def neg_sharpe_ratio_m(weights, mean_returns, cov_matrix, risk_free_rate, alpha):
    p_var, p_ret = portfolio_annualised_performance(weights, mean_returns, cov_matrix)
    m_risk = equal_risk_contributon(weights, cov_matrix)
    return -(p_ret - risk_free_rate)/p_var*alpha + (1-alpha)*m_risk

def max_sharpe_ratio_m(mean_returns, cov_matrix, risk_free_rate, alpha):
    num_assets = mean_returns.shape[0]
    args = (mean_returns, cov_matrix, risk_free_rate, alpha)
    constraints = ({'type': 'eq', 'fun': lambda x: np.sum(x) - 1})
    bound = (0.0,1.0)
    bounds = tuple(bound for asset in range(num_assets))
    result = minimize(neg_sharpe_ratio_m, num_assets*[1./num_assets,], args=args,
                        method='SLSQP', bounds=bounds, constraints=constraints)
    return result.x

weights_alpha =[]
blended_list = []
length = etf_return.shape[0]//66
for alpha in 1/np.exp2(np.arange(0,10,1)):
    i= 0
    risk_free_rate =0.0
    weights = np.empty([0,6])
    while i<length:
        distance = min(66,etf_return.shape[0]-i*66)
        cov_matrix = np.cov(etf_return.iloc[i*66: (i+1)*min(distance, 66) , :].values,
                                            rowvar = False)
        rt = np.mean(etf_return.iloc[i*66: (i+1)*min(distance, 66) , :].values, axis=0)
        result = np.around(max_sharpe_ratio_m(rt, cov_matrix, risk_free_rate, alpha), 3)
        weights = np.vstack((weights, result))
        i+=1
    weights_alpha.append(weights)
    blended = portfolio_performance(weights)
    blended_list.append(blended)