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Research in the Limits of Arbitrage


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									Research on the Limits of Arbitrage

   J.C. Lin
    Collette Endowed Chair of Financial Services and Professor

    Louisiana State University

   Prepared for Presentation at
    University of Vaasa, Finland

   October 2004
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.
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.
Research Design

   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
    (2002, JFE).

   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%.
Findings (continued)

   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
        options markets.
Possible Explanations
   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.
Behavioral Finance
   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.
A Framework
   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.
Forecasting Returns
   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
    pricing models.

   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
    performing stocks.

   Future research??
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
        traded firm.
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
      arbitrageur’s profits.
     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.

   Future research??
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.
Professional Arbitrageurs
   Using other people’s capital.
     Facing the problems of possible interim liquidations before
      mispricing disappears.
     Uncertain the horizon over which mispricing is eliminated.

   Risk averse.

       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

   Future research??

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