迭代測試pandas中投資組合權重的表現

Question

我有x 個（假設 x = 8）股票因子的投資組合，權重為w 。 我可以使用 function F(w) = p以均等加權的方式測試這些因素的性能，其中 output p是性能指標。 第一個測試的投資組合權重 df 如下所示：

    weight
0   12.57
1   12.49
2   12.49
3   12.49
4   12.49
5   12.49
6   12.49
7   12.49

在我使用 100/8 四舍五入到兩位小數的地方，給第一個因素加上余數，如下所示：

pd.DataFrame(columns = ['weight'], data = [(100/factorsdf.shape[0] // 0.01 / 100)]*factorsdf.shape[0])
weights['weight'].iloc[0] = weights['weight'].iloc[0] + round(100 - (100/factorsdf.shape[0] // 0.01 / 100) * factorsdf.shape[0],2)

我現在要做的是迭代改進這些權重。 我想這樣做的方法是逐漸減去底部權重（索引 7）的一半權重（此處：12.49/2 = 6.245）並將其添加到上方權重（索引 6）。

incremental_weight = (100/factorsdf.shape[0] // 0.01 / 100)/2

因此，在第一次迭代中，我將測試同等權重的投資組合。

在下一次迭代中，我將測試：

    weight
0   12.57
1   12.49
2   12.49
3   12.49
4   12.49
5   12.49
6   18.735
7   6.245

如果這不能改善指標p ，我將嘗試將其添加到 dataframe 中的下一個權重元素，如下所示：

    weight
0   12.57
1   12.49
2   12.49
3   12.49
4   12.49
5   18.735
6   12.49
7   6.245

如果確實有所改善，我將再減去底部元素的 6.245，然后嘗試將其添加到上面的元素中。 如果這不能改善p ，我會嘗試將它添加到上面的那個，依此類推，直到我嘗試將它添加到所有其他元素。

之后，我將對底部元素上方的元素（索引為 6）執行相同的過程，減去 6.245 並將其迭代添加到其他元素。 等等。 直到不能再改進度量p 。

以相對有效的方式在 pandas 中對此進行編程的好方法是什么？

Answer 1

如果我完全理解以下內容（我在代碼中添加了注釋），則應該可以工作：

import pandas as pd; import numpy as np
# my random generated factor scores
factorsdf = pd.DataFrame({"Factor": np.random.randint(0, 100, 8)})
# weights evenly allocated (from your code)
weights = pd.DataFrame(columns = ['weight'], data = [(100/factorsdf.shape[0] // 0.01 / 100)]*factorsdf.shape[0])
weights['weight'].iloc[0] = weights['weight'].iloc[0] + round(100 - (100/factorsdf.shape[0] // 0.01 / 100) * factorsdf.shape[0],2)

# weight to increment by (from your code)
incremental_weight = (100/factorsdf.shape[0] // 0.01 / 100)/2

# the F(w) function: weights must be first, from np.apply_along_axis below
def F_w(weights, factorsdf):
    # here it is just the dot product of the random factors and the weights.
    p = np.dot(factorsdf, weights.T/100)
    return p

# initial value of p
p = F_w(np.array(weights["weight"]), np.array(factorsdf["Factor"]))

print("p: ", p)

# rows above the weight that is being decreased
i = len(weights) - 1

# copy of weights to change
weights_c = weights.copy(deep=True)

# can't decrease the top weight, because none above to change
while i >= 1:
    print("i: ", i)
    
    # series with 0s everywhere except on row that will be decreasing the weight
    dec = pd.Series([0]*(len(weights_c)-1) + [incremental_weight]).shift(-len(weights)+1+i).fillna(0)
    # increment array has all possible options for increasing weights above
    inc = np.identity(i)*incremental_weight
    # row that is decreasing should not increase
    inc = np.vstack([inc, [0]*inc.shape[1]])
    # if other rows below have a weight (are not 0) then these won't increase either
    while inc.shape[0] < len(weights_c):
        inc = np.vstack([inc, [0]*inc.shape[1]])
    # if weight will be below 0 then should move up, also if there is only one row left
    if ((weights_c["weight"].sub(dec)<0).sum() > 0) or (inc.shape[0] == 1):
        i -= 1
        continue
    # subtract the increment from the weight
    weights_c["weight"] = weights_c["weight"].sub(dec)
    
    # array of possible weightings when incrementing rows above
    weights_arr = np.repeat(np.array(weights_c), inc.shape[1], axis=1) + inc
    
    print("weights_arr: ", weights_arr)
    print("weights_c: ", weights_c)
    print("factorsdf: ", np.array(factorsdf).T[:, :weights_arr.shape[0]])
    
    # return the p values for F(w) for all the possible variations
    res = np.apply_along_axis(F_w, 0, weights_arr, np.array(factorsdf).T[:, :weights_arr.shape[0]])
    # if any of these are greater than current p...
    if res.max() > p:
        # set new value of p
        p = res.max()
        # find which row the increment should be added to
        x = res.argmax()
    
        # add the increment to the correct row
        weights_c["weight"].iloc[x] += incremental_weight
        
        print("x: ", x)
    # if not, move on
    else:
        weights_c["weight"] = weights_c["weight"].add(dec)
        i -= 1
    
    # if the bottom weight is 0, remove this row from calculations
    if weights_c["weight"].iloc[-1] == 0:
        weights_c = weights_c.iloc[:-1]
        i -= 1
    
    print("weights_c: ", weights_c)

# print final weightings and max value of p
print("weights_c: ", weights_c)
print("p: ", p)

它肯定可以稍微清理一下，刪除一些 while 循環，但這可能會給你一個很好的起點。

如您所見，我使用的 numpy 比 pandas 多得多，如果權重和因子是 arrays 開始，代碼會更少。

如果您有任何問題，請告訴我。