Warren Buffett is on the hunt again and this time he has even more cash to spend. Indeed, Berkshire Hathaway's (BRK.A -0.56%) (BRK.B 0.07%) cash pile has swelled to more than $40 billion and an elephant-sized acquisition had recently got away from him.. 

While it's impossible to know what Buffett will acquire next for sure, we can compile a list of possible candidates based on previous acquisitions.

What to look for
Indeed, we already know that Buffett has around $40 billion of cash at Berkshire. However, we also know that Buffett likes to keep $20 billion on hand to stay "liquid." Still, as with Heinz, Buffett is willing to partner up if the deal is good enough.   

We also know that Buffett likes companies with a strong brand presence and names like Heinz and Coca-Cola. What's more, we can assume that Buffett is unlikely to spend his cash on a company that relies on a commodity for its revenue.

So, where does this leave us? Well, for the sake of simplicity, let's rule out companies that are based outside the U.S., as well as any companies worth less than $10 billion since they're not true "elephants." Furthermore, we know Buffett is a value investor but is willing to pay a bit more for quality.

For example, he brought Heinz at an all-time high price and valuation. In this case then, let's narrow the search down to companies that are currently trading at a trailing-12-months price-to-earnings ratio of less than 20 --  not particularly cheap but not overly expensive, either.

Two possible candidates
Apply these screening criteria to the S&P 500 index and immediately two companies stick out. Travelers (TRV -0.24%) and Chubb (NYSE: CB) would both make great bolt-on acquisitions for Berkshire and greatly expand its presence within the domestic insurance market. Both companies have a strong brand and solid history and are in an industry that Buffett knows extremely well.

There is also another reason why Buffett might target these companies. As you may know, a large portion of Berkshire's revenue comes from insurance, which is the company's main line of business. However, there are some problems plaguing the insurance market, which are likely to affect Berkshire more than most.

Demand for yield
The demand for yield around the world has driven investors into ever more exotic locations when looking for a steady, high-income stream. One region that has seen significant capital inflows is the insurance market. In particular, securities such as catastrophe bonds, which are designed to raise a large amount of capital in exchange for a higher-than-average rate of interest. Catastrophe bonds are high-risk/high-reward assets. The bonds offer a high rate of interest but in the event of a catastrophe, the issuer's obligation to pay interest and/or repay the principal is either deferred or completely forgiven.

The influx of capital and demand for these bonds has removed some of the demand for reinsurance companies, which previously took on this all-or-nothing style of investing. Berkshire Hathaway Reinsurance and General Re are the two main reinsurance operations under Buffett's wing. Together, these two companies accounted for 75% of the insurance float under Berkshire's control during 2012.

Nonetheless, the rise of catastrophe bonds is, according to the Financial Times, giving insurance companies the firepower to demand that reinsurance companies cut their fees by around 10% this year as their services have been replaced by willing private and institutional investors around the world. Indeed, reinsurance prices in Florida have already been compressed by 15% this year.

Unfortunately, this is bad news for Berkshire. However, this could be the catalyst that inspires Buffett to unleash his elephant gun on either Travelers or Chubb as both companies are highly active in the personal insurance market. 

But why have I chosen Chubb and Travelers? For starters, it is widely speculated that Buffett already tried to acquire Chubb in a deal that fell through last November. 

What's more, analysts have consistently expressed belief the both Chubb and Travelers would make great Berkshire add-ons. Indeed, in June last year it was revealed that according to the Bloomberg "Riskless Return Ranking" of insurance companies, Chubb and Travelers were the best-performing companies within the insurance sector, both beating Berkshire.

In addition, both companies remained profitable throughout the financial crisis and their stock prices have gained slowly and steadily during the past decade. This is what makes these two companies so appealing: They are both perfect fits to Buffett's slow and steady methodology without too much risk.

Foolish summary
So overall, pinpointing Buffett's next elephant is tough, but trends within the insurance market as well as studying previous acquisitions lead me to the conclusion that the next acquisition might be within the insurance sector.

Travelers and Chubb both fit the bill and both companies are currently within Buffett's price range. To me, both look like perfect bolt-on acquisitions for Berkshire.