Do Option Prices Reveal Short-Sale Restrictions Impact on Bank

1
Do Option Prices Reveal Short-Sale Restrictions
Impact on Banks Stock Prices?The German Case

• Stefano Corradin
• Marco Lo Duca
• Cristina Sommacampagna
• European Central Bank

() The views and opinions expressed in this
presentation and in the related chapter are those
of the authors only, not of the European Central
Bank.
2
Reading Questions

• Can restrictions on short selling in the spot
  market be circumvented, for example by accessing
  the option market?
• If so, how can investors replicate the price
  behaviour of stocks in the option market?
• How can restrictions on short selling affect the
  stock and option market, and how can such effects
  be tested?
• What is the difference between covered and naked
  short selling?
• Can we find evidence of a decline in market
  efficiency for the stocks affected by the naked
  short-selling ban introduced by BaFin on
  September 22, 2008?

3
Facts on Short-Selling

• On September 18, 2008, the U.K. Financial
  Services Authority (F.S.A.) blocked covered short
  sales of 34 financial stocks.
• On the following day, the U.S. Securities and
  Exchange Commission (S.E.C.) blocked the covered
  short sale of 799 financial stocks.
• Some evidence of a consequent decline in market
  efficiency for the affected stocks in U.K. and
  U.S. has been documented in the literature.
• Following the F.S.A. and the S.E.C., European
  regulators introduced rules prohibiting mainly
  the naked short-selling of financial stocks
• On September 22, 2008, the German federal
  financial supervisory authority (BaFin)
  introduced a naked short-selling ban on eleven
  financial stocks.
• Covered short-selling is the practice of selling
  stocks without owning them but rather borrowing
  them, hoping to buy them later at a lower price,
  thus making a profit.
• Naked short-selling is the practice of selling
  stocks without having the stock nor a lending
  party, hoping to find it later.

4
What we do

• This chapter examines how the naked short-selling
  ban introduced by the BaFin affected stock prices
  of financial companies.
• We replicate the price behaviour of stocks by
  using put-call parity, based on tick trading data
  on eleven major European banks traded on the
  German stock exchange.
• We assess whether the price, implied in the
  synthetic position replicating the price of the
  underlying stock, was lower than the market stock
  price, where restrictions on naked short-selling
  made it difficult to short-sell the stock itself.
• We count the number of put-call parity violations
  before and after the introduction of the naked
  short-selling ban.
• We find no evidence that the naked short-selling
  restriction affected stock or option prices of
  the considered banks, as the number of put-call
  parity violations pre and post ban and comparing
  ban subject stocks to non-subject stocks is not
  statistically significant.

5
Data

• We focus on intra-day tick data of stock and
  American call and put option transactions for
  eleven major European banks, traded on Deutsche
  Borse over the period July 5, 2007 November 28,
  2008.
• The dataset includes four of the eleven European
  banks subject to the BaFins restriction
  Commerzbank, Deutsche Bank, Deutsche Postbank and
  Hypo Real Estate Holding.
• The other banks are BNP Paribas, Credit Suisse,
  Credite Agricole, Fortis, UBS, Unicredito
  Italiano and Société Générale.
• For each traded call, we identify the put, with
  same strike price and same time-to-maturity,
  traded within a millisecond if no match is
  found, a time frame of one second is considered,
  then of one minute, ten minutes or one hour.
• We restrict the sample to options with exercise
  price within 20 of the matched market stock
  price, and with 5 to 90 days time-to-maturity.
• Eventually, 27,338 pairs of option prices are
  used, with the corresponding stock price.

6
Methodology (I)

• Under the condition of no arbitrage, it is well
  known that, for European options on non-paying
  dividend stocks, put-call parity holds
• (1) S PV(K) C P,
• where
• S is the underlying stock price
• PV(K) is the present value of the strike price K
• C and P are the corresponding call and put price,
  of options with strike K and equal maturity.
• Let us define S as the stock price implied by
  the put-call parity, S PV(K)C-P, and lets
  assume the other variables values are as
  observed on the market.
• As the observed prices are of American options,
  we calculate the early exercise premium to obtain
  the corresponding European price.
• Because we assume that no dividend is paid to the
  underlying stock, it is only necessary to derive
  the early exercise premium for the put contract.

7
Methodology (II)

• If S is different from the stock price observed
  on the market, Eq. (1) fails and two violations,
  or categories of arbitrage opportunity, can be
  identified
• Violation 1 S gt S.
• One could arbitrage by selling the stock S and
  buying the synthetic position S.
• Because short-sales on the stock are banned or
  shorting the underlying stock might be costly, an
  arbitrage does not exist that leads to
  convergence of the two values.
• Violation 2 S lt S.
• One could arbitrage by buying the stock S and
  selling the synthetic position S.
• We are interested in violation 1.
• To allow for testing of the naked short-selling
  ban, the sample, of 27,338 pairs of option
  prices, with the corresponding stock price, is
  split in a pre-ban sample, July 5, 2007
  September 22, 2008, and a post-ban sample,
  September 22, 2008 November 28, 2008.

8
Results (I)

• The table in the next slide shows the number of
  times Violation 1 and 2 are observed, by
  percentage of difference between S and S. The
  count for the post-event sample is reported in
  parenthesis.
• In the great majority of cases, Eq. (1) is not
  violated and there are no arbitrage
  opportunities
• Violation 1 S gt S.
• 1,520 in the pre-event sample and 101 in the
  post-event sample.
• Violation 2 S lt S.
• 285 in the pre-event sample and 165 in the
  post-event sample.
• A larger portion of stock trades leads to
  apparent arbitrage opportunities due to Violation
  1 than to Violation 2.
• These apparent arbitrage opportunities do not
  exclusively belong to the financial companies
  subject to the naked short-sale ban, nor to the
  post ban period.

9
Results (II)
10
Model Estimation

• We estimate a Probit model to examine the
  marginal impact of the short sale ban on the
  frequency of apparent arbitrage opportunities.
• We separately estimate the following model for
  banned and non-banned stocks
• (2) PctArbt a0 a1 BanPeriodt A
  Controlst et,
• where
• PctArbt is the proportion of apparent arbitrage
  opportunities due to violation 1 during a day t
• BanPeriodt is a dummy variable, equal to one on
  and after September 22, 2008
• Controlst is a set of explanatory variables to
  capture non linear relations.
• We find the following
• for banned stocks, a1 is -0.309, with a standard
  error estimate of 0.59
• for non-banned stocks, a1 is 0.176, with a
  standard error estimate of 0.911.
• Neither coefficient of the BanPeriod variable is
  statistically significant.

11
Conclusion

• Following the introduction of short-selling bans,
  some evidence of a consequent decline in market
  efficiency for the affected stocks in U.K. and
  U.S. has been documented in the literature.
• We find no evidence that the short-selling
  restrictions, introduced on September 22, 2008 in
  the German market, affected stock prices and
  option prices for four of the eleven major
  European banks subject to the ban.
• We argue that this result depends on the type of
  restrictions introduced
• BaFin introduced a ban for naked short-selling on
  financial stocks
• F.S.A. and S.E.C. introduced a ban for both
  covered and naked short-selling.
• Prohibiting naked short-selling may make the
  short-selling practice more costly, but it is a
  less severe restriction than prohibiting covered
  short-selling.
• Based on our analysis, the impact of the naked
  short-selling ban on the German market efficiency
  was minimal.