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The concept of the market portfolio has been central in both the formulation and application of the CAPM.However,there seems to be an apparent aberration in the concept and construction of the market portfolio by academics and practitioners alike.The objective of this work therefore is to demonstrate that it is feasible and expedient to construct an all-inclusive and market-value weighted market portfolio as well as examine empirically whether or not such an All-Asset market portfolio significantly explains better the risk-return behavior of assets in the capital markets.The Sharpe-Cooper single-index market model was applied to a sample of 70 randomly selected assets listed on the Nigerian Stock Exchange for the period 2002-2005.The results of the study show, among others, that it is indeed feasible to construct an All-Asset market portfolio and that there is a significant difference between the returns on the All-Asset market portfolio and the NSE All-Share market portfolio.These results are very illuminating and would be of immense benefits to academics in financial economics, business management,policy makers, professional investment managers, portfolio managers and analysts.