Suppose a person has a sizable portion of his networth in stocks. He wants to diversify his wealth into the real estate asset class. For the sake of correct diversification, it will be nice to know whether REITs are more correlated with the stock market or the real estate market.
It depends on what you mean by "the real estate market". If you consider that REITs distribute income from real estate lease income and property appreciation, you could say that REITs are the real estate market. Property value appreciation varies greatly from location to location, so REITs should represent a broad overall average.
As far as correlation with stocks, according to NAREIT the correlation has been relatively low (50-80%) but has decreased lately. So I would consider adding REITs to a stock-heavy portfolio a decent strategy for diversification.
REITs are interconnected with both the stock market and the real estate market.
REITs are affected by the interest rates, the economy as well as the stock market. Like all sectors, at times they will outperform the market and at other times they will under perform. During the market collapse from 2008 to 2009, while the market lost 50% of its value, REIT ETFs lost much more. With QE and rates dropping dramatically, REIT ETFs then markedly outperformed the market for 18 months. After a number or years of reasonable correlation, last year REITs severely under performed the market.