I'm going to lay out some logic that may or may not make sense. Feel free to jump in and help sort it out.
1. Rising interest rates mean that fewer individuals can afford to buy property, thus a REIT would have more renters / less vacancy which translates into higher share prices for the REIT.
2. Rising interest rates mean that REITs will spend more to acquire new property (assuming they want to grow larger), which translates to lower share prices for the REIT.
3. Rising interest rates are typically a response to inflation, and inflation is why a lot of people own REITs, thus more people seeking to buy the REIT would translate to higher share prices for the REIT.
1. This only affects mREIT (dealing with mortgages), and only barely at that. When interest rates rise, it means monthly payments go up slightly, but the major barrier to purchasing a home is credit situation and availability of savings, a couple extra hundred dollars (you can go to bankrate and enter in different interest rates to find how payments will be affected - a rise from 4% to 5% is an extra $120 per month on a 200k loan). The main reason share prices will be affected is because most REIT investors are investing for YIELD. When interest rates rise, that means the risk free rate of treasury bonds increases. To hold the equity premium, either dividend payout must increase or share prices on REITs must drop. That's the compensating factor
2. Interest rates have nothing to do with acquisition pace (with the exception of negligible effects on interest expense but down the line when companies have to refinance debt), either the REIT has extra cash or it doesn't
3. You have it reversed, if interest rates go up, people are less likely to buy REITs that have the existing 5% yield, since now the risk free treasury rate is 5% or higher (investors would have to also consider the growth component inherent in REITs but not bonds, of course). They would demand REITs pay them a higher percentage to compensate them for risk of loss
The price of REITs already has the effects of the expected interest rate changes priced in. Given that the Fed has said repeatedly that interest rate hikes will be slow and low, I don't think it's too troublesome for investors.
I strongly disagree with the affinity for efficient market hypothesis/theory around these parts, even though I think forummm usually makes very intelligent points. If assets are always perfectly priced, we wouldn't have random daily fluctuations (sometimes due to how sunny it is in New York, literally) and we wouldn't have Wells Fargo sitting there in 2009 for less than the cash it's holding. It's a nice theory that fits the needs of mathematicians, but doesn't reflect reality