• Boaz Weinstein's Saba Capital detailed its plan for change at 10 BlackRock closed-end funds that trade at a steep discount to net asset value and are underperforming their peers.
• Saba is seeking to oust management at six of those funds.
• The activist fund wants to offer investors the chance to sell out of the funds at the price their shares are worth and to institute broader governance changes.

Boaz Weinstein, the hedge-fund investor on the winning side of JPMorgan Chase's $6.2 billion, "London Whale" trading loss in 2011, is now taking on index fund giant BlackRock. 

On Friday, Weinstein's Saba Capital detailed in a presentation seen by CNBC its plans to push for change at 10 closed-end BlackRock funds that trade at a significant discount to the value of their underlying assets compared to their peers. Saba says the underperformance is a direct result of BlackRock's management.

The hedge fund wants board control at three BlackRock funds and a minority slate at seven others. It also seeks to oust BlackRock as the manager of six of those ten funds.

"In the last three years, nine of the 10 funds that we're even talking about have lost money for investors," Weinstein said on CNBC's "Squawk Box" earlier this week.

At the heart of Saba's "Hey BlackRock" campaign is an argument around governance. Saba says in its presentation that BlackRock runs those closed-end funds the "exact opposite" way it expects companies to run themselves.

BlackRock "is talking out of both sides of its mouth" by doing this, Saba says. That's cost retail investors $1.4 billion in discounts, by Saba's math, on top of the management fees it charges.

BlackRock, Saba says in the deck, "considers itself a leader in governance, but is crushing shareholder rights." At certain BlackRock funds, for example, if an investor doesn't submit their vote in a shareholder meeting, their shares will automatically go to support BlackRock. Saba is suing to change that.

A BlackRock spokesperson called that assertion "very misleading" and said those funds "simply require that most shareholders vote affirmatively in favor."

The index fund manager's rebuttal, "Defend Your Fund," describes Saba as an activist hedge fund seeking to "enrich itself."

The problem and the solution

Closed-end funds have a finite number of shares. Investors who want to sell their positions have to find an interested buyer, which means they may not be able to sell at a price that reflects the value of a fund's holdings.

In open-ended funds, by contrast, an investor can redeem its shares with the manager in exchange for cash. That's how many index funds are structured, like those that track the S&P 500.

Saba says it has a solution. BlackRock should buy back shares from investors at the price they're worth, not where they currently trade.

"Investors who want to come out come out, and those who want to stay will stay for a hundred years, if they want," Weinstein told CNBC earlier this week.

Weinstein, who founded Saba in 2009, made a fortune two years later, when he noticed that a relatively obscure credit derivatives index was behaving abnormally. Saba began buying up the underlying derivatives that, unbeknownst to him, were being sold by JPMorgan's Bruno Iksil. For a time, Saba took tremendous losses on the position, until Iksil's bet turned sour on him, costing JPMorgan billions and netting Saba huge profits.

Saba said in its investor deck that the changes at BlackRock could take the form of a tender offer or a restructuring. The presentation noted that BlackRock previously cast its shares in support of a tender at another closed-end fund where an activist was pushing for similar change.

Saba is seeking shareholder approval to fire the manager at the funds the firm calls the worst-performing relative to their peers over the last three years. In total, BlackRock wants new management at six funds, including the BlackRock California Municipal Income Trust (BFZ), the BlackRock Innovation and Growth Term Trust (BIGZ) and the BlackRock Health Sciences Term Trust (BMEZ).

"BlackRock is failing as a manager by delivering subpar performance compared to relevant benchmarks and worst-in-class corporate governance," the deck says.

If Saba were to win shareholder approval to fire BlackRock as manager at the six funds, the newly constituted boards would then run a review process over at least six months. Saba says that in addition to offering liquidity to investors, its board nominees would push for reduced fees and for other unspecified governance fixes.

A BlackRock spokesperson told CNBC that the firm has historically taken steps to improve returns at closed-end funds when necessary.

"BlackRock's closed-end funds welcome constructive engagement with thoughtful shareholders who act in good faith with the shared goal of enhancing long-term value for all," the spokesperson said.

Weinstein said Saba has run similar campaigns at roughly 60 closed-end funds in the past decade but has only taken over a fund's management twice. The hedge fund sued BlackRock last year to remove that so-called "vote-stripping provision" at certain funds and filed another lawsuit earlier this year.

BlackRock has pitched shareholders via mailings and advertisements. "Your dependable, income-paying investment," BlackRock has told investors, is under threat from Saba.

Saba plans to host a webinar for shareholders on Monday but says BlackRock has refused to provide the shareholder list for several of the funds. The BlackRock spokesperson said that it has "always acted in accordance with all applicable laws" when providing shareholder information, and that it "never blocked Saba's access to shareholders."

"What we want is for shareholders, which we are the largest of but not in any way the majority, to make that $1.4 billion, which can be done at the press of a button," Weinstein told CNBC earlier this week.

WATCH: CNBC's full interview with Saba Capital's Boaz Weinstein