如何设置数据结构以使pandas 和numpy 合作？

编译基于 Pandas 和 numpy 的代码时遇到麻烦。我将尝试通过提供问题所在的缩小工作示例来解释这些问题。

我基本上想做的是 Markowitz 投资组合优化，如下所示。

首先，我有一个 pandas.Dataframe，它以下列方式为给定的股票代码提供收盘价。

df = pd.DataFrame()
df['AAPL'] = [1.2,1.4,1.5]
df['GOOGL'] = [2.1,2.4,2.6]
df['DATE'] = ['2017-01-01', '2017-01-02','2017-01-03']
df = df.set_index('DATE')

接下来我想创建一些基本的统计信息来传递一些函数，我用以下方式做：

returns = df.pct_change()
mean_returns = returns.mean()
cov_matrix = returns.cov()
num_portfolios = 10
risk_free_rate = 0.0178

这些统计的类型是：

pandas.core.series.Series
pandas.core.frame.DataFrame

以下函数是问题开始出现的地方：

def portfolio_annualised_performance(weights, mean_returns, cov_matrix):
    returns = np.sum(mean_returns*weights ) *252
    std = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights))) * np.sqrt(252)
    return std, returns

def random_portfolios(num_portfolios, mean_returns, cov_matrix, risk_free_rate):
    results = np.zeros((3,num_portfolios))
    print('results:',type(results))
    weights_record = []
    for i in range(num_portfolios):
        weights = np.random.random(12)
        weights /= np.sum(weights)
        weights_record.append(weights)
        portfolio_std_dev, portfolio_return = portfolio_annualised_performance(weights, mean_returns, cov_matrix)
        results[0,i] = portfolio_std_dev
        results[1,i] = portfolio_return
        results[2,i] = (portfolio_return - risk_free_rate) / portfolio_std_dev
    #print('results[2,0]:',type(results[2,0]))
    #print('std', type(portfolio_std_dev))
    #print(portfolio_return)
    return results, weights_record


def display_simulated_ef_with_random(mean_returns, cov_matrix, num_portfolios, risk_free_rate):
    results, weights = random_portfolios(num_portfolios, mean_returns, cov_matrix, risk_free_rate)


    max_sharpe_idx = np.argmax(np.array(results[2]))
    sdp, rp = results[0,max_sharpe_idx], results[1,max_sharpe_idx]
    max_sharpe_allocation = pd.DataFrame(weights[max_sharpe_idx],index=df.columns,columns=['allocation'])
    max_sharpe_allocation.allocation = [round(i*100,2)for i in max_sharpe_allocation.allocation]
    max_sharpe_allocation = max_sharpe_allocation.T

    min_vol_idx = np.argmin(results[0])
    sdp_min, rp_min = results[0,min_vol_idx], results[1,min_vol_idx]
    min_vol_allocation = pd.DataFrame(weights[min_vol_idx],index=df.columns,columns=['allocation'])
    min_vol_allocation.allocation = [round(i*100,2)for i in min_vol_allocation.allocation]
    min_vol_allocation = min_vol_allocation.T

尝试运行时：

display_simulated_ef_with_random（cov_matrix，mean_returns，num_portfolios，risk_free_rate）

出现以下错误

----> 2     results, weights = random_portfolios(num_portfolios, mean_returns, cov_matrix, risk_free_rate)

---> 15         results[0,i] = portfolio_std_dev

ValueError: setting an array element with a sequence.

我做错了什么，我该如何解决？