Any tables, graphs, or charts relating to performance, whether hypothetical or simulated, included in this chapter are intended only to illustrate the performance of indices, strategies, or specific accounts for the historical periods shown. When creating such tables, graphs, and charts, Millennium may incorporate assumptions on trading, positions, transactions costs, market impact estimations, and the benefit of hindsight. For example, transaction cost estimates used in simulations are based on historical measured costs and/or modeled costs, and attribution is derived from a process of attributing positions held at a point in time to specific market views and is inherently imprecise. Such tables, graphs, and charts are not intended to predict future performance and should not be used as a basis for making any investment decision. Millennium has no obligation to update or amend such tables, graphs, or charts.