This thesis addresses the issue of developing optimal "ex~ante" global asset allocation strategies from the viewpoint of a UK investor, without the need to resort in fundamental forecasts of the portfolio inputs. In this context, the main emphasis is placed on the market selection, currency hedging and asset mix decisions as opposed to the individual stocklbond selection within each market. Effectively, the principal focus lies in empirically assessing the extent of inter~temporal instability in the inputs to theglobal portfolio optimization problem and in developing appropriate multivariate estimation procedures that aim to assist investors in achieving superior out of sample portfolio performance. The empirical results from application of MANOY A techniques provide strong evidence about the inter~ temporal instability of the global index covariance structure and the necessity of controlling estimation risk in index portfolio inputs. Multifactor models based on unobservable factors are shown to be capable of reducing the "noise" from the historical correlation structure, even though statistically superior correlation estimates do not always result in superior out of sample portfolio performance, since the latter has relatively low sensitivity to misestimation of correlations. Instead, Bayesian and empirical Bayes~Stein type models appear capable of satisfactorily controlling estimation risk in index returns, while very promising results arise from procedures where investors impose prior restrictions on investment weights. Finally "co~integration" analysis reveals significant evidence of common trends andpredictable return components in a number of markets, primarily hedged bond indices.