ローリングβをヒートマップで可視化する

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32

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

np.random.seed(42)
plt.style.use("scripts/k_dm.mplstyle")

dates = pd.date_range("2023-01-01", periods=260, freq="B")
market = np.random.normal(0.0005, 0.01, size=len(dates)).cumsum()
returns = pd.DataFrame(index=dates)
returns["market"] = np.diff(np.insert(market, 0, 0))

for ticker, beta, vol in [
    ("AAA", 1.1, 0.012),
    ("BBB", 0.8, 0.009),
    ("CCC", 1.4, 0.015),
    ("DDD", 0.6, 0.008),
]:
    noise = np.random.normal(0, vol, size=len(dates))
    returns[ticker] = beta * returns["market"] + noise

window = 60
rolling_beta = (
    returns[["AAA", "BBB", "CCC", "DDD"]]
    .rolling(window)
    .apply(
        lambda col: np.cov(col, returns.loc[col.index, "market"])[0, 1]
        / np.var(returns.loc[col.index, "market"]),
        raw=False,
    )
)

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24

fig, ax = plt.subplots(figsize=(10, 4.5))
im = ax.imshow(
    rolling_beta.T,
    aspect="auto",
    cmap="RdYlGn",
    vmin=0.4,
    vmax=1.6,
)

ax.set_yticks(range(len(rolling_beta.columns)))
ax.set_yticklabels(rolling_beta.columns)
ax.set_xticks(np.linspace(0, len(dates) - 1, 6))
ax.set_xticklabels(pd.Series(dates).dt.strftime("%Y-%m-%d").iloc[::len(dates) // 6])
ax.set_title("60日ローリングβ（市場指数との回帰）")
ax.set_xlabel("日付")
ax.set_ylabel("銘柄")

cbar = fig.colorbar(im, ax=ax, pad=0.01)
cbar.ax.set_ylabel("β", rotation=90)

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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12

fig, ax = plt.subplots(figsize=(8, 4))
rolling_beta.dropna().boxplot(ax=ax)
ax.axhline(1.0, color="#ef4444", linestyle="--", linewidth=1, label="β=1")
ax.set_ylabel("ローリングβ")
ax.set_title("銘柄別 ローリングβの分布")
ax.legend()
ax.grid(axis="y", alpha=0.3)
fig.tight_layout()
plt.show()

# 要約統計量
print(rolling_beta.dropna().describe().round(3))

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18

fig, axes = plt.subplots(1, 3, figsize=(14, 3.5), sharey=True)

for ax, w in zip(axes, [30, 60, 120]):
    rb = returns["AAA"].rolling(w).apply(
        lambda col: np.cov(col, returns.loc[col.index, "market"])[0, 1]
        / np.var(returns.loc[col.index, "market"]),
        raw=False,
    )
    ax.plot(dates, rb, linewidth=1.2, color="#3b82f6")
    ax.axhline(1.0, color="#ef4444", linestyle="--", linewidth=0.8)
    ax.set_title(f"ウィンドウ={w}日")
    ax.set_ylabel("β" if w == 30 else "")
    ax.grid(alpha=0.3)
    ax.tick_params(axis="x", rotation=30)

fig.suptitle("AAAのローリングβ: ウィンドウ長の影響", fontsize=13)
fig.tight_layout()
plt.show()