REIT s often pay up to 10% dividends so I would think they should become more valuable when the US bond interest rates go down . For example : In the last 30 days CIM has gone from 19.1 to 18.5 while the US 10 year rate has gone from 2.55% to 2.25 % , approximately.
CIM is not an equity REIT, it is a MORTGAGE REIT (usually abbreviated mREIT). These companies are leveraged to the spread between short and long term interest rates, they borrow at short term rates and invest based on long term rates. When the yield curve inverts (which it just did), then short term bonds pay more interest than longer term bonds (ie 2-year Treasuries yield more than 10-year). This situation is not healthy for mREIT business model, since they're borrowing short term at a higher rate than they're making on long term securities.
Also, the inversion of the yield curve is seen as a leading indicator of recession, and while generally safer than growth stocks, REITS are by no means immune from recession and slowing of the economy risks