He looks sad about it. Photographer: Scott Eells/Bloomberg
He looks sad about it. Photographer: Scott Eells/Bloomberg

Did news of Bill Ackman's $4 billion of Allergan stock purchases leak into the market? Yep! The Wall Street Journal has the gory details -- "Even after stripping out Mr. Ackman's buying, the volume of stock trading in Allergan during the 10-day period before Monday's announcement was 86% higher than its average over the previous year" -- but you don't even need to look at volume; price will do:

Lookit that line go up! Pretty easy to conclude that someone was buying.

Now, the fact that people saw buying and so bought more doesn't necessarily mean that they knew that Bill Ackman was buying, or that it was part of planned takeover bid:

There is no indication investors were tipped off about Pershing's and Valeant's offer. And other traders could have bought based on the higher volume. But such a significant surge in trading suggests that information about the potential buyout bid could have leaked to other investors, analysts said.

So maybe Ackman called his hedge fund buddies and tipped them off to buy some Allergan. (Extremely unlikely.1 ) Or maybe the banks that he hired to accumulate his shares front-ran him a bit, or tipped off their buddies that there was a big buyer. (More likely, surely, though hard to know how much more likely.2 ) Or maybe traders who were paying attention saw the price move on a lot of volume, figured something was coming, and played the momentum.

Or maybe high-frequency traders electronically front-ran Ackman's orders, using algorithms and colocation and direct data feeds to see that he was buying a lot of stock, and then running to other markets ahead of him to push up the price and sell stock back to him at a profit. That, if you haven't been paying attention, is the plot of "Flash Boys." Really, that's the story: Big hedge-fund managers such as David Einhorn and Bill Ackman noticed that, when they wanted to buy a lot of stock, the price of the stock would get pushed up and they would have to pay more than they wanted to.

Whoever did it -- tippees, momentum-seeking tape-reading day traders, or HFT algorithms -- someone traded ahead of Ackman here. On Feb. 24, the day before Ackman started buying, Allergan closed at $124.50. On April 10, the day before he crossed the 5 percent Schedule 13D disclosure threshold and started his "rapid accumulation program" of buying 35 percent of volume, Allergan closed at $116.63. On April 21, the day he finished (and the day before he disclosed his position), it closed at $142. Ackman's average purchase price was $129.28. So he paid an 11 percent premium to the pre-rapid-accumulation price -- but he also bought at a 9 percent discount to the post-rapid accumulation price.3

A fun question is, what price should he have bought at?

One intuition here is: Everyone should own their own order information. If a stock's market price is $120, I should be able to buy a reasonable amount of that stock at $120. If I want to buy a lot of that stock, I will of course push up the price, but it doesn't seem fair for other people to figure out that I want to buy a lot, run ahead of me to buy it, and then sell it back to me at a profit. Particularly if I'm buying it for a good reason, like that I've done a lot of research or have activist or takeover ideas that will benefit all shareholders.4 You want to encourage people to buy stocks for good reasons.

This is the "Flash Boys" intuition, and while it's most evident in colocated high-frequency algorithmic latency arbitrage, you don't need to use any of those words to have the intuition. The momentum-seeking day-trader who saw a lot of volume in Allergan, figured something was up, bought 100 shares in his E*Trade account at $125, and then sold them to Bill Ackman at $130 three days later, did something just as socially useless and predatory as any high-frequency trading firm. He's just not as good at it.

The other intuition is: Everyone should know everyone's order information. If Bill Ackman is accumulating stock, he shouldn't have 10 days to keep his intentions secret. He should tell everyone immediately, because that way they can make an informed judgment about whether or not to sell to him. The people who sold to Ackman at $125 are obviously annoyed that the stock is now in the $160s, and if they'd had complete information they would have behaved differently. Why should Ackman be allowed to buy them out cheap by keeping his intentions secret? Even if it's not insider trading (it's not), it's surely at least a little dicey?

This is the Schedule 13D disclosure intuition: Ackman did his rapid buying over the 10 days between when he accumulated five percent of Allergan's stock, triggering a Schedule 13D disclosure requirement, and when he actually had to make the disclosure. Many people find this 10-day delay unacceptable, as it lets activists such as Ackman accumulate additional stock without letting public investors know. As my Bloomberg View colleague Jonathan Weil puts it: "If the information is truly material, and the investing public has a right to know what a large blockholder's intentions are, why make the public wait 10 days to find out?"

It's worth noticing that these intuitions are opposite intuitions. If you think that Bill Ackman is a crook and an insider trader because he bought a big chunk of Allergan without disclosing what he was up to, you should be happy that other people traded ahead of him, pushing up the price so that public shareholders who sold to him got, on average, a higher price. If you think that high-frequency traders are predators who abuse order information for socially harmful reasons, then you should applaud investors who take steps to keep their order information to themselves.

So which one is right? Neither, of course; the answer is somewhere in the middle. What you want is an optimal amount of inefficiency, in which investors have some right to keep their order information private, to incentivize research and activism and takeover bids and other value-enhancing strategies, but in which some information on trading patterns is public, to make prices more efficient.5

By the way, yes, "to make prices more efficient." Lots of people don't believe that high-frequency trading makes prices more efficient, or that synchronizing prices is actually a good thing, but Allergan is a good example of how it might be. The people or algorithms who traded alongside Ackman's buying pushed up the market price, causing it to better (though not perfectly) reflect Ackman's intentions.6 This means that the public retail shareholders who sold Allergan on April 17 to pay their taxes or whatever got a "fairer" price -- a higher one, closer to the post-disclosure price -- than they would have if no one had been buying alongside Ackman. Is that good? Well, it's good for them, bad for Ackman. The more accurately prices reflect the intentions of big buyers, the less likely it is that uninformed retail investors will get picked off by those big buyers.7

Are equity markets fair? Nope! Some people have faster computers than other people. Some people do better research than other people. And some people buy 9.7 percent of a company quietly in the market before announcing an offer to buy the rest of the company at a big premium. You can quite reasonably get upset about the unfairness of prices reacting too quickly to demand, or you can quite reasonably get upset at the unfairness of prices reacting too slowly to demand. As long as you don't get upset about both.

1 One, because Ackman is less of a fan of those leaks than some other activists are, and has gone after other investors for employing them. But, two, because here that would be illegal insider trading: Ackman had a confidentiality agreement with Valeant, and so his disclosing his buying to his buddies would be a breach of his duty of confidentiality and expose him, and them, to liability. This is distinct from the usual case where an activist is buying shares on his own and can do with his information as he likes.

2 By the way, Ackman bought most of his shares via over-the-counter call options, for antitrust-filing reasons. The Journal:

Mr. Ackman disclosed trading in over-the-counter Allergan options, which are bilateral contracts with Wall Street banks. It isn't clear what role Pershing's trading had in Allergan's exchange-traded options volume, which tripled on Monday.

I will tell you: No role. Active Allergan options have strike prices like $155, not $1.20. Ackman's options are 99 percent in-the-money; there's no optionality at all. They have a delta of around 100.00 percent:

Source: Bloomberg
Source: Bloomberg

You don't hedge a delta-one over-the-counter option by buying listed options. You hedge it by buying stock. Ackman hired dealers to buy stock for him, but the contracts were phrased as options for regulatory purposes. That's all. No optionality. Just stock. So in the rest of the text I say things like "Ackman bought stock," and you can understand something like "Ackman engaged dealers to buy stock on a daily agency pricing basis and then write him delta-one call options on that stock."

Extra credit time: If you are an options dealer, and you sell Bill Ackman those options, how do you hedge? I just told you that you hedge by buying stock, but how much stock? The math is straightforward enough: These options are delta-one, so you buy one share of stock for every share underlying the option. The options are stock, so you hedge them with the same amount of stock.

But! You are a trader, not a robot. When your model tells you that an option has a 70 percent delta, you sometimes hedge with 65 or 75 deltas because you have a view on the stock. Similarly, here, your model tells you that you've sold delta-one options on 25 million shares, give or take (the rest is forwards and physical stock), so you should buy 25 million shares to hedge. But who is to stop you from hedging by buying 20 million shares, or 30 million?

Buying 20 million is super-dumb. Buying 30 million, to hedge the 25 million options that you've sold Bill Ackman right before he announces a big stake in a company through a special vehicle, is ... what? Smart? (You'd have made $100 million or so.) Super-illegal front-running and/or insider trading? Surely the latter, but I've never quite been able to figure out why. There is no general law that you have to hedge an option with the mathematically correct delta, is there?

3 And like a 20+ percent discount to the post-announcing-acquisition-proposal price.

4 Because, remember: 9.7 percent of Allergan's shareholders sold to Ackman "too low," but that means that 90.3 percent of them didn't, and are now billions of dollars richer because of Ackman's and Valeant's efforts.

5 You might ask where current regulators come out on this question. I submit to you that (1) the Securities and Exchange Commission seems pretty concerned about the 10-day window for 13D disclosure, and (2) the SEC seems rather notably unconcerned with high-frequency trading, which is why there's a market opening for Eric Schneiderman (and Michael Lewis!). This suggests that the SEC would prefer an equilibrium with more complete disclosure of order information, which would generally tend to benefit uninformed investors at the expense of informed ones. This is consistent with my hypothesis that the SEC is sub-optimally focused on retail investors.

6 And, really, what is an efficient-market price for Allergan? I submit to you that that's not now a question of Allergan's expected cash flows; it's a question of whether it will be acquired by Valeant and Ackman.

7 And, on the other hand, the less incentive big buyers will have to do research and buy lots of stock. That's the tradeoff.

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.