As the world's third-richest person and most celebrated investor, Warren Buffett attracts a lot of attention. Thousands try to glean what they can from his thinking processes and track his investments.

We can't know for sure whether Buffett is about to buy Sears Holdings (Nasdaq: SHLD) -- he hasn't specifically mentioned anything about it to me -- but we can discover whether it's the sort of stock that might interest him. Answering that question could also reveal whether it's a stock that should interest us. In this series, we do just that.

Writing in his most recent 10-K, Buffett lays out the qualities he looks for in an investment. In addition to adequate size, proven management, and a reasonable valuation, he demands:

  1. Consistent earnings power.
  2. Good returns on equity with limited or no debt.
  3. Management in place.
  4. Simple, non-techno-mumbo-jumbo businesses.

Does Sears Holdings meet Buffett's standards?

1. Earnings power
Buffett is famous for betting on a sure thing. For that reason, he likes to see companies with demonstrated earnings stability.

Let's examine Sears Holdings' earnings and free cash flow history:

Source: S&P Capital IQ.

Sears Holdings has had trouble maintaining its earnings and free cash flow over the past few years because of declining sales.

2. Return on equity and debt
Return on equity is a great metric for measuring both management's effectiveness and the strength of a company's competitive advantage or disadvantage -- a classic Buffett consideration. When considering return on equity, it's important to make sure a company doesn't have an enormous debt burden, because that will skew your calculations and make the company look much more efficient than it is.

Sears Holdings generated a return on equity of negative 4% over the past year and 5% on average over the past five years. It carries a debt-to-equity ratio of 59%.

3. Management
CEO Louis D'Ambrosio has been at the job for about a year. Before that, he was CEO of Avaya for a few years. He spent a number of years in various jobs at IBM.

4. Business
The retail business isn't particularly susceptible to technological disruption.
 
The Foolish conclusion
So is Sears Holdings a Buffett stock? Probably not. Despite its straightforward industry, the company doesn't particularly exhibit the other quintessential characteristics of a Buffett investment: consistent earnings, high returns on equity with limited debt, and tenured management. If you're looking for a fast-growing retail stock our analysts love today, check out "The Motley Fool's Top Stock for 2012."