In a break from historical patterns, returns on large-cap U.S. stocks and U.S. Treasury bonds have been moving in opposite directions, according to an analysis by Factor Advisors, a New York-based asset management firm.

The negative correlation between the two asset classes is the strongest it’s been in 10 years of data, said Stuart Rosenthal, CEO of Factor Advisors. Historically there’s been negligible correlation between the two.

The analysis, which was distributed to financial advisors, shows that the three-month correlation between the SPDR S&P 500 (SPY) and the iShares Barclays 20+ Treasury Bond (TLT) as of Nov. 11, 2011, closed at -0.83, the strongest negative correlation since early 2003. Correlations can range from 1 (completely the same) to minus-1 (completely opposite.) “Investors who sell stocks need a place to park their cash,” said Rosenthal, explaining that T-bonds are seen as safe havens by most investors. (It should be noted that Factor Advisors also sells an ETF that would benefit from the scenario its analysis describes.)

“In spite of the U.S. downgrade in August, investors have been increasingly looking to U.S. Treasury bonds as a flight-to-quality play when equities are under duress,” Rosenthal writes in the analysis.

The negative correlation holds up from a longer-term perspective. The analysis shows that the 30-month correlation between the S&P 500 Stock Price Index and Ryan Labs Index Returns Treasury Yield Curve 30-Year Index hit its lowest point in over three decades on Oct. 31, 2011.