O relatório de final de ano do HyperVolatility 2014 está finalmente pronto e este ano adicionamos mais classes de ativos. Você pode navegar o relatório usando a tabela de conteúdos interativa que permite que você vá diretamente para a análise que deseja ler. O Relatório 2014 da Hipervolatilidade pode ser baixado GRATUITAMENTE no seguinte link (não é requerido registro): Relatório de final de ano da HyperVolatility 2014 (PRINT) A 1ª parte examina os desempenhos das seguintes classes de ativos ao longo de 2014: Patrimônio Líquido Índices: Mini SampP500, DAX 30 Obrigações do Tesouro: Bund alemão, títulos do Tesouro dos Estados Unidos de 10 anos Moedas: Euro, ienes japoneses, britânicos britânicos: WTI Crude, Brent Crude, Gold Volatility Indices: Índice VIX A 2 ª parte analisa o cenário macroeconômico em EUA, Europa, Austrália, Japão e BRICS (Brasil, Rússia, Índia, China e África do Sul). Os indicadores econômicos que foram considerados para o estudo são os seguintes: O Barómetro de janeiro, às vezes também conhecido como efeito de janeiro (embora o efeito de janeiro seja diferente) é a teoria segundo a qual as performances do mercado durante o mês de janeiro podem Ser usado para prever a tendência para o resto do ano. A teoria do Barómetro de janeiro é muitas vezes resumida pelo ditado: como acontece em janeiro, o ano também acontece. As implicações práticas são bastante diretas: se a classe de ativos em análise tiver um retorno positivo em janeiro, a teoria sugere que será um ano de alta, enquanto um desempenho negativo deve prever uma tendência de baixa para os próximos meses. A teoria do Barómetro de janeiro baseia-se no pressuposto de que muitos gestores de fundos e investidores institucionais, particularmente aqueles que estão interessados em investimentos de médio prazo, no início de cada novo ano, tendem a colocar suas posições já descontando sua visão nos próximos 6 12 meses. Conseqüentemente, a teoria sugere que, se a visão for negativa, os gerentes de portfólio se posicionarão no lado curto do mercado no início de janeiro. Caso contrário, se eles acharem que a ação de preços aumentará nos próximos 6 a 12 meses, eles irão por muito tempo. Assim, a teoria é baseada no fato de que a pressão de compra ou venda gerada pela quantidade de dinheiro alocada no mercado pelos grandes jogadores em janeiro deve mover o preço na direção de suas previsões. Esta é a teoria, mas como Albert Einstein afirmou: em teoria, a teoria ea prática são as mesmas. Na prática, eles não são. A presente pesquisa visa investigar e estudar a confiabilidade da teoria do Barómetro de janeiro, a fim de avaliar, sob um ponto de vista probabilístico, quais as chances de ganhar lucros consistentes se forem aplicados aos mercados financeiros. A pesquisa foi realizada nos principais índices de ações do mundo que, por sua vez, foram subdivididos para localização geográfica: América do Norte (SampP500, NASDAQ Composite), Europa (DAX30, FTSE100), AustralAsia (Nikkei225, ASX200) e mercados emergentes (Hang Seng, Bovespa, BSE Sensex). O conjunto de dados que foi utilizado consiste em preços de índices que variam de janeiro de 2004 a dezembro de 2014, o que implica um valor de 11 anos de dados. As análises de back testing que serão expostas e comentadas são simplesmente destinadas a entender se os retornos do mercado de janeiro se comparam, se não forem em tamanho, pelo menos em sinal, com os anuais. Assim, a combinação de retorno negativo no retorno anual janeiro anual, bem como o retorno positivo combinado no retorno anual anual de janeiro, serão calculados como casos de sucesso. Por outro lado, todos os retornos não correspondentes serão tratados como uma falha na teoria. Os resultados das análises serão apresentados e explicados por localização geográfica, portanto, os primeiros índices de ações que serão analisados são os norte-americanos: a tabela acima relatada mostra, na primeira coluna, os retornos lognormal de janeiro calculados para o SampP500 enquanto o A segunda lista o retorno total para cada ano. O lado direito da tabela fornece os mesmos cálculos, mas com base no índice NASDAQ Composite. Em primeiro lugar, vale a pena notar que, nos últimos 11 anos, o retorno médio do índice SampP500 foi de 4,89, enquanto o NASDAQ Composite obteve uma média de 6,78. Em segundo lugar, ambos os índices de ações experimentaram flutuações semelhantes durante as crises, mas o NASDAQ superou de forma consistente o SampP500 desde 2012 até agora. O gráfico a seguir traça as taxas de sucessão da teoria do Barómetro de janeiro aplicada às classes de ativos acima mencionadas nos últimos 11 anos: a taxa de sucesso tanto para o SampP500 como para o NASDAQ Composite é de 54,5 enquanto a taxa de falha é de 45,5. Esses números simplesmente significam que a teoria do JB se manteve verdadeira por 6 anos, mas previu sem sucesso os retornos anuais em 5 ocasiões. No entanto, a taxa de sucesso de 54,5 definitivamente não se enquadra na categoria de estratégias confiáveis, mas resultados diferentes podem vir de diferentes mercados. A tabela seguinte apresenta os resultados de nossas análises sobre o alemão DAX30 e o britânico FTSE100: os quadros mostram, evidentemente, que durante as crises financeiras em 2008, os mercados europeus selecionados se mostraram tão fracos como suas contrapartes americanas (embora o FTSE100 britânico não viole a Limiar 40). Os últimos 3 anos foram bastante bem, tanto quanto os retornos estão em causa, embora em 2014 o britânico FTSE100 (2,62) tenha desempenho inferior ao DAX30 (3,06). Em média, o índice alemão, nos últimos 11 anos, produziu um retorno de 7,26, enquanto os investidores de longo prazo no mercado britânico conseguiram ganhar apenas 2,34. O próximo gráfico traça as taxas de sucessão da teoria do Barómetro de janeiro aplicada nas classes de ativos européias acima mencionadas: os resultados são muito diferentes dos observados para os índices de ações no exterior. Em primeiro lugar, a teoria JB aplicada ao DAX30 apresenta falhas mais altas (54,5) do que os sucessos (45,5). Em particular, a estratégia do Barómetro de janeiro previu com sucesso os retornos futuros 5 vezes, mas falhou 6 vezes, o que implica que mesmo neste mercado levou a resultados ruins. Por outro lado, o JB aplicado ao FTSE100 britânico mostra uma chance vencedora de 63,6, enquanto a probabilidade perdedora é de apenas 36,4. Nesse caso, os retornos registrados no primeiro mês do ano desde 2004 provaram ser bons analistas para retornos anuais. Numericamente, a estratégia JB teria sido rentável em 7 casos, embora não tivesse falhado em 4 ocasiões. A próxima tabela lista os retornos históricos da região AustralAsian: os índices de ações que foram utilizados como proxy para a região geográfica AustralAsian são o japonês Nikkei225 eo australiano ASX200. O 2008 foi um ano muito negativo também na Austrália, na verdade, ambos os retornos anuais são muito próximos do limite de 50. No entanto, também a crise de crédito europeia em 2011 influenciou dramaticamente os índices acima mencionados: 20,58 para o Nikkei225 e 13,16 para o ASX200. Os dados para os retornos médios, calculados nos últimos 11 anos, mostram que o Nikkei225 caiu 2,89 enquanto o índice de ações australiano retornou uma média de 3,57 para potenciais investidores de longo prazo. A estratégia do Barómetro de janeiro oferece ganhos extras O próximo gráfico tentará responder a esta pergunta: O índice japonês exibe a habitual redução de 54,5 45,5 entre taxas de sucesso e falhas, o que implica que a estratégia JB se mostrou rentável apenas 6 vezes e falhou em 5 casos. Por outro lado, a taxa de sucesso para o ASX200 é 63,6 (7 sucessos), enquanto a taxa de falha é de apenas 36,4 (4 falhas), o que implica que a estratégia JB foi definitivamente mais lucrativa quando aplicada ao índice australiano do que ao equivalente japonês. A última tabela da presente pesquisa centra-se nos desempenhos passados de uma área geoeconômica, e não meramente geográfica: mercados emergentes. Os índices de ações que foram selecionados para esta seção são o Hang Seng (Hong Kong), o Bovespa (Brasil) e a BSE Sensex (Índia). A primeira coisa a notar é que durante a crise as perdas incorridas por esses mercados foram maiores que as observadas nos índices que mencionamos até agora. Na verdade, durante a crise do crédito, com a exclusão da Bovespa brasileira que em 2008 teve um retorno negativo de apenas 46,25, o Hang Seng produziu um 55,43, enquanto o retorno indiano para o mesmo ano foi um notável 70,64. No entanto, o cenário muda consideravelmente se o intervalo de tempo 20112014 for levado em consideração. Na verdade, o índice de equidade indiano, inclusive incluindo a queda no 2011, superou consistentemente os outros dois. No que diz respeito aos retornos médios a longo prazo, desde 2004 até agora, o Hong Kongs Hang Seng caiu 5.43, o Bovespa brasileiro retornou 5.81, enquanto a BSE Sensex da Índia calculou uma média impressionante de 13.68. Os retornos médios dos mercados emergentes são claramente muito altos, mas a BSE conseguiu superar todos os outros índices de ações considerados na presente pesquisa (o alemão DAX30 ocupa o segundo lugar com um 7,26 e é imediatamente seguido pelo índice NASDAQ Composite que obteve um retorno médio de 6,78) . O próximo gráfico planeja as taxas de sucessão obtidas ao executar a estratégia do Barómetro de janeiro no Hang Seng, Bovespa e BSE Sensex: as taxas de sucesso para a BSE Sensex (54,5) e a Bovespa (45,5) na verdade não parecem fornecer uma cobertura (embora a A estratégia mostrou-se mais rentável no índice de ações indiano do que no brasileiro). A informação mais significativa que pode ser extraída dessa análise é a alta taxa de falhas no índice de Hong Kongs (63,6). Em particular, a estratégia do Barómetro de janeiro tem consistentemente não conseguido prever os retornos anuais do índice Hang Seng por 7 anos, enquanto ele só foi bem sucedido em 4 casos. De modo geral, as análises realizadas nos 9 índices patrimoniais considerados no estudo parecem salientar que a estratégia JB não oferece nenhuma cobertura especial para os investidores. No entanto, durante a disputa de dados, alguns padrões interessantes surgiram. Os padrões que foram detectados podem ser agrupados em duas categorias: o padrão vencedor e o padrão de perda. A estratégia do Barómetro de janeiro só pode produzir dois resultados mutuamente exclusivos: é rentável ou não (há uma chance de que o retorno anual possa eventualmente ser 0, mas a probabilidade associada, mais de 252 dias de negociação, é tão baixa que a excluímos voluntariamente Da análise de cenários). O padrão vencedor foi extraído simplesmente executando uma análise de freqüência nos tempos em que a estratégia JB provou ser lucrativa. A estratégia JB basicamente afirma que o retorno de janeiro deve corresponder ao anual, no entanto, não faz diferença entre retornos negativos ou positivos. Consequentemente, como indicado no início da pesquisa, um retorno positivo de janeiro em um ano positivo seria contado como um sucesso, mas um retorno negativo de janeiro em um ano negativo também seria contado como um sucesso. A coisa mais importante para a estratégia funcionar é uma combinação entre os retornos. As perguntas que esta seção está tentando dar uma resposta são: há um padrão entre os casos de sucesso Os casos de sucesso têm algo em comum Os casos de sucesso otimista superam os mais baixos ou vice-versa Antes de mostrar os resultados, vale lembrar que valem 11 anos Os dados em 9 classes de ativos diferentes foram filtrados, implicando um total de 99 observações. 52 de 99 observações se enquadram na categoria de padrão vencedora, enquanto as restantes 47 são atribuídas axiomaticamente ao padrão de perda. O seguinte gráfico de torta tenta resumir os resultados obtidos da mineração de dados os dados associados ao primeiro padrão: os casos de sucesso, para a combinação de retorno positivo de janeiro em um ano de retorno positivo (área verde chamada BULL), são 34 enquanto os casos de sucesso, Para a combinação do retorno negativo de janeiro em um ano de baixa (área vermelha chamada BEAR), são apenas 18. Claramente, o resultado desta análise de freqüência é uma conseqüência da tendência geral em cada ano, mas parece que a estratégia JB, quando lucrativa, Funciona melhor em anos de execução positivos, em vez de em negativos (padrão vencedor). Para entender por que esses são os casos que temos de prosseguir e minar os dados por casos de falha. Na seção anterior, observou-se que, numericamente falando, a maioria dos casos de sucesso aconteceu durante a combinação de retorno positivo de janeiro em um ano de rendimento positivo. Também foi afirmado que a estratégia JB funciona melhor em anos positivos e não em negativos. No entanto, para entender por que isso é caso, a seção atual analisará todos os casos de falha. Se a estratégia JB não funcionou, isso significa que o retorno de janeiro não corresponde ao sinal anual. Conseqüentemente, há apenas dois cenários a considerar ao analisar os casos de falha: o retorno em janeiro foi positivo, mas o anual acabou por ser negativo ou o ano começou com um retorno negativo em janeiro, mas terminou com um desempenho positivo. O próximo gráfico de torta traça todos os casos de falha e os agrupa em duas categorias: BEAR TO BULL (retorno negativo em janeiro, mas positivo anualmente) e BULL TO BEAR (retorno positivo em janeiro, mas negativo anualmente): o acima O gráfico reportado está evidenciando que, entre as falhas, há um padrão muito freqüente: a grande maioria das falhas na estratégia JB são devidas a anos que começam com um retorno negativo, mas que posteriormente produzem um padrão positivo (padrão perdedor). Numericamente falando, os casos do BEAR TO BULL contaram 39 observações, enquanto o BULL TO BEAR é apenas 8. A estratégia do Barómetro de janeiro não parece proporcionar lucros consistentes pelo menos para as classes de ativos consideradas e o período de tempo selecionado. A estratégia do Barómetro de janeiro previu com sucesso Retos anuais em 52 casos (52,5 das observações totais) 34 dos 52 casos de sucesso provêm da combinação de retorno positivo de janeiro em um ano de rendimento positivo, enquanto apenas 18 são da combinação de retorno negativo de janeiro em um ano de rendimento negativo. A estratégia do Barómetro de janeiro falhou Para prever os rendimentos anuais em 47 casos (47,5 das observações totais) 39 dos 47 casos de falha caem dentro da categoria BEAR TO BULL, onde janeiro produziu um retorno negativo, mas o ano acabou com um desempenho positivo Apenas 8 casos de falha caíram dentro do BULL PARA A categoria BEAR, onde janeiro produziu um retorno positivo, mas o ano acabou com um desempenho negativo. A pesquisa atual Pode ser expandido de várias maneiras. Na verdade, os possíveis desenvolvimentos de pesquisa podem ser provenientes do aumento dos conjuntos de dados, a fim de permitir observações de 20 ou 30 anos, incluindo mais índices de ações ou expandindo a análise para diferentes tipos de classes de ativos, como títulos do Tesouro, commodities e moedas. A propagação de crack é provavelmente a estratégia financeira mais importante dentro do setor de energia. O preço do spread de crack é tão crucial que é monitorado de perto por comerciais, hedge funds, bancos, empresas de energia e governos. O valor do crack spread resume e combina, em 1 estratégia, o preço do petróleo bruto e seus dois derivados mais importantes: diesel e gasolina. Toda a indústria do petróleo, que ainda desempenha um papel muito importante no que diz respeito à produção de energia, está forte e inevitavelmente ligada ao desempenho da propagação de crack. A presente pesquisa investiga a estrutura da estratégia acima mencionada e as relações quantitativas de e entre seus componentes. Os comerciantes de commodities e os gerentes de portfólio não são estranhos ao conceito de negociação de spread. Na verdade, muitas commodities são fortemente ligadas por fatores comuns, como fundamentos, dinâmicas de demanda, procedimentos de produção de extração, processos importxport, rotas de transporte marítimo, disponibilidade geográfica, variáveis geopolíticas e assim por diante. Existem muitos tipos de spreads dentro do setor de commodities (gás natural versus poder, cobre versus alumínio, ouro vs prata, platina vs paládio) e todos eles são baseados em alguns dos fatores comuns acima mencionados. A propagação da fenda, foco da pesquisa atual, é construída usando os preços WTI Crude Oil, RBOB gasolina e diesel. No entanto, vale a pena mencionar que o termo propagação de fissuras também pode se referir a outra combinação espalhada que envolve WTI, RBOB e óleo de aquecimento ou a menos popular, mas ainda é comercializado, cracking europeu (Brent Crude vs European Gasoil). O spread de crack fornece uma aproximação bastante boa da margem obtida por refinadores e é precisamente por isso que essa estratégia está no cerne da indústria do petróleo. Na verdade, ele simplesmente expressa o valor relativo do custo do petróleo bruto em relação aos produtos refinados (gasolina e diesel). Os refinadores podem entrar em uma simples propagação de crack 1: 1 (petróleo bruto versus gasolina ou petróleo bruto versus diesel), no entanto, em uma refinaria típica, a produção de gasolina geralmente é duas vezes maior que a dos óleos destilados (diesel, óleo de aquecimento, combustível para aviação Óleo, óleo de bunker, etc.). Consequentemente, seria mais apropriado trocar construções diversificadas de propagação de fissuras como uma propagação de 3: 2: 1 ou uma propagação de 5: 3: 2. A análise atual incidirá na propagação de crack 3: 2: 1, que é a construção mais popular e útil porque atende às necessidades de muitas refinarias. A fórmula para calcular o preço de uma propagação de fissuras é a seguinte: (2 RBOB bb 1 ULSD bb) (3 WTI bb) 3 O cálculo é simples. No entanto, os preços de RBOB e ULSD (ou RBOB e preços do óleo de aquecimento) são expressos em por galão e não por barril. Portanto, eles precisam ser multiplicados por 42 (1 barril contém 42 galões) para expressá-los em termos de barril. Por exemplo, no dia 9 de junho de 2014, RBOB e NY Harbour Diesel fecharam em 3.049 e 2.886 por galão respectivamente, portanto, seus preços perbarrel seriam automaticamente (3.049 42) 128.058 para RBOB e (2.88642) 121.21 para ULSD. Os refinadores são, naturalmente, longos o crack porque eles têm que comprar petróleo bruto, refiná-lo e, em seguida, vender os produtos. Assim, a margem de lucro vem da relação entre os preços do petróleo e os preços dos produtos, enquanto as maiores preocupações dos refinadores provêm de mudanças indesejadas nessa relação. Os refinadores dominam predominantemente os preços do petróleo bruto e as quedas dos preços dos produtos porque, nesse caso, sua margem de lucro encolheria. O refinador, a fim de bloquear o preço, irá, portanto, cobrir sua posição física no mercado financeiro. Vamos assumir que um refinador decide bloquear a margem atual porque teme um aumento no preço do petróleo bruto em relação aos preços dos produtos. A melhor estratégia que ele pode implementar envolve a venda de uma propagação de crack, de modo que a longa posição em bruto irá compensar o aumento potencial dos preços do petróleo, enquanto as posições curtas nos produtos compensarão as perdas provenientes de potenciais mergulhos em preços de diesel e gasolina. A WTI está negociando em 100,52, a gasolina da RBOB é comercializada em 2,905 por galão, enquanto o NY Harbor diesel está em 2,927 por galão. Consequentemente, a gasolina RBOB e o diesel NY Harbour em termos de barril são fixados em (2.90542) 122.01 e (2.92742) 122.93. O spread de crack 3: 2: 1 agora pode ser construído, então o refinador comprará 3 contratos de crude WTI em 100.52 e simultaneamente venderá 2 futuros de gasolina em 122.01 e 1 diesel futuros em 122.93. A margem do spread de crack financeiro é equivalente a: (2 122.01 1 122.93) (3 100.52) 3 21.79 O refinador agora trancou uma margem de 21.79 e garantiu sua transação. De fato, qualquer aumento potencial nos preços do petróleo bruto será contrabalançado por um lucro maior na posição de longo prazo do WTI, enquanto qualquer potencial mergulhar nos preços da gasolina ou do diesel será compensado pelos ganhos nas posições curtas financeiras. Claramente, os refinadores tendem a se esconder olhando para a frente, de modo que os contratos que serão utilizados podem expirar em 1, 2 ou 3 meses a partir do tempo de implementação, dependendo da data de entrega. Por outro lado, há momentos em que os refinadores são obrigados a vender petróleo bruto e comprar produtos. Consequentemente, para proteger essa exposição, eles precisam implementar uma propagação de crack reversa (também conhecida como hedge de propagação de crack). O spread de propagação inversa é exatamente o oposto de um crack regular, na verdade, envolve a tomada de uma posição de curto prazo no petróleo bruto WTI e posições longas sobre futuros de gasolina e diesel. Por que um refinador venderá petróleo bruto e comprará produtos. Não é que Refinarias contraproducentes funcionam a plena capacidade para satisfazer a demanda de derivativos de petróleo, no entanto, paradas forçadas, devido a quebras de máquina ou problemas técnicos inesperados, podem acontecer. Os acordos contratuais sempre devem ser honrados, portanto, no evento infeliz de uma quebra técnica, os refinadores devem comprar produtos de outra pessoa e entregá-los aos seus clientes conforme contrato. Além disso, os refinadores tendem a comprar petróleo bruto com 23 meses de antecedência, de modo que uma quebra obrigatória os obrigará a vender o valor já entregue, ou prestes a ser entregue, porque um acidente técnico não permitiria que ele refinasse. Estas situações podem acontecer facilmente, não com frequência, mas acontecem. Assim, a melhor maneira de proteger o negócio é entrar em um spread de crack reverso onde o petróleo cru é curto e os produtos são comprados. A margem final é a diferença entre as operações no mercado físico (venda de barris WTI e compra de barris de produtos) e as do mercado financeiro (venda de futuros WTI ao comprar futuros de gasolina e diesel). Vamos assumir que, no mercado físico, o refinador enfrenta uma perda de 22,52, porque ele é obrigado a comprar milhares de barris de produtos a um preço mais elevado devido à queda inesperada. Por outro lado, graças à estratégia de crack reversa, ele consegue bloquear um lucro de 23,46. A margem final seria 23,46 22,52 0,94. Novamente, os refinadores geralmente não compram produtos e vendem petróleo bruto, a menos que seja obrigado a fazê-lo, portanto, o hedge de propagação de crack é implementado apenas em ocasiões especiais. Vale ressaltar que muitas refinarias podem querer entrar em diferentes tipos de propagação de fissuras para cobrir o chamado risco de base de energia. O risco de base é a diferença de preço entre o mesmo produto entregue ou negociado em 2 locais diferentes. A diferença de preço entre US Gulf Coast Ultra Low Sulphur Diesel e New York Harbor Ultra Low Sulphur Diesel é um exemplo de risco de base. Um refinador que usa apenas NY Harbour diesel irá construir uma propagação de crack usando NY Harbour ULSD futuros, enquanto outro pode querer assumir posições simultâneas em Gulf Coast e NY Harbour diesel, porque ele refina ambos. A seguinte seção da presente pesquisa analisará quantitativamente a propagação da fissura e separará cada componente da estratégia para estudar seu comportamento e flutuações. O primeiro gráfico exibe as oscilações de preços do spread de crack 3: 2: 1 que foi replicado sinteticamente usando os preços de futuros WTI crude, RBOB gasolina e diesel de NY Harbour variando de junho de 2006 a junho de 2014: é evidente que a margem ganha por refinadores Tem flutuado notavelmente nos últimos anos e é seguro dizer que os fatores geopolíticos impactaram fortemente seu desempenho. O gráfico mostra que o preço da propagação de rachaduras predominantemente oscilou dentro de 10 e 40 com desvios ocasionais de tal canal. A queda de preços em 2008 e o pico violento em 2012 são exemplos claros do que acontece com a margem quando os preços do petróleo e dos produtos divergem em termos relativos: o petróleo bruto aumenta quando os preços dos produtos mergulham ou vice-versa. O gráfico a seguir resume o desempenho do crack em uma base anual: os números apresentados em cada bolha representam o preço médio da propagação de fissuras naquele ano. O gráfico mostra de forma bastante eloquente que, no intervalo de tempo 20062010, a ação de preço se moveu entre 13,3 e 17,3. No entanto, a tendência observada durante os 5 anos acima mencionados foi claramente descendente e as margens dos refinadores diminuíram em 23. A segunda parte do gráfico, em vez disso, exibe um cenário diametralmente oposto. Na verdade, os dados para o intervalo 20112014 mostram uma explosão violenta da ação de preço e um consequente alargamento das margens. O preço médio mais alto foi alcançado em 2012 (34,05) enquanto 2013 e no primeiro semestre de 2014 registaram preços médios mais baixos (25,55 e 23,77, respectivamente). É interessante notar que a diferença de preços entre 2010 e 2011 é tão alta quanto 15,94. Mais uma vez, o salto de preço foi devido a uma divergência entre o preço da WTI, que no início de 2011 caiu abaixo de 90 em várias ocasiões e o preço da gasolina e do diesel que, ao contrário, permaneceu constante. O desequilíbrio inicial entre petróleo bruto e produtos, no entanto, persistiu durante o resto do ano, mesmo que a WTI se recuperasse e voltasse para a área 100. É importante ressaltar que, em novembro de 2011, iniciou-se o projeto de encanamento da Seaway, que reverteu o fluxo de petróleo bruto, permitindo o transporte da área de refinação de Cushing para Houstons. Este projeto, que foi concluído em maio de 2012, contribuiu sem dúvida para aumentar a margem para refinadores. O próximo gráfico exibe as flutuações da volatilidade realizada para cada componente da propagação da fissura: óleo bruto WTI, gasolina RBOB e diesel Ultra Low Sulphur: a primeira vista, é claro que o componente mais volátil é a gasolina RBOB porque os picos em A volatilidade é geralmente mais violenta neste mercado do que em todos os outros. O segundo componente, no que diz respeito às flutuações de volatilidade, é WTI Crude Oil porque a sua volatilidade percebida é bastante próxima do RBOB, mas ligeiramente inferior. O componente menos volátil de todo o crack spread é o diesel. De fato, é evidente que a volatilidade do diesel é bem abaixo da RBOB e é menor do que a curva de volatilidade observada para os preços do petróleo. O próximo gráfico, para fornecer uma abordagem mais precisa e quantitativa, traça a distribuição das volatilidades realizadas para cada componente e as classifica: o gráfico acima relatado confirma de forma eloquente que o RBOB é a classe de ativos com maior volatilidade média (37,73) , Seguido por WTI (27.97) e ULSD (26.32). É importante ressaltar que estamos lidando com commodities e, portanto, não é surpreendente observar volatilidades médias bem superiores às usualmente obtidas pela filtragem de dados de índices de ações. O mercado da RBOB é tão volátil que os valores de baixa gama oscilam em torno de 30,28, enquanto a WTI e o diesel experimentam baixos valores que flutuam em torno de 21,16 e 19,76, respectivamente. O mesmo cenário pode ser facilmente observado no segmento Alto da distribuição porque, mesmo neste caso, o RBOB possui o valor mais alto (46.61), enquanto o WTI (35.76) e o ULSD (34.07) são mais baixos. O exame dos valores extremos, Mínimo e Máximo, mostra resultados bastante semelhantes. Em particular, o segmento Mínimo tem o ranking idêntico visto até agora: RBOB ainda é o mais volátil (16.68), o WTI é o segundo mais volátil (11.15), enquanto o diesel continua sendo o terceiro componente mais volátil (8.55). A análise do segmento máximo, em vez disso, fornece algumas evidências interessantes. Em primeiro lugar, os picos de volatilidade realizados nos mercados de energia podem ser bastante violentos e agressivos, portanto, não é surpreendente ver valores muito superiores a 100 para a gasolina RBOB (125,46) e WTI Crude Oil (122,63), enquanto a ULSD ocupa o terceiro lugar (81,26) . Em segundo lugar, é muito interessante notar que no segmento Máximo, os valores de WTI são muito próximos de RBOB, o que implica que explosões de volatilidade realizadas extremas no mercado de petróleo bruto americano podem ser tremendamente violentas. Numericamente falando, uma explosão de volatilidade realizada, que levaria a volatilidade a mudar do segmento Médio para o segmento Alto, significaria um aumento de 232,5 para a gasolina RBOB, mas, no caso da WTI, implicaria um incremento de 365,9. Isso significa que as explosões de volatilidade extremas da WTI podem ser até 57.3 mais agressivas que as da RBOB, que é, em média, o componente mais volátil da rachadura. Até agora, os conceitos que foram discutidos e expandidos são: 1) Os motivos fundamentais por trás da propagação de crack 2) Como construir uma propagação de crack 3) Utilização do spread de crack para fins de cobertura 4) Análise do preço de propagação de crack 5) Análise de volatilidade dos componentes A última seção da presente pesquisa irá concluir a investigação sobre os componentes da propagação de crack. O estudo anterior mostrou que a gasolina RBOB é o componente mais volátil da estratégia, mas, para definir quantitativamente quais das 3 classes de ativos influenciam os preços de propagação de crack, é necessário executar uma análise de correlação: a matriz de correlação é dividida em 2 grupos. O primeiro grupo consiste em 3 conjuntos de barras contendo a distribuição dos coeficientes de correlação calculados executando a análise entre um componente contra o outro: RBOB vs ULSD, WTI vs RBOB e WTI vs ULSD. O segundo grupo, em vez disso, apresenta a distribuição das relações numéricas globais entre cada componente e o crack se espalhou: WTI vs Crack Spread, RBOB vs Crack Spread e ULSD vs Crack Spread. As barras de correlação média serão usadas como proxy para correlação de longo prazo porque fornecem uma avaliação da conexão média entre as variáveis examinadas. O gráfico sugere que todos os componentes estão bem ligados entre si, de fato, a correlação de RBOBULSD é de 0,70, enquanto a relação de WTIRBOB é de 0,67. O coeficiente mais forte é observado para o par WTIULSD e neste caso a figura é tão alta como 0,86. A estratégia de propagação de crack, em vez disso, apresenta uma relação robusta com a gasolina RBOB (0,78), muito fraca em relação ao diesel (0,30) e uma ligação quase inexistente ao WTI (0,09). O alto coeficiente de correlação entre a gasolina ea propagação da fissura deve-se à alta natureza volátil do mercado de RBOB. A alta volatilidade dos preços da gasolina, de fato, é susceptível de produzir mudanças repentinas e mais frequentes no preço do crack. É importante mencionar que o forte relacionamento linear detectado pela análise de correlação, entre RBOB e propagação de crack. Também foi confirmado pela análise de regressão. De fato, os valores de quadrado ajustados obtidos pela regressão de cada componente único contra a propagação de fissuras concluíram que a gasolina de RBOB é, de fato, a classe de ativos que influencia mais o preço do crack. Numericamente falando, o cálculo ajustado ajustado para a regressão WTICrack Spread foi de 6,75 e confirma a relação linear extremamente baixa entre os preços WTI e crack. O ajuste ajustado para a regressão ULSDCrack Spread foi de 24,65 e, mesmo neste caso, a conexão fraca é confirmada. The adjustedR squared for the RBOBCrack Spread regression was 45.5 and it robustly confirms the relevant linear relationship between gasoline prices and the price of the crack spread. The Baltic Dry Index measures shipping activity of raw materials around the world. In particular, the BDI provides a very efficient way to quantify and evaluate the strength of the global demand for commodities and raw materials. The Baltic Dry Index is compiled, on a daily basis, by the Baltic Exchange, and it is built thanks to the information gathered from the largest dry bulk shippers worldwide. Specifically, the Baltic Exchange collects the prices applied by dry bulk shippers for more than 20 shipping routes all over the world. The BDI is actually an average of 4 different components: The Baltic Capesize Index, The Baltic Panamax Index, the Baltic Supramax Index and the Baltic Handysize Index. What these indices are and what do they track The fluctuations of the aforementioned indices are based upon the activity of 4 different types of ships: the Handysize, the Supramax, the Panamax and the Capemax. Lets analyze them one at the time in order to highlight the difference among them: 1) Handysize Ships: they account for approximately 34 of the global fleet and can carry 15,00035,000 dead weight tons of cargo 2) Supramax Ships: they account for approximately 37 of the global fleet and can carry 45,00059,000 dead weight tons of cargo 3) Panamax Ships: they account for approximately 19 of the global fleet and can carry 60,00080,000 dead weight tons of cargo. Panamax ships are the largest ships allowed through the Panama Canal 4) Capemax Ships: they account for approximately 10 of the global fleet and can carry more than 100,000 dead weight tons of cargo and they are too big to pass through the Panama Canal As previously mentioned, every index is specifically created to keep track of the commercial activity connected to the 4 most important type of ship and this is precisely why the BDI is built upon them. Mathematically, the Baltic Dry Index is calculated using the following formula: BDI ((CapesizeTCavg PanamaxTCavg SupramaxTCavg HandysizeTCavg) 4 ) 0.113473601) The 0.113473601 is the multiplier introduced to standardize the calculation while the TCavg refers to the Time Charter average. Time Chartering is simply one of the ways to charter a tramp ship. Specifically, the charter will book the ship that best fits the size of the cargo for a specific period of time and for a predefined route. The hiring fees are expressed on a perton basis because they are structured on the amount of dead weight tons that are transported each month. It is important to point out that the transactional costs (bunker fuel and storage), on time chartering, are covered by the charterer itself. Consequentially, the TCavg is simply a quantification of the average cost for shipping raw materials on a established route on one the four dry bulk carriers. The Baltic Dry Index is a very important leading indicator for worldwide business sentiment for several reasons: 1) It is difficult to modify because it is based on pure demandsupply changes which are, in turn, calculated on real orders 2) It is considered to be a leading indicator because orders are usually booked many months in advance (at least 2-3 months because of high intensity traffic in canals and potential port congestions. Think about the ship traffic concentration in the Panama and Suez canals) 3) It is a reliable index because business activities underlying the calculation are all legally certified, financed and paid upfront (none would hire a Panamax ship without having a paid order in place and none would place an order without actually needing raw materials and commodities) 4) It is a very good macroeconomic indicator. as far as shipping raw materials is concerned, because building a dry bulk carrier (whether it is a Handysize, a Supramax, a Panamax or a Capemax ship is irrelevant) takes many years. Therefore, their limited availability makes the tracking easier and more reliable because it means that the largest quantities of shipped raw materials have to necessarily be transported on one of those ships and, consequently, they are being accounted for in the calculation The Baltic Dry Index is fairly straightforward to understand. In fact, higher or lower fluctuations simply imply a net increase or decrease in the demand for commodities and raw materials. Furthermore, the BDI is an efficient way to measure commodities demand because, given the fact that ships are limited and takes years to build, the amount of cargo that needs to be shipped will largely influence the oscillations of the index. The first chart of the present research displays the performance of the Baltic Dry Index since the 30 th of June 2009 until the 27 th of December 2013: The above reported graph shows that the blue line (the actual BDI) has never fully recovered since the peak touched in November 2001 (4,661 points) while the lowest level ever touched was in February 2012 (647 points). It is evident that the 20112012 time interval has been rather flat in terms of shipping activity and demand for raw materials because both the quarterly and semiannual trend lines oscillated laterally for many consecutive months. Nevertheless, the second half of the 2013 (from June onwards) showed an increased number of business activity but the recovery was far from being robust implying that the shipping of raw materials is still lower than it was before the credit crunch. The next chart will attempt to provide clue regarding the volatility of the index on different time perspectives: First of all, it is important to mention that the Baltic Dry Index has a mean reverting volatility which tends to be confined within the 2040 thresholds. Also, the above reported graph suggests that the divergence between the volatility in the midterm (red curve) and the volatility in the longterm (white curve) tends to be lower than the difference between shortterm and mediumterm volatilities. Volatility analysis is crucial in order to understand the fluctuations of the BDI which is why the next chart has been specifically created to show the volatility distribution of the volatility spectrum over the time period June 2009 December 2013: The above reported chart displays the distribution of the volatility of the Baltic Dry Index in the shortterm (ST VOL), mediumterm (MT VOL) and longterm (LT VOL). The High, MidHigh, Medium, MidLow and Low sections correspond to the different volatility segments in the volatility spectrum. The sections will be now examined one at the time: High . The ST volatility touched its highest point at 63.51 while MT and LT volatilities reached their respective tops at 62.41 and 54.20 MidHigh . MidHigh volatilities are higher in the LT and MT than in the ST. In fact, midhigh volatility is 37.64 in the LT, equals 36.45 in the MT and it is approximately 35.05 in the ST Medium . Medium volatility is higher in the long period than in the short one. Specifically, LT medium volatility is 32.25, MT medium volatility is 30.36 and ST medium volatility is 27.12 MidLow . MidLow volatilities are, even in this case, higher in the LT than in the ST. Specifically, LT midlow volatility fluctuates around 25.51, MT mediumlow volatility is usually 24.31 while STs one is 19.19 Low . LT volatility touched its lowest point at 13.83, MT volatility minimum point was reached at 10.67 while in the ST the volatility has never got lower than 6.45 The distribution analysis of the volatility spectrum has indeed provided very useful information. In fact, the calculation shows that midterm and longterm volatilities, if we exclude the High segment, tend to systematically be more elevated than shortterm volatility. Conversely, the highest spike in volatility was actually achieved in the shortterm, although this volatility segment proved to be the least volatile of all. Why is that What does this entail The reason behind such phenomenon is the following: long and medium term volatilities are higher than the short term one as a consequence of the fact that the mean reverting pressure is lower in the LT and MT than in the ST. Specifically, such phenomenon implies that longterm and mediumterm volatility explosions are more persistent and more ample, in terms of magnitude, and consequentially need more time to be reabsorbed. Besides, the fact that the highest volatility point ever reached by the Baltic Dry Index (63.51) was actually achieved in the shortterm implies that, in this segment, volatility explosions can be immediate and rather large although they tend to mean revert quickly. The strong persistency in medium and long term volatility explosions and the higher propensity to a quicker mean reverting process in the shortterm volatility can be better understood by looking at the following serial correlation plot: The chart shows 4 blocks. Each parallelepiped indicates the serial correlation amongst BDI data. The first on the left displays daily serial correlation, the second one from the left refers to weekly serial correlation, the third one from the left shows the monthly serial correlation while the last one refers to quarterly serial correlation. The interpretation of the above reported chart is fairly simple: the data from Baltic Dry Index tends to have a stronger bond in the very short term, a weak link on a weekly basis and they seem to have no relationship as far as monthly and quarterly data are concerned. The significant spread, between the first and the last two parallelepipeds, proves the point that short term volatility explosions tend to mean revert rather quickly and that actual data do not have any strong relationship in the longterm. The serial correlation plot also gives insights about the nature of the Baltic Dry Index itself: poor serial correlation in the longterm is a clear reflection of an everchanging demand level for commodities and raw materials. The final chart highlights any intermarket relationship between the Baltic Dry Index and the most important asset classes in the world: The correlation matrix emphasizes the rapport with 3 markets in particular: Euro, American Treasury Bonds and German Bunds. The correlation between the Baltic Dry Index and Euro futures, over the 20092013 period, is without a doubt, the most robust (0.47). The strong bond with the Single currency is predominantly due to the fact that approximately the 40 of the shipping transactional costs are due to bunker fuel. Bunker fuel (also known as fuel oil) is priced in US dollar but, since Euro is the largest currency component of the Dollar Index, every fluctuation in the European coinage will cause significant changes in the hiring fees charged to ship raw materials around the world. Consequently, the Baltic Dry Index, which accounts for the hiring fees charged for Handysize, Supramax, Panamax and Capemax ships, will be inevitably influenced by such variable. The remaining asset classes that display a good, although negative, correlation to the BDI are the 2 government debt world benchmarks: American TBonds and German Bunds. The reason American (-0.43) and German (-0.38) sovereign debt securities have an inverse link to the BDI is probably: hedging. In fact, the risk caused by taking positions on Baltic Dry Index futures and options contracts, traded through the Baltic Exchange, is usually counterbalanced via stable government bonds. The low correlation among the BDI and the socalled risky assets (DAX, WTI Crude Oil and Mini SampP500) is predominantly due to business cycles and commercial demand (commercials need to place their orders for raw materials 23 months ahead in order to account for production time, manage risk and ensure a continuous flow of commodity supply). On the other hand, the fact that Japanese Yen and Gold do not have a strong relationship with the BDI implies that fund managers, commercials and commodity traders prefer hedging their BDI market exposure using the aforementioned treasury markets. HyperVolatility Researches related to the present one: The HyperVolatility Forecast Service enables you to receive statistical analysis and projections for 3 asset classes of your choice on a weekly basis. Every member can select up to 3 markets from the following list: E-Mini SampP500 futures, WTI Crude Oil futures, Euro futures, VIX Index, Gold futures, DAX futures, Treasury Bond futures, German Bund futures, Japanese Yen futures and FTSEMIB futures. Send us an email at infohypervolatility with the list of the 3 asset classes you would like to receive the projections for and we will guarantee you a 14 day trial The aims of the actual research are, firstly, to present some of the most efficient methods to hedge option positions and, secondly, to show how important option Greeks are in volatility trading. It is worth mentioning that the present study has been completely developed by Liying Zhao (Quantitative Analyst at HyperVolatility ) and all the simulations have been performed via the HyperVolatility Option ToolBox. If you are interested in learning about the fundamentals of the various option Greeks please read the following studies Options Greeks: Delta, Gamma, Vega, Theta, Rho and Options Greeks: Vanna, Charm, Vomma, DvegaDtime . In this research, we will assume that the implied volatilityis not stochastic, which means that volatility is neither a function of time nor a function of the underlying price. As a practical matter, this is not true, since volatility constantly change over time and can hardly be explicitly forecasted. However, doing researches under the staticvolatility framework, namely, the Generalized BlackScholesMerton (GBSM) framework, we can easily grasp the basic theories and then naturally extend them to stochastic volatility models. Recall that the Generalized BlackScholesMerton formula for pricing European options is: And N ( ) is the cumulative distribution function of the univariate standard normal distribution. C Call Price, P Put Price, S Underlying Price, X Strike Price, T Time to Maturity, r Riskfree Interest Rate, b Cost of Carry Rate, Implied Volatility. Accordingly, first order GBSM option Greeks can be defined as sensitivities of the option price to one unit change in the input variables. Consequentially, second or thirdorder Greeks are the sensitivities of first or secondorder Greeks to unit movements in various inputs. They can also be treated as various dimensions of risk exposures in an option position. 1. Risk Exposures Differently from other papers on volatility trading, we will initially look at the Vega exposure of an option position. 1.1 Vega Exposure Some of the variables in the option pricing formula, including the underlying price S, riskfree interest rate r and cost of carry rate b . can be directly collected from market sources. Strike price X and time to maturity T are agreed with the counterparties. However, the implied volatility , which is the market expectation towards the magnitude of the future underlying price fluctuations, cannot be explicitly derived from any market source. Hence, a number of trading opportunities arise. Likewise directional trading, if a trader believes that the future volatility will rise she should buy it while, if she has a downward bias on future volatility, she should sell it. How can a trader buy or sell volatility We already know that Vega measures options sensitivity to small movements in the implied volatility and it is identical and positive for both call and put options, therefore, a rise in volatility will lead to an increase in the option value and vice versa . As a result, options on the same underlying asset with the same strike price and expiry date may be priced differently by each trader since everyone can input her own implied volatility into the BSM pricing formula. Therefore, trading volatility could be, for simplicity, achieved by simply buying underpriced or selling overpriced options. For finding out if your implied volatility is higher or lower than the market one, you can refer to this research that we previously posted. Lets assume an option trader is holding a socalled naked short option position, where she has sold 1,000 outofthemoney (OTM) call options priced with S 90, X 100, T 30 days, r 0.5, b 0, 30, which is currently valued at 434.3. Suppose the market agreed implied volatility decreases to 20, other things being equal, the option position is now valued at 70.6. Clearly, there is a marktomarket profit of 363.7 (434.3-70.6) for this trader. This is a typical example of Vega exposure. Figure 1 shows the Vega exposure of above the option position. It can be easily observed that the Vega exposure may augment or erode the position value in a nonlinear manner: (Figure 1. Source: HyperVolatility Option Tool Box) A trader can achieve a given Vega exposure by buying or selling options and can make a profit from a better volatility forecast. However, the value of an option is not affected solely by the implied volatility because when exposed to Vega risk, the trader will simultaneously be exposed to other types of risks. 1.2 Theta Exposure Theta is the change in option price with respect to the passage of time. It is also called time decay because Theta is considered to be always negative for long option positions. Given that all other variables are constants, option value declines over time, so Theta can be generally referred to as the price one has to pay when buying options or the reward one receives from selling options. However, this is not always true. It is worth noting that some researchers have reported that Theta can be positive for deep ITM put options on nondividendpaying stocks. Nevertheless, according to our research, which is displayed in Figure 2 . where X 100, T 30 days, r 0.5, b 0, 30, the condition for positive Theta is not that rigorous: (Figure 2. Source: HyperVolatility Option Tool Box) For deep inthemoney (ITM) options (with no other restrictions) Theta can be slightly greater than 0. In this case, Theta cannot be called time decay any longer because the time passage, instead, adds value to bought options. This could be thought of as the compensation for option buyers who decide to give up the opportunity to invest the premiums in riskfree assets. Regarding the aforementioned instance, if an option trader has sold 1,000 OTM call options priced with S 90, X 100, T 30 days, r 0.5, b 0, 30, the Theta exposure of her option position will be shaped like in Figure 3 : (Figure 3. Source: HyperVolatility Option Tool Box) In the real world, none can stop time from elapsing so Theta risk is foreseeable and can hardly be neutralized. We should take Theta exposure into account but do not need to hedge it. 1.3 Interest RateCost of Carry Exposure (RhoCost of Carry Rho) The cost of carry rate b is equal to 0 for options on commodity futures and equals rq for options on other underlying assets (for currency options, r is the riskfree interest rate of the domestic currency while q is the foreign currencys interest rate for stock options, r is the riskfree interest rate and q is the proportional dividend rate). The existence of r . q and b does have an influence on the value of the option. However, these variables are relatively determinated in a given period of time and their change in value has rather insignificant effects on the option price. Consequently, we will not go too deep into these parameters. 1.4 Delta Exposure Delta is the sensitivity of the option price with regard to changes in the underlying price. If we recall the aforementioned scenario (where a trader has sold 1,000 OTM call options priced with S 90, X 100, T 30 days, r 0.5, b 0, 30, valued at 434.3) if the underlying price moves downwards, the position can still be able to make profits because the options will have no intrinsic value and the seller can keep the premiums. However, if the underlying asset is traded at, say, 105, all other things being equal, the option value becomes 6,563.7, which leads to a notable marktomarket loss of 6,129.4 (6,563.7-434.3) for the option writer. This is a typical example of Delta risk one has to face when trading volatility. Figure 4 depicts the Delta exposure of the above mentioned option position, where we can see that the change in the underlying asset price has significant influences on the value of an option position: (Figure 4. Source: HyperVolatility Option Tool Box) Compared to Theta, Rho and cost of carry exposures, Delta risk is definitely much more dominating in volatility trading and it should be hedged in order to isolate volatility exposure. Consequentially, the rest of this paper will focus on the introduction to various approaches for hedging the risk with respect to the movements of the underlying price. 2. Hedging Methods At the beginning of this section, we should clearly define two confusable terms: hedging costs and transaction costs. Generally, hedging costs could consist of transaction costs and the losses caused by buy high and sell low transactions. Transaction costs can be broken down into commissions (paid to brokers, etc. ) and the bidask spread. These two terms are usually confounded because both of them have positive relationships with hedging frequency. Mixing these two terms up may be acceptable, but we should keep them clear in mind. 2.1 Covered Positions A covered position is a static hedging method. To illustrate it, let us assume that an option trader has sold 1,000 OTM call options priced with S 90, X 100, T 30 days, r 0.5, b 0, 30, and has gained 434.3 premium. Compared to the naked position, this time, these options are sold simultaneously with some purchased underlying assets, say, 1,000 stocks at 90. In this case, if the stock price increases to a value above strike price ( e. g. 105) at maturity, the counterparty will have the motivation to exercise these options at 100. Since the option writer has enough amount of stocks on hand to meet the exercise demand, ignoring any commission, she can still get a net profit of 1,000(100-90) 434.3 10,434.3. On the contrary, if the stock price stays under the strike price ( e. g. 85) upon expiry date, the sellers premium is safe but has to suffer a loss in stock position which in total makes the trader a negative profit of 1,000(85-90) 434.4-4565.7. The covered position can offer some degrees of protection but also induces extra risks in the meantime. Thus, it is not a desirable hedging method. 2.2 Stop-Loss Strategy To avoid the risks incurred by stock prices downward trends in the previous instance the option seller could defer the purchase of stocks and monitor the movements of the stock market. If the stock price is higher than the strike price, 1,000 stocks will be bought as soon as possible and the trader will keep this position until the stock price will fall below the strike. This strategy seems like a combination of a covered position and a naked position, where the trader is naked when the position is safe and he is covered when the position is risky. The stop-loss strategy provides some degrees of guarantee for the trader to make profits from option position, regardless of the movements of the stock price. However, in reality, since this strategy involves buy high and sell low types of transactions, it can induce considerable hedging costs if the stock price fluctuates around the strike. A smarter method to hedge the risks from the movements of the underlying price is to directly link the amount of bought (sold) underlying asset to the Delta value of the option position in order to form a Delta neutral portfolio. This approach is referred to as Delta hedging. How to set up a Deltaneutral position Again, if a trader has sold 1,000 call options priced with S 90, X 100, T 30 days, r 0.5, b 0, 30 the Delta of her position will be -119 (-1,0000.119), which means that if the underlying increases by 1, the value of this position will accordingly decrease by 119. In order to offset this loss, the trader can buy 119 units of underlying, say, stocks. This stock position will give the trader 119 profit if the underlying increases by 1. On the other hand, if the stock price decreases by 1, the loss on the stock position will then be covered by the gain in the option position. This combined position seems to make the trader immunized to the movements of the underlying price. However, in the case the underlying trades at 91, we can estimate that the new position Delta will be -146. Obviously, 119 units of stocks can no longer offer full protection to the option position. As a result, the trader should rebalance her position by buying 27 more stocks to make it Deltaneutral again. By doing this continuously, the trader can have her option position well protected and will enjoy the profit deriving from an improved volatility forecasting. Nevertheless, it should be noted that Deltahedging also involves buy high and sell low operations which could cause a loss for every transaction related to the stock position. If the price of the underlying is considerably volatile, the Delta of the option position would change frequently, meaning the option trader has to adjust her stock position accordingly with a very high frequency. As a result, the cumulative hedging costs can reach an unaffordable level within a short period of time. The aforementioned instance show that increasing hedge frequency is effective for eliminating Delta exposure but counterproductive as long as hedging costs are concerned. To reach a compromise between hedge frequency and hedging costs, the following strategies can be taken into considerations. 2.4 DeltaGamma Hedging In the last section, we have found that Delta hedging needs to be rebalanced along with the movements of the underlying. In fact, if we can make our Delta immune to changes in the underlying price, we would not need to rehedge. Gamma hedging techniques can help us accomplishing this goal (recall that Gamma is the speed at which the Delta changes with respect to movements in the underlying price). The previously reported example, where a trader has sold 1,000 call options priced with S90,X100,T30days, r0.5,b0 , 30 had a position Delta equal to -119 and a Gamma of -26. In order to make this position Gammaneutral, the trader needs to buy some options that can offer a Gamma of 26. This can be easily done by buying 1,000 call or put options priced with the same parameters as the sold options. However, buying 1,000 call options would erode all the premiums the trader has gained while buying 1,000 put options would cost the trader more, since put options would be much more expensive in this instance. A positive net premium can be achieved by finding some cheaper options. Let us assume that the trader has decided to choose, as a hedging tool, the call option priced with S 90, X 110, T 30 days, r 0.5, b 0, 30, with 0.011 Delta and 0.00374 Gamma. To offset his sold Gamma, the trader needs to buy 260.00374 6,952 units of this option which cost him 197.3 which leads to an extra Delta of 6,9520.01176. At this point, the trader has a Gammaneutral position with a net premium of 237 (434.3-197.3) and a new Delta of -43(-11976). Therefore, buying 43 units of underlying will provide the trader with Delta neutrality. Now, lets suppose that the underlying trades at 91, the Delta of this position would become -32 but since the trader had already purchased 43 units of stocks, she only needs to sell 12 units to make this position Deltaneutral. This is definitely a better practice than buying 27 units of stocks as explained in section 2.3 where the trader had only Delta neutralized but was still running a nonzero Gamma position. However, DeltaGamma Hedging is not as good as we expected. In order to explain this, let us look at Figure-5 which shows the Gamma curve for an option with S 90, X 110, T 30 days, r 0.5, b 0, 30: (Figure 5. Source: HyperVolatility Option Tool Box) We can see that Gamma is also changing along with the underlying. As the underlying comes closer to 91, Gamma increases to 0.01531 (it was 0.00374 when the underlying was at 90) which means that, at this point, the trader would need 107 (6,9540.01531) Gamma and not 26 to offset her Gamma risk. Hence, she would have to buy more options. In other words, Gammahedging needs to be rebalanced as much as delta hedging. DeltaGamma Hedging cannot offer full protection to the option position, but it can be deemed as a correction of the Deltahedging error because it can reduce the size of each rehedge and thus minimize costs. From section 2.3 and 2.4, we can conclude that if Gamma is very small, we can solely use Delta hedging, or else we could adopt DeltaGamma hedging. However, we should bear in mind that DeltaGamma hedging is good only when Speed is small. Speed is the curvature of Gamma in terms of underlying price, which is shown in Figure 8211 6: (Figure 6. Source: HyperVolatility Option Tool Box) Using the basic knowledge of Calculus or Taylor8217s Series Expansion, we can prove that: We can see that Delta hedging is good if Gamma and Speed are negligible while DeltaGamma hedging is better when Speed is small enough. If any of the last two terms is significant, we should seek to find other hedging methods. 2.5 Hedging Based on Underlying Price Changes Regular Time Intervals To avoid infinite hedging costs, a trader can rebalance her Delta after the underlying price has moved by a certain amount. This method is based on the knowledge that the Delta risk in an option position is due to the underlying movements. Another alternative to avoid overfrequent Delta hedging is to hedge at regular time intervals, where hedging frequency is reduced to a fixed level. This approach is sometimes employed by large financial institutions that may have option positions in several hundred underlying assets. However, both the suitable underlying price changes and regular time intervals are relatively arbitrary. We know that choosing good values for these two parameters is important but so far we have not found any good method to find them. 2.6 Hedging by a Delta Band There exist more advanced strategies involving hedging strategies based on Delta bands. They are effective for finding the best tradeoff between risks and costs. Among those strategies, the Zakamouline band is the most feasible one. The Zakamouline band hedging rule is quite simple: when the Delta of our position moves outside of the band, we need to rehedge and just pull it back to the edge of the band. However, the theory behind it and the derivation of it are not simple. We are going to address these issues in the next research report. Figure-7 provides an example of the Zakamouline bands for hedging a short position consisting of 1,000 European call options priced with S 90, X 110, T 30 days, r0.5, b 0, 30: (Figure 7. Source: HyperVolatility Option Tool Box) In the next report, we will see how the Zakamouline band is derived, how to implement it, and will also see the comparison of Zakamouline band to other Delta bands in a quantitative manner. The HyperVolatility Forecast Service enables you to receive statistical analysis and projections for 3 asset classes of your choice on a weekly basis. Every member can select up to 3 markets from the following list: E-Mini SampP500 futures, WTI Crude Oil futures, Euro futures, VIX Index, Gold futures, DAX futures, Treasury Bond futures, German Bund futures, Japanese Yen futures and FTSEMIB futures. Send us an email at infohypervolatility with the list of the 3 asset classes you would like to receive the projections for and we will guarantee you a 14 day trial Crude oil is a scarce resource which means that at some point the existing oil wells will be exhausted. The current estimations, given the actual extraction and consumption rates, sustain that the black gold will be available for another 40 years but any increase in the demand would reduce the aforementioned projections. The USA has a Strategic Petroleum Reserve which has been specifically created in order to face shortages in the supply, however, rising oil prices and new technologies are pushing towards alternative source of energy. Companies and businesses are considering potential substitute for crude oil and the alternative energy sources, that are increasingly becoming popular, are biofuels (like ethanol), hydrogen fuels, fuel cells, solar energy, nuclear power (even though nuclear power is not an environmentally friendly solution) and wind power. Nevertheless, the demand for refined products is still very high and each oil derivative has its own market and its own price driver. A perfect example of divergence in price drivers for refined products comes for Europe. In the 90s many European governments guaranteed tax incentives to all the drivers who would have bought dieselpowered cars because diesel fuel emits less greenhouse gases than gasoline. Needless to say that such policy provoked a sharp augment in diesel prices but not in other oil derivatives. Lets now have a look at the oil industry as a whole. First of all, it is worth mentioning that the oil industry is subdivided into 3 subsectors: upstream, midstream and downstream. The upstream involves the exploration and the extraction of crude oil, the midstream sector consists of transportation and storage while the downstream segment refers to the refining industry, marketing and distribution of refined products. Upstream The supply chain falls within the upstream segment. Here, the most important thing to determine is the capacity of the onshore or offshore site because this measurement identifies how big the oil well is and, consequently, the extraction rate. It is worth noting that major companies tend to retain a certain amount of unused capacity in order to face unexpected or sudden explosion in demand (usually caused by geopolitical issues). Midstream Once the extraction process is over, the oil enters the second segment: the midstream. This sector has to do, predominantly, with the transportation of the extracted petroleum liquids towards the refining centers. The transition can be processed using pipelines, trucks, barges or rail. Downstream Downstream operations are strongly connected with the refining industry because it is in this segment of the production chain that diesel, kerosene, jet fuel oil and all the other petroleum liquids get synthesized. Now, refining capacity is often closely related to demand for obvious reasons but not all refineries can deal with a broad range of crude oils so there are certain production boundaries. Nevertheless, the business is straightforward: refineries buy crude oil, they refine it and then sell the synthesized outputs. The income generated by refineries is measured with the socalled crack spread (there will be another study entirely focused on this product). The cost of crude oil is not solely influenced by upstream, midstream and downstream operations. In fact, exogenous variables or unexpected events such as natural disasters, political turbulences and quality reduction of a specific oil well can push market players to increase their inventories. Consequentially, an augment in the short term demand and forward delivery would increase the cost of storage and, in turn, the cost of carry. Amongst all of the exogenous factors that can alter oil prices, the geopolitical ones are certainly the most dangerous. Conflicts and political instability in the Middle East have always had a remarkable impact on oil prices. Besides, African or Latin American countries, such as Nigeria and Venezuela, have often hosted violent riots that have increased the buying pressure on the oil market. Geopolitical issues create nervousness among market players and increase prices because internal riots, civil wars, unstable or corrupted governments could jeopardize the supply and limit the amount of oil available. Also, extreme forms of governments (fascism, communism, military controlled countries, etc) are not well seen by oil importing countries because dictators andor nondemocratically elected governments could threaten to limit the extraction or the export of oil. The next chart provides a better clue on the relationship between geopolitical factors and oil prices: The chart shows the fluctuations of WTI Crude Oil futures prices since July 1986 so far. The graph does not really need any comment because the arrows are self explanatory. Wars, civil wars, political turmoil, crises and cuts in the extraction rate have always added a significant pressure on crude prices which have been inevitably pushed higher. The only 3 big events, worth mentioning, that have depressed oil prices have been the Asian Economic Crisis in the mid 90s, the terroristic attack to the Twin Towers in September 2001and the Credit Crunch in 20082009. Clearly, the Middle East is a vital geographical area for oil so any turbulence in this zone is strongly felt by market participants. Likewise, the other OPEC members do not always enjoy a great deal of political and civil stability (the OPEC members are Algeria, Indonesia, Islamic Republic of Iran, Iraq, Kuwait, Libya, Nigeria, Qatar, Saudi Arabia, United Arab Emirates, Venezuela). The following chart shows the weight of each OPEC member in terms of number of daily extracted barrels: As previously mentioned, the chart displays the weight of each country expressed as a percentage of the total OPEC daily barrel production (the data are recent and they refer to the period JanuaryJune 2013). Saudi Arabia (29.68), Iran (11.6), Iraq (9.43), Kuwait (9.17) United Arab Emirates (8.78) and Venezuela (8.63) are the top 6 largest OPEC members. The fact that 5 out of 6 among the largest OPEC members are all located in the Middle East explains very clearly why this world region is so closely monitored by oil importing countries like United States, China, Japan, India and Germany. If you are interested in trading oil or oil derivatives markets you might want to read the following HyperVolatility researches: The HyperVolatility Forecast Service enables you to receive statistical analysis and projections for 3 asset classes of your choice on a weekly basis. Every member can select up to 3 markets from the following list: E-Mini SampP500 futures, WTI Crude Oil futures, Euro futures, VIX Index, Gold futures, DAX futures, Treasury Bond futures, German Bund futures, Japanese Yen futures and FTSEMIB futures. Send us an email at infohypervolatility with the list of the 3 asset classes you would like to receive the projections for and we will guarantee you a 14 day trial . The VIX Index has been introduced by the CBOE in January 1993 and since then it has become the most popular and well known volatility index in the world. The VIX is an index extracted from SampP500 options and its calculation has been changed in September 2003 in order to obtain observations not linked or dependant from any model idiosyncrasy. The present study, inspired by the paper written and compiled by the CBOE, will show how to calculate the VIX Index in a stepbystep fashion. There will be ample explanations about how the index works and we will break down the formula in order to provide a better understanding of the function and weight of every component. Lets start with the general formula for the VIX Index: T Time to expiration F Forward Index price (the ATM strike price) K 0 First strike price below the Forward price F K i Strike of the i th outofthemoney option. A call option strike will be considered if K i gtK 0 while a put option strike will be used if K i K 0 K i it is the midpoint between the strike prices. Specifically, the strikes used will be on both the sides of K i . In other words, K for the lowest strike is just the difference between the lowest strike and the penultimate strike of the option chain while K for the highest strike is equivalent to the difference between the highest strike and the strike immediately below the top one. The formula is the following ampspacebgwhiteampspaceDeltaampspaceKimathampspaceampspacefrac R Risk free interest rate (the interest rate used is usually the Treasury Bond yield that more closely matches the option expiration date) Q (K i ) The midpoint of the spread between bid price and ask price for each option with a strike K i This is the formula that it is currently employed to calculate the most famous risk management index in the world. Before we provide any real example it is necessary to clarify some points. First of all, the VIX index is calculated using 2 expirations: the front month and the second front month contracts. In our study we will be using SampP500 option prices recorded on the 10 th of October 2013 and therefore the front month options will be those expiring on the 18 th of October 2013 (which will provide us with information about the volatility in the near term) while the second front month options will expire on the 15 th of November 2013 and they will provide us with information about the volatility in the medium term. It is important to point out that near term options must have at least 7 days to expiration and when this criteria is no longer met the model automatically rolls to the next available contract. Lets give an example, our front month options expire on the 18 th of October while the medium term options will expire on the 15 th of November, hence, on Friday the 12 th the VIX will mechanically roll. At this point, the front month options used will be the ones expiring on the 15 th of November while the second front month options employed in the calculation will become those expiring in December. This measure has to be adopted in order to avoid mispricing issues that commonly happen when options are about to expire. Another important detail to mention is that T (time to expiration) is calculated in minutes using calendar days, consequently, the time to expiration will be given by M current day minutes remaining until midnight of the same day M settlement day minutes remaining from midnight until 08:30 am on SPX settlement day M other days total minutes in the days between current day and settlement day If we assume that the data have been recorded exactly at 08:30 am on the 10 th of October and that options will expire at 08:30 am of the 18 th of October: Needless to say that T 1 and T 2 refer to near term and medium term options respectively. The yield for 1 month Treasury Bills as of the 9 th of October 2013 was 0.27 and therefore, given that our October options expire in 9 days while the November options will expire in 37 days, we will use this figure for both near and medium terms. We now need to determine the F price of the index and in order to do so we take the strike price at which puts and calls have the smallest difference in absolute terms. The below reported table displays call and put prices with their absolute differential: The red backgrounded figures are the strike prices at which calls and puts have the lowest difference, however, the two expiration dates have 2 different strike prices: ATM for October options is at 1,650 while ATM for November options is 1,655. In order to simplify calculations, and given the fact that the difference is extremely small, we will take 1,650 as F price because it is the front month contract. We can calculate F using the following formula: Obviously, there will be two forward index values, F 1 and F 2 . the first for near term and the second one for medium term options respectively: Now we have both F 1 and F 2 . so we can identify K 0 which is the strike price immediately below the forward prices. In our case, the closest strike right below F 1 and F 2 is 1,650. Consequentially, K 0,1 1,650 and K 0,2 1,650. The next step is to select all put options whose strike is lower than K 0 and all call options whose strike is higher than K 0 . The selection excludes every option with a bid equal to 0 and it terminates when there are 2 consecutive strike prices that equal zero: The above reported table explains very well what stated before. In the month of October the lowest puts are at 790 and 795 but the two red backgrounded options cannot be accepted in our calculation because there are two consecutive 0 in their bid prices and therefore they are our stopping point. In other words, no option with a lower than 800 strike price will be considered into the calculation of the VIX. The same principle applies to calls and in fact 2,095 and 2,100 are the highest call option strike prices that will be considered. The same procedure will be applied to November options. It is important to point out that the option chains will rarely have the same amount of strikes available because according to volatility fluctuations the number of strikes that will be priced by market makers will vary. It goes without saying that high volatility explosions will obligate market makers to price even FarAwayFromTheMoney options on both sides because the demand for these instruments will rise. Consequentially, the number of strikes that will be used for the purpose of calculating the VIX will vary according to volatility fluctuations and swings in SampP500 futures. The following table lists the options that will be used for calculating the volatility index: The ATM strike is highlighted in blue. The put options in the near term contract that will be used start from strike 800 until strike 1,645 while the call options range from strike 1,655 until strike 2,100. The medium term strikes, instead, goes from 985 until 1,645 for put options and from strike 1,655 until strike 2,100 for calls. We now calculate the specific weight that every single strike will have in the calculation by using the following formula and we will take the 800 put as an example: Please bear in mind that Q is the midpoint between bid and ask while K is the difference between the last options strike and the closest next strike, hence, in our case K is (805 800) 5. Lets proceed with the calculation: The next table summarizes the contribution of each option strike to the overall computation of the VIX Index: Now, the weights need to be added up and multiplied by 2T 1 for the near term and by 2T 2 for the medium term and by performing this calculation we would have 0.074319519775 for the near term and 0.041553088 for the medium term. The equation (1) that we presented at the beginning of this study is almost completed, in fact, the final part is the only one yet to be estimated. Lets proceed: We can now complete the calculation by subtracting the two members of equation (1) : Near Term 2 1 . 0.074319519775 0.000016423 0.074303096 Medium Term 2 2 . 0.041553088 0.000021750 0.041531338 The final VIX computation is given by the following formula: The second term of the equation is nothing but the computation of the square root of the 30 day average of 2 1 and 2 2 which are subsequently multiplied by the first term 100. The weights of 2 1 and 2 2 are less than 1 or almost equal to 1 when the near term options have less 30 days and the medium term options have more than 30 days to expiration. However, it is worth noting that when the VIX rolls both near and medium term options have more than 30 days to expiration. Lets now conclude the VIX estimation: N T1 minutes left before the settlement of near term options N T2 minutes left before the settlement of medium term options N 30 number of minutes in 30 days N 365 number of minutes in a year composed by 365 days If we plug in the numbers we have the following outcome: This leads to the very last step: VIX 100 x 0.209736087 20.9 Now, the number we came out with is fairly accurate but it is limited to the moment in which the option prices have been frozen. Consequentially, the aforementioned procedure and calculation, in order to be precise, has to be automated and repeated every instant because any changes in option premiums will inevitable affect the final assessment of the VIX. The HyperVolatility Forecast Service enables you to receive statistical analysis and projections for 3 asset classes of your choice on a weekly basis. Every member can select up to 3 markets from the following list: E-Mini SampP500 futures, WTI Crude Oil futures, Euro futures, VIX Index, Gold futures, DAX futures, Treasury Bond futures, German Bund futures, Japanese Yen futures and FTSEMIB futures. Send us an email at infohypervolatility with the list of the 3 asset classes you would like to receive the projections for and we will guarantee you a 14 day trial . Option markets are multidimensional, in fact, options spreads can be created using different strikes, different maturities or different type of options (calls puts). Besides, option traders cannot track instantaneous price changes on the entire option chain, hence, it is easy to derive that the most important factor in option trading is not the price of the option itself. The variable that has to be accurately tracked and monitored at all times is, in fact, what drives and determines the price of the option: volatility. In reality, there are different types of volatilities but the one extracted from option premiums is called implied volatility (the volatility extracted from futures prices is instead referred to as realized volatility) and its shapes and fluctuations are crucial to any market player involved in options trading. The present research will try to describe the dynamics of the implied volatility shape and to analyze its most common evolutions: Smile, Smirk and Forward Skew. In particular, the implied volatility figures used in the present examination have been extracted from front month WTI option premiums traded on the 30 th of August 2013 which expire in October. All calculations and charts have been respectively performed and created with the HyperVolatility Option Toolbox . The following chart displays the socalled volatility smile: (Source: HyperVolatility Option Toolbox) As we can see from the above reported graph, the curve is higher at the extremes but rather low in the middle (bear in mind that the AttheMoney strike was 107.5). This is the typical shape for a front month implied volatility curve where the high demand for ITM calls and OTM puts as well as for ITM puts and OTM calls drives the volatility higher. In many cases, you will hear that the volatility for OutoftheMoney options is higher but such statement is clearly incorrect because without further specification it implies that only OTM puts and calls experience such high volatility. The chart evidently shows that the volatility for ITM and OTM options is higher but, for obvious reasons, the volatility for the strike where a call option is IntheMoney will be almost as high as the volatility for the OutoftheMoney put option and vice versa. Consequentially, saying that AwayfromtheMoney options (both calls and puts) have a higher implied volatility than AttheMoney options is without a doubt the most correct statement. The most natural questions at this point would be: Why What does a smileshaped curve tell us The most obvious thing to say is that the volatility on AFTM options is higher because investors tend to trade them more often and they consequently push the volatility on the upside. The reason why investors buy wings is that ITM options have more intrinsic value than the ATM ones while OTM options have more extrinsic value than an option struck AttheMoney. Consequentially, the presence of an implied volatility smileshaped curve is typical of more speculative markets. The smile suggests that, when large volatility shifts happen, many market players rush to buy OTM options for speculative reasons while ITM options are primarily purchased to stabilize portfolio gains. The next chart shows how the curve moves: (Source: HyperVolatility Option Toolbox) Many researches on implied volatility curve dynamics showed that the 75 of volatility changes can be defined by a total shift, up or down, of the entire curve as you can see from the chart. A further 15 of the movements consist of curve twisting (the right hand side of the curve goes deeper down while the left side gets pulled on the right or vice versa) while the remaining 10 is the product of a change in convexity (wings getting wider or tighter). Smileshaped curves are frequently found in equity index options, stock options and popular commodities currencies (Euro, WTI, Gold, etc). Nevertheless, it is worth noting that the shape of the curve can even evolve over time. This concept can be better explained by looking at the following chart: (Source: HyperVolatility Option Toolbox) The smirk is a particular volatility profile where ITM calls and OTM puts are priced with a much higher implied volatility. This phenomenon is commonly found in equity markets and risky assets. In this simulation the ATM strike is 116 and its volatility is 13.1 but OTM puts and ITM calls are much more expensive because they are trading above the 70 level. As previously mentioned, the implied volatility curve can change and evolve and a volatility smile can turn into a smirk if investors, traders and market players are expecting a market crash or if the plunge in price has already happened. Smirks are simply telling us that lower strikes are more traded than higher strikes and OTM puts as well as ITM calls are being heavily traded. If the market is heading south, a smile would easily evolve into a smirk because of the great buying pressure generated by market players rushing to buy OTM puts to protect their portfolios. The purchase of ITM calls, even during market crashes, makes sense because ITM call options have already an established intrinsic value and they have the highest probability to expire IntheMoney in other words they are safer. However, in the event of market downtrends the evolution of a volatility smile into a smirk would predominantly be caused by the large buying volume on OTM puts. The Volatility smile, nevertheless, can go through another metamorphosis whose final output is the socalled forward skew: (Source: HyperVolatility Option Toolbox) The forward skew is nothing but a reversed form of smirk, in fact, the volatility here tends to become higher for ITM puts and OTM calls. This type of curve is more frequently found in commodity markets, particularly agricultural products, than equity indices or stock options. Even in this case the increase in volatility is provoked by an augment in demand for these options. However, the strong buying pressure concentrated on OTM calls is often the main cause of such shape. Let us break it down. Many players in commodity markets are commercials (mining and energy companies, grain wheat sugar coffee producers) and therefore a disruption in the supply chain of a particular commodity can generate serious problems. A shortage in oil supply due to geopolitical variables, a disappointing crop due to a frost or to challenging meteorological conditions, continuous strikes in a particularly large mine are all factors that would force companies to buy as quickly as possible the commodity they need in order to lock in the order. Consequentially, the remarkable buying pressure on OTM calls would inevitably drive their price up and that is why the implied volatility of higher strikes is more elevated than others. Let us now summarize the main concepts in order to avoid confusion: 1) An implied volatility smile means that AwayfromtheMoney options have a higher implied volatility than AttheMoney options 2) Implied volatility smileshaped curves are typical of highly speculative markets 3) Many researches on implied volatility curve dynamics showed that the 75 of all volatility changes consist of a shift, up or down, of the entire curve 4) Smileshaped curves are frequently found in equity index options, stock options and the most popular commodities currencies 5) The smirk is a particular volatility profile where ITM calls and OTM puts are priced with a much higher implied volatility 6) Volatility smile curves can turn into a smirk if investors, traders and market players are expecting a market crash or if the plunge in price has already happened 7) The forward skew is a reversed form of smirk, in fact, the volatility here tends to become higher for ITM puts and OTM calls 8) The forward skew curve is more frequently found in commodity markets (particularly in agricultural products) 9) The formation of a forward skew curve is often the consequence of a shortage in the supply chain due to transportation issues, geopolitical problems, adverse meteorological conditions, etc The HyperVolatility Forecast Service enables you to receive statistical analysis and projections for 3 asset classes of your choice on a weekly basis. Every member can select up to 3 markets from the following list: E-Mini SampP500 futures, WTI Crude Oil futures, Euro futures, VIX Index, Gold futures, DAX futures, Treasury Bond futures, German Bund futures, Japanese Yen futures and FTSEMIB futures. Send us an email at infohypervolatility with the list of the 3 asset classes you would like to receive the projections for and we will guarantee you a 14 day trial. Trading volume and volatility in the shipping forward freight market This paper investigates the price volatility and trading volume relationship in the forward freight agreement (FFA) market for dry bulk ships over the period 2007ndash2011. It is found that FFA price changes have a positive impact on trading volume, suggesting a momentum effect as higher capital gains encourage more transactions. Também há evidências de uma relação contemporânea e positiva entre o volume de negócios e a volatilidade, o que está de acordo com a evidência dos mercados financeiros e a Hipótese da Mistura de Distribuição. No entanto, os aumentos na volatilidade dos preços levam a menores atividades de negociação futura no mercado FFA. Destaques O estudo investiga a volatilidade dos preços e a relação de volume no mercado FFA. Observa-se que um efeito de impulso impulsiona o mercado FFA e a atividade comercial. Os negócios da FFA são principalmente informações geradas por especuladores em vez de hedgers. Existe uma relação positiva contemporânea entre volatilidade e volume de negócios. Além disso, a volatilidade do preço atrasada tem um impacto negativo no volume de negócios da FFA. Shipping Forward freight agreement Volatility Trading volume Causality
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