Market Add and Subtract? Mispriced Stocks Break the
Rules of Efficient Markets
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 longer possible.
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 ,
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
Not One Price
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 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 per share.
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
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
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 2000.
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.
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
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 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, 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 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, 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
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.
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
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."