The Market Impact Model™ —First in a series

by Nicolo Torre

Superior investment performance is the product of careful attention to four elements:

• forming reasonable return expectations
• controlling risk so that the pursuit of opportunities remains tempered by prudence
• controlling costs so that investment profits are not dissipated in excessive or inefficient trading
• controlling and monitoring the total investment process to maintain a consistent investment program

These four elements are present in any investment management problem, be it a strategic asset allocation decision, an actively managed portfolio, or an index fund. The Market Impact Model focuses on cost control.

FIGURE 1. Elements of superior investment management.

Portfolio transaction costs are incurred each time assets are bought or sold in a portfolio. The total transaction cost is the sum of two components:

• order processing costs
• market impact cost

The order processing costs are all costs explicitly incurred to accomplish the transaction. The most important such cost is brokerage commissions, but processing costs may also include taxes and other transaction-related costs. The market impact cost occurs because the transaction itself may change the market price of the asset. The difference between the transaction price and what the market price would have been in the absence of the transaction is termed the market impact of the transaction. The market impact is a price-per-share amount. Multiplying the market impact by the number of shares traded gives the market impact cost of the transaction.

Often an order is worked in multiple transactions. In this case, the market impact should be measured from the price that would have pertained in the absence of all the transactions, and the market impact cost of the order is the sum of the cost of the constituent components.

The result of both the processing costs and impact costs is that some portion of portfolio funds are expended in effecting the transaction, rather than being productively invested in the portfolio. Thus, there is also the loss of investment income which these funds would have produced had they been invested. This lost income is an indirect cost of transacting. However, we take the simpler course of restricting the meaning of transaction cost to direct costs.

Market impact is a hidden cost

Market impact is the difference between the transaction price and what the market price would have been in the absence of the transaction. Since we cannot observe both the occurrence and non-occurrence of the transaction, the market impact cost cannot be directly measured. The best we can do is estimate what the price would have been in the absence of the transaction and compare this estimated price with the actual transaction price.

The simplest way to estimate market impact is to look at quoted prices just prior to the transactions. Quoted prices on a stock are the prices at which other market participants have offered to buy (bid quotes) or to sell (ask quotes). These offers are usually made with respect to fairly limited quantities of the stock, termed the quote depth. The average of the bid and ask prices is the midquote. The difference between the ask and bid prices is the spread. Hence the difference between either quote and the midquote is the halfspread.

FIGURE 2. Price points and their relationship to market impact.

If the transaction size is less than the quote depth, then the transaction will usually occur at the bid or ask price respectively. Taking the midquote as an estimate of the market price in the absence of the transaction, the halfspread then becomes an estimate of the market impact. If the transaction size exceeds the quote depth, then the transaction price will usually be on less favorable terms than the quoted prices. The amount by which the execution price exceeds the halfspread is termed the incremental market impact.¹

Although comparing transaction prices to the midquote can give a useful estimate of market impact, this calculation is only an estimate of market impact and not the definition of market impact. Market impact occurs even if quotes are unavailable and the estimate cannot be made.

Typical transaction costs

As a first step toward understanding market impact, it is useful to form a rough estimate of these different transaction costs. The size of the order processing costs is the easiest to determine. In principle, it would be enough to look at brokerage house statements. In actuality, brokerage commissions often represent compensation for services which are not directly transaction-related, such as payment for security research. Thus, making an appropriate allocation of a portion of commissions to transaction cost may not be entirely straightforward. For U.S. institutional investors, however, a ball park figure for the order processing costs would be about 5¢ per share.

The magnitude of market impact depends very much on the type of asset traded. Let us consider the assets which form the S&P 500. For these assets the average halfspread is about 7¢. The median quote depth is typically 3,500 shares and the median share price is approximately $40. If we assume the typical institutional order is for 10,000 shares (i.e., about $400,000), we see that the order size will usually exceed the quote depth, and so some incremental market impact will be incurred. In fact, from the Market Impact Model we will learn that the average market impact of such a trade is about 20¢, which cost indicates an incremental impact of 13¢.

The transaction costs are summarized as:

Table 1. Transaction cost ledger

We see at once that market impact costs represent the largest portion of total transaction cost. Furthermore, the incremental market impact by itself accounts for roughly half of the cost. Since it is difficult to estimate the amount of incremental market impact prior to trading, there is also uncertainty about what the exact cost will be. Clearly, if the cost is unknown ahead of time, it may be difficult to control these costs.

The economic significance of transaction costs

Next we ask how significant are costs of this magnitude. To answer this question, we need some standard of comparison. One possible comparison is the return to be earned from the assets. The expected annual return from the S&P 500 is about 12% per annum. The median share price is about $40, so the expected annual return is about $4.80 per share. If each transaction generates costs of 25¢ per share and the annual turnover is 100% (implying two transactions per year), then annual costs will be 50¢ per share, or about 10% of annual return.

Transactions are often undertaken to implement an active management strategy. Therefore, another valid standard of comparison is the value added by active management. The value added by a manager is measured by the information ratio, which is defined as:

information ratio =

Consider the case of an active manager who runs a large-cap U.S. equity portfolio. A common benchmark for such a manager would be the S&P 500 Index, and so we may suppose active risks and returns are measured with respect to this benchmark. Suppose that the manager is in the top quartile of active managers; then the manager's information ratio is about 0.5. Suppose also that the manager takes on an active risk of about 4% per annum. Given the assumed information ratio, we conclude that the manager's skill will contribute a 2% active return increment to the portfolio. For a median-priced stock, a 2% annual return amounts to 80¢ per share.

Let us further suppose that the manager has an average holding period of one year. This means that each year the manager will make two decisions about an asset (to buy and to sell). Furthermore, the total value of these decisions is 80¢ per share, so each individual management decision contributes on average 40¢ per share to total portfolio performance. The estimate of 40¢ per share is the value added net of transaction costs. Based on the estimate of 25¢ per share of transaction cost, one concludes that the value before transaction costs of the manager's information is about 65¢ per share. Thus, transaction costs consume about 40% of the gross value of the manager's information. This comparison suggests that careful cost control may be an effective means for active managers to improve their performance.

We can also consider transaction costs in the context of passive management. The basic thesis of passive management is that it is difficult to forecast returns, while it is easy to pay transaction costs. Thus, passive management seeks to maintain a broad exposure to economic opportunity while incurring minimal costs. Typically, an ideal portfolio is defined. The actual portfolio will tend to deviate from this ideal as cash flows occur and the assets held experience different returns from the assets in the ideal portfolio. The basic management decision is, therefore, to decide when deviations from the ideal are sufficiently large as to justify the costs of bringing the portfolio composition back toward the ideal. Estimating and controlling transaction costs is thus central to the passive management strategy. Cost experience reflects the total investment process Having assessed the significance of transaction costs, our attention shifts to controlling them. Here a key insight is that the cost experience is the outcome of decision-making at many levels of the portfolio management process:

• At the strategic level, choices are made regarding asset classes and management style. Clearly, the choice between a large-cap passive strategy and a micro-cap high-turnover active strategy will have important consequences for the cost experience of the portfolio.
• At the portfolio level, specific asset holding decisions are taken and, in consequence, trade lists are generated. Generally, there are many different ways to implement investment ideas in portfolios, and some ways naturally lead to lower transaction costs.
• At the trade level, individual positions are transacted. Here there is some scope for affecting transaction costs, although it can be limited by time constraints and the need to efficiently process a large number of orders.

We see that each decision contributes to the total result and that each decision limits the scope of what can be achieved at the following level.

On further examination of the investment management process, we see that there is a significant opportunity to improve transaction cost control at the portfolio management level. At this level, a delicate balance must be struck between return, risk, and cost. Achieving this balance requires asset-level estimates of each quantity. The basic difficulty, therefore, is to develop and integrate the necessary information. In many investment management firms, cost expertise is concentrated in the trading desk, whereas return expertise is the domain of the portfolio manager. This division of knowledge can lead to inefficiencies in the integration process.

FIGURE 3. Levels of decision-making.

A hypothetical example illustrates the practical difficulties. Consider a manager who develops return expectations and constructs a portfolio with an optimal balance of risk and return characteristics. During the portfolio construction, the manager may control transaction costs by placing a limit on total turnover, but no true cost-benefit analysis occurs. Transforming the current portfolio into the optimal portfolio requires a certain number of trades. The manager reviews the projected trade list, perhaps in consultation with a senior trader. Typically, the list is found to contain untradable positions, and so the manager adjusts the list by hand. The resulting target portfolio is now no longer optimal. Furthermore, it may be unclear at the time adjustments are made whether an asset is being purchased primarily for return reasons or for risk control. Hence, the best way to adjust the portfolio is unclear.

Once the manager decides on the target portfolio, the trading desk begins implementing the trades. As the trading progresses, market impact is observed to drive up the price of some assets—i.e., the assets run away from the traders. The manager then decides either to pay up or to abandon the attempted trades. Generally these decisions must be made on an asset-by-asset basis, so a portfolio viewpoint is lost. The portfolio that finally emerges from the trading process can differ from the original optimal portfolio in a fairly ad hoc way.

The weakness in this process is that transaction costs were not incorporated in the portfolio construction decision at the start and thus no true cost-benefit analysis occurred. Had the cost been incorporated into the portfolio construction from the beginning, the trade list would have been inherently more tradable. Hence the need for hand-tuning would have been reduced or eliminated. During the trading process, the handling of runaway assets could also be guided —e.g., by a simple rule: If the cost of implementing the program reaches the forecast costs before completion of the program, then the target portfolio can be adjusted based on the new current holdings. Thus, incorporating transaction cost estimates into the portfolio construction decision should permit a more streamlined process that ensures the portfolio owned is actually the optimal portfolio (see Figure 4).

FIGURE 4. Portfolio management: typical vs. ideal

Requirements for the Market Impact Model

The goal of the Market Impact Model is to provide transaction cost forecasts suitable for portfolio construction purposes. To realize this goal the model must meet the following criteria:

• The model must provide a priori forecasts rather than ex-post measurements.
• Based on information available at close of market today, the model must provide forecasts valid for the trading conditions likely to apply over the next few days.
• The model must cover a wide universe of assets with uniform accuracy.
• The model must cover a wide range of transaction sizes.

These requirements make construction of the Market Impact Model a difficult task. On the one hand, requiring forecasts to remain valid over a few days limits the data that can be applied to the problem. Thus, information which is hard to forecast, such as price trend, is not directly useful. On the other hand, the breadth requirements demand high performance from the model.

Econometric challenges faced by the Market Impact Model

At first, it might seem that forecasts of market impact costs could be developed in a fairly straightforward manner. Seemingly, it would be enough to monitor the costs of past trades. One might categorize the trades by asset traded and trade size. Then the mean of past costs at a given trade size would provide a forecast of future costs. Three econometric difficulties guarantee that such a methodology will fail, however:

• Market impact is not directly observable; rather it must be estimated. To reduce estimation error, large statistical samples are required, which implies gathering data over extended time periods. Thus, only time-averaged behavior can be measured with any precision. But the underlying phenomenon is a product of the highly dynamic market environment. Thus, long-term averages end up having little forecasting ability.
• Trade data suffers from a censoring problem. Since investors avoid costly trades, we never see the most costly trades in the record. Unless we somehow compensate for this circumstance, estimates derived from trade data will systematically underestimate market impact costs.
• There is an uneven level of information available for assets. We see market impact for an asset by watching how it trades. Therefore, we know more about heavily traded assets and less about thinly traded assets. Yet it is the thinly traded assets that tend to have the higher market impact costs, and it is the more costly-to-trade assets that are most important for the portfolio construction problem. Again, we need to adjust for the data problems to avoid introducing a methodological bias into the results.

Choice of modeling strategy

Of the three econometric challenges, the data censoring problem exerts the greatest influence over the choice of modeling strategy. The key assumption in the naïve modeling approach is that the data contain the information we need, and so all we have to do is to extract it. However, the data does not contain the information we want, at least not in any directly extractable form. As a result, the naïve approach cannot succeed.

A successful modeling strategy must begin with a more sophisticated approach to the data. Although the data may not directly answer our question, they can still answer many questions about market functioning. If we knew how the market mechanism determines impact, then we could hope to assemble the measurements of market function drawn from the data into an answer to the question of true interest—namely, what will be the impact of a prospective trade? For this approach to succeed we need an understanding of the economic fundamentals determining impact.

Our model-building exercise begins, therefore, with an economic analysis of the markets and trading. The result of this analysis is the identification of the factors determining market impact and the structure relating the factors. Once the model components have been identified, we turn to empirical analysis to complete their estimation.

The ultimate modeling strategy is thus a combination of the analytical and empirical approaches. We feel that a marriage of these two approaches is especially suitable to the market impact problem—since the economic analysis can overcome the limitations of the data, while the empirical approach ensures that the results are closely tied to the realities of the market.

Summary

We have seen that the portfolio management process benefits from timely a priori estimates of trading costs covering a wide range of assets and position sizes. Providing these estimates is the goal of the Market Impact Model. Because of econometric difficulties, a purely data-driven approach to this modeling problem cannot succeed; a combination of analytical and empirical methods is required. Future articles in this series will address these issues and describe the construction and implementation of the Market Impact Model.

Footnotes

¹ This account simplifies somewhat, since there can be more volume available inside the quote than is revealed in the quoted depth and since there can be volume available inside the quoted spread. The realized spread (i.e., what investors experience) is thus different from the quoted spread. (return to text)