According to the law of one price, identical assets should have identical prices. Driving this law is arbitrage, in which an investor buys and sells the same security for two different prices to make a profit. In a well functioning capital market, arbitrage prevents the law of one price from being broken, and in fact, violations of the law are rarely seen.

Consider the investor who buys an ounce of gold in London for $100 and sells the gold in New York for $150, locking in a profit of $50. This is an example of arbitrage. As a result, the price in London should be driven up, and the price in New York should be driven down so that arbitrage is no longer possible.

During the recent boom in technology stocks, several cases emerged where the law of one price was violated, and high transaction costs limited arbitrage, allowing the mispricing to persist.

Two University of Chicago Graduate School of Business professors, Owen A. Lamont and Richard H. Thaler, investigate these unusual cases in their paper, "Can the Market Add and Subtract? Mispricing in Tech Stock Carve-Outs."

Their study focuses on recent equity carve-outs in technology stocks in which the parent company has stated its intention to spin-off its remaining shares. Lamont and Thaler examine several cases of mispriced stocks and document the precise market friction that allows prices to be wrong, concluding that two things are necessary for mispricing: trading costs and irrational investors.

Not One Price But Two

Also known as a partial public offering, an equity carve-out is defined as an IPO for shares (typically a minority stake) in a subsidiary company. A spin-off occurs when the parent firm gives remaining shares in the subsidiary to the parent's shareholders.

The most prominent example of mispricing in this study is the case of Palm and 3Com. Palm, which makes hand-held computers, was owned by 3Com, a profitable company selling computer network systems and services. On March 2, 2000, 3Com sold 5 percent of its stake in Palm to the public through an IPO for Palm. Pending IRS approval, 3Com planned to spin off its remaining shares of Palm to 3Com's shareholders before the end of the year. 3Com shareholders would receive about 1.5 shares of Palm for every share of 3Com that they owned, thus the price of 3Com should have been 1.5 times that of Palm. Investors could therefore buy shares of Palm directly or by buying shares embedded within shares of 3Com. Given 3Com's other profitable business assets, it was expected that 3Com's price would also be well above 1.5 times that of Palm.

The day before the Palm IPO, the price of 3Com closed at $104.13 per share. After the first day of trading, Palm closed at $95.06 per share, implying that the price of 3Com should have jumped to at least $145. Instead, 3Com fell to $81.81.

The day after the IPO, the mispricing of Palm was noted by the Wall Street Journal and the New York Times. The nature of the mispricing was easy to see, yet it persisted for months.

In cases of equity carve-outs, a negative "stub value" indicates an extreme case of mispricing. The stub value represents the implied stand-alone value of the parent company's assets without the subsidiary, a projection of what the company will be worth after it distributes these shares.

In the case of Palm and 3Com, after the first day of trading, the stub value of 3Com, representing all non-Palm assets and businesses, was estimated to be negative $63, a total of negative $22 billion. Since stock prices can never fall below zero, a negative stub value is highly unusual.

To study this and other cases of mispricing, Lamont and Thaler built a sample of all equity carve-outs from April 1985 to May 2000 using a list from Securities Data Corporation. They combined this list with information on intended spin-offs from the Securities and Exchange Commission's Edgar database. The final sample contained 18 issues from April 1996 to August 2000.

In order to focus on cases of clear violations of the law of one price, they looked for potential cases of negative stubs. Besides Palm, they found five other cases of unambiguously negative stubs in their sample, all technology stocks: UBID, Retek, PFSWeb, Xpedior, and Stratos Lightwave. While the number of negative stubs is not significant, even a single case raises important questions about market efficiency. The fact that five other such cases of mispricing existed indicates that the highly publicized Palm example was not unique.

The time pattern of these six negative stubs suggests that the stubs generally start negative, gradually get closer to zero, and eventually become positive. This implies that market forces act to correct the mispricing, but do so slowly, reflecting the sluggish functioning of the market for lending stocks.

Problems with Shorting

To determine ways that an investor could profit from the mispricing, Lamont and Thaler tested an investment strategy of buying the parent and shorting the subsidiary, which on paper yielded high returns with low risk for these six cases.

In order to short a stock, an investor bets that a stock will go down in value and looks for an institution or individual willing to lend shares of this stock. The investor then borrows the shares, sells them to another individual, and later buys the shares back at a hopefully lower price to cover the short. Buying the shares back at this lower price yields a profit for the initial investor.

While these negative stub situations present attractive arbitrage opportunities, the high returns Lamont and Thaler calculated are difficult to realize due to problems with shorting the subsidiary.

The chief obstacles to arbitrage in these cases were short sale constraints, which make shorting very costly or impossible. In some cases, institutions or individuals may be unwilling to lend their shares to short sellers, the cost of borrowing the share may be too high, or the demand for shares may exceed what the market can supply, creating a price which is too high.

Many investors were interested in selling the subsidiaries short for the six cases in question. In the case of Palm, at the peak level of short interest, short sales were 147.6 percent, indicating that more than all floating shares had been sold short. Given that the typical stock has very little short interest, it is extremely unusual that more than 100 percent of the float was shorted.

As the supply of shares grows via short sales, the stub value gets more positive, indicating less demand from irrational investors, and causing the subsidiary to fall relative to the parent.

Next, Lamont and Thaler studied the options market for more evidence on how high shorting costs eliminate exploitable arbitrage opportunities. Options can make shorting easier, both because options can be a cheaper way of obtaining a short position and because options allow short-sale constrained investors to trade with other investors who have better access to shorting.

In a well-functioning options market, one expects to observe put-call parity. A put is the right to sell a stock at a certain price, and a call is the right to buy a stock at a certain price. These two rights together allow an investor to reproduce the stock itself, synthetically creating a security identical to Palm, for example. Under the law of one price, this bundle of securities that mimics Palm should have the same price as Palm.

"The concept that a bundle of securities should have exactly same price as whatever it replicates is the most fundamental thing in all of finance-the law of one price," says Lamont.

The options on Palm display unusually large violations of put-call parity, with puts about twice as expensive as calls. Calculating the implied price of synthetic securities, Lamont and Thaler found that on March 16, 2000, the price of the synthetic short was about $39.12, far below the actual trading price of Palm, which was $55.25 at the time. This difference in prices indicates a significant violation of the law of one price, since the synthetic security was worth 29 percent less than the actual security.

The options prices confirm that shorting Palm was either incredibly expensive or that there was a large excess demand for borrowing Palm shares that could not be met by the market.

"Given that arbitrage cannot correct the mispricing, why would anyone buy the overpriced security?" write Lamont and Thaler. One plausible explanation is that the type of investor buying the overpriced stock is ignorant about the options market and unaware of the cheaper alternative. In looking at who buys the expensive shares and how long they hold them, Lamont and Thaler find numerous patterns consistent with irrational investors.

Larger Problems for the Market?

While Lamont and Thaler do not generalize that these overpriced stocks reflect problems with all stock prices, their evidence casts doubt on the claim that market prices reflect fundamental values because these cases should have been easy for the market to get right. Their analysis offers evidence that arbitrage doesn't always enforce rational pricing.

If irrational investors are willing to buy Palm at an unrealistically high price, and rational but risk averse investors are unwilling or unable to sell enough shares short, then two inconsistent prices can co-exist.

One law of economics that still holds is the law of supply and demand, namely that prices are set where the number of shares demanded equals the number of shares supplied. If optimists are willing to bid up the shares of some faddish stocks, and not enough courageous investors are willing to meet that demand by selling short, then optimists will set the price.

"Regarding tech stocks in general, I don't think that there were enough pessimists shorting the NASDAQ in March 2000," says Lamont. "The short sale constraints that applied to Palm were not true for the entire NASDAQ. It would have been easy to short the whole market with futures, for example, but basically no one shorts. This means that sometimes the optimists go crazy, and things get overpriced."

Lamont adds, "Whether you are an executive doing a takeover or buying the stock for your own account, if stocks can get overpriced, the key to success is identifying what's overpriced and avoiding it."

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