L’indice CAC40 est la première chose à laquelle on pense lorsqu’on parle de bourse en France. Cependant il n’est pas négociable. C’est pourquoi sont apparus des contrats dérivés comme le contrat future FCE dont le sous-jacent est le CAC40 qui peuvent être achetés et vendus. Leurs valeurs sont très proches mais non égales. Quel est donc la relation qui lie le contrat FCE au CAC40 ? A l’aide de données téléchargeables quotidiennement sur Internet et accessibles à tous une réponse va être apportée. Dans une première partie nous présentons le contrat à terme dérivé du CAC40, les raisons de le « trader » et le comparons aux autres contrats future dérivés d’indices boursiers dans le monde. Nous étudions ensuite la relation FCE/CAC40 en terme d’efficience informationnelle. Pour cela nous allons étudier différentes notions de base et tenter de les modéliser. Enfin dans une dernière partie nous nous intéressons à cette même relation d’un point de vue microstructure, en étudiant en particulier des variables non prix (volume et position ouverte), et la volatilité. Nous allons enfin tenter d’apporter une modélisation de la volatilité en fonction de ces variables. / The CAC 40 index is the first thing that comes to mind when talking about financial markets. However it is not negotiable. Therefore appeared derivative contracts such as futures contract FCE whose underlying is the CAC40 index which can be bought and sold. Their values are very close but not equal. So what is the relationship between the FCE contract and the CAC40? Using daily downloadable data on the Internet and accessible to everyone, answers will be given. In the first part we present the future contracts derived from the CAC40, the reasons to trade it, and we compare it to other stock index futures in the world. We then study the relationship FCE / CAC40 in terms of informational efficiency. For that we will study different notions of basis and try to model them. Finally in the last part we are interested in the same relationship but with a microstructure point of view, studying in particular non-price variables: volume and open interest, and volatility. Finally, we will try to modelise volatility with these variables.

Most of Indiana corn and soybeans are placed into storage at harvest time to be delivered to market at a later date. Indiana farmers have many options regarding how and when to sell this grain. The present research addresses the issue of how to maximize the expected net returns to storage. The three central questions are: (i) which crop produces better returns? (ii) should the grain be stored unpriced or hedged using futures? and (iii) how long should grain be stored? Expected net returns for corn were maximized by storing unpriced until spring. However, unpriced corn storage provided positive returns less frequently than storage hedging. Unpriced soybean storage was better on average, and also produced positive returns more frequently than storage hedging. Returns were higher for soybeans than corn.

Yes / This paper examines the existence of dynamic spillover effects across petroleum based commodities and among spot-futures volatilities, trading volume and open interest. Realized volatilities of spot-futures markets are used as inputs to estimate a VAR model following Diebold and Yilmaz (2014, 2015) and distinguish dynamic spillovers in total and net effects. Results reveal the existence of large and time-varying spillovers among the spot-futures volatilities and across petroleum-based commodities when examined pairwise. In addition, speculative pressures, as reflected by futures trading volume, and hedging pressures, as reflected by open interest, are shown to transmit large and persistent spillovers to the spot and futures volatilities of crude oil and heating oil-gasoline markets, respectively.

The first chapter of this dissertation examines the returns to frequent acquirers from emerging markets and analyzes the cross-country variations in cumulative abnormal returns. The sample consists of 5,147 transactions carried out by firms from 17 common and civil-law countries during the period of January 1985 to June 2008. I find that the cumulative abnormal returns decline over the deal order and it is more pronounced in civil-law countries than in common-law countries. There is also evidence that the premiums paid by acquirers from civillaw countries with a first successful acquisition are higher than those from common-law countries. These findings are consistent with agency problems and the hubris hypothesis, first introduced by Roll (1986). The second chapter examines the information links across futures markets in different nations, using Vector Autoregressive (VAR)-Dynamic Conditional Correlation (DCC) model. The data comprise a large set of commodity and financial futures traded in U.S., U.K., China, Japan, Canada, and Brazil during the period from August 1998 to December 2008. The primary finding is that market interactions are relatively high for commodities for which information production generally is more diverse (metal commodities), while moderate for commodities for which information is more concentrated (agricultural commodities). Furthermore, the strength and persistence of interactions among futures markets decline after excluding the most informative markets. These findings indirectly support the breadth of information being a relevant factor in the extent of information linkage. The results also indicate that the dynamic correlation in futures markets is high in most commodity and financial futures if there is a significant bi-directional return and volatility spillover. Additionally, I estimate a market’s contribution to the price discovery process. In general, the market that has a stronger price impact and a stronger volatility spillover tends to be the market that has greater contribution or leadership in price discovery.

Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Management Graduate School of Business Administration University of the Witwatersrand April 2016 / This thesis examined commodity futures on the South African Futures Exchange (SAFEX) from two angles; the investors’ perspective and that of the futures exchange. For the former, the research looked at market inefficiencies and resultant arbitrage opportunities while for the latter, extraordinary market movements are examined by exploring how extreme value analysis (EVA) is ideal for exchange risk management and maintaining market integrity. This broadly leads to four empirical contributions to the literature on commodity futures. Using a variety of time series models, wheat contract anomalies are identified by developing new trading rules whose outcomes are superior to any approach based on chance. Monte Carlo simulation employed in an out-of-sample period after accounting for transaction costs establishes that the trading rules are financially profitable. An examination of information flows across four major markets indicated that the Zhengzhou Commodity Exchange (ZCE) is the most endogenous market, Euronext and the London International Financial Futures Exchange (LIFFE) the most exogenous, while Kansas City Board of Trade (KCBT) is the most influential and sensitive wheat market. SAFEX is a significant receiver of information but does not impact the other markets. Another contribution, analysing maturity effects by incorporating traded volume, change in open interest, and the bid-ask spread while accounting for multicollinearity and seasonality indicates that only wheat supports the so called maturity effect. Lastly, asymmetry is found in long and short positions in SAFEX contracts, and using extreme value theory (EVT) in margin optimization, evidence is found that price limits significantly impact large contract returns. Several implications arise from these results. SAFEX wheat contract inefficiencies could be attractive to speculators. Wheat margins should be higher nearer maturity. Optimizing margins using EVT could reduce trading costs, increase market attractiveness and liquidity while enhancing price discovery. South Africa should increase wheat production since reducing imports will lower vulnerability to adverse price transmission. JEL Classification: C13, C14, C58, G01, G13, G17 Keywords: Futures market; commodities; volatility; seasonality; information flows, margins / MB2016

Die erste Studie analysiert den Einfluss spekulativer Aktivität auf die Renditen und die Volatilität von Edelmetallterminpreisen. Die Ergebnisse zeigen, dass die spekulative Aktivität kurzfristig keinen Einfluss auf die Edelmetallterminpreise hat. Langfristig, auf monatlicher Basis, beeinflussen sie jedoch die Renditen der Edelmetallterminpreise. Die zweite Studie untersucht, ob Händleraktivitäten unterschiedlicher Marktteilnehmer den Beitrag des Terminmarktes zur Preisfindung und die Konvergenzgeschwindigkeit zwischen Rohstoffkassa- und Terminpreisen beeinflussen. Die Ergebnisse zeigen, dass Händleraktivitäten den Beitrag der Rohstoffterminmärkte zur Preisfindung nicht signifikant beeinflussen. Spekulanten verbessern die Konvergenzrate und Index Trader verschlechtern sie. Die dritte Studie analysiert den Einfluss der Marktstruktur auf Weizenterminpreise. Die Ergebnisse zeigen, dass sich aufgrund der Dominanz physischer Händler, in Verbindung mit einer geringen Beteiligung anderer Händler, der Terminpreis des harten Frühlingsweizens von der fundamentalen Entwicklung abgekoppelt hat. Die vierte Studie vergleicht den Einfluss von Nachrichten zum Angebot und Nachfrage mit dem Einfluss der Veröffentlichungen von Händlerpositionen auf die Getreideterminpreise. Während fundamentale Nachrichten weiterhin wichtig für die Preisbildung auf Getreideterminmärkten sind, ist die Bedeutung der Veröffentlichung von Händlerpositionen auf dem Mais- und Weizenterminmarkt verhältnismäßig gestiegen. Die fünfte Studie untersucht die Absichten unterschiedlicher Händler und inwieweit die Interaktion zwischen verschiedenen Händlern die Preisbildung an Rohstoffterminmärkten beeinflusst. Wir zeigen, dass Spekulanten Momentum-Strategien verfolgen und Hedger gegen den Markt handeln. Die Interaktions-Analyse zeigt, dass Spekulanten und Hedger die wichtigsten Händlergruppen für die Preisbildung auf Rohstoffterminmärkten sind. / The first study analyzes the impact of speculative activity on precious metals’ futures returns and volatility. Our results demonstrate that speculative activity does not affect precious metals’ futures returns in the short run. However, in long-term they influence precious metals’ futures returns on a monthly base. The second study examines how trading activities of different market participants influence the contribution of the futures market to price discovery and the rate of convergence between commodity spot and futures markets. The results show that the trading activities do not significantly contribute to price discovery in commodity futures markets. Considering the rate of convergence between spot and futures prices, we find that speculators improve while index traders impair the rate of convergence. The third study analyzes the impact of the market structure on wheat futures prices. The findings reveal that the price of hard red spring futures decoupled from its fundamental development because of the dominant presence of physical traders, combined with a low participation of other traders. The fourth study analyzes the impact of fundamental news on grain futures prices compared to the impact of the publication of traders’ positions. The results show that fundamental news remain an important source for pricing in grain futures markets. Nevertheless, a shift of importance from fundamental news to the publication of traders’ positions is observed in corn and wheat futures markets. The fifth study aims to reveal the motives behind the position changes of different market participants and how the interaction between the different traders affects prices in commodity futures markets. We find that speculators are driven by momentum trading and hedgers are contrarian traders. The interaction analysis demonstrates that on average speculators and hedgers appear to be the most important traders influencing pricing in commodity markets.

O objetivo deste trabalho foi investigar motivos pelos quais os produtores brasileiros de boi gordo e milho fazem relativamente pouco uso dos mercados futuros como ferramenta de gerenciamento de risco de preços. Duas abordagens diferentes foram apresentadas na pesquisa. Para o mercado de boi gordo, onde a presença de hedgers parece ser maior, um modelo de razão de hedge ótima alternativo ao tradicional modelo de mínima variância foi utilizado. O modelo alternativo faz uso de uma função de utilidade com aversão relativa ao risco constante para modelar as preferências dos indivíduos. Esta abordagem é considerada mais realista, por permitir que o nível absoluto de aversão ao risco se altere com a riqueza. Além disso, uma medida de downside risk e o relaxamento das hipóteses do modelo tradicional de mínima variância foram adicionados na análise. De acordo com os resultados, quando consideradas a possibilidade de se realizar investimento em um ativo alternativo ao mercado agropecuário, e a presença de custos de transação, o incentivo ao hedge se reduz acentuadamente. A utilização de uma medida alternativa de risco colaborou para esta redução, que foi mais acentuada para indivíduos menos aversos ao risco. Isto pode ser concluído observando-se que as razões de hedge ótimas, obtidas através da maximização da utilidade esperada dos indivíduos, foram, em grande parte, inferiores àquelas obtidas pelo modelo tradicional. Além disso, na maior parte dos casos, a utilização das razões de hedge ótimas alternativas mostrou-se mais eficiente que a obtida pelo modelo tradicional, pois possibilitou a obtenção de maiores razões retorno/risco no período selecionado para teste. Para o mercado de milho, um questionário foi aplicado a 90 produtores no sul e centro-oeste do Brasil. O questionário teve o objetivo de verificar se existem sinais de excesso de confiança nos preços por parte dos produtores de milho entrevistados. Adicionalmente, perguntas sobre o conhecimento do mercado futuro na BM&FBOVESPA foram também apresentadas. Em relação a este último tema, a maior parte dos produtores respondeu que conhece sobre o mercado futuro na bolsa brasileira, mas não fazem uso do mesmo. O principal motivo apontado pelos produtores foi não possuir informação suficiente sobre os mercados futuros. Associado a este resultado, descobriu-se que existe pouco incentivo para que os produtores realizem proteção de preços da produção, pois, para a maior parte dos entrevistados, as variâncias subjetivas de preços foram significativamente inferiores às variâncias dos preços históricos no mercado físico e futuro. Este resultado permitiu concluir que o excesso de confiança nos preços pode ser considerado uma explicação alternativa para o baixo uso dos mercados futuros como ferramenta de gestão de risco de preços. Como conclusões gerais, ações que visem promover reduções de custos de transação no mercado futuro e uma maior divulgação dos benefícios desta importante ferramenta na redução de risco de preços devem ser mais exploradas pela BM&FBOVESPA. Além disso, a promoção do maior conhecimento a respeito de como se negociar nesse mercado pode ser também uma boa estratégia para se fazer com que um maior número de produtores passe a negociar nesse mercado. / This research aimed to investigate the significant underuse of futures markets as a risk management tool by Brazilian live cattle and corn producers. To this end, the paper used two different approaches. In the live cattle market, where there appears a higher participation of hedgers trading, an alternative hedge ratio model was used instead of the standard minimum variance model. The alternative model uses a constant relative risk aversion utility function to model individual preferences. This approach is considered more realistic as use of the constant relative risk aversion utility function allows for the absolute level of risk aversion to change with wealth. In addition, a downside risk measure was introduced and certain restrictive assumptions to the minimum variance model were relaxed. According to the results, when the possibility of investment in an alternative asset and transaction costs are considered, the incentive to hedge is dramatically reduced. The use of an alternative risk measure also proved important to this reduction, which was higher for less risk averse individuals. This conclusion may be drawn after observing that the optimal hedge ratios obtained from the expected utility maximization are, in most cases, lower than those obtained by the standard model. Moreover, in most cases the use of alternative optimal hedge ratios provides higher return/risk ratios during the test period. For the corn market, a survey questionnaire was conducted of ninety producers in South and Central- West Brazil. The survey was conducted in order to verify the presence of overconfidence in prices among corn producers. The survey also asked questions regarding their knowledge of futures markets at BM&FBOVESPA. Most respondents answered that while they know about futures markets at the Brazilian board of trade, they do not trade on it because they do not have enough information about trading. The results also revealed that there is a low incentive for producers to hedge their production in futures markets because for most producers, subjective price variances are significantly lower than the variance of historical futures and spot prices. Given the results, one may conclude that the overconfidence effect in prices can be considered an alternative explanation to the low use of futures markets as a price risk management tool. Furthermore, actions which promote transaction costs reductions and promote the benefits to producers of using this important risk management tool while trading in the futures markets must be more carefully explored by the BM&FBOVESPA. Moreover, promoting knowledge of trading in futures markets may likely be a successful strategy for the wider adoption of futures trading among corn and live cattle producers.

Made available in DSpace on 2015-04-16T14:49:06Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1909548 bytes, checksum: f063691d27b5e27e8ff2e452860bc508 (MD5) Previous issue date: 2013-01-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The beef sector is one of the main highlights of the Brazilian agribusiness in the global scenario, the recent stabilization of the economy, the advantages of production costs based on abundant natural resources and few environmental restrictions have ensured the growth and competitiveness of the sector. With decreasing government intervention, the policies private of risk management began to become a concern among those involved in agribusiness and also between agents of the beef sector that started to seek ways of managing risk, among them the futures markets and options, to ensure profitability by reducing exposure to the risk of price fluctuations. Given the importance of the beef sector, the developments presented by derivative instruments and use yet inexpressive these contracts for risk management, sought to apply the pricing model for options on futures contracts, developed by Black, to the reality of the beef cattle future market. The method consisted of applying different types of volatility (historical, implied and deterministic) to pricing model of Black and then held the performance analysis of the models by calculating the errors. The results show that historical volatility for the different windows mobile subpricing values prizes traded in the market, whereas the models calculated with EWMA and THARCH volatility superprecificam the option premiums. Generally the pricing model with historical volatility by moving window showed the best performance in analysis. The results were also evaluated according to the maturity periods and degrees of moneyness, seeking to provide information that most agents have access to these instruments familiarizing themselves with the existing pricing methods and thus improve market liquidity. / O setor de carne bovina é um dos principais destaques do agronegócio brasileiro no cenário mundial, o recente processo de estabilização da economia, as vantagens de custos de produção com base em recursos naturais abundantes e poucas restrições ambientais têm garantido o crescimento e a competitividade do setor. Com a diminuição da intervenção governamental as políticas privadas de gestão de risco começaram a tornar-se uma preocupação entre os agentes envolvidos no agronegócio e também entre os agentes do setor de carne bovina que passaram a buscar formas de gerenciamento de risco, dentre elas os mercados futuros e de opções, a fim de garantir antecipadamente a lucratividade, reduzindo à exposição ao risco de oscilações dos preços. Em face à importância do setor de carne bovina, e a evolução apresentada pelos instrumentos derivativos, e o uso, ainda pouco expressivo, desses contratos para a administração do risco, buscou-se aplicar o modelo de precificação de opções sobre contratos futuros, desenvolvido por Black, à realidade do mercado futuro de boi gordo. O método consistiu em aplicar diferentes tipos de volatilidade (histórica, implícita e determinística) ao modelo de precificação de Black e em seguida realizou-se a análise de desempenho dos modelos por meio do cálculo dos erros. Foi encontrado que volatilidade histórica para as diferentes janelas móveis, subprecifica os valores dos prêmios negociados no mercado; enquanto que os modelos calculados com volatilidade EWMA e TARCH superprecificam os prêmios das opções. De modo geral o modelo de precificação com volatilidade histórica por janela móvel foi o que apresentou melhor desempenho nas análises realizadas. Os resultados foram avaliados ainda de acordo com os períodos de maturidade e os graus de moneyness, buscando proporcionar informações para que mais agentes tenham acesso a esses instrumentos familiarizando-se com os métodos de precificação existentes e assim melhorando a liquidez desse mercado.

O objetivo deste trabalho foi investigar motivos pelos quais os produtores brasileiros de boi gordo e milho fazem relativamente pouco uso dos mercados futuros como ferramenta de gerenciamento de risco de preços. Duas abordagens diferentes foram apresentadas na pesquisa. Para o mercado de boi gordo, onde a presença de hedgers parece ser maior, um modelo de razão de hedge ótima alternativo ao tradicional modelo de mínima variância foi utilizado. O modelo alternativo faz uso de uma função de utilidade com aversão relativa ao risco constante para modelar as preferências dos indivíduos. Esta abordagem é considerada mais realista, por permitir que o nível absoluto de aversão ao risco se altere com a riqueza. Além disso, uma medida de downside risk e o relaxamento das hipóteses do modelo tradicional de mínima variância foram adicionados na análise. De acordo com os resultados, quando consideradas a possibilidade de se realizar investimento em um ativo alternativo ao mercado agropecuário, e a presença de custos de transação, o incentivo ao hedge se reduz acentuadamente. A utilização de uma medida alternativa de risco colaborou para esta redução, que foi mais acentuada para indivíduos menos aversos ao risco. Isto pode ser concluído observando-se que as razões de hedge ótimas, obtidas através da maximização da utilidade esperada dos indivíduos, foram, em grande parte, inferiores àquelas obtidas pelo modelo tradicional. Além disso, na maior parte dos casos, a utilização das razões de hedge ótimas alternativas mostrou-se mais eficiente que a obtida pelo modelo tradicional, pois possibilitou a obtenção de maiores razões retorno/risco no período selecionado para teste. Para o mercado de milho, um questionário foi aplicado a 90 produtores no sul e centro-oeste do Brasil. O questionário teve o objetivo de verificar se existem sinais de excesso de confiança nos preços por parte dos produtores de milho entrevistados. Adicionalmente, perguntas sobre o conhecimento do mercado futuro na BM&FBOVESPA foram também apresentadas. Em relação a este último tema, a maior parte dos produtores respondeu que conhece sobre o mercado futuro na bolsa brasileira, mas não fazem uso do mesmo. O principal motivo apontado pelos produtores foi não possuir informação suficiente sobre os mercados futuros. Associado a este resultado, descobriu-se que existe pouco incentivo para que os produtores realizem proteção de preços da produção, pois, para a maior parte dos entrevistados, as variâncias subjetivas de preços foram significativamente inferiores às variâncias dos preços históricos no mercado físico e futuro. Este resultado permitiu concluir que o excesso de confiança nos preços pode ser considerado uma explicação alternativa para o baixo uso dos mercados futuros como ferramenta de gestão de risco de preços. Como conclusões gerais, ações que visem promover reduções de custos de transação no mercado futuro e uma maior divulgação dos benefícios desta importante ferramenta na redução de risco de preços devem ser mais exploradas pela BM&FBOVESPA. Além disso, a promoção do maior conhecimento a respeito de como se negociar nesse mercado pode ser também uma boa estratégia para se fazer com que um maior número de produtores passe a negociar nesse mercado. / This research aimed to investigate the significant underuse of futures markets as a risk management tool by Brazilian live cattle and corn producers. To this end, the paper used two different approaches. In the live cattle market, where there appears a higher participation of hedgers trading, an alternative hedge ratio model was used instead of the standard minimum variance model. The alternative model uses a constant relative risk aversion utility function to model individual preferences. This approach is considered more realistic as use of the constant relative risk aversion utility function allows for the absolute level of risk aversion to change with wealth. In addition, a downside risk measure was introduced and certain restrictive assumptions to the minimum variance model were relaxed. According to the results, when the possibility of investment in an alternative asset and transaction costs are considered, the incentive to hedge is dramatically reduced. The use of an alternative risk measure also proved important to this reduction, which was higher for less risk averse individuals. This conclusion may be drawn after observing that the optimal hedge ratios obtained from the expected utility maximization are, in most cases, lower than those obtained by the standard model. Moreover, in most cases the use of alternative optimal hedge ratios provides higher return/risk ratios during the test period. For the corn market, a survey questionnaire was conducted of ninety producers in South and Central- West Brazil. The survey was conducted in order to verify the presence of overconfidence in prices among corn producers. The survey also asked questions regarding their knowledge of futures markets at BM&FBOVESPA. Most respondents answered that while they know about futures markets at the Brazilian board of trade, they do not trade on it because they do not have enough information about trading. The results also revealed that there is a low incentive for producers to hedge their production in futures markets because for most producers, subjective price variances are significantly lower than the variance of historical futures and spot prices. Given the results, one may conclude that the overconfidence effect in prices can be considered an alternative explanation to the low use of futures markets as a price risk management tool. Furthermore, actions which promote transaction costs reductions and promote the benefits to producers of using this important risk management tool while trading in the futures markets must be more carefully explored by the BM&FBOVESPA. Moreover, promoting knowledge of trading in futures markets may likely be a successful strategy for the wider adoption of futures trading among corn and live cattle producers.

This dissertation consists of three essays. The first essay focuses on idiosyncratic volatility as a primary arbitrage cost for short sellers. Previous studies document (i) negative abnormal returns for high relative short interest (RSI) stocks, and (ii) positive abnormal returns for low RSI stocks. We examine whether these market inefficiencies can be explained by arbitrage limitations, especially firms' idiosyncratic risk. Consistent with limits to arbitrage hypothesis, we document an abnormal return of -1.74% per month for high RSI stocks (>=95th percentile) with high idiosyncratic volatility. However, for similar level of high RSI, abnormal returns are economically and statistically insignificant for stocks with low idiosyncratic volatility. For stocks with low RSI, the returns are positively related to idiosyncratic volatility. These results imply that idiosyncratic risk is a potential reason for the inability of arbitrageurs to extract returns from high and low RSI portfolios. The second essay investigates market efficiency in the absence of limits to arbitrage on short selling. Theoretical predictions and empirical results are ambiguous about the effect of short sale constraints on security prices. Since these constraints cannot be eliminated in equity markets, we use trades from futures markets where there is no distinction between short and long positions. With no external constraints on short positions, we document a weekend effect in futures markets which is a result of asymmetric risk between long and short positions around weekends. The premium is higher in periods of high volatility when short sellers are unwilling to accept higher levels of risk. On the other hand, riskiness of long positions does not seem to have a similar impact on prices. The third essay studies investor behaviors that generate mispricing by examining relationship between stock price and future returns. Based on traditional finance theory, valuation should not depend on nominal stock prices. However, recent literature documents that preference of retail investors for low price stocks results in their overvaluation. Motivated by this preference, we re-examine the relationship between stock price and expected return for the entire U.S. stock market. We find that stock price and expected returns are positively related if price is not confounded with size. Results in this paper show that, controlled for size, high price stocks significantly outperform low price stocks by an abnormal 0.40% per month. This return premium is attributed to individual investors' preference for low price stocks. Consistent with costly arbitrage, the return differential between high and low price stocks is highest for the stocks which are difficulty to arbitrage. The results are robust to price cut-off of $5, and in different sub-periods. / Ph. D.