Do Option Prices Reveal Short-Sale Restrictions Impact on Bank’s Stock Prices? The German Case

1. Do Option Prices Reveal Short-Sale Restrictions Impact on Bank’s 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 BaFin’s 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 let’s 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) PctArbt = α0 + α1 · BanPeriodt + A · Controlst + εt, 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, α1 is -0.309, with a standard error estimate of 0.59; • for non-banned stocks, α1 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.