- b) is the tracking error relative to benchmark of the combined completion and overlay portfolio, and t(w - tuQ) is the estimated total transaction costs implied by a given optimal portfolio. Then, for attribution purposes, the completion portfolio is defined as Mm{{w -byi(w -b)} W where wc represents the vector of weights in the completion portfolio. This optimization also yields the pure overlay weights, which are defined as w - w . Note that while every asset in the benchmark is represented in w and wc, only the subset of assets with liquid futures and forwards are traded, so the tracking error of the completion portfolio is not zero. Also, this is a purely hypothetical completion portfolio that ignores transaction costs, since transaction costs are already considered in the total GTAA optimization. If the completion and pure overlay portfolios are managed separately, transaction costs must be considered in each of them independently. Given the reduced transaction costs, does it always make sense to combine the completion and pure overlay portfolios? Although generally managing these two portfolios together is easier and less costly, this is not always the case. The exceptions are typically very large and complex portfolios, or portfolios with significant contributions and redemptions. In these cases, the custodian or a specialized completion manager is often closer to the information flow and can more quickly and more accurately remove unintentional asset allocation risk, and the gains from reducing transaction costs from netting are typically small since the pure overlay portfolio is usually not rebalanced every time there is a new cash inflow or outflow.15 Where Does GTAA Fit Into a Portfolio? GTAA is generally implemented in a small overlay account using liquid derivative instruments such as futures and forwards, although the strategy can also use swaps or cash instruments such as country index funds to increase the opportunity set. Why? The small account size required is a tremendous advantage from a risk budgeting viewpoint. This is because in practice the dollars allocated and limited tracking error of traditional managers severely limit the achievable active risk in a portfolio. It is exactly this problem that drives investors to seek absolute return strategies. Another practical motivation for limiting the size of the GTAA overlay 15In practice, one could rebalance both completion and overlay every time anything changed in the underlying holdings of the portfolio. Because there is noise in any model's expected return estimates, trading too frequently results in trading on noise, and therefore only reduces performance. Based on our experiences with our forecasting models, we believe the optimal rebalance frequency for a pure overlay account is somewhere between three and seven weeks.