Yes, Herbalife has a logo, and this is it. Photographer: Patrick Fallon/Bloomberg.
Yes, Herbalife has a logo, and this is it. Photographer: Patrick Fallon/Bloomberg.

Herbalife is the battlefield for an epic war between billionaire hedge fund managers, but it is also more or less a textbook on the many uses of corporate equity derivatives. I have never been a billionaire hedge fund manager, but I was a corporate equity derivatives salesman, so let's talk about that instead.

As it happens, we talked the other day about how Herbalife, after buying back around $700 million of stock in the first quarter of the year in interesting ways, and buying around $300 million in April in normal but very speedy ways, had $266 million more to buy in May and June. Never ones to sleep on their buybacks, Herbalife signed up to do all of it this week:

On May 6, 2014, Herbalife Ltd. ("Herbalife" or the "Company") entered into an agreement with Merrill Lynch International to repurchase $266 million of Herbalife's common shares as part of the Company's previously announced share repurchase program. Under the terms of the repurchase agreement, Herbalife will pay $266 million on May 7, 2014 from the Company’s cash on hand. Herbalife will receive a portion of the repurchased shares on pre-determined dates and the remainder upon completion of the program. The total number of shares ultimately repurchased under the agreement will be determined based generally upon a discounted volume-weighted average share price of Herbalife's common shares over the course of the program. The transaction is currently expected to be completed no later than June 2014. Shares that are repurchased will be retired.

A good phrase to start with there is "discounted volume-weighted average share price." Why does Herbalife get to buy stock at a discount? It's paying Merrill Lynch International $266 million and buying back more than $266 million worth of stock -- $266 million divided by the average price of the stock, less a discount. If the discount is a dollar, and the stock trades at around $62, then Herbalife is buying $270 million worth of stock for $266 million.1 Why would Merrill do that?

The answer is in the words "completed no later than June 2014": The program could be completed earlier; that is, there's some optionality in when the program ends. Herbalife has sold Merrill that optionality -- it's referred to as a "variable maturity option" -- and Merrill has paid for it in the form of a discount to the share price.2

Why would Merrill pay for that optionality? Well, because it's got a derivatives desk, and derivatives desks pay for optionality. Where the option value comes from here is a little wizardy, but you can get the gist simply enough. Assume that the program can end no later than June 30, but that Merrill can end it as early as June 2.3 Then imagine that the stock bops around in the low $60s for the rest of May, and then plummets in early June:

In early June, Merrill has bought around half of Herbalife's shares for an average price of around $60. Then the stock falls out of bed and Merrill can buy the rest for around $40. So it does that quickly: It ends the contract on June 5th, delivers stock to Herbalife at an average price of around $60 (minus a discount, so maybe $59), but ends up buying it for an average price of around $50.4 So it makes several dollars a share on a 4-million-ish share contract.

This is the simplest and biggest way for Merrill to make money, but Merrill is not really betting that Herbalife's stock will plummet in June. Merrill would also do very well if Herbalife's stock jumps up in June; this is less obvious but follows similar principles.5 And it does quite well if Herbalife's stock bounces around a lot, because Merrill owns an option and volatility makes options more valuable.6 Each time the stock goes down, Merrill buys more; each time it goes up, it buys less; and the variable-maturity option lets Merrill beat the average price.

On the other hand, if the stock doesn't move much, Merrill doesn't make any money on the optionality. And since it pays for the optionality in the form of a discount, it loses money on the trade if the stock stays put.7 Merrill and Herbalife are betting on volatility: Merrill's bet is that Herbalife's stock will be more volatile than the company expects.

I mean, they didn't put it like that. One reason this trade is so lovely -- and it's a pretty common trade8 -- is that the story for the client and the math for the bank are so unrelated. The pitch to the client is: You want to buy shares in May and June. You want to be done by the end of June, but you don't particularly care whether you buy the shares over five weeks or eight weeks. Let us decide, and we'll pay you a buck a share for that privilege. It's not like you were doing anything with it anyway.

The pitch to the derivatives desk is: We're buying a floating-strike put on a very volatile stock, and pricing it using a pretty conservative volatility, so in expectation we'll make a lot of money. There are like no overlapping words in those two descriptions.

You can have thoughts about the social value, or lack thereof, of Wall Street financial engineering, and this simple piece of engineering is a good test case. In expectation, Merrill is making money here (though it's at risk and might end up losing money). That means that, in expectation, Herbalife is overpaying for its stock. But Herbalife is getting a pleasing story, and not an inaccurate one: It probably really doesn't care whether it buys its shares over five weeks or eight. At the end of the five, or eight, or whatever, weeks, it will buy back shares at a discount to the average price over those few weeks. It will feel like it's underpaying for its stock. In some real sense, it will be. In another sense, it won't be. The sense in which it is underpaying is the sense that is visible to Herbalife (it beats the realized average price). The sense in which it is overpaying is the sense that is visible to Merrill (it overpays in Black-Scholes expectation). Everyone wins, on the same zero-sum financial transaction.

That's neat! But if you take this trade simply as a volatility bet, it's still interesting, no? Merrill Lynch is now in line for a big payday if the Federal Trade Commission announces Bad Things About Herbalife in June -- or, on the other hand, if the Securities and Exchange Commission announces Bad Things About Bill Ackman.9 So that gives them sort of a fun rooting interest in this drama. And the right one: They don't care if Ackman wins or Herbalife does; they just want a dramatic (and volatile) fight.10

On the other hand, a thing about volatility trading is that it has the effect of dampening volatility. If Herbalife's stock goes up, Merrill will buy it slowly. If it goes down, though, Merrill will step in to be a big buyer, doing more to prop up the stock price the more rapidly it falls. Merrill wants volatility, but its trading will have the effect of reducing volatility. Herbalife's stock is the subject of a tug-of-war between those who want to prop it up and those who want to tear it down, and the company has now pulled in Merrill as a useful ally.

1 Numbers are extremely illustrative; I don't know what the discount is. Math was just $266 million divided by $61 per share price is 4.36 million shares; 4.36 million shares times $62 per share value is $270.4 million.

2 I mean, I confidently assume that that's what's going on. There are other imaginable possibilities, but the discount plus the "no later than" are pretty good giveaways.

3 That would be less than four weeks to buy 4.3-ish million shares, or around a quarter million shares a day. Herbalife trades around 3 million shares a day, so to buy in four weeks Merrill would be buying over eight percent of volume every day, which is kind of a lot.

4 Like, if you buy half at $60 and half at $40, your average cost is $50. Really Merrill would have bought more than half by that point, so its average cost will be higher, more like $53. That's a $6 a share profit on 4.4 million shares, or around $25 million.

5 The intuition is basically that you start out buying at a medium speed. If the stock plunges in early June, you start buying really fast (at low prices) and end the program early, while the average is still high. If the stock soars in early June, you start buying really slowly, averaging in higher prices even though you've done a majority of your buying in May.

6 The particular flavor of option is sometimes referred to as a floating-strike put: Merrill has the right to sell Herbalife stock at the trailing average price, which looks like a put option (right to sell stock at a fixed price), albeit one with a changing strike price. Intuitively, you make money owning puts when stocks plummet. But when you're a hedged option owner, as Merrill is, you mostly make money on volatility, not direction.

7 Or drifts slowly up, or down. What you want is rapid sudden movements.

8 One allegedly invented by Harvey Schwarz, now chief financial officer of Goldman Sachs! Er, wait, no. Harvey allegedly invented the accelerated stock buyback. This trade appears to be the accelerated stock buyback, without the acceleration. Normally the trade involves the bank delivering most of the shares to the customer day one, and then truing up at the end. (This helps the customer's accounting.) It's not clear that this trade does ("Herbalife will receive a portion of the repurchased shares on pre-determined dates ..."). The reason is that to deliver shares day one, the bank needs to borrow the stock: It's effectively short selling the shares to the company. And it's tough to borrow Herbalife stock, since Bill Ackman pretty much borrowed all of it and then Herbalife's convertible investors went and borrowed some more. The non-accelerated accelerated stock buyback is less common than the accelerated kind, but certainly not unheard-of.

(That paragraph was a little speculative; perhaps Merrill is shorting shares to Herbalife to accelerate this buyback, it's hard to tell. This would not have much effect on the economics; it would just improve Herbalife's earnings-per-share treatment very slightly. And perhaps the "pre-determined dates" refers instead to the possibility that Merrill is providing a collar on this trade, in which Herbalife won't pay more than $X or less than $Y per share, and the delay is to hedge the collar. My guess would be that that's not the case, but I don't really know. Part of my guess against it is that it would be a little goofy for Merrill to sell Herbalife a cap on its stock price, since Herbalife is living in exciting times. But you never know.)

9 Or if the FTC announces Good Things About Herbalife, though structurally that seems less common? I feel like regulators are rarely in the business of saying "that Herbalife, great company, I buy their shakes all the time, not a pyramid at all, gold star," even when it's true.

10 That's not quite true. They might make a little more money on this trade if Herbalife plummets than if it soars. But that's surely outweighed by the fact that Herbalife is a client and they want more business. Also, if Herbalife goes to zero, as Bill Ackman keeps promising, then Merrill will make a huge paper profit on this trade -- but share buybacks near insolvency tend to be treated with suspicion, as Ackman has mentioned in his threatening correspondence with Herbalife's board, which might put Merrill's profits at risk.

To contact the writer of this article: Matt Levine at mlevine51@bloomberg.net.

To contact the editor responsible for this article: Tobin Harshaw at tharshaw@bloomberg.net.