Bill Ackman's fund, Pershing Square, is one of the highest profile hedge funds in the world. As the company takes large, concentrated bets on major American companies, and often works to change their business structure, the actions of the fund can have a real impact on investors' portfolios. Anyone holding shares of J.C. Penney (JCPN.Q) or Canadian Pacific (CP -6.60%) is no doubt aware of Pershing Square's ability to move stocks. If the fund gets involved with a company, there's going to be some volatility, one way or the other.

While Pershing Square's second quarter letter to investors touches on all of the fund's positions, I've highlighted what I consider to be the three biggest investment takeaways.

J.C. Penney: Admitting defeat
After two arduous years, Ackman has finally admitted his investment in J.C. Penney was a mistake.

Perhaps to soothe his investors, Ackman deflects blame for the failure of former CEO Ron Johnson, noting that all members of the retailer's board (not just him) wanted to hire Johnson back in 2011. At the same time, Ackman says he has been upfront about the high risk/high reward nature of his J.C. Penney investment. Interestingly, he notes that his fund's two biggest failures (J.C. Penney and Target) have been retail stocks. Perhaps the activist will avoid retailers for the foreseeable future.

After reaching an agreement with J.C. Penney's board, Ackman unloaded his shares earlier this week. He had said he was prepared to hold J.C. Penney shares until more interesting investment opportunities come along -- something else must have caught his eye. Since Ackman's sale, J.C. Penney shares have moved lower, but some analysts see it as a positive. Oppenheimer's Brian Nagel wrote that it would be positive for the company in the long-run.

With Ackman out, J.C. Penney is an interesting situation. Management appears to be committed to bringing back the old J.C. Penney with coupons and private label clothing like St. John's Bay. That could help stabilize the situation, and should the customers driven away by Johnson return, J.C. Penney could see same-store sales growth. On the company's recent earnings call, it said each month of the recent quarter was better than the last, and it expects this trend to continue through the end of the year. 

Not backing down from Herbalife
Currently, Pershing Square's bet against multi-level marketing firm Herbalife (HLF -0.43%) is underwater. Ackman has lost about $300 million on the position, according to Reuters.

Yet, he's not backing down. Instead, he reaffirmed his position on the company -- that it's a pyramid scheme destined to collapse -- and rebuked many of the bullish arguments for the stock.

Ackman notes that last quarter, the company saw its earnings growth decline. Herbalife is still profitable, but earnings are growing at a lesser pace. Herbalife bulls have argued that the company should be able to authorize a large share repurchase program in the near-future, but Ackman isn't buying it. Given that much of its cash is overseas, Ackman believes that the company would have to borrow money to repurchase shares. If, as he alleges, the company is a pyramid scheme, any institution that loaned Herbalife money would be out of luck if the FTC shuts the company down.

And that's still what Ackman expects, with more certainty than ever. Although he didn't explain exactly why, Ackman writes that he's now more confident in regulators taking action against the company.

In Canadian Pacific for the long-haul
Canadian railroad giant Canadian Pacific has been one of Ackman's biggest wins in recent years. After installing a new CEO last year, Canadian Pacific shares are up better than 60%.

Pershing Square trimmed some of its investment in the railroad last quarter, but Ackman writes that it sold stock simply to balance the portfolio. In light of the large appreciation, Canadian Pacific accounted for almost one-third of Pershing Square's capital. Ackman reaffirmed his commitment to the company, writing that turnaround is just beginning to take place, and that Pershing Square is in for the long haul.

That seems reasonable. Pershing Square makes big bets, but with so much capital invested in just one stock, a black swan event could've blown up the fund.

With Ackman reaffirming his commitment, it should be good for Canadian Pacific shareholders. When Ackman began to trim his stake, some analysts saw it as a sign that the top was in. RBC, for example, downgraded the stock in June and cut its price target to $104 based largely on Pershing Square's sales.

Investing alongside Pershing Square

Ackman has had some impressive home runs in recent years (Canadian Pacific, General Growth Properties, Fortune Brands) but he's also had some big losses (J.C Penney, Borders, Target).

In this case, Ackman has accepted his failure with J.C. Penney, and is preparing to unload his shares. On paper, Herbalife also looks like a failure, but Ackman continues to be as adamant as ever about the company's problems. As for Canadian Pacific, it's been a great investment, but Pershing Square isn't selling out yet.

One thing's for certain: whenever Pershing Square gets involved in a stock, it's going to move. For that reason, investors holding stocks that Ackman is involved in, need to keep a close eye on the fund's activities.