are macroeconomic growth, fund flows, and proxies for risk premiums. IMPLEMENTATION ISSUES Portfolio Construction The forecast models of country and asset-class returns drive the desire to create deviations from the strategic asset allocation in a GTAA portfolio. However, knowing that cheap countries outperform expensive ones on average is not enough. We must also use a method of portfolio construction that translates our forecasts into meaningful estimates of expected return. We desire portfolios that balance risk and return, but traditional mean-variance optimizers struggle to construct reasonable portfolios due to the inconsistency between estimates of expected return and risk. To avoid these undesirable results, users of optimizers often impose constraints, which unfortunately also hinder the optimizer's ability to find the best portfolio. As described more fully in Chapter 7, the Black-Litterman asset allocation model provides the natural solution to this problem by estimating expected returns more consistent with risk assumptions. It achieves this by blending views from forecasting models with the market's implicit equilibrium views to create a new set of expected returns. In principle, the model works by "shrinking" the weights on extreme views toward equilibrium, and the weights on correlated views toward each other. The degree of shrinkage depends on how much confidence we place in our forecasting model views relative to the market's implicit views. The resulting expected returns more consistently reflect estimated volatilities and correlations. In this way, the Black-Litterman approach produces better-specified expected returns and results in better-balanced portfolios than traditional methods, while requiring fewer artificial constraints. Conceptually, a GTAA portfolio is constructed in two steps. First, the completion portfolio is built to minimize tracking error to the benchmark, and second, the pure overlay portfolio is created to maximize expected return per unit of intentional active risk. In practice, we solve for these two portfolios jointly along with transaction costs projections in order to create an aggregate GTAA overlay portfolio that maximizes expected return per unit of risk net of transaction costs. Determining the completion and pure overlay positions at the same time minimizes overall transaction costs. After using Black-Litterman to estimate expected returns, the actual joint completion and pure overlay portfolio optimization is straightforward: Max{E[R]'(w -b)-X(w- b)'lL{w -b)-$t(w- wQ)} where E[R] represents the vector of Black-Litterman expected returns, w represents the vector of asset weights, b represents the vector of benchmark weights, £ represents the covariance matrix of asset returns, t{ ) represents the transaction cost function that depends on the size of trades, wQ represents the vector of current weights, and X and 0 represent the risk aversion and transaction cost aversion parameters calibrated for the desired risk and GTAA-process-specific transaction costs.