relevant costs, including transaction costs. Ignoring transaction costs when forming portfolios can lead to poor performance because implementation costs can reduce, or even eliminate, the advantages achieved through superior stock selection. Conversely, taking account of transaction costs can help produce portfolios with gross returns that exceed the costs of trading. Accurate trading-cost forecasts are also important after portfolio formation, when monitoring the realized costs of trading. A good transaction-cost model can provide a benchmark for what realized costs should be, and hence whether actual execution costs are reasonable. Detailed trade-cost monitoring can help traders and brokers achieve best execution by driving improvements in trading methods-such as more patient trading or the selective use of alternative trading mechanisms. Transaction costs have two components: (1) explicit costs, such as commissions and ticket charges; and (2) implicit costs, or market impact. Commissions and ticket charges tend to be relatively small, and the cost per share does not depend on the number of shares traded. In contrast, market impact costs can be substantial. They reflect the costs of consuming liquidity from the market, costs that increase on a per-share basis with the total number of shares traded.7 Forecasting price impact is difficult. Because researchers observe prices only for completed trades, they cannot determine what a stock's price would have been without these trades. It is therefore impossible to know for sure how much prices moved as a result of the trades. Price impact costs, then, are statistical estimates that are more accurate for larger data samples. One approach to estimating trade costs is to directly examine the complete record of market prices, tick by tick.8 These data are noisy due to discrete prices, nonsynchronous reporting of trades and quotes, and input errors. Also, the record does not show orders placed, just those that eventually got executed (which may have been split up from the original, larger order). Lee and Radhakrishna (2000) suggest empirical analysis should be done using aggregated samples of trades rather than individual trades at the tick-by-tick level. Another approach is for portfolio managers to estimate a proprietary transaction cost model using their own trades and, if available, those of comparable managers. If a sufficient sample is available, this approach is ideal because the resulting 7Market impact costs arise because suppliers of liquidity incur risk. One component of these costs is inventory risk. The liquidity supplier has a risk/return trade-off, and will demand a price concession to compensate for this inventory risk. The larger the trade size and the more illiquid or volatile the stock, the larger are inventory risk and market impact costs. Another consideration is adverse selection risk. Liquidity suppliers are willing to provide a better price to uninformed than informed traders, but since there is no reliable way to distinguish between these two types of traders, the market maker sets an average price, with expected gains from trading with uninformed traders compensating for losses incurred from trading with informed traders. Market impact costs tend to be higher for low-price and small-cap stocks for which greater adverse selection risk and informational asymmetry tend to be more severe. 8For example, see Breen, Hodrick, and Korajczyk (2000).