Python for Finance

Monte Carlo Simulation
R0[i,j]=sp.random.normal(loc=mean_0[j],scale=std_0[j],size=1)
if(R0.any()<=-1.0):
print ('Error: return is <=-100%')
#
# Step 4: generate correlated return matrix: Cholesky
R=np.dot(R0,U)
R=np.array(R)
#
# Step 5: define a few functions
def objFunction(W, R, target_ret):
stock_mean=np.mean(R,axis=0)
port_mean=np.dot(W,stock_mean)
# portfolio mean
cov=np.cov(R.T)
# var-covar matrix
port_var=np.dot(np.dot(W,cov),W.T) # portfolio variance
penalty = 2000*abs(port_mean-target_ret) # penalty 4 deviation
return np.sqrt(port_var) + penalty # objective function
#
# Step 6: estimate optimal portfolo for a given return
out_mean,out_std,out_weight=[],[],[]
stockMean=np.mean(R,axis=0)
#
for r in np.linspace(np.min(stockMean), np.max(stockMean), num=100):
W = sp.ones([nStocks])/nStocks
# starting:equal w
b_ = [(0,1) for i in range(nStocks)] # bounds
c_ = ({'type':'eq', 'fun': lambda W: sum(W)-1. })# constraint
result=minimize(objFunction,W,(R,r),method='SLSQP',constraints=c_,
bounds=b_)
if not result.success:
# handle error
raise BaseException(result.message)
out_mean.append(round(r,4))
# a few decimal places
std_=round(np.std(np.sum(R*result.x,axis=1)),6)
out_std.append(std_)
out_weight.append(result.x)
#
# Step 7: plot the efficient frontier
plt.title('Simulation for an Efficient Frontier: '+str(nStocks)+'
stocks')
plt.xlabel('Standard Deviation of the Porfolio')
plt.ylabel('Return of the2-stock portfolio')
plt.plot(out_std,out_mean,'--',linewidth=3)
plt.show()
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