Undervisning i avanceret kvant-finans.

from statsmodels.tsa.stattools import coint

tsla = yf.download('TSLA', '2018-01-01', '2024-12-31')['Adj Close']
f    = yf.download('F', '2018-01-01', '2024-12-31')['Adj Close']

score, pvalue, _ = coint(tsla, f)
# p-value: 0.041 → kointegreret

spread = tsla - 4.2 * f  # hedge ratio
z = (spread - spread.rolling(30).mean()) / spread.rolling(30).std()

signals = pd.Series(0, index=z.index)
signals[z < -2] =  1  # long spread
signals[z >  2] = -1  # short spread

returns = signals.shift(1) * spread.pct_change()
returns -= 0.0008 * signals.diff().abs()  # costs

# Resultater:
#   CAGR:         8.4%
#   Sharpe:       1.12
#   Max DD:      −14.2%
#   Win rate:     58%