投資組合最佳化

用 ILP 做資產配置

import pulp
import numpy as np

# === 資產資料 ===
assets = ["台積電", "聯發科", "台達電", "中華電", "富邦金"]
expected_return = [0.15, 0.12, 0.10, 0.04, 0.08]  # 預期年報酬
risk_score = [0.35, 0.30, 0.25, 0.10, 0.20]  # 風險分數（標準差）
min_investment = [10, 5, 5, 10, 5]  # 最低投資額（萬）

# 建立問題
prob = pulp.LpProblem("投資組合最佳化", pulp.LpMaximize)

# 變數：每個資產的投資比例（0-1 連續變數）
weights = {a: pulp.LpVariable(f"w_{a}", lowBound=0, upBound=1) for a in assets}

# 二元變數：是否投資該資產
selected = {a: pulp.LpVariable(f"sel_{a}", cat="Binary") for a in assets}

# 目標：最大化預期報酬
prob += pulp.lpSum(expected_return[i] * weights[assets[i]] for i in range(len(assets)))

# 限制 1：總比例為 1
prob += pulp.lpSum([weights[a] for a in assets]) == 1

# 限制 2：風險上限
max_risk = 0.25
prob += pulp.lpSum(risk_score[i] * weights[assets[i]] for i in range(len(assets))) <= max_risk

# 限制 3：如果投資某資產，比例不能低於最低要求
budget = 1000  # 總預算 1000 萬
for i, a in enumerate(assets):
    min_ratio = min_investment[i] / budget
    prob += weights[a] >= min_ratio * selected[a]
    prob += weights[a] <= selected[a]  # 沒選中就不能投資

# 限制 4：至少要投資 3 個資產
prob += pulp.lpSum([selected[a] for a in assets]) >= 3

# 求解
prob.solve()

print(f"\n=== 投資組合結果 ===")
print(f"求解狀態: {pulp.LpStatus[prob.status]}")
print(f"預期報酬率: {pulp.value(prob.objective)*100:.2f}%")
print(f"組合風險: {max_risk*100:.0f}% (上限)")

print(f"\n資產配置:")
for i, a in enumerate(assets):
    w = weights[a].value()
    if w and w > 0.001:
        print(f"  {a}: {w*100:.1f}% (報酬 {expected_return[i]*100:.0f}%, 風險 {risk_score[i]*100:.0f}%)")