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Implementation
Subtracts Value

The Market
Impact Model™ -
Second in a Series

Should You Worry about
Transaction Costs?

The BARRA Brainteaser
for Spting 1998

Solution to the Winter
1998 Brainteaser

The BARRA Convertible
Bond System (CBS)

Should You Worry about Transaction Costs?

Two Case Studies

Cars and portfolios

"You can have your model T in any color, so long as it's black." This famous ad ran in 1914, six years after the introduction of the Model T, when Henry Ford decided to stop offering his famous automobile in red, green, and French gray in order to streamline the production process and reduce manufacturing costs. Cost reduction, he determined, was a more important element in attracting new customers than a choice of colors.

Like the automobile industry then, the investment management industry today is in its late infancy. Unlike the automobile industry, reducing production costs has been less important than providing customers with a variety of choices in order to attract new business. Nevertheless, as the investment management industry matures and consolidates, cost considerations will become an increasingly important competitive factor in the marketplace–especially for non-niche products that will be broadly grouped according to style and capitalization dimensions.

The investment management industry today is indeed undergoing increased competition caused by recent waves of consolidation, highlighting, among other things, the importance of cost control in the "manufacturing process." In fact, cost control has become an essential element of superior performance.

Components of transaction costs¹

Transaction costs are of two types: processing costs and market impact costs. Processing costs are commissions paid to brokers, taxes, and fees. These costs are known and easily measurable. Market impact costs consist of the halfspread and additional market impact, if the order exceeds the quote depth for the security to be purchased or sold. The market impact can be seen as the price concession we must pay to liquidity providers in order to accommodate our trade. Market impact is intrinsically difficult to measure and represents the bulk of the total transaction costs. As a rule, that which is not easily measurable or quantifiable tends to receive less of our attention. Fortunately, the Market Impact Model^TM (MIM), which BARRA has developed over the last five years, is a tool we can use to measure and control total transaction costs.

Are transaction costs large enough to bother with?

How large are the various components of transaction costs? For U.S. institutional investors, a ballpark figure for order processing costs would be about 5¢ per share. The magnitude of the market impact cost depends on the type of asset traded and the size of the order. Let's consider a typical institutional transaction of a stock in the S&P 500. The average halfspread for an S&P 500 stock is approximately 7¢. The median quote depth is typically 3,500 shares, and the median share price is $40. If we assume a typical institutional order of 10,000 shares, we will expect an additional market impact to execute the trade, since it exceeds the typical quote depth of 3,500. According to the Market Impact Model the average total market impact for such a trade is 20¢, which indicates an incremental market impact of 13¢.

TABLE 1

Transaction cost comparisons for a typical institutional trade

 

Processing cost		5¢/share
Halfspread	7¢/share
Incremental market impact	13¢/share
Total marketr impact		20¢/share
Total costs		25¢/share

From this simplified example we see that the measurable processing costs are only the tip of the iceberg, representing roughly 20% of the total cost of trading for S&P 500 stocks. Total transaction costs thus might be even more than five times the processing costs for funds investing in medium- or small-cap stocks, or for larger and more actively traded funds.

The impact of transaction costs on performance

Is the cost of 25¢ per share worth worrying about? How does this cost impact performance? Assuming a portfolio turnover of 100% per year, each stock will be bought and sold each year. The total yearly transaction costs for each stock will therefore be 50¢. Assuming 12% total return and a price of approximately $40 for the average stock, the yearly transaction cost of 50¢ per share represents roughly 10% of the total stock return.

However, since most active managers are selected and rewarded based on their performance relative to a benchmark, a more meaningful analysis would compare the transaction costs to the active return rather than the total return of the portfolio. Let's assume the manager is in the top quartile, with an information ratio of 0.5. Let's further assume an active risk of 4%. Given the hypothetical information ratio, the manager will contribute 2% of active return. For a median-priced stock, a 2% annual return amounts to 80¢ per share. Again assuming a portfolio turnover of 100% per year, each trading decision (to buy or to sell) will contribute 40¢ to the active portfolio performance, net of transaction costs, and 65¢ before transaction costs. The 25¢ of transaction costs represents, therefore, approximately 40% of the gross value of the manager's information.

It is clear from this very simple "back of the envelope" calculation that careful control of transaction costs can be an effective way for active managers to improve their performance.

FIGURE 1
Transaciton cost relative to total realized returns and manager value added

Two case studies

We recently had the opportunity to analyze an actual rebalancing of a manager's portfolio and to quantify the benefits of using the Market Impact Model. The client manages a $750 million U.S. midcap portfolio. The portfolio is rebalanced monthly and has an annual turnover of roughly 80%. The manager uses the Aegis Optimizer and creates new alphas and estimates of transaction costs based on recent liquidity for each stock on a monthly basis. We performed two rebalancings: For the first, we optimized using the manager’s estimates of unit transaction costs and a linear assumption for the transaction cost function. For the second, we optimized using the Market Impact Model estimated transaction costs and a step-wise linear assumption for the transaction cost function. We compared the costs (as estimated by MIM) of trading the trade lists obtained from these two optimizations. We considered three portfolio sizes: $300 million, $750 million, and $3 billion. The results are shown in TABLE 2.

TABLE 2
Portfolio rebalancing turnover and costs: linear cost estimates ve. MIM cost estimates

 

		$300 million portfolio	$750 million portfolio	$3 billion portfolio
Turnover	linear MIM	6.30% 5.60%	6.64% 3.81%	6.47% 2.60%
Total cost (from MIM)	linear MIM	$208,000 $148,000	$623,000 $287,000	$3,749,000 $958,000
$ savings	MIM vs. linear	$60,000	$336,000	$2,791,000
cost savings	basis points	2.0	4.5	9.3

This study puts the Market Impact Model in the best possible light, since it uses MIM to estimate transaction costs and to measure the magnitude of those costs. Nevertheless, the cost advantage for the MIM method would persist, after adjusting for the measurement bias.

We can derive a number of insights from these results. The importance of using a transaction cost function that reflects the increasing cost of trading larger and larger positions is clear. The linear transaction cost assumption does not sufficiently limit the turnover as the size of the portfolio, and therefore the market impact, increases. We could also argue that, since market impact costs are very hard to measure, the manager might not have realized the need for reducing the monthly turnover for the $750 million and $3 billion portfolio from more than 6% down to 3.8% and 2.6%, respectively. This means that, all other factors being equal, as the size of the portfolio increases, the optimal level of turnover decreases.

We conducted one further study in which we assume that the manager is aware of the exact relationship between the size of the portfolio and the amount of market impact, and therefore adjusts the linear transaction costs upward to obtain the optimal level of turnover–i.e., 5.6% for the $300 million portfolio, 3.8% for the $750 million portfolio, and 2.6% for the $3 billion portfolio. Even in this case there is an advantage to using MIM, since the Optimizer will favor stocks which are easier to trade. TABLE 3 shows the results of this study.

TABLE 3
Portfolio rebalancing turnover and costs: adjusted linear cost estimates vs. MIM cost estimates

 

		$300 million portfolio	$750 million portfolio	$3 billion portfolio
Turnover	adjusted linear MIM	5.60% 5.60%	3.80% 3.81%	2.70% 2.60%
Total cost (from MIM)	adjusted linear MIM	$178,000 $148,000	$336,000 $287,000	$1,364,000 $958,000
$ savings	MIM vs. adjusted linear	$30,000	$49,000	$406,000
cost savings	basis points	1.0	0.7	1.4

This second study shows how the manager–even assuming that he or she is able to come up with the optimal scaling factor for the transaction costs based on the size of the portfolio and the current market conditions–can use MIM in conjunction with the Aegis Optimizer to realize large savings in transaction costs.

Summary

Transaction costs can potentially erode a large part of an active manager's value added. The market impact, the largest component of transaction costs, has been for the most part neglected–primarily because it is the hardest to measure and therefore to control. As a result of five years of research, BARRA has developed a tool you can use to forecast and control market impact costs, and, in conjunction with the Aegis portfolio construction tool, reduce transaction costs and consequently improve performance.

Just a final thought: Take the annual processing costs for your portfolio and multiply by four. That represents a ballpark estimate of the amount paid to the liquidity providers–i.e., the market impact. What percentage of this amount, if saved, would have a material positive impact on your active performance?