# Chapter 2 : Portfolio Investing

portfolio_weights = np.array([0.12, 0.15, 0.08, 0.05, 0.09, 0.10, 0.11, 0.14, 0.16])

# Calculate the weighted stock returns
WeightedReturns = StockReturns.mul(portfolio_weights, axis=1)

# Calculate the portfolio returns
StockReturns['Portfolio'] = WeightedReturns.sum(axis=1)

# Plot the cumulative portfolio returns over time
CumulativeReturns = ((1+StockReturns["Portfolio"]).cumprod()-1)
CumulativeReturns.plot()
plt.show()

numstocks = 9

# Create an array of equal weights across all assets
portfolio_weights_ew = np.repeat(1/numstocks, numstocks)

# Calculate the equally-weighted portfolio returns
StockReturns['Portfolio_EW'] = StockReturns.iloc[:, 0:numstocks].mul(portfolio_weights_ew, axis=1).sum(axis=1)
cumulative_returns_plot(['Portfolio', 'Portfolio_EW'])

# Create an array of market capitalizations (in billions)
market_capitalizations = np.array([601.51, 469.25, 349.5, 310.48, 299.77, 356.94, 268.88, 331.57, 246.09])

# Calculate the market cap weights
mcap_weights = market_capitalizations/sum(market_capitalizations)

# Calculate the market cap weighted portfolio returns
StockReturns['Portfolio_MCap'] = StockReturns.iloc[:, 0:9].mul(mcap_weights, axis=1).sum(axis=1)
cumulative_returns_plot(['Portfolio', 'Portfolio_EW', 'Portfolio_MCap'])

correlation_matrix = StockReturns.corr()

# Import seaborn as sns
import seaborn as sns

# Create a heatmap
sns.heatmap(correlation_matrix,
            annot=True,
            cmap="YlGnBu",
            linewidths=0.3,
            annot_kws={"size": 8})

# Plot aesthetics
plt.xticks(rotation=90)
plt.yticks(rotation=0)
plt.show()

# Calculate the covariance matrix
cov_mat = StockReturns.cov()

# Annualize the co-variance matrix
cov_mat_annual = cov_mat*252

# Print the annualized co-variance matrix
print(cov_mat_annual)

# Calculate the portfolio standard deviation
portfolio_volatility = np.sqrt(np.dot(portfolio_weights.T, np.dot(cov_mat_annual, portfolio_weights)))
print(portfolio_volatility)

# Risk free rate
risk_free = 0

# Calculate the Sharpe Ratio for each asset
RandomPortfolios['Sharpe'] = (RandomPortfolios["Returns"]-risk_free)/RandomPortfolios["Volatility"]

# Print the range of Sharpe ratios
print(RandomPortfolios['Sharpe'].describe()[['min', 'max']])

# Sort the portfolios by Sharpe ratio
sorted_portfolios = RandomPortfolios.sort_values(by=['Sharpe'], ascending=True)

# Extract the corresponding weights
MSR_weights = sorted_portfolios.iloc[0, 0:numstocks]

# Cast the MSR weights as a numpy array
MSR_weights_array = np.array(MSR_weights)

# Calculate the MSR portfolio returns
StockReturns['Portfolio_MSR'] = StockReturns.iloc[:, 0:numstocks].mul(MSR_weights_array, axis=1).sum(axis=1)

# Plot the cumulative returns
cumulative_returns_plot(['Portfolio_EW', 'Portfolio_MCap', 'Portfolio_MSR'])