如何在Python中为Efficient Frontier添加附加约束？

Question

我有一个表，列出了每种资产的预期收益和波动率，还有这些资产的协方差矩阵，最后，这些资产中的一部分是寻求回报的一部分，其余的资产是寻求负债的一部分，我想添加寻求回报和寻求负债的权重约束。

我正在使用一种优化方法来解决有效边界，但我想在我的优化问题中添加两个约束。我的优化问题是：

                 Minimise  Volatility 
                    x
                subject to portfolio returns = target
                           Sum of weights = 1

我想添加两个额外的约束条件寻求权重的回报总和= 0.65寻求权重的负债总和= 0.35我的代码写成：

def efficient_return(mean_returns, cov_matrix, target):
    num_assets = len(mean_returns)
    args = (mean_returns, cov_matrix)

    def portfolio_return(weights):
        return portfolio_annualised_performance(weights, mean_returns, cov_matrix)[1]

    constraints = ({'type': 'eq', 'fun': lambda x: portfolio_return(x) - target},
                   {'type': 'eq', 'fun': lambda x: np.sum(x) - 1})
    bounds = tuple((0,1) for asset in range(num_assets))
    result = sco.minimize(portfolio_volatility, num_assets*[1./num_assets,], args=args, method='SLSQP', bounds=bounds, constraints=constraints)
    return result


def efficient_frontier(mean_returns, cov_matrix, returns_range):
    efficients = []
    for ret in returns_range:
        efficients.append(efficient_return(mean_returns, cov_matrix, ret))
    return efficients

我的投资组合列表是：

lista_labels = ['Global Equity', 'TIPS','Long Duration Bonds – Gov’t / Credit', 'Long Duration Bonds – Credit',
               'High Yield Bonds','Emerging Market Bonds','Real Estate (Broad Market)','Global REITs',
               'Commodities','Private Infrastructure','25-year Government Bond','Broad Hedge Funds (Universe)'
                ,'Public Infrastructure','Tactical Asset Allocation','Core Plus Fixed Income']

我的退货清单是：

lista_RS = ['Global Equity','High Yield Bonds','Emerging Market Bonds','Real Estate (Broad Market)',
           'Global REITs','Commodities','Private Infrastructure','Broad Hedge Funds (Universe)',
           'Public Infrastructure','Tactical Asset Allocation']

我的责任是：

lista_LS = ['TIPS','Long Duration Bonds – Gov’t / Credit','Long Duration Bonds – Credit','25-year Government Bond',
           'Core Plus Fixed Income'] 

我想复制这个表http://prntscr.com/twredz。提前谢谢。

Answer 1

constraints = (
{'type': 'eq', 'fun': lambda x: portfolio_return(x) - target},
{'type': 'eq', 'fun': lambda x: np.sum(x) - 1},
{'type': 'eq', 'fun': lambda x: np.sum(x[x>0]) - 0.65},
{'type': 'eq', 'fun': lambda x: np.sum(x[x>0]) - 0.35}
)