Use Pandas to read the HW3.xlsx

arrays and construct the corresponding simple returns.

2. Perform a PCA analysis on the factors’ returns using numpy linalg.eig, find the minimum number of principal 

components to cover a required explanatory power (set as 0.8). Extract the principal components using 

statsmodels.sandbox.tools.tools_pca. 

3. Run a multivariate linear regression of the standardized equity index returns over the PCs from Q2 using 

sklearn.linear_model, output all the beta coefficients into dataframe and save it as coef.csv.

4. Run a multiple regression for each standardized equity index return over the PCs: the OLS (statsmodels.api) with 

intercept (‘add_constant’ function). retrieve the beta, t-value and the R-square. Output all of them into beta.csv, 

tvalue.csv, Rsq.csv.

5. Use the HSI stocks monthly return series from HW2 to find the weight vector using the following smart beta 

schemes. Use an upper bound weight of 10% for each stock 

a. Maximum Diversification Ratio (MDR)

b. Global Minimum Variance (GMV)

c. Maximum Sharpe Ratio (MSR)

You will need to import ‘minimize’ from scipy.optimize. To help you understand how to use an optimizer, a sample code 

for the objective function and the optimization for Equal Risk Contribution (ERC) is provided for you (you need to 

understand and change the code).

def risk_parity_function(weights, cov):

temp = np.dot(cov,weights) / np.dot(np.dot(weights, cov),weights)**(1/2)

MC = weights[:] * temp[:]

return (sum(((np.dot(np.dot(weights,cov),weights))**(1/2) / len(weights) -MC)**2))

def risk_parity(data):

cov = data.cov()

n = cov.shape[0]

weights = np.ones(n) /n

cons = ({'type': 'eq', 'fun': lambda x: 1 - sum(x)})

bnds = [(0,0.1) for i in weights]

res = minimize(risk_parity_function, x0 = weights, args = (cov), method = 'SLSQP', constraints = cons, 

bounds = bnds, tol = 1e-30)

return res.x