Optimal Portfolios of Natural Gas Futures

Abstract

In this thesis we investigate portfolios consisting of a collection of positions in natural gas futures. The logarithms of the futures prices follow correlated Ornstein-Uhlenbeck processes which are mean-reverting. Under the assumption that the portfolios are constant and short-selling is allowed, formulae for the portfolio that is optimal in terms of minimizing Capital at Risk (CaR) in a continuous-time context are obtained following an adapted version of the theory in [14]. We show that the results in this paper hold with small modifications in our situation and we apply them to portfolios of positions in AB NIT natural gas futures contracts. Furthermore, we allow the portfolio to be reoptimized periodically, showing dramatically better performance of portfolio with regard to the final wealth. And finally we consider the contract size limitation so that the portfolio is tradeable, and demonstrate the unsurprising underperformance of the portfolio that results.