Imperial College London
                     Business School
      Trading Strategies in Futures Markets
                     James Grant
        Submitted in partial fulfillment of the requirements for the degree of
             Doctor of Philosophy of Imperial College London
      Abstract
       The purpose of this thesis is to investigate trading strategies based on futures contracts. The
      first chapter demonstrates and analyzes the exceptional performance of both carry and momentum
      strategies in future markets across asset classes (commodities, bonds, equities, and currencies). In-
      dividual carry and momentum returns have low correlation, generating a significant diversification
      benefit in the combined portfolio and a Sharpe ratio of 1.4. Individually and combined, carry and
      momentum strategies have significant returns not explained by the CAPM or risk factor models.
      However, carry returns disappear after adjusting for lagged macroeconomic variables, suggesting
      performance is related to business cycle risk. Expected momentum returns are only weakly related
      to macroeconomic variables, but co-vary significantly with hedge fund capital flow - indicating
      returns are related to limits to arbitrage constraints of hedge funds.
       The second chapter establishes the economic significance of carry and momentum trading sig-
      nals. We use a model incorporating a time varying investment opportunity set into a parametric
      portfolio framework and derive optimal portfolio parameters. Without any ex-ante imposed rela-
      tion, in-sample portfolio parameters are found to be consistent with the results of the first chapter.
      Furthermore, out-of-sample returns are found to be highly significant, robust to transaction costs
      and not compensation for traditional risk exposure, time-varying risk due to macroeconomic cy-
      cles, or funding liquidity. Out-of-sample returns are significantly related to pro-cyclical hedge fund
      capital flows, suggesting expected returns decrease with speculative capital.
       The third chapter applies our parametric portfolio framework to assess the economic signif-
      icance of predictors important in commodity markets since 2001. The studied predictors are
      widened to include hedging pressure and three market wide predictors found in the literature to
      forecast returns. In contrast to our results for the whole futures market, we find little evidence for
      economically significant commodity strategy returns for either individual or combined predictors.
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             Contents
             Abstract                                                                                                 1
             Acknowledgments                                                                                          9
             Introduction                                                                                           11
             1 The Returns to Carry and Momentum Strategies                                                         18
                I     Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   18
                II    Returns, Leverage and Trading Strategies . . . . . . . . . . . . . . . . . . . . . . . .       22
                      A       Data Set and Sample Contracts . . . . . . . . . . . . . . . . . . . . . . . . . 22
                      B       Excess Futures Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     22
                      C       Leverage Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    23
                      D       Trading signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    24
                      E       Trading Rules and Portfolio Construction        . . . . . . . . . . . . . . . . . . .  25
                      F       Market, Macroeconomic and Hedge Fund Data Sources . . . . . . . . . . . . 27
                III   Characterizing Carry and Momentum Returns . . . . . . . . . . . . . . . . . . . . . 28
                      A       Return Premia of Global Strategies . . . . . . . . . . . . . . . . . . . . . . .       28
                      B       Return Premia within Asset Classes . . . . . . . . . . . . . . . . . . . . . . .       32
                      C       Comovement Structure Globally and within Asset Classes            . . . . . . . . . .  34
                IV    Understanding the Return Premia to Carry and Momentum . . . . . . . . . . . . . 35
                      A       Risk Factor Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     36
                      B       Time Varying Expected Returns and Business Cycles . . . . . . . . . . . . . 37
                      C       Hedge Funds and Limits to Arbitrage . . . . . . . . . . . . . . . . . . . . . . 40
                V     What Can We Learn About Momentum by Observing Carry? . . . . . . . . . . . . 43
                      A       Time Trend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     43
                      B       Recessions and Hedge Fund Liquidity . . . . . . . . . . . . . . . . . . . . . . 44
                VI    Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   46
                VII Appendix: Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       48
                VIII Appendix: Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       60
                IX    Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     71
             2 Optimal futures portfolios and hedge fund capital                                                    72
                I     Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   72
                II    Portfolio Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     76
                      A       Optimal Futures Portfolios with Predictable Returns . . . . . . . . . . . . . 76
                      B       Portfolio Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     78
                      C       Construction of Tradable Futures Return Series . . . . . . . . . . . . . . . . 79
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                      D       Transaction Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    79
                III   Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   80
                      A       Price Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   80
                      B       Macroeconomic and Liquidity Data . . . . . . . . . . . . . . . . . . . . . . . 81
                      C       Hedge Fund Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      81
                IV    Characterising Optimal Futures Portfolios . . . . . . . . . . . . . . . . . . . . . . .        82
                      A       Carry and Momentum Portfolio Returns Across Asset Classes . . . . . . . . 82
                      B       Effects of Changing Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . .       86
                      C       Diversified Investor with Optimal Futures Portfolio . . . . . . . . . . . . . . 87
                V     Business Cycles, Limits to Arbitrage and Hedge Fund Capital . . . . . . . . . . . . 89
                      A       Optimal Futures Returns with Transaction Costs . . . . . . . . . . . . . . . 89
                      B       Risk Factor Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     90
                      C       Macroeconomic Influences and Funding Liquidity . . . . . . . . . . . . . . . 91
                      D       Hedge Fund Activity and Capital Flows         . . . . . . . . . . . . . . . . . . . .  94
                VI    Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   97
                VII Appendix: Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       99
                VIII Appendix: Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
                IX    Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
                      A       Statistical Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
             3 Assessing the Economic Significance of Commodity Futures Price Predictors 114
                I     Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
                II    Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
                      A       Parametrization of portfolio weights . . . . . . . . . . . . . . . . . . . . . . . 117
                      B       Out-of-sample parametric portfolios . . . . . . . . . . . . . . . . . . . . . . . 119
                      C       Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
                III   Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
                      A       Futures Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
                      B       Commodity Characteristics        . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
                      C       Macroeconomic Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 125
                IV    Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
                      A       In-sample optimal portfolio performance . . . . . . . . . . . . . . . . . . . . 126
                      B       Out-of-sample optimal portfolio performance . . . . . . . . . . . . . . . . . . 128
                V     Robustness     . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
                      A       Sub-sample Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
                      B       Varying Risk Aversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
                      C       Strategy performance across commodity classes . . . . . . . . . . . . . . . . 133
                VI    Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
                VII Appendix: Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
                VIII Appendix: Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
             4 Conclusions                                                                                         147
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