Can the Market Add and Subtract? The 3Com and Palm Absurdity

Most tests of market efficiency are arguments. Someone finds a return pattern, someone else says it is a risk premium, and twenty years later there is still a conference panel about it.

Lamont and Thaler found something different. They found a case where the market was provably, arithmetically wrong, in a way that requires no model, no risk adjustment, and no theory of anything. Just addition.

And then they explained why nobody fixed it, which is the part that actually matters.

The problem: a company worth less than one of its parts

In March 2000, at the absolute peak of the dot-com bubble, the tech company 3Com did an equity carve-out. It sold a small slice of its subsidiary Palm (the maker of the PalmPilot, the hot gadget of the era) to the public in an IPO. 3Com kept the vast majority of Palm.

And here is the crucial fact: 3Com announced in advance that within a matter of months it would distribute its remaining Palm shares to its own shareholders. Specifically, every holder of one 3Com share would receive roughly 1.5 shares of Palm.

So now do the arithmetic, because that is all this requires.

If you own one share of 3Com, you own:

• About 1.5 shares of Palm, which you will physically receive shortly, and
• All the rest of 3Com: its other businesses, its equipment, its customers, and a very large pile of cash.

Therefore, ignoring everything except logic, one share of 3Com must be worth at least 1.5 times the price of a Palm share. The rest of 3Com is a real, profitable business with cash in the bank. Its value cannot be negative. A share of stock cannot be worth less than nothing, because you can always walk away.

So: price of 3Com must be greater than 1.5 times the price of Palm.

What actually happened on the day Palm started trading? Palm's shares went berserk. And 3Com's stock price ended the day below 1.5 times Palm's price.

Read that again. The market was saying that 3Com's stake in Palm alone was worth more than the whole of 3Com. Which means the market was assigning a negative value to everything else in the company: the other businesses, the assets, and the several billion dollars in actual cash sitting in the bank.

The market was pricing a large pile of cash at less than zero.

This is not a subtle mispricing that depends on your discount rate. This is the market failing at subtraction. And it persisted for months, not minutes.

The key idea via analogy: the wallet worth less than the twenty inside it

Imagine a wallet. Everyone can see there is a twenty dollar note inside it, plus some other stuff (a gift card, some coins, an unknown but definitely non-negative amount of value).

The wallet is being sold for eighteen dollars.

You should be able to buy the wallet, take out the twenty, and be up two dollars plus whatever else is in there. Free money, no risk, no forecasting required.

Why doesn't everyone do this until the wallet costs more than twenty? Lamont and Thaler's answer is the whole point of the paper.

The arbitrage requires two legs:

1. Buy 3Com (buy the cheap wallet). Easy. Anyone can buy a stock.
2. Short Palm (sell the expensive contents). Nearly impossible.

To short a stock you must borrow shares from someone who owns them. And in the days after Palm's IPO, only a tiny fraction of Palm's shares were actually floating in the market. Almost all of them were still inside 3Com, unavailable to lend. So the borrow was unavailable, or ruinously expensive. Traders who could find shares to borrow were paying enormous fees for the privilege, sometimes at annualized rates that consumed the entire profit of the trade.

And even for the few who could put it on, there was the noise trader risk that De Long, Shleifer, Summers and Waldmann had described: the mispricing could get worse before it got better. A short seller facing a rising Palm price gets margin calls, and can be forced out of a position that is guaranteed to be correct eventually. Being right is not a defence against being liquidated.

So the arbitrage was blocked. And with the arbitrage blocked, the price of Palm was set by whoever was left: the most optimistic buyers in the market, with no counterweight from the pessimists, because the pessimists had been locked out.

This is the deepest point in the paper, and it deserves its own line. When short selling is constrained, the price does not reflect the average opinion. It reflects the opinion of the most enthusiastic buyer. Everyone who thinks Palm is overpriced simply cannot express that view. Their information never reaches the price. The price becomes a survey of optimists only.

Lamont and Thaler showed this was not a one-off oddity. They documented several other carve-outs in the 1998 to 2000 tech period with the same structure and the same absurdity. It was a pattern, not an accident.

Why it mattered

• It is the cleanest possible refutation of "prices are always right". You cannot argue this one away with a risk model. There is no risk story where cash is worth less than nothing. This is the exhibit you produce when someone tells you the market is efficient because arbitrage forces prices to be correct.
• It proves the limits of arbitrage empirically. Shleifer and Vishny had argued in theory that arbitrage is capital-constrained and risky. Lamont and Thaler produced a case where the profit was arithmetically certain and it still did not get arbitraged away, because of a plumbing problem: you could not borrow the shares. Theory confirmed, in the most vivid way possible.
• It made short-sale constraints a central topic. After this, "how hard is it to short?" became a standard question about any anomaly. If a mispricing lives in stocks that are expensive or impossible to short, it can survive indefinitely, and a whole literature (on short interest, borrow fees, and overpricing) grew from this insight.
• It has a lovely implication for bubbles. If pessimists cannot short, then during a mania the price reflects only the believers. The bubble is not evidence that everyone believed. It is evidence that only the believers could trade.

The honest limitations

• It is a small number of extreme cases. A handful of tech carve-outs during the most deranged market episode in modern history. That is a spectacular demonstration, but it is not a broad statistical fact about markets in general. Efficiency defenders can quite reasonably say: yes, and how much capital was actually mispriced, in the scheme of things?
• The distribution was not literally guaranteed. 3Com's plan to distribute the Palm shares was contingent on a favourable tax ruling from the IRS. It was highly likely, not certain. That sliver of uncertainty is what a determined critic will point at, and it is technically a real risk, though nothing like large enough to justify a negative valuation on billions in cash.
• The trade was, in fact, unprofitable to attempt for most people. This is the paper's darkest joke. It identifies a guaranteed arbitrage that you could not have executed. That is a lesson about markets, not a trading strategy, and anyone who reads it as the latter has misunderstood.
• It does not tell you how common this is. The frightening question is: how many smaller, less visible mispricings persist right now for exactly the same reason, in the vast number of stocks that are hard to borrow? The paper implies "probably a lot" and cannot prove it.

The one-line takeaway

Lamont and Thaler documented a market that valued 3Com's stake in Palm at more than all of 3Com, implying the rest of the company plus billions in cash was worth less than zero, and showed the absurdity survived for months because you could not borrow Palm shares to short, which means a price is only as sane as the arbitrage that is allowed to police it.