Research on the Limits of Arbitrage
Collette Endowed Chair of Financial Services and Professor
Louisiana State University
Prepared for Presentation at
University of Vaasa, Finland
Limited Arbitrage and Short Sales Restrictions: Evidence from
the Option Markets
by Ofek, Richardson, and Whitelaw, 2002, JFE
Law of one price: Two assets with the same payoffs
should have the same price.
If this restriction is violated, then at least two
conditions must be met.
1. there must be some limits to arbitrage.
2. there must be a reason why these assets have diverging
prices in the first place.
The goal of this paper is to analyze the impact of
these two conditions under put-call parity.
For European options on non-dividend paying
stocks, S=PV(K) +C-P.
For American options, the put will be more valuable
because at every point in time there is positive
probability of early exercise, implying S>=PV(K)+C-
With an early exercise premium, EEP, it can be
rewritten as S=PV(K)+C-P+EEP.
Investigate violations of the modified put-call
parity, S=PV(K)+C-P+EEP, and relate them
to the following conditions:
(i) limited arbitrage via either short sales
restrictions or transaction costs, and
(ii) potential periods of mispricing.
expected maturity effects,
potential structural shifts in mispricing,
forecastability of future returns.
Short Sales Restrictions
Two reasons why short sales restrictions exist:
Investors are either unwilling to sell stock short or find it too
difficult to do so.
Because of the Investment Company Act of 1940, mutual fund
managers are unwilling to short stock (Chen, Hong, and Stein
Almazan, Brown, Carlson, and Chapman (2002) show
only a small fraction of mutual funds short stocks; and
greater mispricing occurs when mutual funds are absent from the
Short Sales Restrictions (continued)
It is difficult to short stocks on a large scale.
To short a stock, the investor must be able to borrow it.
Not many shares available.
There is no guarantee that the short position will not
get called through either the lender demanding the
stock be returned or a margin call.
no guarantee that the investor will be able to re-short the
Short Sales Restrictions (continued)
When an investor shorts a stock, she places a cash deposit
equal to the proceeds of the shorted stock.
That deposit carries an interest rate referred to as the rebate rate.
One way to measure the difficulty in short selling is to compare
the rebate rate on a stock against the median rebate rate.
The rebate rate spread can be used as the actual cost of
borrowing a stock.
It can also be used as a signal of the difficulty of shorting.
Violations of the put-call parity are asymmetric in the
direction of short sales restrictions.
For example, after shorting costs, 13.63% of stock prices
still exceed the upper bound implied by the option market,
while only 4.36% are below the lower bound.
The mean difference between the option-implied
stock price and the actual stock price for these
violations is 2.71%.
Both the probability and magnitude of the
violations can be linked directly to the
magnitude of the rebate rate.
A one standard deviation decrease in the rebate
rate spread implies a 0.67% increase in the
deviation between the prices in the stock and
The results suggest that the relative prices of similar assets with
identical payoffs can deviate from each other when arbitrage is not
What possible explanations exist?
If markets are segmented such that the marginal investors across these
markets are different, it is possible that prices can differ.
In the absence of some friction that prevents trading in both markets, this
segmentation will not be rational.
Behavioral finance argues that prices can deviate from fundamental
values because a significant part of the investor class is irrational.
Irrational investors look to market sentiment or are driven by
psychological (rather than financial) motivations.
In the presence of limited arbitrage, there is no immediate
mechanism for correcting the resulting mispricings.
If the equity and options markets are segmented, i.e., have
different investors, then mispricing in the equity market do not
necessarily carry through to the options market.
In other words, irrational investors do not use the options market.
Consider a framework in which the stock and options markets are
segmented and the equity markets are “less rational” than the options
This framework allows us to interpret the price differences as mispricing
in the equity markets.
The framework also generates predictions about the relation between
put-call parity violations, short sales constraints, and future returns.
Stock returns are expected to fall over the life of the options conditional
on a put-call parity violation and/or a negative rebate rate spread.
Conditional on a rebate rate spread of less than -0.5%, the mean
excess return over the life of the option is -9.96%, versus 0.70%
for zero rebate rate stocks.
Conditioning on put-call parity violations of greater than 1.0%, the
mean excess returns over the life of the option is -4.49% versus
0.13% for violations of less than zero.
Combining these signals produces an average excess returns of
-12.57%, which illustrates that the rebate rate and the violation
contain independent information about future stock price
Put-call parity violations pose considerable problems for rational asset
The results support the foundations of behavioral finance,
i.e., there are enough irrational investors to matter for pricing assets.
The forces of arbitrage do appear to limit the relative mispricing of
i.e., there is clear relation between arbitrage constraints (e.g., transaction
costs and rebate rates) and the level of mispricing.
It is a puzzle why any investor would ever wish to purchase poorly
Limited Arbitrage in Equity Markets
by Mitchell, Pulvino, and Stafford, 2002,JF
Consider the situation where a firm’s market
value is less than the value of its ownership
stake in a publicly traded subsidiary.
Commonly referred to as “negative stub value.”
It can arise following equity carve out of
subsidiaries or from partial acquisition of a public
Research Design and Findings
Examine 82 situations with negative stub values.
The link between parent and subsidiary firms disappears without
convergence of the arbitrage spread 30 percent of the time.
This happens when a corporate event permanently alters the
relative mispricing in a manner that is detrimental to the
For example, going bankrupt.
• Negative stub values are not risk-free arbitrage opportunities.
There is substantial variability in the time to termination.
The average time between the initial mispricing and a termination
event is 236 days, the median is 92 days, the minimum is 1 day,
and the maximum is 2,796 days.
As a result of this uncertainty, even if convergence is eventually
achieved, the negative-stub-value investment often
underperforms the risk-free rate.
Discouraging investments by arbitrageurs who are uncertain of
the time to convergence.
There are costs that limit arbitrage in equity
Uncertainty about the distribution of returns
and characteristics of risks limits arbitrage.
The Limits of Arbitrage
by Shleifer and Vishny, 1997, JF
Textbook arbitrage in financial markets
requires no capital and entails no risk.
In reality, almost all arbitrage requires capital,
and is typically risky.
The absolute and relative values of different
securities are hard to calculate.
Using other people’s capital.
Facing the problems of possible interim liquidations before
Uncertain the horizon over which mispricing is eliminated.
Avoiding extremely volatile markets.
High volatility could make arbitrage less attractive if expected
alpha does not increase in proportion to volatility.
They may prefer bond markets over equity markets.
Anomalies in financial markets are likely to
appear, and why arbitrage fails to eliminate