Measuring risk is mandatory in every form of responsible asset management; be it mitigating losses or maximizing performance, the level of risk dictates the magnitude of the effect of the strategy the asset manager has chosen to execute. Many common risk measures rely on simple statistics computed from historic data. In this thesis, we present a more dynamic risk measure explicitly aimed at the commodity futures market.
The basis of our risk measure is built on a stochastic model of the commodity spot price, namely the Schwartz two-factor model. The model is essentially determined by a system of stochastic differential equations, where the spot price and the convenience yield of the commodity are modelled separately. The spot price is modelled as a Geometric Brownian Motion with a correction factor (the convenience yield) applied to the drift of the process, whereas the convenience yield is modelled as an Ornstein-Uhlenbeck process. Within this framework, we show that the price of a commodity futures contract has a closed form solution. The pricing of futures contracts works as a coupling between the unobservable spot price and the observable futures contract price, rendering model fitting and filtering techniques applicable to our theoretic model.
The parameter fitting of the system parameters of our model is done by utilizing the prediction error decomposition algorithm. The core of the algorithm is actually obtained from a by-product of a filtering algorithm called Kalman filter; the Kalman filter enables the extraction of the likelihood of a single parameter set. By subjecting the likelihood extraction process to numerical optimization, the optimal parameter set is acquired, given that the process converges.
Once we have attained the optimal parameter sets for all of the commodity futures included in the portfolio, we are ready to perform the risk measurement procedure. The first phase of the process is to generate multiple future trajectories of the commodity spot prices and convenience yields. The trajectories are then subjected to the trading algorithm, generating a distribution of the returns for every commodity. Finally, the distributions are aggregated, resulting in a returns distribution on a portfolio level for a given target time frame. We show that the properties of this distribution can be used as an indicator for possible anomalies in the returns within the given time frame.
