Equity Program Trading

by Michael Bishopp and Rakesh Manani

The BARRA Aegis System is BARRA's Windows-based equity risk management system. Aegis risk models cover over 27,000 equities in more than 50 countries. The U.K. Equity Trading Model, profiled in the Winter 1997 Horizon, is one of these models. In this article we explore the usage of Aegis with the U.K. Equity Trading Model for program trading in the U.K. market, but Aegis can be used for this purpose for any market covered by the system.

The mechanism of a program trade calls for the seller of the portfolio to exchange information with the quoting broker so that he or she is able to determine the trade's price. The characteristics exchanged often vary with the sophistication of the client, but they typically cover the number of names, the liquidity of the assets, and whether there are any sector imbalances contained within the portfolio. Structural questions are often considered, such as how many stocks are exchange-listed versus over-the-counter or what percentage of the portfolio is in FTSE as opposed to non-FTSE names.

BARRA risk reports have become a popular medium for communicating the risk characteristics of a program. Using the information in these reports along with the Aegis unit exposure assets, a trader can create a composite asset¹ with the same common factor and specific risk exposures as the client's portfolio. This composite can then be used to more accurately assess the impact of the program on a trader's held inventory and hence more accurately price the trade.²

What are unit exposure assets?

Unit exposure assets are fictitious assets that represent each of the common factors in a BARRA equity country model. If the asset represents a risk index, it has an exposure of 1.0 to that factor and an exposure of zero to every other common factor. If the asset represents an industry, it has an exposure of 100% to that industry and zero exposure to all other common factors. For each country model there is also a unit exposure asset for specific risk, which has a specific risk of 10% and zero exposure to all common factors.

Unit exposure assets are named after the risk indices and industries they represent. The Reference section of the Aegis User's Guide lists the unit exposure assets and their identifiers available for each country model.

An example

Figure 1 shows a sample BARRA Factor Summary, one of the risk reports available from Aegis. Using this information we can construct a portfolio to replicate the risk profile of the program, which can then be processed as a composite and added to the trader's inventory. Once added, we will then use this composite to analyze how taking on the trade will change the overall risk profile of the trader's position.

FIGURE 1. BARRA Aegis System Factor Summary Report for a proposed U.K. equity program.

Let us assume that the trader's current inventory has the risk characteristics shown in Figure 2. Here the residual risk characteristics are relative to the FTSE 100 index.

FIGURE 2. Aegis Risk Decomposition for a U.K. equity inventory held by a trader.

This Risk Decomposition report shows us that the trader's book has an annual predicted volatility of 16.14%. However, the most important risk number here is the total residual risk of 2.99%, since this is the risk in the inventory that will remain after a futures hedge. Now, by adding a composite asset constructed to approximate the client's portfolio, we can assess the impact on the residual risk of the inventory by taking on the program. If the trade has a favorable impact, the trader may be more aggressive in pricing the program, compared with pricing in isolation, and vice versa.

In addition, the trader may want to assess some other dimensions of risk, such as the actual number and profile of stocks within the position and the availability of a suitable hedge instrument to offset the component of risk associated with the market (systematic risk).

Figure 3 shows the risk of our inventory after adding the composite asset. Note that the residual risk has decreased by 4 basis points, demonstrating that the incoming program is in fact a risk-reducing trade.

FIGURE 3. Aegis Risk Decomposition of a U.K. equity trader's inventory after adding a composite representing a client's program trade.

Unwinding positions

Traders must often manage an inventory of long/short positions that are, for example, the result of a buy program and sell program. Here we show how we can sequence a series of trades to optimally unwind the book by using the U.K. Trading Model within the Aegis System.

For our example we shall use a hypothetical U.K. book with 24 assets long and 16 assets short, and with a net value of £1,507,501 (£4,141,488 - £2,633,987). In general, to optimally manage the book, the trader will choose to offset the market component of the total risk he or she is bearing with a futures hedge. This can be calculated from within the U.K. Trading Model by using the Best Hedge tool. Once this is applied, the trader is left bearing non-market or residual risk.

The Best Hedge tool is flexible and can calculate the optimal hedge using single or multiple futures contracts. Note that a common misconception is that a position is market-neutral when the value of the portfolio is zero. In our example, the naïve trader who believed in this misconception would short FTSE 100 futures contracts equal in value to the net value of the position, in the hope of achieving market-neutrality. This method will yield a position beta that is different from zero, and thus the trader will bear some market risk. Aegis's Best Hedge tool will yield a position beta of zero, as intended and desired. In this case the net value of the book will not be zero but will remain constant and result in a lower book volatility.

Figure 4 shows our example hedged long/short portfolio.

FIGURE 4. Hedged long/short U.K. equity book with minimum market exposure.

In deciding the sequence of trades, the trader needs to know the impact of an individual trade on overall position volatility. To do this we use the marginal contribution to risk (MC-Risk) calculated by the Aegis System. The system tells us that the optimal trade will be to sell the asset with the highest MC-Risk and, with the realized money, to buy the asset with the lowest MC-Risk.

The simplest way to calculate the optimal amount of each stock to trade is to use the Aegis Trade Scenario tool. This interactive function allows the user to trade high MC-Risk positions for low MC-Risk ones, iteratively lowering portfolio risk. Figure 5 shows an example with a trade between Glaxo Wellcome and Halifax. Here the most risk-reducing first trade would be to reduce our short position in Glaxo (MC-Risk = -0.13) from -5.40% (the starting position) to -3.14%, which would be financed by completely unwinding our long position in Halifax (MC-Risk = 0.22). The impact on portfolio predicted total risk would be a reduction from 2.49% to 1.85%. (Recall that we have offset the market risk with a short position in FTSE 100 futures contracts.)

FIGURE 5. Aegis Trade Scenario can be used to trade out of high risk positions into lower risk positions into lower risk positions.

The trader may now continue this process until the whole position, including the short futures position, is unwound. In implementing this scheme it is important to remember that the trade order is entirely determined by risk factors. The trader must also use skill and judgment in considering other factors such as daily trading volume and market impact when deciding the sequence and value of each trade.

Summary

This article illustrates another application of BARRA's Aegis System with the U.K. Equity Trading Model. The U.K. Equity Trading Model uses the latest risk-modeling techniques to help equity traders manage the short-term risk within their books, and is the first of a series of planned enhancements to BARRA's risk models and applications to meet and exceed the demands of the trading community.

Footnotes

¹ A composite asset consist of two or more assets or composites, and has the risk characteristics of those assets as if they were to be treated as a portfolio.
(return to text)

² Note that the composite asset is only an approximation of the client's portfolio, because the risk model will assume that the specific covariance of the assets in the trader's inventory with the assets in the composite are all zero. This would not be true if any of the assets in the inventory were in the client's portfolio; however, this efect is in general not significant for typical portfolios.
(return to text)