Outline StatisticalArbitrageFramework CommodityMarketsandInefficiencies StatArbMethodology Investigating Statistical Arbitrage in Commodity Markets Viviana Fanelli UniversityofBari MDEF, Urbino, September 20, 2014 VivianaFanelli UniversityofBari InvestigatingStatisticalArbitrageinCommodityMarkets Outline StatisticalArbitrageFramework CommodityMarketsandInefficiencies StatArbMethodology Outline 1. Statistical Arbitrage Framework 2. Commodity Markets and Inefficiencies 3. StatArb Methodology VivianaFanelli UniversityofBari InvestigatingStatisticalArbitrageinCommodityMarkets Outline StatisticalArbitrageFramework CommodityMarketsandInefficiencies StatArbMethodology Outline 1. Statistical Arbitrage Framework 2. Commodity Markets and Inefficiencies 3. StatArb Methodology VivianaFanelli UniversityofBari InvestigatingStatisticalArbitrageinCommodityMarkets Outline StatisticalArbitrageFramework CommodityMarketsandInefficiencies StatArbMethodology EfficientMarketHypothesis Efficient Market Hypothesis: Fama 1970 Market Efficiency implies stock prices fully reflect all publicly available information instantaneously, thus no investment strategies can systematically earn abnormal returns. ⇓ Stock market anomalies are violations of Efficient Market Hypothesis in whichconsistentlyabnormalreturnscanbeearnedbyonsomeinvestment strategies that are constructed based on potential market inefficiencies. ⇓ The Joint Hypothesis problem refers to that testing for market efficiency is problematic, or even impossible. Any attempts to test for market (in)efficiency must involve an equilibrium asset pricing models. VivianaFanelli UniversityofBari InvestigatingStatisticalArbitrageinCommodityMarkets Outline StatisticalArbitrageFramework CommodityMarketsandInefficiencies StatArbMethodology AbitofHistory A bit of History Statistical Arbitrage: long horizon trading opportunity that generates riskless profits. (cid:73) 1980: Pairs Trading: Nunzio Tartaglia. (cid:73) 1990: Statistical Arbitrage (StatArb): statistical-mathematical models are used to individuate pricing inefficiencies and to profit from mispricing. (cid:73) 2002: Losing interest in StatArb models. Bad performance and poor confidence. (cid:73) 2005: New interest in StatArb models. VivianaFanelli UniversityofBari InvestigatingStatisticalArbitrageinCommodityMarkets Outline StatisticalArbitrageFramework CommodityMarketsandInefficiencies StatArbMethodology StatisticalArbitrageDefinition Definition: Bondarenko (2003) (cid:73) For Bondarenko (2003) the definition of statistical arbitrage opportunity derives from the concept of pure arbitrage opportunity. A pure arbitrage opportunity is a zero cost trading strategy by which gains are received with no possibility of losses. Instead, a statistical arbitrage opportunity is a zero-cost trading strategy for which the expected payoff is positive and the conditional expected payoff in each state of the economy is nonnegative, meaning that the strategy payoff can be negative in some elementary states, as long as the average payoff in each final state is nonnegative. VivianaFanelli UniversityofBari InvestigatingStatisticalArbitrageinCommodityMarkets Outline StatisticalArbitrageFramework CommodityMarketsandInefficiencies StatArbMethodology StatisticalArbitrageDefinition Definition: Bondarenko (2003) A zero-cost trading strategy with a payoff Z =Z(I ) is called a T T statistical arbitrage opportunity if 1. E[Z |I ]>0, and T 0 2. E[Z |IξT]≥0 for all ξ , T 0 T where IξT :=(I ;ξ )=(ξ ,...,ξ ;ξ ) denotes the augmented t t T 1 t T information set which in addition to the market information at time-t also includes the knowledge of the final state of the economy. VivianaFanelli UniversityofBari InvestigatingStatisticalArbitrageinCommodityMarkets Outline StatisticalArbitrageFramework CommodityMarketsandInefficiencies StatArbMethodology StatisticalArbitrageDefinition Definition: Jarrow et al. (2003, 2005) (cid:73) ForJarrowetal. (2003, 2005)astatisticalarbitrageisalonghorizon trading opportunity that generates riskless profits. It is a natural extension of the trading strategies utilized in the existing empirical literature on anomalies. Statistical arbitrage is defined without any reference to any equilibrium model, therefore, its existence is inconsistent with market equilibrium and, by inference, market efficiency. The notion of statistical arbitrage enables the rejection of market efficiency without invoking the joint hypothesis of an equilibrium model. The joint hypothesis of an equilibrium model is replaced with an assumed stochastic process for trading profit. VivianaFanelli UniversityofBari InvestigatingStatisticalArbitrageinCommodityMarkets Outline StatisticalArbitrageFramework CommodityMarketsandInefficiencies StatArbMethodology StatisticalArbitrageDefinition Definition: Jarrow et al. (2003, 2005) A statistical arbitrage is a zero initial cost, self-financing trading strategy with cumulative discounted trading profits v(n) and incremental trading profits ∆v(n) such that: (cid:73) v(0)=0 (cid:73) lim EP[v(n)]>0 n→∞ (cid:73) lim P(v(n)<0)=0 and n→∞ (cid:73) lim Var[∆v(n)] =0 if P[v(n)<0]>0,∀n<∞ n→∞ n [lim Var[∆v(n)|∆v(n)<0]=0] n→∞ P is the statistical probability measure. VivianaFanelli UniversityofBari InvestigatingStatisticalArbitrageinCommodityMarkets Outline StatisticalArbitrageFramework CommodityMarketsandInefficiencies StatArbMethodology StatisticalArbitrageDefinition Financial meaning Statistical fair-price long-term relationship between assets (cid:8) Exploiting predictability in price dynamics VivianaFanelli UniversityofBari InvestigatingStatisticalArbitrageinCommodityMarkets