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, 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)+CP, 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 > 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 < 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 > S*. 1,520 in the pre-event sample and 101 in the post-event sample. Violation 2: S < 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)PctArb t = α 0 + α 1 · BanPeriod t + A · Controls t + ε t, where PctArb t is the proportion of apparent arbitrage opportunities due to violation 1 during a day t; BanPeriod t is a dummy variable, equal to one on and after September 22, 2008; Controls t is a set of explanatory variables to capture non linear relations. We find the following: for banned stocks, α 1 is , with a standard error estimate of 0.59; for non-banned stocks, α 1 is 0.176, with a standard error estimate of 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.