After a rough stock market in May, large cap blue chip stocks bounced back nicely in the beginning of June. Then these stock picks gave it all back with most large cap investments looking to close out the month about where they started. In a rocky investing environment right now, it’s hard to find investment advice that produces profits that stick — even in low-risk large cap blue chip stocks right now.

But unfortunately, some stock investors are throwing good money after bad by refusing to unload their battered blue chip stock picks. That’s why I’m going to tell you about my 10 top large cap stocks to sell right now based on my entire Portfolio Grader database of 5,000 investments. If you own shares, sell them immediately — and if you’re an options investors looking for a trading strategy, consider playing the downside on these “dogs with fleas.”

The largest blue chip stock to sell I have identified is Exxon Mobil (XOM). This large cap stock is down -14% year-to-date — about 7 times worse than the broader market. Exxon stock has seen some negative sentiment thanks to the BP plc (BP) Gulf of Mexico oil spill, fairly or not, along with the rest of the oil industry. To top it off, Exxon has missed estimates in three of its four last quarterly earnings reports. Not a sign of growth, and not an encouraging sign for large cap stock investing strategies.

Though about half of Exxon’s size but just as influential in the crude oil industry is BRIC investment Petroleo Brasileiro (PBR) or Petrobras. Like XOM stock, this Brazil investment has been weighed down by negative sentiment in the sector. It also has hurt PBR stock to suffer a  downgrade in April from “Outperform” to “Market Perform” by Bernstein. PBR stock is down -26% year to date, proving that not all BRIC investments are sound right now.

Third largest by size on my list of 10 large cap stocks to sell this week is automaker Toyota Motor Corp. (TM). Recalls plagued Toyota earlier in the year and that continues to darken TM stock looking forward. Shares have shed about -17.5% since January 1. While Toyota has managed to keep impressing Wall Street with its earnings, four consecutive quarterly reports all projected a loss for the company. It’s only a matter of time before this negative sentiment catches up with this Japanese automaker in the wake of recent quality concerns and vehicle recalls.

One of the “smaller” stocks on this list of large caps is BlackBerry maker Research in Motion (RIMM). RIMM has a tough road ahead if it wants to topple red hot Apple Inc. iPhone sales, and with the Google Android going like gangbusters it’s likely that the BlackBerry is on the way out. RIM stock is down -22% year to date.

The complete roll of my top 10 blue chip stocks to sell is below, including market capitalization and sector for each of these large cap stocks — along with my proprietary ranking from Portfolio Grader on shares. Some of the more noteworthy stocks to sell include euro zone investments like Telefonica (TEF) that have suffered due to the Europe debt crisis and financial stock Credit Suisse (CS) which is trending down due to the prospect of financial reform limiting derivitave trading.

You can also get last week’s list of 10 blue chip stocks to sell here. Some of the companies are the same, such as France energy giant Total (TOT) and Italy integrated energy stock ENI S.p.A. (E).

Here’s the complete list of this week’s large cap stocks to sell:

To any shareholders of these stocks afraid to lock in a loss: Simple trading strategies are often the most effective, especially when it comes to blue chips. Don’t worry about PE ratios or the potential of a rebound — just remember that even if one of these stocks jumps 5% in the next few weeks, that’s only good if those returns beat the broader market. If you sell out of these picks and invest in stronger stocks, you will likely make up your lost ground faster than simply wishing and hoping for these blue chips to get back to square. Don’t be emotional about the loss — protect your portfolio and move on with your investing strategy.

As of this writing, Louis Navellier did not own a position in any of the blue chip stocks named here.

About Portfolio Grader: Every Sunday, renowned growth stock expert Louis Navellier runs a fundamental analysis on the top 5,000 Wall Street companies. Armed with this research, Navellier offers a rating for each company reflected as a simple letter grade, with A being “strong buy” and F being “strong sell.” Portfolio Grader’s stock data is free and open to the public and can be accessed online here.

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