Testing the Effects of the Volatility of a Gaussian Distribution Monthly Returns of Commodity Futures Contracts of a Hedge Fund Portfolio

In this article, we test the effects of the volatility of Gaussian distribution monthly returns of commodity futures contracts of a hedge fund portfolio. We test a linear Gaussian state space model and the Kalman filter ARMA(2,4) model of the natural logarithmic monthly market returns of the of the commodity futures contracts. The purpose of this article is to estimate expectations that arise from the interaction of arbitrageurs and noise traders. An arbitrageur buying or selling an asset has to be cautious and limited about his investment positions. Noise traders could become more pessimistic or more bullish, so the arbitrageur has to take into consideration a risk for a further rise or fall of the commodity futures prices. This fact motivates us to use state space model that will reveal to us the final one – step ahead values of the signal and state vector. This one – step – ahead signal and state prediction is very important for the arbitrageurs to craft their investment strategy concerning holding, buying or selling commodity futures. The state space model is composed from the observation and the state equation. It is analyzed by using the Kalman recursive algorithm filter to calculate finite sample forecasts for Gaussian ARMA models. The sample is provided from Data Feeder dataset. It includes managed futures hedge funds for the period 1990 to 2003. The database includes defunct funds and funds that ceased to operate and, therefore, is free from survivorship bias, selection and backfill bias