Billionaire investor Nelson Peltz had a tough second quarter with his Trian Partners funds vastly underperforming the S&P 500, according to an investor letter obtained by CNBC.
Trian said that most of its long portfolio "kept pace" with the broader market's near 3 percent gain, but its "short portfolio detracted."
The investment firm's Onshore Fund returned 0.35 percent in the second quarter and 11.81 percent year-to-date.
The S&P has increased about 18.5 percent in 2013.
The Offshore Fund had similar results, up 11.70 percent on the year and 0.24 percent for the quarter.
"Second-quarter performance: Like a duck—calm on the surface, but paddling furiously underneath."
In the July 31 letter, Trian equates its second-quarter performance to "a duck—calm on the surface, but paddling furiously underneath."
Assets under management also reached an all-time high of $6.83 billion, partially attributable to a $500 million fund-raise completed in June for "Position C in a new co-investment vehicle."
The letter describes "Position C" as a "company comprised of world class businesses where we see a path to superior value creation."
"Position C" remains officially undisclosed.
But "Squawk Box" co-host Andrew Ross Sorkin reported on July 17 at the Delivering Alpha Conference, which was presented by CNBC and Institutional Investor, that Trian bought a stake in DuPont, which jumped 5 percent on the news that day.
(Read more: Nelson Peltz amasses big stake in DuPont)
It's unclear if DuPont is "Position C" or another investment.
The new position was funded, in part, by liquidating the funds' stake in Danone and trimming State Street. Trian also scaled-back its stakes in Family Dollar and Ingersoll Rand, according to the letter.
The investor letter also summarized Trian's current proposal for PepsiCo to buy Mondelez, the snack food company spun off from Kraft last year, which was also outlined in a white paper released on July 17—the same day that Peltz talked extensively about the idea at the Delivering Alpha Conference.
(Read more: Nelson Peltz calls on Pepsi to buy Mondelez)
As of March 31, Trian owned 12 million shares of PepsiCo and 40 million shares of Mondelez, according to regulatory filings.
Trian says PepsiCo is "increasingly unmanageable" and states the company has "underperformed its peers as it grapples with the differing needs of its fast-growth (snacks) and slow-growth (beverages) and resulting inherent conflict in allocating its resources."
Trian's plan to maximize shareholder value would mean PepsiCo would acquire Mondelez, creating "a leading global snacks company with one of the most valuable brand portfolios in the world."
(Read more: Pepsi profits beat; CFO answers Peltz on Mondelez)
The fund proposes the merger would serve as a catalyst for PepsiCo to spin off its beverage business, creating "substantial cost and revenue synergies and the opportunity for margin and capital structure efficiencies."
Trian estimates the merger may lead to approximately $175 of implied value per PepsiCo share and $72 of implied value per Mondelez share by the end of 2015—more than double the current prices of those stocks.
The letter went on to disclose that PepsiCo indicated "it is not inclined to pursue a Mondelez transaction" but conceded that as a "constructivist" investor, the fund understands "a company cannot be compelled to complete a transformational merger but we hope they reconsider their position."