Rolling Beta

Intuição

O Rolling Beta mede a sensibilidade do retorno do ativo em relação ao retorno de um benchmark (CAPM), estimado em uma janela móvel.

Definição

Em uma janela n, com retornos r_a (ativo) e r_b (benchmark):

beta = Cov(r_a, r_b) / Var(r_b)

Uso

from quantmaster.features.statistical import rolling_beta

beta = rolling_beta(df, benchmark_series, window=60)

API

Source code in src/quantmaster/features/statistical.py

def rolling_beta(
    data: pd.DataFrame | pd.Series,
    benchmark: pd.Series,
    *,
    window: int = 60,
    price_col: str = "close",
    log_returns: bool = True,
) -> pd.Series:
    window = validate_positive_int(window, name="window")

    asset_price = get_price_series(data, price_col=price_col).astype(float)
    bench_price = pd.to_numeric(benchmark, errors="coerce").astype(float)

    if log_returns:
        r_asset = np.log(asset_price.where(asset_price > 0)).diff()
        r_bench = np.log(bench_price.where(bench_price > 0)).diff()
    else:
        r_asset = asset_price.pct_change()
        r_bench = bench_price.pct_change()

    df = pd.concat([r_asset.rename("asset"), r_bench.rename("bench")], axis=1)
    out = pd.Series(np.nan, index=df.index, dtype=float)
    out.name = f"rolling_beta_{window}"

    if len(df) < window:
        return out

    x = df["asset"].to_numpy(dtype=float)
    y = df["bench"].to_numpy(dtype=float)

    xw = np.lib.stride_tricks.sliding_window_view(x, window_shape=window)
    yw = np.lib.stride_tricks.sliding_window_view(y, window_shape=window)

    beta_arr = np.full(xw.shape[0], np.nan, dtype=float)
    for i in range(xw.shape[0]):
        beta_arr[i] = _beta_from_windows(xw[i], yw[i])

    out.iloc[window - 1 :] = beta_arr
    return out