TLT-SPY Return Delta as Stock Market Crash Indicator

A subscriber hypothesized that a very large delta between daily iShares 20+ Year Treasury Bond (TLT) and SPDR S&P 500 (SPY) returns presages a stock market collapse, and asked for verification. To investigate, we consider two tests:

1. Calculate correlations between daily TLT-SPY return delta and daily SPY returns over the next month (21 trading days). A stock market collapse during this interval should exhibit very negative correlations.
2. Compute average next-day SPY returns by ranked tenth (decile) of daily TLT-SPY return deltas. Average SPY returns should be relatively very low for high deciles.

Using daily dividend-adjusted prices for TLT and SPY during late July 2002 (limited by TLT) through mid-December 2021, we find that: