using the Black-Litterman model to produce final return forecasts that are more consistent with risk estimates, and with each other. Finally, portfolio managers should impose sensible, but simple constraints on the optimizer to help guard against the effects of noisy inputs. These constraints could include maximum active weights on individual stocks, industries, or sectors, as well as limitations on the portfolio's active exposure to factors such as size or market beta. TRADING Trading is the process of executing the orders derived in the portfolio construction step. To trade a list of stocks efficiently, investors must balance opportunity costs and execution price risk against market impact costs. Trading each stock quickly minimizes lost alpha and price uncertainty due to delay, but impatient trading incurs maximum market impact. In contrast, trading more patiently over a longer period reduces market impact but incurs larger opportunity costs and short-term execution price risk. Striking the right balance is one of the keys to successful trade execution. The concept of striking a balance suggests optimization. Investors can use a trade optimizer to balance the gains from patient trading (e.g., lower market-impact cost) against the risks (e.g., greater deviation between the execution price and the decision price; potentially higher short-term tracking error). Such an optimizer will tend to suggest aggressive trading for names that are liquid and/or have a large effect on portfolio risk, while suggesting patient trading for illiquid names that have less impact on risk. A trade optimizer can also easily handle most real-world trading constraints, such as the need to balance cash in each of many accounts across the trading period (which may last several days). A trade optimizer can also easily accommodate the time horizon of a manager's views. That is, if a manager is buying a stock primarily for long-term valuation reasons, and the excess return is expected to accrue gradually over time, then the optimizer will likely suggest a patient trading strategy (all else being equal). Conversely, if the manager is buying a stock in expectation of a positive earnings surprise tomorrow, the optimizer is likely to suggest an aggressive trading strategy (again, all else being equal). The trade optimizer can also be programmed to consider short-term return regularities, such as the tendency of stocks with dramatic price moves on one day to continue those moves on the next day before reversing the following day. For example, if a manager wants to buy a stock that was up significantly yesterday, it may pay to wait until tomorrow to execute the trade given the likelihood it will decline tomorrow relative to today's price. To induce traders to follow the desired strategy (i.e., that suggested by the trade optimizer), the portfolio manager needs to give the trader an appropriate benchmark, which provides guidance about how aggressively or patiently to trade. Two widely used benchmarks for aggressive trades are the closing price on the previous day and the opening price on the trade date. Because the values of these two benchmarks are