Balancing Execution Risk and Trading Cost in Portfolio Algorithms

Transcription

1 Balancing Execution Risk and Trading Cost in Portfolio Algorithms Jeff Bacidore Di Wu Wenjie Xu Algorithmic Trading ITG June, 2013

2 Introduction For a portfolio trader, achieving best execution requires balancing execution risk and transaction cost across a basket of securities. Naturally, reducing risk and minimizing cost have opposing effects on execution. Simply put, trading aggressively incurs higher cost but lower risk, while trading patiently yields lower cost but higher risk. Furthermore, traders often have secondary considerations such as maintaining cash- or beta-neutrality, which makes this trade-off even more challenging. In this paper, we discuss the cost-risk trade-off in a portfolio trading context. We provide examples of how trading a basket in a coordinated manner can lead to more efficient execution than by trading each stock independently. Specifically, by trading buy and sell orders in a synchronized way, traders are able to trade more passively, reducing cost without increasing risk. We discuss how this cost-risk trade-off can be operationalized via an optimization approach, even when traders apply additional constraints like cash- or beta-neutrality. Finally, we address the importance of incorporating intraday variation in cost and risk when formulating an optimal trading strategy. Managing Risk in Portfolio Transactions When trading a single stock, the only means of managing risk is to execute quickly to reduce the chance of an adverse price movement. In the context of portfolio transactions, however, traders can also control risk by exploiting the correlations between stocks. For example, consider a trade basket that has more sells than buys and is therefore vulnerable to sudden market declines. Single-stock algorithms would trade each stock independently and would likely frontload both the buys and sells to reduce risk (Figure 1a). In contrast, portfolio algorithms would trade the orders in a coordinated way to exploit the natural negative correlation between the buys and sells. In this example, a portfolio algorithm would execute the sells more aggressively, while trading the buys more slowly possibly even backloading them to reduce the imbalance and help immunize the basket from market moves (Figure 1b). 1

3 Figure 1a: Risk reduction in single-stock algorithms Figure 1b: Risk reduction in portfolio algorithms Another benefit of managing risk in a portfolio context is that it allows traders to trade more passively, leading to lower trading cost. Given that buy and sell orders are typically negatively correlated, one naturally hedges the other and hence both can be executed more passively without increasing risk. For example, as noted above, a single-stock implementation shortfall algorithm will generally frontload both the buys and sells to shorten the time over which a basket is exposed to market volatility (Figure 2a). Had the trader executed the orders as part of a coordinated portfolio trade, she could have controlled risk by pairing correlated buys and sells together to offset future market swings. This would have allowed her to lower cost by spreading the order out without increasing her risk exposure (Figure 2b). Figure 2a: Aggressive trading with higher cost Figure 2b: Passive trading with lower cost Successful risk management also requires efficient utilization of dark liquidity. When stocks are executed independently, a block crossed in dark pools is generally welcomed since it reduces both cost and risk. In a portfolio context, however, block fills may result in lower trading cost but 2

4 unwanted market exposures as well. For example, if a basket is risk-balanced, receiving a large block on one side of the market could substantially increase risk. When this happens, a portfolio algorithm must quickly bring risk under control through actions such as executing the slow side more quickly. 1 Therefore, a well-designed portfolio algorithm needs to be careful when exposing orders to dark pools and, following dark fills, it must bring risk back in line in the most efficient way. Minimizing Cost and Risk under Constraints One way to operationalize the cost-risk tradeoff is via an optimization. 2 However, the basic cost-risk optimization can become challenging in a real-world context. For example, the scale of the optimization can be quite large given that a portfolio trader could include thousands of orders. In addition, traders may have other objectives that must be satisfied, such as maintaining beta- or cash-neutrality. For an optimization to be practical, it must incorporate these constraints in a way that generates intuitive solutions, and not simply apply them mechanically. For example, if an algorithm receives a beta-imbalanced basket but the trader wants to eventually reach beta neutrality, the algorithm should not simply remove the imbalance immediately (and at high cost) just to meet the constraint. Rather, the algorithm should use the same cost-risk approach when determining how quickly to meet these additional cash or beta considerations. An added benefit of incorporating constraints in the optimization directly is that it allows the optimization to formulate a trading strategy that will adhere to these secondary considerations while still meeting the primary trading objectives. For example, consider a common scenario in which a trader wants to manage both total risk and beta risk explicitly. The conventional method that only takes total risk into consideration may often end up with a solution with a slow decrease in beta exposure, since the optimizer may find it more efficient to lower total risk by managing the firm-specific portion of risk as opposed to beta (Figure 3a). Specifically, if the basket has some positions that have large firm-specific risk, the optimizer may accept additional beta risk in order 1 See for example Wu and Xu (2012). 2 See for example Almgren and Chriss (2001), Kissell and Malamut (2007), and Engle and Ferstenberg (2007). 3

5 to reduce the firm-specific risk. If, on the other hand, the optimization directly incorporated the trader s secondary consideration to neutralize beta exposure, the result would be a trading strategy that reduced beta risk much more rapidly (Figure 3b). Figure 3a: Cost-risk minimization without constraints Figure 3b: Cost-risk minimization with constraints The Time-of-Day Effect of Cost and Risk The ability to manage risk by controlling the composition of a trade basket allows portfolio trades to be executed passively, over a relatively long time period (e.g., hours). Therefore, an optimal trading strategy must consider not only the differences in cost and risk across stocks, but also how cost and risk vary over time. For example, the cost of liquidity is generally at its peak right around market open, then declines uniformly as the day progresses (Figure 4a). This implies that if one executes the same order at different times of day, the expected cost and therefore the inherent cost-risk tradeoff will vary. Figure 4b displays four curves that represent the cost of trading a given quantity at different points in time. The clear distinction between these curves demonstrates how intraday variation in liquidity can significantly affect costs. A well-designed algorithm therefore needs to recognize this effect and use time-dependent cost variables in its optimization process. 4

6 Figure 4a: The intraday pattern of cost Figure 4b: Time-dependent cost Similarly, price volatility also exhibits a time-varying pattern (Figure 5). In general, the price of a stock is most volatile in early morning, especially around the open. As the day goes on, volatility tapers off, but often with a slight increase just prior to the close. As was the case with time-varying cost, a well-designed portfolio algorithm must also consider time-varying volatility in its risk estimate in order to make the trading schedule to be optimal. Figure 5: The intraday pattern of volatility Figures 6a and 6b show how ignoring time-variation can lead to suboptimal schedules. Given the same amount of risk, time-dependent cost will lead to a more backloaded strategy as the algorithm tries to avoid the costly liquidity at the start of the day and exploit the cheap liquidity at the end of the day (Figure 6a). Equivalently, for a fixed level of cost, time-dependent volatility results in a strategy that is more frontloaded so that risk is reduced more quickly given the unusually high volatility around market open (Figure 6b). 5

7 Figure 6a: Time-dependent vs. constant cost Figure 6b: Time-dependent vs. constant volatility Conclusion Execution risk and transaction cost are the two main drivers of trading performance. However, reducing one driver often leads to increasing the other. Achieving best execution therefore requires traders to strike a balance between these two. In the context of portfolio trading, risk can be managed not only through speeding up the trade, but also through exploiting the correlations across stocks. A trader executing a two-sided basket for example can use the buys as a hedge against the sells, making it possible for the trader to effectively lower costs by trading more passively without dramatically increasing risk. In practice, this balance can be effectively achieved via the use of portfolio trading algorithms. Such algorithms can balance cost against risk by executing a basket in a coordinated manner, e.g., speeding up certain orders while slowing down others to keep the basket risk-balanced. Algorithms are often best suited for this task since they can consider the full correlation matrix when formulating an optimal trading strategy. Such a framework also makes it possible to efficiently incorporate other considerations, e.g. maintaining beta- or cash-neutrality and even factoring in time-varying cost and risk. Equipped with these advanced quantitative trading techniques, portfolio algorithms will be able to help traders improve execution performance and eventually increase overall investment returns. 6

8 REFERENCES Almgren R., and Chriss N., Optimal Execution of Portfolio Transactions, Journal of Risk, Winter 2000/2001. Kissell R., and Malamut R., Investing and Trading Consistency, Journal of Trading, Fall Engle R., and Ferstenberg R., Execution Risk, Journal of Portfolio Management, Winter Wu D., and Xu W. J., Algorithmic Portfolio Trading: A Primer, ITG White Paper, July