There are almost 9 percent fewer homes on the market than a year ago, and the majority of those are unaffordable for most first-time homebuyers. More than half of all homes for sale across the U.S. are at the high end of the market, according to the March Zillow Real Estate Market Report.

More millennials are aging into their prime home buying years and looking to buy their first home, but there are very few homes on the market that are affordable for them. Among all homes on the market right now, just 22 percent are entry-level, among the least expensive on the market.

This year's home-shopping season will be one of the most competitive ever recorded. Inventory has been falling since the beginning of 2015, and with so few homes for sale, many are going for over asking price.

"This year's home-shopping season is shaping up to be even crazier than last, and sadly, the group that will have the hardest time is first-time and lower-income homebuyers," said Zillow Chief Economist Svenja Gudell. "These buyers will be competing for the few entry-level homes on the market, which are also the ones appreciating the fastest because of extremely high demand. One way to take the edge off would be an increase in inventory, but that is easier said than done. There are some signals a shift may be coming – construction activity is at its highest point in a decade – but buyers shouldn't hold their breath. Getting pre-approved for a mortgage and finding an agent you trust can go a long way in helping buyers act quickly once the right home does become available in this otherwise tight and stressful housing landscape."

Inventory is down the most in San Jose, Las Vegas and Indianapolis. Home shoppers in San Jose will have 26 percent fewer homes to choose from than a year ago. In Las Vegas, inventory is down 23.5 percent, and among the homes on the market, almost 70 percent are high-end homes, among the most expensive on the market.

While inventory remains low, home value appreciation is soaring. The median home value in the U.S. rose 8 percent since last March to $213,146. Home values in San Jose, Las Vegas and Seattle are rising the fastest. The median home value in San Jose rose 25 percent over the past year to $1,252,424. In Las Vegas, home values rose 17 percent year-over-year, and 15 percent in Seattle.

Median rent across the nation rose 2.7 percent over the past year to a median payment of $1,447 per month. Sacramento, Calif., Riverside, Calif., and Seattle reported the greatest year-over-year rent appreciation among the 35 largest U.S. metros. In Sacramento, median rent rose 7.7 percent to $1,852. Median rent in Riverside and Seattle rose 7 percent and 4.7 percent, respectively.

March ended with mortgage rates on Zillowⁱⁱ at 4.19 percent, the lowest rate of the month. March mortgage rates peaked toward the end of the month at 4.30 percent, after starting the month at 4.20 percent. Zillow's real-time mortgage rates are based on thousands of custom mortgage quotes submitted daily to anonymous borrowers on the Zillow Mortgages site and reflect the most recent changes in the market.