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Dynamic Futures Portfolio Under a Multifactor Gaussian Framework

Futures are standardized exchange-traded bilateral contracts of agreement to buy or sell an asset at a pre-determined price at a pre-specified time in the future. At the Chicago Mercantile Exchange (CME), futures trading volume averages over 15 million contracts per day. 

Managed futures portfolios play an integral role in hedge funds and alternative investments, with hundreds of billions under management. These investments are managed by professional investment individuals or management companies known as Commodity Trading Advisors (CTAs), and typically involve trading futures on commodities, currencies, interest rates, and other assets. This class of assets has averaged over US$300 billion annually during 2011–2020. 

One appeal of managed futures strategies is their advertised potential to produce uncorrelated and superior returns, as well as different risk-return profiles, compared to the equity market. The classes of strategies are conceivably diverse among managed futures funds, with the popular ones being long-short strategy and momentum strategy. 

In our new paper, we discuss a new approach to generate dynamic futures trading strategies under a general Gaussian framework where the underlying asset’s log price is modeled by a multifactor diffusion process. Our framework is very general and able to capture different forms of futures curves, such as contango and backwardation. It also encapsulates some famous two-factor models, like the Schwartz (1997) model and Central Tendency Ornstein-Uhlenbeck (CTOU) model. 

We first derive the no-arbitrage prices and historical price dynamics of the futures contracts. The optimal futures trading strategy is determined by solving a stochastic control problem. Our portfolio optimization approach allows for trading different numbers of futures. By analyzing and solving the associated Hamilton-Jacobi-Bellman (HJB) equations, we present the value function and optimal trading strategies explicitly. 

In order to quantify the value of the futures trading opportunity, we define the portfolio manager’s certainty equivalent. Intuitively, it should be more beneficial to be able to trade a larger set of securities. Using certainty equivalent, we quantify the value of trading different sets of futures and show that the highest certainty equivalent is achieved from trading all available contracts.   

We apply our stochastic framework to the Schwartz model and CTOU model. In addition, we introduce a new multiscale CTOU model that is driven by a fast and slow mean-reverting process. We provide numerical examples to examine model parameters for our new model. 

One challenge in the empirical estimation of multifactor models is that some factors are not directly observable. To address this issue, a popular approach is to apply Kalman filter. This is facilitated by the fact that, under the multifactor Gaussian model, the log-futures price is an affine function of all the state variables. 

The full paper is available for download here


T. Leung and Y. Zhou (2021), Optimal Dynamic Futures Portfolio Under a Multifactor Gaussian Framework [pdf], International Journal of Theoretical & Applied Finance 

T. Leung and Y. Zhou (2021), Optimal Dynamic Futures Portfolios Under a Multiscale Central Tendency Ornstein-Uhlenbeck Model [pdf], in the Proceedings of the American Control Conference 2021 

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