The anatomy of a bar

import numpy as np
import pandas as pd
import qadata

close = qadata.trending_prices()            # 756 seeded daily closes
n = len(close)
rng = np.random.default_rng(7)               # fixed seed: same bars forever

open_ = close.shift(1).fillna(close.iloc[0] / 1.0004) * (1 + 0.0015 * rng.standard_normal(n))
wick_hi = np.abs(0.004 * rng.standard_normal(n))
wick_lo = np.abs(0.004 * rng.standard_normal(n))
bars = pd.DataFrame({
    "open": open_,
    "high": np.maximum(open_, close) * (1 + wick_hi),
    "low": np.minimum(open_, close) * (1 - wick_lo),
    "close": close,
    "volume": np.round(1e6 * np.exp(0.3 * rng.standard_normal(n))).astype(int),
})

print(bars.head(3).round(4))
ok_hi = (bars.high >= bars[["open", "close"]].max(axis=1) - 1e-12).all()
ok_lo = (bars.low <= bars[["open", "close"]].min(axis=1) + 1e-12).all()
print("high is the envelope top:", bool(ok_hi), "| low is the bottom:", bool(ok_lo))
print(f"mean intraday range: {((bars.high - bars.low) / bars.close).mean():.4%}")
print(f"mean close-to-close : {close.pct_change().abs().mean():.4%}")

import numpy as np
import qadata

adj = qadata.trending_prices()               # the truth, split-adjusted
raw = adj.copy()
raw[raw.index < "2021-12-02"] *= 2.0          # vendor's unadjusted file: 2:1 split

raw_rets, adj_rets = raw.pct_change(), adj.pct_change()
d = "2021-12-02"
print(f"split day 'return' raw: {raw_rets[d]:+.4%}   truth: {adj_rets[d]:+.4%}")
print(f"worst day          raw: {raw_rets.min():+.4%}   truth: {adj_rets.min():+.4%}")
print(f"ann vol            raw: {raw_rets.std() * np.sqrt(252):.4%}  truth: {adj_rets.std() * np.sqrt(252):.4%}")

close_before = 60.00     # cum-dividend close
dividend = 1.20          # cash paid per share on the ex-date
close_exdiv = 58.80      # stock opens lower by the payout, nothing else happens

raw_ret = close_exdiv / close_before - 1
total_ret = (close_exdiv + dividend) / close_before - 1

factor = 1 - dividend / close_before          # back-adjustment factor
adj_before = close_before * factor
adj_ret = close_exdiv / adj_before - 1

print(f"raw price return : {raw_ret:+.4%}   (looks like a loss)")
print(f"holder's truth   : {total_ret:+.4%}   (price drop + cash in hand)")
print(f"factor {factor:.4f} -> adjusted prior close {adj_before:.2f} -> return {adj_ret:+.4%}")
print(f"2% yield ignored for 40 years compounds to: {0.98 ** 40 - 1:+.2%}")