The prices of homes on the market are climbing, as inventory levels are falling, offering hopes of a market on its way to recovery, according to recent housing reports. The prices of properties listed for sale rose in 22 of 26 major markets during April, according to the Real-Time Housing Report, published by Altos Research and Real IQ. The Altos 10-City Composite Price Index increased by 2.2% during April and 3.3% during the most recent three month period, which Stephen Bedikian, partner and research director for Real IQ, contributes largely to the “powerful effect of seasonality.” Listing prices rose at the fastest rate in the California markets with San Jose up 3.7%, Los Angeles up 3.2% and San Diego up 2.8% in April.  Prices in 18 markets are now showing three months of sequential listing price increases. Asking prices fell at the fastest rate during April in Las Vegas, followed by Salt Lake City, down 3.8% and 2.6% respectively. “We expect to see continued strength during the next few months of the spring selling season fueled by historically low mortgage rates,” Bedikian says. “We won’t be able to call a bottoming of the market until we see stability continue into the seasonally weak fall and winter months.” And and one of the most important questions is whether inventory growth will remain restrained — as it fell in 15 of 26 major markets in April, according to the report — or whether pent-up supply will come on to the market in succeeding months. “There is no surer way to snuff out a recovery in housing prices than a flood of inventory that overwhelms demand,” says Michael Simonsen, CEO of Altos Research. A recent report by Zillow.com shows one-third of homeowners indicate they would like to put their home on the market if conditions improve, which presents some fear that shadow inventory will inundate the market. “By our calculations, this could translate into as many as 20 million homes that could seep into the market as prices stabilize, maintaining a constant stream of supply that far outpaces demand, thus keeping prices flat,” Zillow said in a press release. During April, all markets except Portland, San Francisco and Salt Lake City still had a median days-on-market of 100 or more.  By far, the market with the slowest rate of inventory turnover was again Miami, now at a median of 246 days-on-market — or more than eight months. Portland experienced the fastest rate of inventory turnover at a median of 82 days-on-market, followed by San Francisco at 96 days. But pending home sales offer hope that sales will pick-up in the coming months. The National Association of Realtors’ pending home sales index, a forward-looking indicator based on contracts signed in March, increased 3.2% in March, as it’s Affordability Index sat at a record high. Write to Kelly Curran.