配当再投資で総リターンをシミュレーションする

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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from pathlib import Path

np.random.seed(21)
plt.style.use("scripts/k_dm.mplstyle")

dates = pd.date_range("2015-01-01", periods=9 * 12, freq="M")
price = 100 * np.exp(np.cumsum(np.random.normal(0.005, 0.04, len(dates))))
dividend_yield = np.random.uniform(0.015, 0.025, len(dates))  # 年率1.5〜2.5%

frame = pd.DataFrame({"price": price, "dividend_yield": dividend_yield}, index=dates)
frame["dividend_cash"] = frame["price"] * frame["dividend_yield"] / 12

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cash_hold = frame["dividend_cash"].cumsum()
total_value_cash = frame["price"] + cash_hold

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shares = 1.0
cash = 0.0
portfolio_value = []

for price, dividend in zip(frame["price"], frame["dividend_cash"]):
    cash += dividend
    additional_shares = cash / price
    shares += additional_shares
    cash = 0.0
    portfolio_value.append(shares * price)

total_value_reinvest = pd.Series(portfolio_value, index=frame.index)

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comparison = pd.DataFrame(
    {
        "現金保持": total_value_cash,
        "再投資": total_value_reinvest,
    }
)

fig, ax = plt.subplots(figsize=(9, 4.2))
comparison.plot(ax=ax)
ax.set_title("配当再投資シミュレーション（擬似データ）")
ax.set_ylabel("評価額（基準=100）")
ax.grid(alpha=0.3)

output = Path("static/images/finance/main/dividend_reinvestment.svg")
output.parent.mkdir(parents=True, exist_ok=True)
fig.tight_layout()
fig.savefig(output)

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final_cash = total_value_cash.iloc[-1]
final_reinvest = total_value_reinvest.iloc[-1]
reinvest_bonus = final_reinvest - final_cash

print(f"現金保持の最終評価額:  {final_cash:.1f}")
print(f"再投資の最終評価額:    {final_reinvest:.1f}")
print(f"再投資による上乗せ:    {reinvest_bonus:.1f} ({reinvest_bonus/final_cash*100:.1f}%)")

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years = len(dates) / 12

cagr_cash = (total_value_cash.iloc[-1] / 100) ** (1 / years) - 1
cagr_reinvest = (total_value_reinvest.iloc[-1] / 100) ** (1 / years) - 1

print(f"CAGR（現金保持）: {cagr_cash:.2%}")
print(f"CAGR（再投資）:   {cagr_reinvest:.2%}")
print(f"差分:             {cagr_reinvest - cagr_cash:.2%}")

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def max_drawdown(series: pd.Series) -> float:
    cummax = series.cummax()
    drawdown = (series - cummax) / cummax
    return drawdown.min()

mdd_cash = max_drawdown(total_value_cash)
mdd_reinvest = max_drawdown(total_value_reinvest)

print(f"最大ドローダウン（現金保持）: {mdd_cash:.2%}")
print(f"最大ドローダウン（再投資）:   {mdd_reinvest:.2%}")