Shares of real estate services companies rallied Thursday, after data showing that existing-home sales fell again in September, but managed to beat expectations. Zillow Group Inc.’s stock          Z,         +2.02%         ZG,         +2.07%        surged 1.9% in morning trading, reversing an earlier decline of as much as 0.8%, while Redfin Corp. shares          RDFN,         +4.17%        jumped 4.6% after being down 0.3% at its intraday low. Elsewhere, shares of Anywhere Real Estate Inc.          HOUS,         +1.10%        gained 1.5%, RE/MAX Holdings Inc.          RMAX,         +0.66%        tacked on 1.3% and Douglas Elliman Inc.          DOUG,         +1.33%        advanced 1.2%. They all outperformed the S&P 500          SPX,         +0.75%,        which gained 0.7%. The National Association of Realtors said existing-home sales fell 1.5% to a seasonally adjusted annual rate of 4.71 million in September, the eighth straight monthly decline but above expectations of an annual rate of 4.70 million.