Mispriced Stocks Break the Rules of Efficient Markets
Research by Richard H. Thaler
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
During the late 1990s 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. University of Chicago Graduate School of Business
professor Richard H. Thaler and Owen A. Lamont of the Yale
School of Management investigate these unusual cases in their
paper, "Can the Market Add and Subtract? Mispricing in
Tech Stock Carve-Outs."
The study focuses on recent equity carve-outs in technology
stocks in which the parent company stated its intention to
spin-off its remaining shares. The authors 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
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
The most prominent example of mispricing in the 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 buy 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
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, the authors
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
In order to focus on cases of clear violations of the law
of one price, the authors 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, the authors 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 the authors 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
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
Next, the authors 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
"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, the
authors 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
Thaler and Lamont. 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, the authors find numerous patterns consistent with
Larger Problems for the Market?
While the authors 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."