Stocks Down, Treasuries Up

• When institutions sell stocks, they seek a safe place to park the cash, such as short-term Treasury securities, which typically go up when stocks sell off.
  
  

Bonds Down, Stocks Down

• When interest rates rise, both stocks and bonds go down because inflation is generally considered bad for both stocks and bonds. Investors sell both, seeking safety in cash or gold.
  
  

No or Limited Correlation

• Stocks generally decline when the economy goes into a recession. Interest rates typically fall in a recession, which is generally bullish for bonds, so they should rise. However, a recession may be bad for high-yield bonds whose issuers may not be able to make interest payments in an economic downturn, so high-yield bonds decline.
  
  State tax receipts also decline in a recession, raising fears of default in lower-quality municipal bonds, so those can decline too. On the other hand, U.S. Government debt and high-quality bonds issued by blue-chip companies are considered safe havens in a recession and may rise.