This is a brain teaser. You’ve been warned.
The S&P 500 is in a bear market (defined as the 50-day MA being below the 200-day MA) 30.8% of the time. Also, the S&P 500 has experienced single-day 4% declines 0.242% of the time. Of the times we experienced single-day selloffs exceeding 4%, 75.7% of the time we were in a bear market.
How much more likely are we to experience single-day losses exceeding 4% now that we’re in a bear market?
Odds are you stopped reading this puzzle after the first three sentences. In the unlikely event that you’re still with me, I’ve created a link to some code that holds the answer. It’s a prolog script whose knowledge-base is derived from data-mining in R.