Gun safety in the home hasn’t been discussed much in the recent national conversation on gun violence, but the head of the nation’s largest homeowners and auto insurance company acknowledges that it could be.

Edward B. Rust Jr., CEO and chairman of the board of State Farm Mutual Insurance Co., said this week that gun ownership “could be among a multitude of things” considered among the risk factors used by insurance companies to determine the cost of homeowners insurance policies. “But,” he added, “whether someone owns a gun doesn’t necessarily make them a risk. . . . The bigger debate is, Are people competent in gun ownership?”

Rust made his comments following a panel discussion at a forum for property and casualty insurers held at the Waldorf-Astoria hotel in New York on Monday.

In recent weeks, some commentators have suggested that insurance could play a role in mitigating gun violence. Insurers could offer discounts for gun owners who indicated they use gun locks and other safety features, suggests Marsha N. Cohen, a law professor at the University of California Hastings College of the Law. Another option: Consumers would have to show proof of coverage before buying guns.

Accidents represent just 2.6 percent of all gun fatalities, according to the Centers for Disease Control and Prevention. But that figure rose by 37 percent, from 1.9 percent, from 2010 to 2011.

State Farm does not specifically ask applicants whether they own firearms, says Jeff McCollum, a company spokesman. In most states, the company’s standard homeowners policy covers up to $2,500 of loss if guns are stolen or destroyed. Owners of expensive collectible guns can buy a separate “personal articles policy” for the value of what they own.

State Farm does not give special discounts for people who use gun locks and other safety devices, McCollum said. The company sells policies in every state and has 20 to 25 percent of the homeowners and auto insurance market. (Check our buying guide and Ratings for homeowners insurance.)

Rust seemed reluctant to insert himself or the industry in the gun-violence debate. He acknowledged that “compliance and safety” had to be part of people’s thinking about guns. But, he said, while there was a need for a “healthy debate” on the subject, insurers weren’t geared up to police policyholders on whether they’re taking proper gun-safety measures in the home. “It’s like seat belt laws,” he said. “Wearing a seat belt can mitigate injuries. But we can’t pull everyone over to make sure they’re wearing a belt.”

Demand for foreclosures is so great and supplies are so low in some of the nation’s hottest foreclosure markets popular with investors that the price differences between REOs and full-price homes have virtually disappeared.

According to data from Home Value Forecast, during 2012 foreclosure discounts shriveled in some but not all of the markets suffering the greatest record foreclosure activity in past years. Foreclosure inventories have declined in these markers, largely due to residential real estate investors, both individual and hedge funds, who buy up foreclosed properties to convert into single family rentals. While full-price homes and short sales have appreciated slightly in these markets, REO prices have zoomed, a sign that investor demand-especially hedge funds who have been buying up thousands of REOs since the end of 2011-is driving the decline in foreclosure discounts.

Foreclosure discounts are critical to most investors’ business plans. To bring foreclosures up to market-ready or rent-ready status, investors spend a media of $7500 per property, or $9.2 billion per year according to a survey of investors by BiggerPockets.com and Memphis Invest. Should the foreclosure discount evaporate, it will be cheaper simply to purchase a full-price home that needs no repair.

Foreclosure discounts also have toxic effect home values. Their reduced values often are used by automatic valuation models and by appraisers in calculating comparable sales values for full-priced properties, resulting in lower appraised values.

In Las Vegas, the discount between full price homes and foreclosures was only was only 1 percent in the third quarter of 2012, and price differential between full-price properties are REOs has fallen to only $2000. Third quarter 2012 data from Home Value Forecast provides trend lines for REO, full-pricne and short sale prices, sales volume and time on market.. HVF provides insight into the current and future state of the U.S. housing market, and delivers 14 market snapshot graphs from the top 30 CBSAs. Home Value Forecast was created from a strategic partnership between Pro Teck Valuation Services and Collateral Analytics and uses numerous data sources including public records, local market MLS and general economic data.

The foreclosure discount in Phoenix has shrunk to about 5 percent. REO prices have risen to a median of $88,000 from $62,000 in January 2011, and today are only $6000 less than the median full-price home in the Phoenix market. At $70,000, short sales trail both REOs and full-price homes.

In Orlando, REO prices have been rising throughout 2012, but they still trail full-price homes by $17,000. The discount in the third quarter was still sizeable, about 21 percent, but down significantly from 33 percent in 2009. Tampa also saw in increase in REO prices at the same time that full-price homes rose, keeping the discount at about 32 percent.

Yet in Detroit, a major source of foreclosures but not a popular market for most inestors, the discount actually grew. REO prices in the third quarter were at the same level, $26,000, as they were in the third quarter of 2011, while full-price homes rose from $41,000 to $50,000.

The massive amounts of money hedge funds are spending on foreclosures clearing impacting the real estate economy. Last year several dozen investment firms backed by $6 to 8 billion in private equity hedge funds announced plans to purchase between 40,000 and 80,000 previously foreclosed homes. In September investment bankers at Keefe Bruyette and Woods estimated the dollars raised so far may only trim 15 percent of the foreclosure supply and there is room for even more growth that could last for years.

Just last week Blackstone Group LP, the largest U.S. private real estate owner, accelerated purchases of single- family homes as prices jumped faster than it expected. According to Bloomberg, Blackstone has spent more than $2.5 billion on 16,000 homes to manage as rentals, deploying capital from the $13.3 billion fund it raised last year, said Jonathan Gray, global head of real estate for the world’s largest private equity firm. That’s up from $1 billion of homes owned in October, when Blackstone Chairman Stephen Schwarzman said the company was spending $100 million a week on houses.

“The market is moving much faster than anybody thought possible,” Gray said during an interview in Blackstone’s New York headquarters. “Housing is much stronger than people anticipated.”

Santa Monica-based Colony Capital LLC, last week raised at least $45 million to finance additional REO purchases. It has invested $355 million in the REO-to-rental business since July, according to regulatory filings.

Meanwhile, Colony, Blackstone, Waypoint Real Estate Group LLC and American Homes 4 Rent have reportedly converged on Atlanta in search of low-priced properties to buy and rent out, after helping drive prices up 34 percent in Phoenix from a year ago.

Southern California’s housing market ended the year with sharp gains, rounding out the first solid year of sustained improvement after nearly five years of real estate malaise — and helping set up further improvement in 2013.

The region’s median home price registered a sizable 19.6% pop in December compared with the same month last year to hit $323,000, real estate firm DataQuick reported Tuesday. A record level of cash buyers flooded into the market and more move-up homes sold last month.

While Southland housing is on the mend, the steep increase in the region’s median price last month probably reflects a variety of factors, such as the mix of what sold in December, and the run-up may not continue at that brisk pace, experts said. The median is the point at which half the homes in the region sold for more and half for less.

“There is no possible way that number can be sustained nor should anybody look at that as a long-term trend,” said Stuart Gabriel, director of the Ziman Center for Real Estate at UCLA. “We haven’t shifted from bust back to bubble, and nobody should think we have, and nor likely will we.”

When compared with the prior month, the median was essentially flat, up only 0.6%. San Bernardino and Riverside counties posted the strongest year-over-year increases, up 20.0% and 19.1%, respectively, indicating that the once hard-hit Inland Empire is now probably in recovery.

The median is heavily influenced by the types of homes selling, and some of last month’s pricier sales may have been driven by fears of increased tax burdens on the wealthy, as Washington wrangled with the “fiscal cliff” negotiations.

A rise in prices will mean more homeowners who had been underwater — owing more on their mortgages than their homes are worth, a condition also known as negative equity — can now put their properties on the market. That would help ease the region’s inventory squeeze, which is another major factor driving up prices.

Last year was the first year of solid improvement since housing crashed in 2007. The strong performance last month indicates that 2013 will continue to bring home price gains, analysts said.

“Our forecast over the next 12 months is for equally strong appreciation,” Zillow.com chief economist Stan Humphries said. “Even though we have got a lot of homes still in negative equity in Southern California, the tight inventory is definitely creating some price appreciation.”

An estimated total of 20,274 new and previously owned homes and condominiums sold throughout the six-county region in December. That was a 5.1% increase from November and up 5.3% from December 2011. Last month’s tally was the highest for a December since 2009.

The 2012 housing rebound came after foreclosures declined, housing inventory plummeted, mortgage interest rates hit record lows and demand from investors surged last year.

In addition, the overhang of the last housing bust resulted in some unexpected benefits.

For instance, the high number of underwater borrowers actually served as a boost to the market rather than being a drag, as people kept their homes off the market, decreasing inventory.

“The lock-out phenomenon, combined with the rise in investors converting foreclosures into rentals, led to a lack of for-sale inventory,” CoreLogic economist Sam Khater wrote in a research note. “With home prices rising in 2012 and 2013, tight for-sale inventory will begin to ease.”

Nationally, CoreLogic reported that home prices were on a sharp upward trajectory in November, with almost all states posting gains that month. The firm’s home price index report, also released Tuesday, showed that home prices nationwide increased 7.4% year-over-year.

“Consistent price increases throughout 2012 have started the process of lifting households out of negative equity, which will support home sales and refinancing volumes,” Paul Diggle, an economist for Capital Economics, wrote in an emailed analysis. “Lower levels of negative equity is good news for housing market activity and sets up a virtuous circle of rising activity leading to rising prices and pushing negative equity down further.”

In California, buyers can anticipate a tight market in the near term. A supply of only about 2 1/2 months’ worth of single-family homes for sale was available statewide at the end of December, the California Assn. of Realtors reported Tuesday. A supply of six or seven months is considered healthy by most economists.

Supply from distressed sales, particularly from foreclosed homes, will remain limited as those homes are being quickly snapped up by investors while the number of troubled borrowers entering foreclosure continues to decline. The number of notices of default — the first step in the formal foreclosure process — fell 14.5% in December from November and dropped 39.8% from December 2011, according to foreclosure tracker ForeclosureRadar.com.

The decline in foreclosures has been aided by an increase in short sales, as The Times recently reported, as well as other loan aid for borrowers. The drop in foreclosures should continue to help lift prices.

“For 2013, we largely expect more of the same,” Sean O’Toole, chief executive of ForeclosureRadar, wrote in a blog post this week. “Demand will remain strong thanks to Federal Reserve-manipulated low interest rates and affordability. Housing supply will remain constrained, largely due to government foreclosure intervention. As a result, prices will rise, though likely at a slower pace.”

The increase in the median home price in Southern California reflects market dynamics as fewer sales are logged in cheaper neighborhoods and pricier places take off.

Throughout Southern California, sales of mid-to-higher-cost markets rose in December, DataQuick reported. Sales of homes between $300,000 and $800,000, the typical move-up range, jumped 31.4% year-over-year. Sales of homes above $500,000 soared 40.0% year-over-year, while sales of homes of more than $800,000 were up 36.3%.

Meanwhile, cheaper neighborhoods posted weak sales. Most notably, the number of homes throughout the region that sold below $200,000 dropped 28.1% while those below $300,000 fell 18.2%.

Sales of foreclosed homes made up just 14.8% of the market last month, down from 15.4% the month before and 32.4% in December 2011. That compares with a high of 56.7% of the market in February 2009.

Cash buyers and investors are playing a big part in snapping up home inventory. Cash buyers bought up 33.8% of all resale homes last month, while absentee buyers purchased 29.1% of Southland homes in December, DataQuick said.