Mean-Variance Analysis

1. Content
   (1) Calculate the vector of mean returns and covariance matrix of returns for the ten industry portfolios. Create a table showing the mean returns and standard deviation of returns for the ten industry portfolios.
   (2) Plot the minimum-variance frontier generated by the ten industry portfolios (x: standard deviation of return, range from 0% to 2%; y: mean return)
   (3) Plot the efficient frontier (with the riskless asset) on the same plot
   (4) Calculate the weights of the ten industry portfolios at the tangency portfolio

2. code

file = 'Industry_Portfolios.xlsx'
df = pd.read_excel(file)

# describe df
df=DataFrame.drop(df,'Date',axis=1)
des=DataFrame.describe(df)
 
# caculate mean returns and covariance matrix of returns
table=des[1:3]

mean_return=np.mean(df,axis=0)
mean_return = np.array(mean_return/100)

covariance=np.cov(df/100,rowvar=0)
covariance=np.array(covariance)


e= np.ones(10)
rp=np.linspace(0.0013,0.02,100)
a = np.dot(np.dot(np.transpose(mean_return),(np.linalg.inv(covariance))),e)
b=  np.dot(np.dot(np.transpose(mean_return),(np.linalg.inv(covariance))),mean_return)
c= np.dot(np.dot(np.transpose(e),(np.linalg.inv(covariance))),e)
minVariance =np.sqrt(1/c+c/(b*c-a**2)*(rp-a/c)**2)


#with riskless asset
rf=0.0013
minVariance1=np.sqrt((rp-rf)**2/(b-2*a*rf+c*rf**2))

plt.plot(minVariance,rp)
plt.plot(minVariance1,rp)
plt.xlabel("variance")
plt.ylabel("Rp")
plt.legend()
plt.show
plt.savefig('tupian.png')

# Calculate the weights of the ten industry portfolios at tangency portfolio
r_tg=(a*rf-b)/(c*rf-a)
lamda=(r_tg-rf)/(b-2*a*rf+c*rf**2)
weight=lamda*np.dot(np.linalg.inv(covariance),(mean_return-rf*e))
print(weight)

result: