Avon Products ( NYSE: AVP ) hasn’t exactly been the belle of the ball lately, but that isn’t stopping its management from snubbing a suitor.

Private company Coty, which has traditionally focused on fragrance, offered $10 billion in cash to buy struggling Avon, but it’s being rebuffed — even though the market values Avon at only about $8 billion. Coty’s bid of about $23.25 per share represented a 20% premium to Avon’s closing stock price last Friday.

Avon’s aggressive take: The bid substantially undervalues the company. Coty’s response: It would consider a higher offer if Avon is willing to let it take a look at its books. In other words, prove it .

It’s pretty amazing when corporate managements take the hard line even when they possess a glaring lack of bargaining power. Avon’s been floundering for quite some time now; my November 2010 underperform CAPScall on Avon and my negative take with fellow Fool Dayana Yochim have proved right so far. (View my CAPS track record here.)

Avon’s many issues include slowing sales in emerging markets such as Eastern Europe and Brazil, and even a bribery probe in China. Furthermore, the Avon Lady has lost popularity in more developed markets, like right here at home, and the company’s still searching for a replacement for longtime CEO Andrea Jung, who is staying on as board chair.

The frump factor

The situation parallels retailer Talbots ‘ ( NYSE: TLB ) recent spurning of potential suitor Sycamore Partners, despite its own dire competitive positioning. Much like we saw with today’s action in Avon’s stock price, some investors started piling in on the mere whiff of a possible acquisition. forgetting that there’s absolutely no guarantee such an outcome will come to pass.

Has the Talbots buyout materialized yet? Nope.

Meanwhile, another struggler, Liz Claiborne ( NYSE: LIZ ). is rumored to have garnered some private-equity interest recently, too. When such interest is more about companies’ weaknesses than their strengths, investors should beware.

Stick with strength

Forget the acquisitive speculation: Investors should seek strong companies to invest in instead. Estee Lauder ( NYSE: EL ) is a highly successful cosmetics company with a strong portfolio of stellar brands. Although Estee Lauder’s not cheap — it’s currently trading at 24 times forward earnings — it’s also not a longtime struggler. It would be better to patiently wait for a cheaper price for Estee Lauder than plow money into shares of Avon now.

Likewise, with cases such as Talbots, investors would be better off buying shares of retailers that are proving their competitive mettle. Take Buckle ( NYSE: BKE ). which recently increased profit by 13% and total sales by 11%; its same-store sales increased an amazing 8%. That retail stock is reasonably priced, too, trading at 13 times forward earnings. Although it’s about on par with or a little higher than the forward multiples on American Eagle Outfitters and Abercrombie & Fitch. it’s also consistently proved itself to be operationally strong over long periods of time.

People who are buying up shares of Avon today at nearly 20% more than Friday’s closing price are taking a serious gamble with their money. Investing in messed-up companies based solely on the notion of possible acquisitions isn’t the high road in investing; in fact, it’s an incredibly risky one.

Forget the speculative stocks — here’s another high-quality retail stock idea: an emerging-market play our analytical team dubbed The Motley Fool’s Top Stock for 2012. The report is absolutely free, so act now.

Alyce Lomax owns no shares of any of the companies mentioned. The Motley Fool has a disclosure policy . We Fools don’t all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. Try any of our Foolish newsletter services free for 30 days .