import requests # math operations from numpy import inf import datetime as dt import yfinance as yf # time operations from datetime import timedelta # for numerical analyiss import numpy as np # to store and process data in dataframe import pandas as pd # basic visualization package import matplotlib.pyplot as plt import io # advanced ploting import seaborn as sns # interactive visualization import plotly.express as px import plotly.graph_objs as go # import plotly.figure_factory as ff # from plotly.subplots import make_subplots # for offline ploting from plotly.offline import plot, iplot, init_notebook_mode init_notebook_mode(connected=True) # hide warnings import warnings warnings.filterwarnings("ignore") import scipy.stats as st

# color pallette cnf, dth, rec, act = "#393e46", "#ff2e63", "#21bf73", "#fe9801"

url = 'https://raw.githubusercontent.com/owid/covid-19-data/master/public/data/owid-covid-data.csv' download = requests.get(url).content covid = pd.read_csv(io.StringIO(download.decode('utf-8')), parse_dates=['date']) covid.info() covid.tail(5)

#Analysing Covid cases in Taiwan taiwan = covid[covid['location'] == 'Taiwan'] taiwan.index = (pd.to_datetime(taiwan['date'],format='%m/%d/%y %I:%M%p')) taiwan.groupby(by=[taiwan.index.month, taiwan.index.year]) taiwan.info()

new_cases = taiwan['new_cases_smoothed_per_million'] new_deaths = taiwan['new_deaths_smoothed_per_million'] icu_patients = taiwan['icu_patients_per_million'] hosp_patients = taiwan['hosp_patients_per_million'] new_tests = taiwan['new_tests'] new_vaccinations_smoothed = taiwan['new_vaccinations_smoothed'] date = taiwan['date'] stringency_index = taiwan['stringency_index']

QUESTION 1

1. Pick a country and evaluate the Covid19 situation in the country.

#EVALUATING COVID IN TAIWAN fig,ax=plt.subplots() sns.lineplot(date, new_cases, color='orange', label='New Cases') sns.lineplot(date, new_deaths,color='red', label='New Deaths') plt.xlabel('Date') plt.ylabel('New Cases & New Deaths') plt.xticks(rotation=90) ax2= plt.twinx() sns.lineplot(date, new_vaccinations_smoothed,color='blue', alpha=0.5, label='New vaccinations') ax2.set_ylabel('New Vaccination') ax2.legend(frameon=False, loc='center left') plt.title('COVID IN TAIWAN') plt.show()

Answer to Question 1:

In this question, we are evaluating Taiwan's Covid19 situation. As we can see from the graph, the spike of Covid19 happens in late May 2021 and lasts till July 2021. It all started with a case outbreak caused by a tested positive pilot. We can assume that a positive outbreak is a direct result from the accidental release of the virus from a confined person. We believe had this not happened then the country's outbreak wouldn't have happened, and therefore the spike in cases, and subsequent deaths would have been avoided.

Overall, there are not many death cases, and the death cases only have its spike as the new cases increased in May. Moreover, by plotting the new vaccination in Taiwan, we can see more and more people are taking vaccination after the rise in Covid19 cases. Also, from the plot, we can imply that the vaccination actually help cease the new cases. we must still be on alert as studies have shown that people with the vaccine are in some instances more likely to get the disease in a variant, however, it shouldn't be as bad and their effects will be 'supposedly' in a lesser manner.

# EVALUATING COVID IN THE WORLD world_new_cases = covid['new_cases_smoothed_per_million'] world_new_deaths = covid['new_deaths_smoothed_per_million'] world_new_vaccinations_smoothed = covid['new_vaccinations_smoothed'] world_date = covid['date']

fig,ax=plt.subplots() sns.lineplot(world_date, world_new_cases, color='green', label='World_New Cases') sns.lineplot(world_date, world_new_deaths,color='yellow', label='World_New Deaths') plt.xlabel('Date') plt.ylabel('World_New Cases & World_New Deaths') plt.xticks(rotation=90) ax2= plt.twinx() sns.lineplot(world_date, world_new_vaccinations_smoothed,color='gray', alpha=0.5, label='New vaccinations') ax2.set_ylabel('World_New Vaccination') ax2.legend(frameon=False, loc='upper left') plt.title('WORLD COVID CASES & DEATHS') plt.show()

Here we plot the new cases, new deaths, and new vaccination of the world. We can see that compared to the world's new cases, Taiwan's new cases are relatively low and seem controllable. However, the vaccination level of Taiwan is also low compared to the world. This is caused by a vaccine shortage in Taiwan.

QUESTION 2

2. Evaluate the potential hidden cases (e.g., case positivity rate) and deaths (e.g., estimated infection fatality rate, excess death).

covid['world_positivity'] = (covid['total_cases']/covid['total_tests'])*100 covid[covid['world_positivity'] == inf] = 0 avg_world_positivity= np.mean(covid['world_positivity']) taiwan['case_positivity'] = (taiwan['total_cases']/taiwan['total_tests'])*100 avg_taiwan_case_positivity = np.mean(taiwan['case_positivity'])

#IDENTIFYING BENCHMARK COUNTRIES benchmark_countries = covid[covid['world_positivity']<=0.5] benchmark_countries.tail() #NO OF BENCHMARK COUNTRIES print(len(benchmark_countries['iso_code'].unique())) #THESE ARE THE COUNTRIES THAT GO FOR RIGOROUS TESTING REGIMES benchmark_countries['benchmark_case_positivity'] = (benchmark_countries['total_cases']/benchmark_countries['total_tests'])*100 benchmark_case_positivity_rate = np.mean(benchmark_countries['benchmark_case_positivity'])

#COMPARING CASE POSITIVITY OF THE WORLD, THE BENCHMARK, AND TAIWAN print("Average World Positivity: " + str(avg_world_positivity)) print("Average Taiwan Case Positivity: " + str(avg_taiwan_case_positivity)) print("Benchmark Case Positivity Rate: " + str(benchmark_case_positivity_rate))

Here we compare the average world positivity, benchmark positivity, and the case positivity in Taiwan. Taiwan appears to be well below the average world positivity rate of 9.66% with only 0.67%. However, above the benchmark positivity rate 0.26%. So, we conclude that there aren't much hidden cases in Taiwan, given the enough number of tested people country can reflect a more accurate positivity rate.

#COMPARING CASE FATILITY OF THE WORLD, THE BENCHMARK, AND TAIWAN covid['world_fatality']=(covid['total_deaths']/covid['total_cases'])*100 avg_world_fatality = np.mean(covid['world_fatality']) print("Average World Fatality: " + str(avg_world_fatality) ) taiwan['case_fatality'] = (taiwan['total_deaths']/taiwan['total_cases'])*100 avg_taiwan_fatality = np.mean(taiwan['case_fatality']) print("Average Taiwan Fatality: " + str(avg_taiwan_fatality)) benchmark_countries['case_fatality'] = (benchmark_countries['total_deaths']/benchmark_countries['total_cases'])*100 benchmark_fatality_rate = np.mean(benchmark_countries['case_fatality']) print("Benchmark Fatality Rate: " + str(benchmark_fatality_rate))

Here we compare the average world fatality, benchmark infection fatality, and the case fatality in Taiwan. Taiwan appears to be below the average world fatality rate of 2.76% and benchmark fatality of 2.17% with only 1.92%. There could be potential hidden death due to the disparity in the fatality rate. Yet, shouldn't be much since 1.92% isn't far from 2.17%.

#COMPARING THE FATALITY RATE BEFORE AND AFTER COVID OF TAIWAN #Taiwan's fatality rate per 1000 people before covid is 7.631 #Source:https://www.macrotrends.net/countries/TWN/taiwan/death-rate taiwan_after_covid = taiwan[taiwan['date'] > '2020-01-20'] avg_taiwan_fatality_after_covid= np.mean(taiwan_after_covid['new_deaths_per_million']*1000) print(avg_taiwan_fatality_after_covid)

There is a big gap between the fatality before 7.63 and after 60.76 Covid19 in Taiwan. So, we can infer that there is not much hidden death in Taiwan.

#COMPARING THE CASE POSITIVITY AND FATALITY IN TAIWAN sns.lineplot(date,taiwan['case_positivity'], label='Case Positivity') sns.lineplot(date, taiwan['case_fatality'], label='Case Fatality') plt.legend() plt.xticks(rotation=90) #COMPARING THE CASE POSITIVITY AND FATALITY IN TAIWAN sns.jointplot(x='case_positivity', y='case_fatality', data=taiwan, kind='reg', color='b')

fig,ax=plt.subplots() sns.lineplot(date, taiwan['new_vaccinations_smoothed_per_million'],label='Taiwan Vaccinations') sns.lineplot(world_date, covid['new_vaccinations_smoothed_per_million'],label='World Vaccinations') plt.xticks(rotation=90) plt.legend() ax2= plt.twinx() sns.lineplot(date, new_deaths,color='red', alpha=0.5, label='New Deaths') ax2.set_ylabel('Taiwan Death') ax2.legend(frameon=False, loc='center left') plt.title('Vaccinations and Taiwan Death') plt.show()

There seems to be positive correlation between the case fatality and the spread of the infection as seen in the regression above. The line plot below also suggests the same, where increases in the case positivity have been followed by increases in case fatality. We can infer from the graph that the community spread has a relationship with fatality. Taiwan has also started vaccinating its residents long after the world began rolling out vaccines. This is because there are not enough capacity in health care and medical centers in Taiwan when it comes to community spread with many people ending up in severe cases and need a lot of medical resources. Since the vaccination rate is low, so the likelihood for patients to be in severe case is higher and need more medical capacity.

We also can see from the graph that, once the vaccination rate in creases, the death rate lowers.

#COMPARING THE TOTAL TESTS DONE TO THE TOTAL POSITIVE CASES sns.jointplot(x='total_tests', y='total_cases', data=taiwan, kind='reg', color='b')

Here, we see a positive correlation between the total tests taken and the total cases. The more total_tests, the more likely we are going to capture more Covid19 cases. However, there is a diminishing return effect. When total_test reaches 3 million, it seems that the more tests taken wouldn't help much in capturing more cases since most cases are already identified. As a result, when we set the benchmark country, we use a positivity rate that's below 0.5% (15000 cases/ 3000000 tests).

QUESTION 3

3.  Explore the relationship between the country's Covid19 cases and deaths and government health intervention policies (e.g., vaccination rate, closure), as well as Google community mobility reports.

#STRINGENCY INDEX fig,ax=plt.subplots() sns.lineplot(date, new_cases, color='orange', label='New Cases') sns.lineplot(date, new_deaths,color='red', label='New Deaths') plt.xlabel('Date') plt.ylabel('New Cases & New Deaths') plt.xticks(rotation=90) ax2= plt.twinx() sns.lineplot(date, stringency_index,color='blue', alpha=0.5, label='Stringency Index') ax2.set_ylabel('Stringency Index') ax2.legend(frameon=False, loc='center left') plt.show()

The Stringency Index measures the strictness go government intervention policies but doesn't imply the effectiveness or appropriateness of the country's response. The graph for the index remains flat in many areas indicating that the index has remained the same and new cases, new deaths have remained low. We can infer that the government intervention is taking effect. However, recently there has been a huge spike and outbreak in the number of Covid19 cases in Taiwan in May 2021. The Stringency Index had increased right away to reflect this spike from an average of about 30 to 70. Given that the number of cases have fallen, it can be understood that the Government's quick Intervention reflected by the Index has played a part in this decrease.

#TAIWAN MOBILITY INDEX Taiwan_mobility_2020 = pd.read_csv('/work/TW mobility.csv') Taiwan_mobility_2021 = pd.read_csv('/work/2021_TW_Region_Mobility_Report.csv') Taiwan_mobility_data = Taiwan_mobility_2020.append(Taiwan_mobility_2021) Taiwan_mobility_data.index = (pd.to_datetime(Taiwan_mobility_data['date'])) Taiwan_mobility_data.groupby(by=[Taiwan_mobility_data.index.month, Taiwan_mobility_data.index.year])

taiwan_mobility = pd.merge(Taiwan_mobility_data, taiwan, left_index=True, right_index=True) taiwan_mobility.info()

#EXAMINING THE MOBILITY INDICES fig,ax=plt.subplots() sns.lineplot(date, taiwan_mobility['parks_percent_change_from_baseline'],color='lightpink', label='Parks') sns.lineplot(date, taiwan_mobility['grocery_and_pharmacy_percent_change_from_baseline'], color='yellow', label='Grocery and Pharmacy') sns.lineplot(date, taiwan_mobility['retail_and_recreation_percent_change_from_baseline'],color='lightblue', label='Retail and Recreation') plt.xlabel('Date') plt.ylabel('Grocery, Retail and Parks') plt.xticks(rotation=90) ax2= plt.twinx() sns.lineplot(date,taiwan['case_positivity'] ,color='gray', alpha=0.5, label='Case Positivity') ax2.set_ylabel('Case Positivity') ax2.legend(frameon=False, loc='upper left') plt.title('MOBILITY INDICES') plt.show()

Upon comparing the changes in retail, parks and grocery with the case positivity, the recent sudden spike in cases have been met by a fall in grocery and pharmaceutical runs, parks and retail and recreation. This may be due to voluntary avoidance by the residents of Taiwan. But a portion of it can also be attributed to restrictions imposed by the government as indicated by the stringency levels which increased during this period. Taiwan immediately went into level 3 soft lock down right after the outbreak of cases in May 2021.

#EXAMINING THE MOBILITY INDICES fig,ax=plt.subplots() sns.lineplot(date, taiwan_mobility['residential_percent_change_from_baseline'],color='lightpink', label='Residential') sns.lineplot(date, taiwan_mobility['workplaces_percent_change_from_baseline'], color='violet', label='Workplace') sns.lineplot(date, taiwan_mobility['transit_stations_percent_change_from_baseline'],color='lightblue', label='Transit Stations') plt.xlabel('Date') plt.ylabel('Residential, Workplaces and Transit') plt.xticks(rotation=90) ax2= plt.twinx() sns.lineplot(date,taiwan['case_positivity'] ,color='gray', alpha=0.5, label='Case Positivity') ax2.set_ylabel('Case Positivity') ax2.legend(frameon=False, loc='upper left') plt.title('MOBILITY INDICES') plt.show()

Upon comparing the changes in residential, workplace and transit stations with the case positivity, the recent sudden spike in cases have been met by a surprising rise in the residential percentage. There has however been a fall in the workspaces and the transit stations. As see above this could be due to higher stringency levels and imposition of lockdowns.

Overall we can say the government reacted pretty fast in leveling up the restriction after the Covid19 outbreak, and Taiwanese also tighten their mobility according to the policy. We observe the decrease of cases right after that.

LAB 5

Industries:

#NEED TO FIND STOCKS WE WANT TO OBSERVE AND A MARKET INDEX symbols_list = ['TSM','TLC', 'BNTX', 'CHT', 'ASX','UMC', 'EWT'] start = dt.datetime(2016,7,15) end = dt.datetime(2021,9,15) data = yf.download(symbols_list, start=start, end=end) # filter column adjusted close df = data['Adj Close'] df = df.ffill()

!pip install PyPortfolioOpt==1.2.1

from pypfopt.efficient_frontier import EfficientFrontier from pypfopt import risk_models from pypfopt import expected_returns from pypfopt import cla from pypfopt.plotting import Plotting from pypfopt.discrete_allocation import DiscreteAllocation, get_latest_prices from matplotlib.ticker import FuncFormatter import seaborn as sns

# Check NaN values in the data nullin_df = pd.DataFrame(df,columns=symbols_list) print(nullin_df.isnull().sum()) # Calculate portfolio mean return mu = expected_returns.mean_historical_return(df) print(mu) # Calculate portfolio return variance sigma = risk_models.sample_cov(df) print(sigma)

QUESTION 1

1. Based on your investment strategy (i.e., chosen stocks, industries, asset classes), identify the maximum Sharpe ratio and minimum volatility portfolios.

# Note max sharpe ratio is the tangency portfolio # weight bounds in negative allows shorting of stocks ef = EfficientFrontier(mu, sigma, weight_bounds=(-1,1)) # optional constraints possible, read pypfopt documentation. sharpe_portfolio=ef.max_sharpe(risk_free_rate=0.008) sharpe_portfolio_wt=ef.clean_weights() print(sharpe_portfolio_wt) Plotting.plot_weights(sharpe_portfolio_wt)

Maximum Shape Ratio Portfolio {'ASX': -0.32434, 'BNTX': 0.33452, 'CHT': -0.21005, 'EWT': 0.30105, 'TLC': 0.06969, 'TSM': 0.43368, 'UMC': 0.39544}.

QUESTION 2

2. If you have USD 1 million now, how much should you invest in each?

latest_prices = get_latest_prices(df) # Allocate Portfolio Value in $ as required to show number of shares/stocks to buy, # also bounds for shorting will affect allocation # Maximum Sharpe Portfolio Allocation $1000000 da = DiscreteAllocation(sharpe_portfolio_wt, latest_prices, total_portfolio_value=1000000) allocation, leftover = da.greedy_portfolio() #change allocation in line above print(allocation) print("Leftover Fund value for the maximum Sharpe portfolio is ${:.2f}".format(leftover))

Out of the $1000000 available for allocation, the amounts have been invested in the stocks as shown above. The leftover fund in the maximum Sharpe portfolio is $69.73. The portfolio indicates that we short the stocks of ASX a tech company and CHT a telecom company.

max_sharpe_cla = cla.CLA(mu, sigma) max_sharpe_cla.max_sharpe() Plotting.plot_efficient_frontier(max_sharpe_cla, show_assets="True")

sharpe_portfolio_wt_list = list(sharpe_portfolio_wt.values()) ret_data = df.pct_change()[1:] weighted_returns = (sharpe_portfolio_wt_list * ret_data) portfolio_ret = pd.DataFrame(weighted_returns.sum(axis=1)) ret_data = ret_data.merge(portfolio_ret, on="Date", how="left") ret_data = ret_data.rename(columns={0: "portfolio_ret"}) ret_data.tail()

ret_data['cumulative_portfolio_ret'] = (ret_data['portfolio_ret'] + 1).cumprod() ret_data['cumulative_EWT_ret'] = (ret_data['EWT'] + 1).cumprod() ret_data.tail()

QUESTION 3

3. Plot a graph showing how your portfolios (maximum Sharpe and minimum volatility portfolios) perform relative to the market (i.e., SPY)

sns.scatterplot('Date', 'cumulative_portfolio_ret', data=ret_data) sns.scatterplot('Date', 'cumulative_EWT_ret', data=ret_data)

plt.hist(ret_data['portfolio_ret'], bins=10)

st.norm.interval(alpha=0.95, loc=np.mean(ret_data['portfolio_ret']), scale=st.sem(ret_data['portfolio_ret']))

QUESTION 1

1. Calculate the Minimum Volatility Portfolio

#Minimum Volatility Portfolio ef = EfficientFrontier(mu, sigma, weight_bounds=(-1,1)) min_vol_portfolio=ef.min_volatility() min_vol_portfolio_wt=ef.clean_weights() print(min_vol_portfolio_wt) Plotting.plot_weights(min_vol_portfolio_wt)

For our MVP we calculated that we need a majority of CHT for our portfolio, along with smaller amounts EWT, UMC, TLC. We had to short stocks for TSM, BNTX, and ASX for the portfolio as well.

da = DiscreteAllocation(min_vol_portfolio_wt, latest_prices, total_portfolio_value=1000000) allocation, leftover = da.greedy_portfolio() print(allocation) print("Leftover Fund value for the maximum Sharpe portfolio is ${:.2f}".format(leftover))

As per MVP, the funds are allocated as shown above. We short the stocks of ASX a tech company, TSM a semi-conductor manufacturing company and BNTX a pharma company. The leftover fund for the maximum Sharpe portfolio is now $102.48.

min_vol_cla = cla.CLA(mu, sigma) min_vol_cla.min_volatility() Plotting.plot_efficient_frontier(min_vol_cla, show_assets="True")

min_vol_portfolio_wt_list = list(min_vol_portfolio_wt.values()) ret_data2 = df.pct_change()[1:] weighted_returns2 = (min_vol_portfolio_wt_list * ret_data2) portfolio_ret2 = pd.DataFrame(weighted_returns2.sum(axis=1)) ret_data2 = ret_data2.merge(portfolio_ret2, on="Date", how="left") ret_data2 = ret_data2.rename(columns={0: "portfolio_ret"}) ret_data2.head()

df = df.stack() df.head()

df = df.reset_index() df = df.rename(columns={"level_1": "ticker", 0: "price"}) df.head()

df = df.dropna() df.head()

sns.scatterplot('Date', 'price', data=df, hue='ticker')

QUESTION 4

4. Comment on your strategy note and highlight the potential future issues/risks.

We chose to diversify our portfolio by choosing Taiwanese stocks or companies critical to Taiwan traded in USD. The portfolio comprises stocks of TSM, an electricity manufacturing company; TLC and BNTX pharma companies; CHT in the telecom industry; and ASX a tech & hardware manufacturing company; and UMC a tech company. The market index we chose is EWT which comprises of the top 85% of Taiwanese companies.

The sharpe portfolio helps provide the weights of each stock. TSM appears to be the largest by weight with us shorting ASX. Based on our observation of the covid situation in Taiwan, we believe that technology sector represents the strongest growth in the Taiwan economy. As a result we take portfolio is consisting to take the advantage of technology sector. As our portfolio is tech sector weighted heavy, We choose to put CHT(Taiwan Telecom Company) in our portfolio to reduce the risk variance of our portfolio. As CHT is in defense industry(Telecom), it will add diversification in our portfolio. As a result we take advantage of the technology sector. Although shorting could be inherently volatile, it could help the portfolio in long-term risk exposure.

The potential qualitative risk will be global competition on semiconductor, the rising shortage on semiconductor and competition in manufacture in future.

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Answer to Question 1:

QUESTION 2

QUESTION 3

LAB 5

QUESTION 1

QUESTION 2

QUESTION 3

QUESTION 1

QUESTION 4

QUESTION 1