Degree Name

Doctor of Philosophy (PhD)


Department of Accounting and Finance - Faculty of Commerce


The thesis investigates the problems involved in effectively modelling the (time-varying basis risk (the risk of large movements in the relationship between the spot price and the derivatives price) and the subsequent calculation of effective hedge ratios. The specific purpose of this research involves the identification of conditional variance models that accommodate the time series properties commonly encountered in many spot and futures return series, by targeting changes in basis volatility over time. The research analyses the problem of incorporating conditional basis variance into the time series model by extending popular specifications to include long-run (cointegration) information. The analysis investigates whether the omission of cointegration information in the underlying econometric time series model leads to inappropriate modelling of long-run and short-run time series behaviour. Cointegration information, through the squared spread between spot and futures rates, may potentially provide predictive power in modelling volatility of asset returns, volatility that is not captured effectively by GARCH (1,1) model. Consequences of omitting dynamic adjustments include inadequate modelling of the time series behaviour, sub-optimal decision making and the possible progressive degeneration of such modelling and decision making over time. The research determines hedging criteria that enables the comparison of the effectiveness of different constant hedge ratios. The comparison of conditional variance measures of various hedge ratios is of interest to the hedger who would like to implement a constant hedge but does not wish to be constrained to choosing either the na�ve or minimum-variance hedge. An alternative constant hedge ratio to the na�ve and minimum-variance hedges, termed the forecasted hedge, is proposed. The forecasted hedge ratio is based upon the forecasting curves of both the conditional covariance between spot and figures returns and the conditional variance of futures returns, extracting information embedded in the time-varying distribution of spot and futures returns. Dynamic hedges are compared to constant procedures to determine the conditions under which allowance for conditional variance substantially increases hedging effectiveness. Hedging effectiveness is subsequently defined as the percentage reduction in the variance of the portfolio achieved by implementing a hedged rather than and unhedged position. Where dynamic variance-covariance matrices are effectively modelled, hedge ratios may be constructed that subsequently minimise basis risk. Another major objective of the research involves the determination of the conditions where periodic re-balancing of the optimal hedge ratio leads to increased hedging effectiveness. The analysis determines criteria that must be triggered in order for an alternative hedging strategy to be better (in terms of risk-reduction) than the strategy currently in effect. The most important contribution of the thesis is to ensure that in time series modelling of financial series, the basic model adopted is capable of accounting for any significant short-run and long-run characteristics found to be typical of these series. Concentration is focussed on the calculation of optimal hedge ratios in order to simplify that analysis, by using a very common example of the conditional variance situation. However, the fundamental contribution involves attempting to ensure the basic econometric specification is appropriate in modelling typical time series behaviour so it does not need further adjustment.

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