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Connolly, Kevin Brendan (1985) A study of the multivariate distribution of commodity futures prices with a view to the development of portfolios and trading systems. Doctoral thesis, City of London Polytechnic.
The univariate and multivariate distribution of daily returns on contracts in the London cocoa, coffee, sugar and rubber futures markets over the period 1975-79 are studied. In the analysis, two relatively recent multivariate procedures (the multivariate serial correlation coefficient and the multivariate extension of the W- test for normality) are investigated. The four dimensional vector of returns with one component from each futures market can be viewed as being generated from a serially independent multivariate normal process with non - constant variance/covariance structure and occasional contaminating extreme realisations.
Examining the multivariate distribution in which all the components are returns on contracts in the same futures market, however, produced different and very unexpected results. Highly significant multivariate serial correlation coefficients of lag one day and significant departures from multivariate normality were discovered.
The multivariate temporal dependence was shown to be due to correlation between certain linear combinations of returns on contracts of differing maturities. Studying the distribution of the linear combination estimates led to the discovery that much of the observed phenomenon can be explained by negatively correlated multivariate spread portfolios. Multivariate trading rules were devised to exploit the observed temporal behaviour and when applied to all four series produced large, positive and highly statistically significant returns. The introduction of non zero transaction costs reduced returns but still produced positive profits in the cocoa and coffee series.
Models of processes that could explain the observed multivariate temporal behaviour and the multivariate non - normality are presented.
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