Foreclosures made up 31% of existing-home sales in Phoenix last month, down from 35% in May and 43% from the beginning of the year, according to a report from the W.P. Carey School of Business at Arizona State University. The author of the foreclosure study says it is unclear why the numbers are down, but despite four consecutive months of foreclosure sale declines, the report stops short of calling the trend a recovery. “Things are showing a lot of improvement, but we still have a long way to go, and some conditions affecting the housing market remain uncertain,” said W. P. Carey School of Business Professor Emeritus Jay Butler, who released the report Tuesday. “Even though the number of foreclosure pre-filings has been declining for the last year, foreclosures continue to be the dominant force in the market. Recovery is moving at a glacial pace.” In June, the Phoenix area reported 3,300 single-family home foreclosures, down from 3,500 in May and 3,800 in June 2010. The median price for a single-family home resold in the Phoenix market rose slightly to $126,500 in June, up from $125,000 in May. Overall, 10,500 homes were sold last month, down slightly from 10,720 transactions last year. Write to Kerri Panchuk.