When I first started learning about investing, I heard the age-old adage “Buy Low, Sell High” everywhere. Turns out, that’s not the best advice. For one, it can make investors hold on to stocks too long in the hopes of getting back to even. Two, it scares investors away from good stocks trading near their highest prices.

In fact, research shows that buying when the market makes a new 52-week high is much more profitable than buying when it hits a 52-week low, and crushes the average market returns as well.

With that in mind, here are three stocks fresh off of new 52-week highs that make great investments.

Arris Group, Inc. (NASDAQ:ARRS)

Last December, Arris bought the Motorola Home division from Google Inc (NASDAQ:GOOG) for $2.05 billion in cash and $300 million in stock. A month later, the company sold half of Google’s stake to Comcast Corporation (NASDAQ:CMCSA) giving them each 7.85% of the total outstanding shares.

What’s important is Arris now has two very big partners with direct interest in the company’s success. Arris will be the beneficiary of licensing deals with one of the biggest innovators in tech, particularly as they move into the high-speed video and internet delivery market. The deal with Comcast ensures that the company’s largest customer isn’t going to drop them.

The acquisition of Motorola Home also creates a more diversified customer base for Arris Group, Inc. (NASDAQ:ARRS). Last quarter, the company reported 51.7% of total revenue came from just two companies – Comcast and Time Warner Cable. By adding a slew of smaller cable companies that rely on Motorola set-top boxes, the company now has a stronger foothold on the market.

Even while the company is hitting a new high, it looks like it has room to continue growing. The company is already seeing traction with its newly launched Moxi home gateway and E6000 router. Order backlog at the end of 2012 was $222.6 million compared to $148.5 million at the end of 2011. And the company is starting to diversify internationally, where big opportunities exist, specifically in China.

American Express Company (NYSE:AXP)

One of the few financial companies to have completely retraced back to its pre-financial crisis highs, American Express looks like another great buy-high opportunity. Where competitors Visa Inc (NYSE:V) and Mastercard Inc (NYSE:MA) focus on the nascent e-wallet revolution, American Express is following the money and investing heavily in the e-commerce market.

Most recently, the company made a partnership with Twitter to sync its credit cards with the social network, allowing cardholders to purchase items through special hashtagged tweets. This comes after establishing relationships with Facebook Inc (NASDAQ:FB), Foursquare, and Microsoft Corporation (NASDAQ:MSFT)’s Xbox Live.

E-commerce has grown into a $1 trillion market, and grew at 21.1% rate last year. American Express Company (NYSE:AXP) is beating its competition to the punch as it harnesses the growing number of social network users to bring customers and vendors together with their credit cards. As money transforms from paper and metal to bits of data, American Express is positioned well to ride the trend of electronic payments.