of the individual portfolio manager.9 To demonstrate how transaction costs can vary across trade characteristics, we estimated a nonlinear regression model on a large sample of our own trades. The sample represented over 60,000 trades over the nine months from October 2001 to June 2002. We measured costs using implementation shortfall. For purchases, implementation shortfall is equal to the decision price (or the price at the time we decided to trade) minus the average execution price (including commissions), all expressed as a proportion of the decision price. For sales, the terms in the numerator are reversed: Implementation shortfall is the execution price minus the decision price, divided by the decision price. Thus, with slippage (i.e., positive transaction costs), implementation shortfall is negative for both buys and sells. For example, if the decision price is $10 and a purchase is executed at $10.15, then the implementation shortfall is -0.015, for a cost of 1.5 percent. To predict trade costs, our model uses five proxies for trading liquidity: order size, average trading volume, market capitalization, stock price volatility, and stock price level. We also control for contemporaneous sector returns, since mar-ketwide price movements usually account for much of the difference between the decision price and the execution price, although ex ante these movements are generally unpredictable. Figure 23.1 presents the model's cost estimates, expressed as a proportion of trade value, for trading two baskets of stocks: (1) a large-cap basket comprising the stocks in the S&P 500 and (2) a small-cap basket comprising the stocks in the FR 2000 index. Figure 23.1 also shows the liquidity characteristics of an average large- and small-cap stock as of June 2002. Not surprisingly, the cost of trading a basket of large-cap stocks is lower than the cost of trading a basket of small-cap stocks with similar liquidity. For example, a $500-million basket of S&P 500 stocks is expected to incur transaction costs of about 18 basis points. A trade this size represents about 1.3 percent of the average daily volume of the underlying stocks. In contrast, the average cost of trading a $25 million basket of Russell 2000 stocks, which represents 1.1 percent of average daily volume, is 25 basis points. Liquidity is more costly for small-cap stocks because their prices are more volatile, their prices are lower, and their average daily trading volume is smaller. Moreover, as the concave curves in Figure 23.1 show, trading costs increase with order size, but at a decreasing rate. sThere is a large academic literature on measuring transaction costs. One paper that is especially relevant to portfolio managers interested in developing a model based on their own trades is Keim and Madhavan (1997), who investigate the impact of investment style on total transaction costs for a sample of 21 institutions over the period January 1991 to March 1993. They study transaction costs by trade direction (i.e., buyer- vs. seller-initiated trades) and investment style: value-fundamental, technical-momentum, and index. The study concludes that total transaction costs are increasing in order size, and decreasing in firm size and the magnitude of the stock price. Further, costs differ by investment style. Technical and index investors, who demand immediacy, incur higher costs than the more patient value investors.