full$return))
)

ggplot(all_eff_clean, aes(x = Risk, y = Return, color = Group)) +
  geom_line(size = 1.2) +
  # MVP point: Circle
  geom_point(data = mvp_points, aes(x = Risk, y = Return, fill = Group),
             shape = 21, size = 4, color = "black", stroke = 1.2, show.legend = FALSE) +
  # ORP point: Triangle
  geom_point(data = orp_points, aes(x = Risk, y = Return, fill = Group),
             shape = 24, size = 4, color = "black", stroke = 1.2, show.legend = FALSE) +
  # CML lines
  geom_line(data = cml_data, aes(x = x, y = y, color = Group), linetype = "dashed", size = 0.8) +
  scale_color_manual(values = c(
    "20 Stocks" = "blue",
    "20 + Gold" = "orange",
    "20 + Gold + Crypto" = "green",
    "20 + Gold + Crypto + ESG" = "red"
  )) +
  scale_fill_manual(values = c(
    "20 Stocks" = "blue",
    "20 + Gold" = "orange",
    "20 + Gold + Crypto" = "green",
    "20 + Gold + Crypto + ESG" = "red"
  )) +
  labs(title = "Efficient Frontiers with MVP (●), ORP (▼), and Capital Market Line",
       x = "Annualized Risk (σ)", y = "Annualized Return") +
  theme_minimal()

# Build per-group datasets
eff_20_clean$Group <- "20 Stocks"
eff_gold_clean$Group <- "20 + Gold"
eff_crypto_clean$Group <- "20 + Gold + Crypto"
eff_full_clean$Group <- "20 + Gold + Crypto + ESG"

# Points
mvp_df <- data.frame(
  Group = c("20 Stocks", "20 + Gold", "20 + Gold + Crypto", "20 + Gold + Crypto + ESG"),
  Return = c(mvp_20$return, mvp_gold$return, mvp_crypto$return, mvp_full$return),
  Risk = c(mvp_20$risk, mvp_gold$risk, mvp_crypto$risk, mvp_full$risk)
)

orp_df <- data.frame(
  Group = c("20 Stocks", "20 + Gold", "20 + Gold + Crypto", "20 + Gold + Crypto + ESG"),
  Return = c(orp_20$return, orp_gold$return, orp_crypto$return, orp_full$return),
  Risk = c(orp_20$risk, orp_gold$risk, orp_crypto$risk, orp_full$risk)
)

# CML lines (start = rf, end = ORP)
cml_df <- bind_rows(
  data.frame(Group = "20 Stocks", x = c(0, orp_20$risk), y = c(rf_annual, orp_20$return)),
  data.frame(Group = "20 + Gold", x = c(0, orp_gold$risk), y = c(rf_annual, orp_gold$return)),
  data.frame(Group = "20 + Gold + Crypto", x = c(0, orp_crypto$risk), y = c(rf_annual, orp_crypto$return)),
  data.frame(Group = "20 + Gold + Crypto + ESG", x = c(0, orp_full$risk), y = c(rf_annual, orp_full$return))
)

plot_frontier_group <- function(eff, mvp, orp, cml, group_name, color) {
  ggplot() +
    geom_line(data = eff, aes(x = Risk, y = Return), color = color, size = 1.3) +
    geom_point(data = mvp, aes(x = Risk, y = Return), shape = 21, size = 4, fill = color, color = "black") +
    geom_point(data = orp, aes(x = Risk, y = Return), shape = 24, size = 4, fill = color, color = "black") +
    geom_line(data = cml, aes(x = x, y = y), linetype = "dashed", color = color, linewidth = 1) +
    labs(title = paste("Efficient Frontier with MVP (●), ORP (▼) and CML:", group_name),
         x = "Annualized Risk (σ)", y = "Annualized Return") +
    theme_minimal()
}

plot_frontier_group(eff_20_clean,
                    filter(mvp_df, Group == "20 Stocks"),
                    filter(orp_df, Group == "20 Stocks"),
                    filter(cml_df, Group == "20 Stocks"),
                    "20 Stocks", "blue")

plot_frontier_group(eff_gold_clean,
                    filter(mvp_df, Group == "20 + Gold"),
                    filter(orp_df, Group == "20 + Gold"),
                    filter(cml_df, Group == "20 + Gold"),
                    "20 Stocks + Gold", "orange")

plot_frontier_group(eff_crypto_clean,
                    filter(mvp_df, Group == "20 + Gold + Crypto"),
                    filter(orp_df, Group == "20 + Gold + Crypto"),
                    filter(cml_df, Group == "20 + Gold + Crypto"),
                    "20 Stocks + Gold + Crypto", "green")

plot_frontier_group(eff_full_clean,
                    filter(mvp_df, Group == "20 + Gold + Crypto + ESG"),
                    filter(orp_df, Group == "20 + Gold + Crypto + ESG"),
                    filter(cml_df, Group == "20 + Gold + Crypto + ESG"),
                    "20 Stocks + Gold + Crypto + ESG", "red")

library(dplyr)
library(knitr)

orp_weights_20 <- data.frame(Asset = names(orp_20$weights), Weight = round(orp_20$weights, 4)) 
orp_weights_gold <- data.frame(Asset = names(orp_gold$weights), Weight = round(orp_gold$weights, 4))
orp_weights_crypto <- data.frame(Asset = names(orp_crypto$weights), Weight = round(orp_crypto$weights, 4))
orp_weights_full <- data.frame(Asset = names(orp_full$weights), Weight = round(orp_full$weights, 4))

kable(orp_weights_20, caption = "ORP Weights: 20 Stocks")

ORP Weights: 20 Stocks

	Asset	Weight
AAPL	AAPL	0.1352
MSFT	MSFT	0.0041
GOOGL	GOOGL	0.1697
AMZN	AMZN	-0.3524
NVDA	NVDA	0.6854
TSLA	TSLA	0.1641
F	F	-0.1661
GM	GM	-0.0382
APTV	APTV	-0.7897
BWA	BWA	-0.2070
JPM	JPM	1.0919
BAC	BAC	-1.1096
WFC	WFC	-0.1586
GS	GS	0.9630
MS	MS	0.3367
JNJ	JNJ	-0.5811
PFE	PFE	-0.5379
MRK	MRK	0.2512
UNH	UNH	0.2424
ABBV	ABBV	0.8970

kable(orp_weights_gold, caption = "ORP Weights: 20 Stocks + Gold")

ORP Weights: 20 Stocks + Gold

	Asset	Weight
AAPL	AAPL	0.0836
MSFT	MSFT	-0.0386
GOOGL	GOOGL	0.1153
AMZN	AMZN	-0.2191
NVDA	NVDA	0.3756
TSLA	TSLA	0.0986
F	F	-0.0882
GM	GM	-0.0122
APTV	APTV	-0.4639
BWA	BWA	-0.1566
JPM	JPM	0.6592
BAC	BAC	-0.5780
WFC	WFC	-0.0894
GS	GS	0.5350
MS	MS	0.1496
JNJ	JNJ	-0.3354
PFE	PFE	-0.3139
MRK	MRK	0.1395
UNH	UNH	0.1603
ABBV	ABBV	0.4996
GLD	GLD	0.4788

kable(orp_weights_crypto, caption = "ORP Weights: 20 + Gold + Crypto")

ORP Weights: 20 + Gold + Crypto

	Asset	Weight
AAPL	AAPL	0.1215
MSFT	MSFT	-0.0631
GOOGL	GOOGL	0.0959
AMZN	AMZN	-0.2462
NVDA	NVDA	0.3795
TSLA	TSLA	0.0948
F	F	-0.0707
GM	GM	-0.0303
APTV	APTV	-0.5158
BWA	BWA	-0.1502
JPM	JPM	0.7353
BAC	BAC	-0.6651
WFC	WFC	-0.1068
GS	GS	0.5483
MS	MS	0.1669
JNJ	JNJ	-0.3461
PFE	PFE	-0.3197
MRK	MRK	0.1354
UNH	UNH	0.1506
ABBV	ABBV	0.5331
GLD	GLD	0.4448
BTC-USD	BTC-USD	0.1079

kable(orp_weights_full, caption = "ORP Weights: 20 + Gold + Crypto + ESG")

ORP Weights: 20 + Gold + Crypto + ESG

	Asset	Weight
AAPL	AAPL	0.4539
MSFT	MSFT	0.2306
GOOGL	GOOGL	0.2955
AMZN	AMZN	-0.1378
NVDA	NVDA	0.6263
TSLA	TSLA	0.1374
F	F	-0.0160
GM	GM	0.0268
APTV	APTV	-0.5435
BWA	BWA	-0.1456
JPM	JPM	0.9574
BAC	BAC	-0.7186
WFC	WFC	-0.0274
GS	GS	0.8282
MS	MS	0.3380
JNJ	JNJ	-0.1421
PFE	PFE	-0.3291
MRK	MRK	0.3147
UNH	UNH	0.3227
ABBV	ABBV	0.7026
GLD	GLD	0.6927
BTC-USD	BTC-USD	0.1482
ESGU	ESGU	-3.0147

d) Optimal risky portfolio no short selling

library(quadprog)

compute_mvp_constrained <- function(returns_data) {
  R <- as.matrix(returns_data[, -1])  
  Sigma <- cov(R)                     # covariance matrix
  n_assets <- ncol(R)

  Dmat <- 2 * Sigma
  dvec <- rep(0, n_assets)

  # Constraints:
  # - sum(w) = 1  (equality)
  # - w_i >= 0    (inequality)
  Amat <- cbind(rep(1, n_assets), diag(n_assets))  # first column: sum(w)=1, rest: w_i >= 0
  bvec <- c(1, rep(0, n_assets))
  meq <- 1

  result <- solve.QP(Dmat, dvec, Amat, bvec, meq)
  weights <- result$solution
  names(weights) <- colnames(R)

  # Calculate return and risk (annualized)
  mu <- colMeans(R)
  port_return <- sum(weights * mu) * 52
  port_risk <- sqrt(t(weights) %*% Sigma %*% weights) * sqrt(52)

  list(
    weights = weights,
    return = port_return,
    risk = port_risk
  )
}

mvp_20_constrained     <- compute_mvp_constrained(returns_20)
mvp_gold_constrained   <- compute_mvp_constrained(returns_gold)
mvp_crypto_constrained <- compute_mvp_constrained(returns_crypto)
mvp_full_constrained   <- compute_mvp_constrained(returns_full)

library(dplyr)
library(knitr)

kable(data.frame(
  Asset = names(mvp_20_constrained$weights),
  Weight = round(mvp_20_constrained$weights, 4)
),
caption = "MVP Weights (No Shorting): 20 Stocks")

MVP Weights (No Shorting): 20 Stocks

	Asset	Weight
AAPL	AAPL	0.0000
MSFT	MSFT	0.1061
GOOGL	GOOGL	0.0830
AMZN	AMZN	0.0072
NVDA	NVDA	0.0069
TSLA	TSLA	0.0000
F	F	0.0000
GM	GM	0.0000
APTV	APTV	0.0000
BWA	BWA	0.0095
JPM	JPM	0.0859
BAC	BAC	0.0000
WFC	WFC	0.0000
GS	GS	0.0000
MS	MS	0.0000
JNJ	JNJ	0.4174
PFE	PFE	0.0129
MRK	MRK	0.1993
UNH	UNH	0.0341
ABBV	ABBV	0.0377

kable(data.frame(
  Asset = names(mvp_gold_constrained$weights),
  Weight = round(mvp_gold_constrained$weights, 4)
) ,
caption = "MVP Weights (No Shorting): 20 Stocks + Gold")

MVP Weights (No Shorting): 20 Stocks + Gold

	Asset	Weight
AAPL	AAPL	0.0000
MSFT	MSFT	0.0002
GOOGL	GOOGL	0.0534
AMZN	AMZN	0.0000
NVDA	NVDA	0.0000
TSLA	TSLA	0.0000
F	F	0.0000
GM	GM	0.0000
APTV	APTV	0.0000
BWA	BWA	0.0000
JPM	JPM	0.0791
BAC	BAC	0.0000
WFC	WFC	0.0000
GS	GS	0.0000
MS	MS	0.0000
JNJ	JNJ	0.2363
PFE	PFE	0.0000
MRK	MRK	0.1135
UNH	UNH	0.0366
ABBV	ABBV	0.0016
GLD	GLD	0.4793

kable(data.frame(
  Asset = names(mvp_crypto_constrained$weights),
  Weight = round(mvp_crypto_constrained$weights, 4)
) ,
caption = "MVP Weights (No Shorting): 20 Stocks + Gold + Crypto")

MVP Weights (No Shorting): 20 Stocks + Gold + Crypto

	Asset	Weight
AAPL	AAPL	0.0000
MSFT	MSFT	0.0002
GOOGL	GOOGL	0.0534
AMZN	AMZN	0.0000
NVDA	NVDA	0.0000
TSLA	TSLA	0.0000
F	F	0.0000
GM	GM	0.0000
APTV	APTV	0.0000
BWA	BWA	0.0000
JPM	JPM	0.0791
BAC	BAC	0.0000
WFC	WFC	0.0000
GS	GS	0.0000
MS	MS	0.0000
JNJ	JNJ	0.2363
PFE	PFE	0.0000
MRK	MRK	0.1135
UNH	UNH	0.0366
ABBV	ABBV	0.0016
GLD	GLD	0.4793
BTC-USD	BTC-USD	0.0000

kable(data.frame(
  Asset = names(mvp_full_constrained$weights),
  Weight = round(mvp_full_constrained$weights, 4)
) ,
caption = "MVP Weights (No Shorting): 20 Stocks + Gold + Crypto + ESG")

MVP Weights (No Shorting): 20 Stocks + Gold + Crypto + ESG

	Asset	Weight
AAPL	AAPL	0.0000
MSFT	MSFT	0.0002
GOOGL	GOOGL	0.0534
AMZN	AMZN	0.0000
NVDA	NVDA	0.0000
TSLA	TSLA	0.0000
F	F	0.0000
GM	GM	0.0000
APTV	APTV	0.0000
BWA	BWA	0.0000
JPM	JPM	0.0791
BAC	BAC	0.0000
WFC	WFC	0.0000
GS	GS	0.0000
MS	MS	0.0000
JNJ	JNJ	0.2363
PFE	PFE	0.0000
MRK	MRK	0.1135
UNH	UNH	0.0366
ABBV	ABBV	0.0016
GLD	GLD	0.4793
BTC-USD	BTC-USD	0.0000
ESGU	ESGU	0.0000

library(nloptr)

compute_orp_constrained_maxsharpe <- function(returns_data, rf_annual) {
  R <- as.matrix(returns_data[, -1])
  mu <- colMeans(R)
  Sigma <- cov(R)
  n_assets <- ncol(R)
  excess_mu <- mu - rf_annual / 52  # weekly excess return

  eval_f <- function(w) {
    port_ret <- sum(w * excess_mu)
    port_risk <- sqrt(as.numeric(t(w) %*% Sigma %*% w))
    -port_ret / port_risk  # negate Sharpe for minimization
  }

  eval_grad_f <- function(w) {
    port_ret <- sum(w * excess_mu)
    port_risk <- sqrt(as.numeric(t(w) %*% Sigma %*% w))
    grad_ret <- excess_mu
    grad_risk <- as.vector(Sigma %*% w) / port_risk  
    - (grad_ret * port_risk - port_ret * grad_risk) / (port_risk^2)
  }

  eval_g_eq <- function(w) sum(w) - 1
  eval_jac_g_eq <- function(w) rep(1, n_assets)

  result <- nloptr::nloptr(
    x0 = rep(1 / n_assets, n_assets),
    eval_f = eval_f,
    eval_grad_f = eval_grad_f,
    lb = rep(0, n_assets),
    ub = rep(1, n_assets),
    eval_g_eq = eval_g_eq,
    eval_jac_g_eq = eval_jac_g_eq,
    opts = list(
      "algorithm" = "NLOPT_LD_SLSQP",
      "xtol_rel" = 1e-8,
      "maxeval" = 10000
    )
  )

  w <- result$solution
  names(w) <- colnames(R)

  port_return <- sum(w * mu) * 52
  port_risk <- sqrt(as.numeric(t(w) %*% Sigma %*% w)) * sqrt(52)
  sharpe <- (port_return - rf_annual) / port_risk

  list(
    weights = w,
    return = port_return,
    risk = port_risk,
    sharpe = sharpe
  )
}

orp_20_constrained<- compute_orp_constrained_maxsharpe(returns_20, rf_annual)
orp_gold_constrained<- compute_orp_constrained_maxsharpe(returns_gold, rf_annual)
orp_crypto_constrained<- compute_orp_constrained_maxsharpe(returns_crypto, rf_annual)
orp_full_constrained<- compute_orp_constrained_maxsharpe(returns_full, rf_annual)

library(dplyr)
library(knitr)

# 1. ORP Weights: 20 Stocks
kable(data.frame(
  Asset = names(orp_20_constrained$weights),
  Weight = round(orp_20_constrained$weights, 4)
) ,
caption = "ORP Weights (No Shorting): 20 Stocks")

ORP Weights (No Shorting): 20 Stocks

	Asset	Weight
AAPL	AAPL	0.0000
MSFT	MSFT	0.0000
GOOGL	GOOGL	0.0000
AMZN	AMZN	0.0000
NVDA	NVDA	0.4149
TSLA	TSLA	0.0416
F	F	0.0000
GM	GM	0.0000
APTV	APTV	0.0000
BWA	BWA	0.0000
JPM	JPM	0.0000
BAC	BAC	0.0000
WFC	WFC	0.0000
GS	GS	0.0492
MS	MS	0.0000
JNJ	JNJ	0.0000
PFE	PFE	0.0000
MRK	MRK	0.0000
UNH	UNH	0.0425
ABBV	ABBV	0.4518

# 2. ORP Weights: 20 Stocks + Gold
kable(data.frame(
  Asset = names(orp_gold_constrained$weights),
  Weight = round(orp_gold_constrained$weights, 4)
),
caption = "ORP Weights (No Shorting): 20 Stocks + Gold")

ORP Weights (No Shorting): 20 Stocks + Gold

	Asset	Weight
AAPL	AAPL	0.0000
MSFT	MSFT	0.0000
GOOGL	GOOGL	0.0000
AMZN	AMZN	0.0000
NVDA	NVDA	0.2876
TSLA	TSLA	0.0295
F	F	0.0000
GM	GM	0.0000
APTV	APTV	0.0000
BWA	BWA	0.0000
JPM	JPM	0.0000
BAC	BAC	0.0000
WFC	WFC	0.0000
GS	GS	0.0394
MS	MS	0.0000
JNJ	JNJ	0.0000
PFE	PFE	0.0000
MRK	MRK	0.0000
UNH	UNH	0.0390
ABBV	ABBV	0.3181
GLD	GLD	0.2864

# 3. ORP Weights: 20 Stocks + Gold + Crypto
kable(data.frame(
  Asset = names(orp_crypto_constrained$weights),
  Weight = round(orp_crypto_constrained$weights, 4)
),
caption = "ORP Weights (No Shorting): 20 + Gold + Crypto")

ORP Weights (No Shorting): 20 + Gold + Crypto

	Asset	Weight
AAPL	AAPL	0.0000
MSFT	MSFT	0.0000
GOOGL	GOOGL	0.0000
AMZN	AMZN	0.0000
NVDA	NVDA	0.2826
TSLA	TSLA	0.0239
F	F	0.0000
GM	GM	0.0000
APTV	APTV	0.0000
BWA	BWA	0.0000
JPM	JPM	0.0000
BAC	BAC	0.0000
WFC	WFC	0.0000
GS	GS	0.0158
MS	MS	0.0000
JNJ	JNJ	0.0000
PFE	PFE	0.0000
MRK	MRK	0.0000
UNH	UNH	0.0328
ABBV	ABBV	0.3290
GLD	GLD	0.2633
BTC-USD	BTC-USD	0.0527

# 4. ORP Weights: 20 Stocks + Gold + Crypto + ESG
kable(data.frame(
  Asset = names(orp_full_constrained$weights),
  Weight = round(orp_full_constrained$weights, 4)
),
caption = "ORP Weights (No Shorting): 20 + Gold + Crypto + ESG")

ORP Weights (No Shorting): 20 + Gold + Crypto + ESG

	Asset	Weight
AAPL	AAPL	0.0000
MSFT	MSFT	0.0000
GOOGL	GOOGL	0.0000
AMZN	AMZN	0.0000
NVDA	NVDA	0.2826
TSLA	TSLA	0.0239
F	F	0.0000
GM	GM	0.0000
APTV	APTV	0.0000
BWA	BWA	0.0000
JPM	JPM	0.0000
BAC	BAC	0.0000
WFC	WFC	0.0000
GS	GS	0.0158
MS	MS	0.0000
JNJ	JNJ	0.0000
PFE	PFE	0.0000
MRK	MRK	0.0000
UNH	UNH	0.0328
ABBV	ABBV	0.3290
GLD	GLD	0.2633
BTC-USD	BTC-USD	0.0527
ESGU	ESGU	0.0000

compute_efficient_frontier_qp <- function(returns_data, n_points = 100, rf = rf_annual) {
  R <- as.matrix(returns_data[, -1])
  mu <- colMeans(R)
  Sigma <- cov(R)
  n_assets <- ncol(R)

  Dmat <- 2 * Sigma
  dvec <- rep(0, n_assets)
  Amat <- cbind(rep(1, n_assets), mu, diag(n_assets))  # constraints: sum(w)=1, mu'w = target, w ≥ 0

  min_return <- quantile(mu, 0.4)
  max_return <- max(mu) * 1.2
  target_returns <- seq(min_return, max_return, length.out = n_points)

  result <- data.frame(Return = numeric(0), Risk = numeric(0), Sharpe = numeric(0))

  for (i in 1:n_points) {
    bvec <- c(1, target_returns[i], rep(0, n_assets))

    sol <- tryCatch({
      solve.QP(Dmat, dvec, Amat, bvec, meq = 2)
    }, error = function(e) return(NULL))

    if (!is.null(sol)) {
      w <- sol$solution
      port_return <- sum(w * mu) * 52
      port_sd <- sqrt(t(w) %*% Sigma %*% w) * sqrt(52)
      sharpe <- (port_return - rf) / port_sd

      result <- rbind(result, data.frame(Return = port_return, Risk = port_sd, Sharpe = sharpe))
    }
  }

  result <- result[result$Return == cummax(result$Return), ]
  return(result)
}

eff_20_constrained <- compute_efficient_frontier_qp(returns_20)
eff_20_constrained$Group <- "20 Stocks"

eff_gold_constrained <- compute_efficient_frontier_qp(returns_gold)
eff_gold_constrained$Group <- "20 Stocks + Gold"

eff_crypto_constrained <- compute_efficient_frontier_qp(returns_crypto)
eff_crypto_constrained$Group <- "20 Stocks + Gold + Crypto"

eff_full_constrained <- compute_efficient_frontier_qp(returns_full)
eff_full_constrained$Group <- "20 Stocks + Gold + Crypto + ESG"

# Combine all into one frame
all_constrained_frontiers <- bind_rows(
  eff_20_constrained,
  eff_gold_constrained,
  eff_crypto_constrained,
  eff_full_constrained
)

ggplot(all_constrained_frontiers, aes(x = Risk, y = Return, color = Group)) +
  geom_line(size = 1.2) +
  labs(title = "Efficient Frontiers (No Shorting)",
       x = "Annualized Risk (σ)", y = "Annualized Return") +
  theme_minimal() +
  scale_color_manual(values = c("purple", "red", "blue", "orange"))

get_mvp_orp <- function(frontier_df) {
  mvp_index <- which.min(frontier_df$Risk)
  orp_index <- which.max(frontier_df$Sharpe)
  list(
    mvp = frontier_df[mvp_index, ],
    orp = frontier_df[orp_index, ]
  )
}

eff_20 <- compute_efficient_frontier_qp(returns_20);       eff_20$Group <- "20 Stocks"
eff_gold <- compute_efficient_frontier_qp(returns_gold);   eff_gold$Group <- "20 + Gold"
eff_crypto <- compute_efficient_frontier_qp(returns_crypto); eff_crypto$Group <- "20 + Gold + Crypto"
eff_full <- compute_efficient_frontier_qp(returns_full);   eff_full$Group <- "20 + Gold + Crypto + ESG"

# Extracting MVP and ORP
pts_20 <- get_mvp_orp(eff_20)
pts_gold <- get_mvp_orp(eff_gold)
pts_crypto <- get_mvp_orp(eff_crypto)
pts_full <- get_mvp_orp(eff_full)

plot_frontier_with_points <- function(frontier_df, mvp, orp, title, color = "black") {
  points_df <- rbind(
    mvp %>% mutate(Type = "MVP"),
    orp %>% mutate(Type = "ORP")
  )

  ggplot(frontier_df, aes(x = Risk, y = Return)) +
    geom_line(color = color, size = 1.2) +
    geom_point(data = points_df, aes(shape = Type), size = 4, fill = "white", color = color) +
    scale_shape_manual(values = c("MVP" = 21, "ORP" = 24),
                       name = "Portfolio Type") +
    labs(title = title,
         x = "Annualized Risk (σ)",
         y = "Annualized Return") +
    theme_minimal() +
    theme(legend.position = "right")
}

plot_frontier_with_points(eff_20, pts_20$mvp, pts_20$orp, "Efficient Frontier non shorting: 20 Stocks", "purple")

plot_frontier_with_points(eff_gold, pts_gold$mvp, pts_gold$orp, "Efficient Frontier non shorting: 20 Stocks + Gold", "red")

plot_frontier_with_points(eff_crypto, pts_crypto$mvp, pts_crypto$orp, "Efficient Frontier non shorting: 20 Stocks + Gold + Crypto", "blue")

plot_frontier_with_points(eff_full, pts_full$mvp, pts_full$orp, "Efficient Frontier non shorting: 20 Stocks + Gold + Crypto + ESG", "orange")

pts_20     <- get_mvp_orp(eff_20)
pts_gold   <- get_mvp_orp(eff_gold)
pts_crypto <- get_mvp_orp(eff_crypto)
pts_full   <- get_mvp_orp(eff_full)

# Combine all MVP and ORP into one frame
summary_table <- bind_rows(
  pts_20$mvp %>% mutate(Point = "MVP", Portfolio = "20 Stocks"),
  pts_20$orp %>% mutate(Point = "ORP", Portfolio = "20 Stocks"),
  pts_gold$mvp %>% mutate(Point = "MVP", Portfolio = "20 Stocks + Gold"),
  pts_gold$orp %>% mutate(Point = "ORP", Portfolio = "20 Stocks + Gold"),
  pts_crypto$mvp %>% mutate(Point = "MVP", Portfolio = "20 Stocks + Gold + Crypto"),
  pts_crypto$orp %>% mutate(Point = "ORP", Portfolio = "20 Stocks+ Gold + Crypto"),
  pts_full$mvp %>% mutate(Point = "MVP", Portfolio = "20 Stocks+ Gold + Crypto + ESG"),
  pts_full$orp %>% mutate(Point = "ORP", Portfolio = "20 Stocks+ Gold + Crypto + ESG")
) %>%
  select(Portfolio, Point, Return, Risk, Sharpe) %>%
  arrange(Portfolio, Point)

summary_table <- summary_table %>%
  mutate(across(c(Return, Risk, Sharpe), ~ round(., 4)))

kable(summary_table, caption = "MVP and ORP Performance Summary (No Shorting)")

MVP and ORP Performance Summary (No Shorting)

Portfolio	Point	Return	Risk	Sharpe
20 Stocks	MVP	0.0881	0.1455	0.4956
20 Stocks	ORP	0.3743	0.2664	1.3451
20 Stocks + Gold	MVP	0.0907	0.1093	0.6836
20 Stocks + Gold	ORP	0.2962	0.2034	1.3777
20 Stocks + Gold + Crypto	MVP	0.0938	0.1094	0.7112
20 Stocks+ Gold + Crypto	ORP	0.3050	0.2074	1.3931
20 Stocks+ Gold + Crypto + ESG	MVP	0.0969	0.1097	0.7383
20 Stocks+ Gold + Crypto + ESG	ORP	0.3071	0.2090	1.3931

e.1.) Optimal risky portfolio only 2 industries shorting allowed

# Defineing industry 
industries <- c(
  AAPL = "Technology", MSFT = "Technology", GOOGL = "Technology", AMZN = "Technology",
  NVDA = "Technology", TSLA = "Automotive", F = "Automotive", GM = "Automotive",
  APTV = "Automotive", BWA = "Automotive", 
  JPM = "Financial", BAC = "Financial", WFC = "Financial", GS = "Financial", MS = "Financial",
  JNJ = "Healthcare", PFE = "Healthcare", MRK = "Healthcare", UNH = "Healthcare", ABBV = "Healthcare"
)

# Drop Automotive and Healthcare
selected_tickers <- names(industries)[!(industries %in% c("Automotive", "Healthcare"))]

returns_10 <- returns_20[, c("date", selected_tickers)]

compute_orp_unconstrained <- function(returns_data, rf = rf_annual) {
  R <- as.matrix(returns_data[, -1])
  mu <- colMeans(R)
  Sigma <- cov(R)

  # Max Sharpe portfolio
  excess_mu <- mu - rf / 52  
  weights <- solve(Sigma) %*% excess_mu
  weights <- as.numeric(weights / sum(weights)) 

  # Portfolio stats
  port_return <- sum(weights * mu) * 52
  port_sd <- sqrt(t(weights) %*% Sigma %*% weights) * sqrt(52)
  sharpe <- (port_return - rf) / port_sd

  list(
    weights = setNames(round(weights, 4), colnames(R)),
    return = round(port_return, 4),
    risk = round(port_sd, 4),
    sharpe = round(sharpe, 4)
  )
}


orp_unconstrained_10 <- compute_orp_unconstrained(returns_10)

library(knitr)

orp_table <- data.frame(
  Asset = names(orp_unconstrained_10$weights),
  Weight = round(orp_unconstrained_10$weights, 4)
)

orp_table <- rbind(
  orp_table,
  data.frame(Asset = "Expected Return", Weight = round(orp_unconstrained_10$return, 4)),
  data.frame(Asset = "Risk (SD)", Weight = round(orp_unconstrained_10$risk, 4)),
  data.frame(Asset = "Sharpe Ratio", Weight = round(orp_unconstrained_10$sharpe, 4))
)

kable(orp_table, caption = "Optimal Risky Portfolio (Unconstrained, 10 Stocks)")

Optimal Risky Portfolio (Unconstrained, 10 Stocks)

	Asset	Weight
AAPL	AAPL	0.2531
MSFT	MSFT	0.0104
GOOGL	GOOGL	0.0672
AMZN	AMZN	-0.3331
NVDA	NVDA	0.6332
JPM	JPM	0.9756
BAC	BAC	-1.3910
WFC	WFC	-0.1308
GS	GS	0.6768
MS	MS	0.2387
1	Expected Return	0.6318
11	Risk (SD)	0.4269
12	Sharpe Ratio	1.4428

compute_mvp_unconstrained <- function(returns_data) {
  R <- as.matrix(returns_data[, -1])  
  mu <- colMeans(R)
  Sigma <- cov(R)

  # Minimum variance
  n <- ncol(R)
  Dmat <- 2 * Sigma
  dvec <- rep(0, n)
  Amat <- matrix(1, nrow = n, ncol = 1)  # constraint: sum(w) = 1
  bvec <- 1

  sol <- solve.QP(Dmat, dvec, Amat, bvec, meq = 1)
  w <- sol$solution
  w <- as.numeric(w)

  port_return <- sum(w * mu) * 52
  port_sd <- sqrt(t(w) %*% Sigma %*% w) * sqrt(52)

  list(
    weights = setNames(round(w, 4), colnames(R)),
    return = round(port_return, 4),
    risk = round(port_sd, 4)
  )
}

mvp_unconstrained_10 <- compute_mvp_unconstrained(returns_10)

library(knitr)

sharpe <- (mvp_unconstrained_10$return - rf_annual) / mvp_unconstrained_10$risk

mvp_table <- data.frame(
  Asset = names(mvp_unconstrained_10$weights),
  Weight = round(mvp_unconstrained_10$weights, 4)
)

summary_row_mvp <- data.frame(
  Asset = c("Expected Return", "Risk (SD)", "Sharpe Ratio"),
  Weight = round(c(mvp_unconstrained_10$return,
                   mvp_unconstrained_10$risk,
                   sharpe), 4)
)

mvp_full_table <- rbind(mvp_table, summary_row_mvp)

kable(mvp_full_table, caption = "Minimum Variance Portfolio (Unconstrained, 10 Stocks)")

Minimum Variance Portfolio (Unconstrained, 10 Stocks)

	Asset	Weight
AAPL	AAPL	0.2087
MSFT	MSFT	0.4419
GOOGL	GOOGL	0.1283
AMZN	AMZN	-0.0228
NVDA	NVDA	-0.1352
JPM	JPM	0.5284
BAC	BAC	-0.2295
WFC	WFC	0.0333
GS	GS	0.2578
MS	MS	-0.2108
1	Expected Return	0.1491
2	Risk (SD)	0.1984
3	Sharpe Ratio	0.6711

compute_efficient_frontier_unconstrained_10 <- function(returns_data, n_points = 100, rf = rf_annual) {
  R <- as.matrix(returns_data[, -1])
  mu <- colMeans(R)
  Sigma <- cov(R)
  n_assets <- ncol(R)

  Dmat <- 2 * Sigma
  dvec <- rep(0, n_assets)
  Aeq <- cbind(rep(1, n_assets), mu)
  frontier <- data.frame(Return = numeric(), Risk = numeric(), Sharpe = numeric())
  weights_list <- list()

  min_return <- min(mu, 0.4)
  max_return <- max(mu) * 1.2
  target_returns <- seq(min_return, max_return, length.out = n_points)

  for (i in 1:n_points) {
    bvec <- c(1, target_returns[i])
    sol <- tryCatch({
      solve.QP(Dmat, dvec, Aeq, bvec, meq = 2)
    }, error = function(e) return(NULL))

    if (!is.null(sol)) {
      w <- sol$solution
      port_return <- sum(w * mu) * 52
      port_sd <- sqrt(t(w) %*% Sigma %*% w) * sqrt(52)
      sharpe <- (port_return - rf) / port_sd

      frontier <- rbind(frontier, data.frame(Return = port_return, Risk = port_sd, Sharpe = sharpe))
      weights_list[[length(weights_list) + 1]] <- w
    }
  }

  frontier$Weights <- weights_list
  return(frontier)
}

clean_efficient_curve_unconstrained_10 <- function(frontier_df) {
  df <- frontier_df[order(frontier_df$Risk), ]
  
  efficient <- df[1, , drop = FALSE]
  for (i in 2:nrow(df)) {
    if (df$Return[i] >= efficient$Return[nrow(efficient)]) {
      efficient <- rbind(efficient, df[i, , drop = FALSE])
    }
  }
  return(efficient)
}

extract_mvp_orp_unconstrained_10 <- function(frontier_df) {
  mvp <- frontier_df[which.min(frontier_df$Risk), ]
  orp <- frontier_df[which.max(frontier_df$Sharpe), ]
  mvp$Type <- "MVP"
  orp$Type <- "ORP"
  rbind(mvp, orp)
}

extract_mvp_orp_unconstrained_10 <- function(frontier_df) {
  mvp <- frontier_df[which.min(frontier_df$Risk), ]
  orp <- frontier_df[which.max(frontier_df$Sharpe), ]
  mvp$Type <- "MVP"
  orp$Type <- "ORP"
  rbind(mvp, orp)
}

# Compute frontier
frontier_unconstrained_10 <- compute_efficient_frontier_unconstrained_10(returns_10)

frontier_unconstrained_10_clean <- clean_efficient_curve_unconstrained_10(frontier_unconstrained_10)

# Extract key points
points_unconstrained_10 <- extract_mvp_orp_unconstrained_10(frontier_unconstrained_10_clean)

ggplot(frontier_unconstrained_10_clean, aes(x = Risk, y = Return)) +
  geom_line(color = "darkgreen", size = 1.2) +
  geom_point(data = points_unconstrained_10,
             aes(shape = Type),
             size = 4,
             fill = "white",
             color = "darkgreen") +
  scale_shape_manual(values = c("MVP" = 21, "ORP" = 24),
                     name = "Portfolio Type",
                     labels = c("MVP (Min Variance)", "ORP (Max Sharpe)")) +
  labs(title = "Efficient Frontier: 10-Stock Universe (Unconstrained)",
       x = "Annualized Risk (σ)",
       y = "Annualized Return") +
  theme_minimal() +
  theme(legend.position = "right")

e.2.) Optimal risky portfolio only 2 industries no shorting allowed

compute_mvp_constrained_10 <- function(returns_data) {
  R <- as.matrix(returns_data[, -1])  
  Sigma <- cov(R)
  n_assets <- ncol(R)

  Dmat <- 2 * Sigma
  dvec <- rep(0, n_assets)
  Amat <- cbind(rep(1, n_assets), diag(n_assets))  # sum of weights = 1 and w >= 0
  bvec <- c(1, rep(0, n_assets))

  sol <- solve.QP(Dmat, dvec, Amat, bvec, meq = 1)
  w <- sol$solution
  names(w) <- colnames(R)
  return(w)
}

library(knitr)

R <- as.matrix(returns_10[, -1])  
mvp_weights_constrained_10 <- compute_mvp_constrained_10(returns_10)
mvp_return <- as.numeric(sum(mvp_weights_constrained_10 * colMeans(R)) * 52)
mvp_risk <- as.numeric(sqrt(t(mvp_weights_constrained_10) %*% cov(R) %*% mvp_weights_constrained_10) * sqrt(52))
mvp_sharpe <- (mvp_return - rf_annual) / mvp_risk


mvp_weights_table <- data.frame(
  Asset = names(mvp_weights_constrained_10),
  Weight = round(mvp_weights_constrained_10, 4)
)


summary_rows <- data.frame(
  Asset = c("Expected Return", "Risk (SD)", "Sharpe Ratio"),
  Weight = round(c(mvp_return, mvp_risk, mvp_sharpe), 4)
)


mvp_full_table <- rbind(mvp_weights_table, summary_rows)


kable(mvp_full_table, caption = "MVP (10-Stock Portfolio, No Shorting) — Weights and Performance")

MVP (10-Stock Portfolio, No Shorting) — Weights and Performance

	Asset	Weight
AAPL	AAPL	0.1588
MSFT	MSFT	0.3433
GOOGL	GOOGL	0.0946
AMZN	AMZN	0.0000
NVDA	NVDA	0.0000
JPM	JPM	0.3452
BAC	BAC	0.0000
WFC	WFC	0.0000
GS	GS	0.0581
MS	MS	0.0000
1	Expected Return	0.1899
2	Risk (SD)	0.2120
3	Sharpe Ratio	0.8208

compute_orp_constrained_10 <- function(returns_data, rf = rf_annual, n_points = 100) {
  R <- as.matrix(returns_data[, -1])
  mu <- colMeans(R)
  Sigma <- cov(R)
  n_assets <- ncol(R)

  Dmat <- 2 * Sigma
  dvec <- rep(0, n_assets)
  Amat <- cbind(rep(1, n_assets), mu, diag(n_assets))  # sum(w)=1, target return, w≥0

  frontier <- data.frame(Return = numeric(), Risk = numeric(), Sharpe = numeric())
  weights_list <- list()

  min_target <- min(mu)
  max_target <- max(mu) * 1.2
  target_returns <- seq(min_target, max_target, length.out = n_points)

  for (i in 1:n_points) {
    bvec <- c(1, target_returns[i], rep(0, n_assets))
    sol <- tryCatch({
      solve.QP(Dmat, dvec, Amat, bvec, meq = 2)
    }, error = function(e) return(NULL))

    if (!is.null(sol)) {
      w <- sol$solution
      port_return <- sum(w * mu) * 52
      port_sd <- sqrt(t(w) %*% Sigma %*% w) * sqrt(52)
      sharpe <- (port_return - rf) / port_sd

      frontier <- rbind(frontier, data.frame(Return = port_return, Risk = port_sd, Sharpe = sharpe))
      weights_list[[length(weights_list) + 1]] <- w
    }
  }

  # ORP (max Sharpe)
  best_index <- which.max(frontier$Sharpe)
  orp_weights <- weights_list[[best_index]]

  list(
    weights = setNames(round(orp_weights, 4), colnames(R)),
    return = round(frontier$Return[best_index], 4),
    risk = round(frontier$Risk[best_index], 4),
    sharpe = round(frontier$Sharpe[best_index], 4)
  )
}

orp_constrained_10 <- compute_orp_constrained_10(returns_10)

library(knitr)

orp_table <- data.frame(
  Asset = names(orp_constrained_10$weights),
  Weight = orp_constrained_10$weights
)

orp_table <- rbind(
  orp_table,
  data.frame(Asset = "Expected Return", Weight = orp_constrained_10$return),
  data.frame(Asset = "Risk (SD)", Weight = orp_constrained_10$risk),
  data.frame(Asset = "Sharpe Ratio", Weight = orp_constrained_10$sharpe)
)

kable(orp_table, caption = "ORP (10-Stock, No Shorting) — Weights and Performance")

ORP (10-Stock, No Shorting) — Weights and Performance

	Asset	Weight
AAPL	AAPL	0.1204
MSFT	MSFT	0.0000
GOOGL	GOOGL	0.0000
AMZN	AMZN	0.0000
NVDA	NVDA	0.6185
JPM	JPM	0.0000
BAC	BAC	0.0000
WFC	WFC	0.0000
GS	GS	0.2611
MS	MS	0.0000
1	Expected Return	0.4677
11	Risk (SD)	0.3718
12	Sharpe Ratio	1.2149

compute_efficient_frontier_constrained_10 <- function(returns_data, n_points = 100, rf = rf_annual) {
  R <- as.matrix(returns_data[, -1])
  mu <- colMeans(R)
  Sigma <- cov(R)
  n_assets <- ncol(R)

  Dmat <- 2 * Sigma
  dvec <- rep(0, n_assets)
  Amat <- cbind(rep(1, n_assets), mu, diag(n_assets))  # constraints: sum(w)=1, mu'w = target, w ≥ 0

  frontier <- data.frame(Return = numeric(), Risk = numeric(), Sharpe = numeric())
  weights_list <- list()

  target_returns <- seq(min(mu), max(mu) * 1.2, length.out = n_points)

  for (i in 1:n_points) {
    bvec <- c(1, target_returns[i], rep(0, n_assets))
    sol <- tryCatch({
      solve.QP(Dmat, dvec, Amat, bvec, meq = 2)
    }, error = function(e) return(NULL))

    if (!is.null(sol)) {
      w <- sol$solution
      port_return <- sum(w * mu) * 52
      port_sd <- sqrt(t(w) %*% Sigma %*% w) * sqrt(52)
      sharpe <- (port_return - rf) / port_sd

      frontier <- rbind(frontier, data.frame(Return = port_return, Risk = port_sd, Sharpe = sharpe))
      weights_list[[length(weights_list) + 1]] <- w
    }
  }

  frontier$Weights <- weights_list
  return(frontier)
}

clean_efficient_curve_constrained_10 <- function(frontier_df) {
  df <- frontier_df[order(frontier_df$Risk), ]
  efficient <- df[1, , drop = FALSE]
  for (i in 2:nrow(df)) {
    if (df$Return[i] >= efficient$Return[nrow(efficient)]) {
      efficient <- rbind(efficient, df[i, , drop = FALSE])
    }
  }
  return(efficient)
}

extract_mvp_orp_constrained_10 <- function(frontier_df) {
  mvp <- frontier_df[which.min(frontier_df$Risk), ]
  orp <- frontier_df[which.max(frontier_df$Sharpe), ]
  mvp$Type <- "MVP"
  orp$Type <- "ORP"
  rbind(mvp, orp)
}

# Compute full frontier
frontier_constrained_10 <- compute_efficient_frontier_constrained_10(returns_10)

frontier_constrained_10_clean <- clean_efficient_curve_constrained_10(frontier_constrained_10)

# Extract MVP & ORP
points_constrained_10 <- extract_mvp_orp_constrained_10(frontier_constrained_10_clean)

ggplot(frontier_constrained_10_clean, aes(x = Risk, y = Return)) +
  geom_line(color = "steelblue", size = 1.2) +
  geom_point(data = points_constrained_10,
             aes(shape = Type),
             size = 4,
             fill = "white",
             color = "steelblue") +
  scale_shape_manual(values = c("MVP" = 21, "ORP" = 24),
                     name = "Portfolio Type",
                     labels = c("MVP (Min Variance)", "ORP (Max Sharpe)")) +
  labs(title = "Efficient Frontier: 10-Stock Universe (Constrained)",
       x = "Annualized Risk (σ)",
       y = "Annualized Return") +
  theme_minimal() +
  theme(legend.position = "right")

f) Index model and Treynor Black

# Use SPY as the market return
market_returns <- weekly_returns %>%
  select(date, Market = SPY)

# Remove date from market returns before merging
returns_all <- weekly_returns %>%
  select(-SPY)

returns_merged_all <- left_join(returns_all, market_returns, by = "date")

estimate_index_model_verbose <- function(stock, data) {
  df <- na.omit(data[, c("Market", stock)])
  model <- lm(df[[stock]] ~ df$Market)

  summary_model <- summary(model)

  alpha <- coef(model)[1]
  beta <- coef(model)[2]
  resid_var <- var(resid(model))
  r_squared <- summary_model$r.squared
  p_alpha <- coef(summary_model)[1, 4]
  p_beta <- coef(summary_model)[2, 4]

  return(data.frame(
    stock = stock,
    alpha = round(alpha, 5),
    beta = round(beta, 5),
    resid_var = round(resid_var, 5),
    R_squared = round(r_squared, 4),
    p_alpha = round(p_alpha, 5),
    p_beta = round(p_beta, 5)
  ))
}

regression_outputs <- bind_rows(
  lapply(colnames(returns_all)[-1], estimate_index_model_verbose, data = returns_merged_all)
)

rownames(regression_outputs) <- NULL

regression_outputs <- head(regression_outputs, -1)

kable(regression_outputs, caption = "Index Model Regressions for All 23 Assets")

Index Model Regressions for All 23 Assets

stock	alpha	beta	resid_var	R_squared	p_alpha	p_beta
AAPL	0.00174	1.17304	0.00078	0.5176	0.31789	0.00000
MSFT	0.00117	1.07762	0.00060	0.5410	0.44478	0.00000
GOOGL	0.00091	1.13828	0.00089	0.4683	0.62611	0.00000
AMZN	-0.00013	1.29102	0.00139	0.4203	0.95456	0.00000
NVDA	0.00711	1.87842	0.00291	0.4236	0.03579	0.00000
TSLA	0.00434	2.12861	0.00710	0.2791	0.41090	0.00000
F	-0.00288	1.54479	0.00237	0.3796	0.34389	0.00000
GM	-0.00193	1.42188	0.00194	0.3867	0.48357	0.00000
APTV	-0.00563	1.56970	0.00225	0.3993	0.05854	0.00000
BWA	-0.00337	1.17960	0.00151	0.3585	0.16577	0.00000
JPM	0.00008	1.02674	0.00094	0.4041	0.96503	0.00000
BAC	-0.00176	1.22232	0.00118	0.4337	0.41232	0.00000
WFC	-0.00156	1.23030	0.00160	0.3648	0.53242	0.00000
GS	0.00083	1.18113	0.00077	0.5243	0.63037	0.00000
MS	0.00059	1.35582	0.00092	0.5490	0.75459	0.00000
JNJ	-0.00045	0.37566	0.00053	0.1387	0.75628	0.00000
PFE	-0.00182	0.53747	0.00117	0.1299	0.39558	0.00000
MRK	0.00010	0.42274	0.00078	0.1221	0.95636	0.00000
ABBV	0.00217	0.51142	0.00109	0.1273	0.29402	0.00000
UNH	0.00078	0.63797	0.00100	0.1973	0.69557	0.00000
GLD	0.00150	0.15413	0.00045	0.0313	0.25840	0.00425
BTC-USD	0.00520	1.61340	0.00679	0.1887	0.31298	0.00000
ESGU	-0.00009	1.01266	0.00001	0.9834	0.66771	0.00000

tb_params <- regression_outputs %>%
  select(stock, alpha, beta, resid_var)

tb_params <- tb_params %>%
  mutate(
    # MVP (unconstrained)
    score_mvp = 1 / resid_var,
    weight_mvp_tb = score_mvp / sum(score_mvp),

    # ORP (constrained): only assets with alpha > 0
    score_orp = ifelse(alpha > 0, alpha / resid_var, 0),
    weight_orp_tb = score_orp / sum(score_orp)
  )

# Market stats (SPY assumed already cleaned)
r_M <- mean(returns_merged_all$Market, na.rm = TRUE) * 52
sd_M <- sd(returns_merged_all$Market, na.rm = TRUE) * sqrt(52)
rf <- rf_annual  # already in annualized decimal format

compute_tb_metrics <- function(w, alpha, beta, resid_var, r_f, r_M, sd_M) {
  w <- w / sum(abs(w))  

  alpha_A <- sum(w * alpha)
  beta_A  <- sum(w * beta)
  var_eA  <- sum((w^2) * resid_var)

  var_eA <- max(var_eA, 1e-4)

  tb_score <- alpha_A / var_eA
  tb_score <- min(tb_score, 10) 

  # Calculation for optimal weights for active vs. passive (market) portfolio
  w_A <- tb_score / ((r_M - r_f) / sd_M^2 + tb_score)
  w_M <- 1 - w_A
  
  # Computation of portfolio return, risk, Sharpe
  expected_return <- r_f + w_A * alpha_A + (w_A * beta_A + w_M) * (r_M - r_f)
  risk <- sqrt((w_A * beta_A + w_M)^2 * sd_M^2 + w_A^2 * var_eA)
  sharpe <- (expected_return - r_f) / risk

  return(c(
    Return = expected_return,
    Risk = risk,
    Sharpe = sharpe,
    ActiveWeight = w_A,
    MarketWeight = w_M
  ))
}

res_mvp <- compute_tb_metrics(
  tb_params$weight_mvp_tb,
  tb_params$alpha, tb_params$beta, tb_params$resid_var,
  rf, r_M, sd_M
)

res_orp <- compute_tb_metrics(
  tb_params$weight_orp_tb,
  tb_params$alpha, tb_params$beta, tb_params$resid_var,
  rf, r_M, sd_M
)

tb_summary <- data.frame(
  Portfolio = c("MVP (Treynor-Black)", "ORP (Treynor-Black, No Shorting)"),
  Expected_Return = c(res_mvp["Return"], res_orp["Return"]),
  Risk = c(res_mvp["Risk"], res_orp["Risk"]),
  Sharpe_Ratio = c(res_mvp["Sharpe"], res_orp["Sharpe"]),
  Active_Weight = c(res_mvp["ActiveWeight"], res_orp["ActiveWeight"]),
  Market_Weight = c(res_mvp["MarketWeight"], res_orp["MarketWeight"])
)

kable(tb_summary, digits = 4, caption = "Treynor-Black Portfolio Summary (MVP & ORP)")

Treynor-Black Portfolio Summary (MVP & ORP)

Portfolio	Expected_Return	Risk	Sharpe_Ratio	Active_Weight	Market_Weight
MVP (Treynor-Black)	0.1345	0.1777	0.6673	-0.0928	1.0928
ORP (Treynor-Black, No Shorting)	0.1376	0.1798	0.6765	0.7269	0.2731

tb_weights <- tb_params %>%
  select(stock, weight_mvp_tb, weight_orp_tb) %>%
  rename(MVP_Weight = weight_mvp_tb, ORP_Weight = weight_orp_tb)

kable(tb_weights, digits = 4, caption = "Active Portfolio Weights (including Crypto, Gold, ESG)")

Active Portfolio Weights (including Crypto, Gold, ESG)

stock	MVP_Weight	ORP_Weight
AAPL	0.0106	0.1308
MSFT	0.0138	0.1143
GOOGL	0.0093	0.0599
AMZN	0.0060	0.0000
NVDA	0.0029	0.1432
TSLA	0.0012	0.0358
F	0.0035	0.0000
GM	0.0043	0.0000
APTV	0.0037	0.0000
BWA	0.0055	0.0000
JPM	0.0088	0.0050
BAC	0.0070	0.0000
WFC	0.0052	0.0000
GS	0.0108	0.0632
MS	0.0090	0.0376
JNJ	0.0157	0.0000
PFE	0.0071	0.0000
MRK	0.0106	0.0075
ABBV	0.0076	0.1167
UNH	0.0083	0.0457
GLD	0.0184	0.1954
BTC-USD	0.0012	0.0449
ESGU	0.8295	0.0000