This paper portfolio allocation strategies based on a recently developed autoregressive conditional heteroscedasticity model (QTARCH) are constructed for the US and UK and compared with strategies relying on the conventional Markowitz approach. The procedure is based on partitioning the historical data into 'state of the world' which are used to produce expectations of return and risk. Several different approaches, including clustering methods, are developed to partition an initial in-sample period from 1978 to 1983 using quarterly asset returns and economic data. These partitions are then used to test out-of-sample strategies for the next quarter. The QTARCH results are compared with those from Markowitz strategies. A further quarter is added to the in-sample period and the procedure repeated, successively adding one additional quarter, until 1995. Although, the QTARCH results are sensitive to the method of partitioning and are generally better for the US, it is demonstrated that the approach can improve portfolio performance in both countries