Kogan Capital

How the books move with the S&P 500

Daily results of our same-day options book in backtesting have shown almost no linear relationship with the index. Books that also hold multi-day positions are more connected to it, especially in large selloffs.

0.03Daily correlation with the S&P 500, same-day book, 2023 to October 2026
0.02Beta: a 1% index move has lined up with about 0.02% on the book
0.25–0.27Daily correlation of the two more connected multi-day books, 2022 to October 2026
Same-day book

Index moves explain very little of the daily result.

Book vs S&P 500, each trading day959 backtested days. The dashed line shows a book that moved one-for-one with the index.
Rolling 63-day correlationThe range was −0.29 to +0.40, so it does drift from quarter to quarter.
Every book

Correlation differs by book and rises on big days.

The more connected books hold multi-day positions. In 2022 their beta reached 0.71 and 0.57, and their rolling correlation peaked near 0.7.

BookDaily correlationBetaVariance explained by indexHighest 63-day correlationCorrelation on ±1% daysAverage on index's 20 worst days
Same-day book2023 to Oct 20260.030.020.1%0.400.14−0.08%
Book A2022 to Oct 20260.270.367.5%0.720.42−2.25%
Book B2022 to Oct 20260.250.286.1%0.680.39−1.99%
Book C2022 to Oct 2026−0.04−0.070.2%0.320.02+0.84%
By year

2022 was the hardest test, and 2025 was the next most connected.

Daily correlation20222023202420252026 to date
Same-day booknot tested0.07−0.060.040.10
Book A0.370.130.110.380.30
Book B0.370.06−0.060.290.12
Book C−0.04−0.08−0.120.000.07
Worst index days

The five largest S&P 500 falls in the same-day test.

DateS&P 500Same-day book
April 4, 2025−5.97%−0.63%
April 3, 2025−4.84%−0.84%
April 10, 2025−3.46%+0.36%
August 5, 2024−3.00%+0.18%
December 18, 2024−2.95%+0.94%
Live trading

The live record is still too short to confirm this.

Over 42 sessions from September 1 to October 29, 2026, the two live accounts with enough history had daily correlations of −0.31 and −0.23 with the index, with a margin of error of about 0.15. Their betas were −1.64 and −2.56, measured against fixed account bases. Both accounts changed strategies during this period.