The goal of Transaction Cost Analysis is to provide a framework that can determine whether a trade was conducted well, and to offer benchmarks to identify trading skill. But if our concern is to identify trading alpha, we first need to determine what constitutes trading beta.
Bertsimas and Lo (1998) define best execution as the dynamic trading strategy that provides the minimum expected cost of trading over a fixed period of time. This definition provides a useful framework to think about the concerns a trader has when they bring an order to market. Trading is an optimisation problem.
A short while ago I had an opportunity to read a white paper by Dr Jamie Walton which offers a fairer, more efficient way of establishing the 4pm Fixing price for currencies. His model proposes a dynamic optimisation process using New Change FXs independent benchmark mid-rates. The SIREN benchmark methodology is based on the optimisation framework first put forward by Almgren and Chriss (2000). This optimisation framework was further developed by Kissel & Glantz (2003) and promoted by Edhec (Transaction Cost Analysis A-Z). Whereas the idea of an efficient trading frontier is fairly well known in equities, FX has been slower to implement it in the trading decision process.
FX markets are of course quite different from equities. One crucial factor is that the majority of FX trades are motivated by liquidity rather than information. This means that the information quotient of FX trades is low. Most FX trades are a derivative of another transaction, buying foreign currency denomination goods or services for example, rather than a speculative bet that one currency will perform better than another. This makes for noisy trading.
Is a three-pip spread to buy $50 million worth of euro really enough to compensate the dealer for their inventory risk? (Osler et al 2006). Only if the dealer thinks the adverse selection risk is low. (If a customer wants to sell because they correctly anticipate prices will decline, the dealer risks buying high and selling low). The edge that FX dealers have over clients stems from bigger networks, enabling them to take riskless profit by internalizing trades, rather than taking a bet that they have better (faster access to) information. The players with the largest networks have a distinct advantage.
The dealer’s advantage arises from the structural opacity of the FX market. The prices that clients see are not necessarily the whole picture. Independent FX mid rates are a relatively recent development. Dealers quote the prices at which they will trade. As we mentioned earlier, bids and offers are skews away from equilibrium. Prices adjust in anticipation of order flow. But also, there is variation between dealers’ quotes. A common misunderstanding is that if a customer could aggregate all dealer quotes, then they would have an unbiased estimate of the mid-rate.
This would be true only if this data could be collected anonymously; a condition that is not present in Request for Quote data for example, or streaming data that allows last look. Each time a dealer makes a two-way price they are essentially guessing which way the customer is likely to go. The more often the customer trades, the more data can be collected. More data allows market-makers better odds of guessing correctly. Even the act of asking for a price causes market impact.
In order to measure transaction costs accurately we need to know what the market would have been had we not traded, or better yet, where the market was trading had we not asked to see a price. This is akin to trying to follow a single pair of footprints through a snow field, when a thousand people are simultaneously traipsing across it. How do we determine whose footprints are whose?
Independent benchmark price
Our first goal then on the journey to an efficient frontier is to establish an independent benchmark price. A clean, anonymised mid-rate price captured before anyone has walked across the snow. Truly independent ex-ante prices will look something like the product of a synthetic ECN which perpetually asks for prices from other ECNs, but never trades.
Armed with an independent mid-rate we are now able to tackle the trader’s dilemma. When we have a large transaction to undertake, we could either trade in equal amounts over time, or trade all in one go. If we could trade in increments of equal size, employing a time weighted average technique we should minimize expected market impact costs, but the exposure to variance could be large if the time horizon is long.
A very risk averse participant would prefer to trade everything immediately, incurring a higher market impact penalty, whereas a risk seeking participant might be happy to extend their time horizon indefinitely to minimize market impact. But how much time should we allocate to complete a trade?
One method of estimating this is to think about the difference between permanent and temporary market impact. As we noted earlier, dealers quote bids and offers as compensation for providing liquidity to take the other side of a trade. If the size of the trade is less than the capacity of the market to absorb the trade, the mid prices before and after the trade will be the same. Conversely, if the market flow capacity in GBPUSD is running $5 million a second and we were to trade $6 million, we should expect that bid ask spreads should widen further, and the mid-rate post trade will have changed. The price skew away from mid is the temporary market impact. The change in the mid-rate is a permanent effect. To calculate it we must have some way to estimate what the absorption rate of the market is. This capacity is the liquidity replenishment cycle.
Unfortunately, there is no consolidated FX market tape that will provide us with the actual market volumes, but we can make an educated guess. Using triennial BIS data, and updated with the semi annual regional Joint Standing FX Committtee data we can estimate daily average turnover volumes per currency pair and adjust them for the daily liquidity cycle. Research by Marsh et al (2017) shows that there are a fairly regular series of bursts in activity around sensitive times during the trading day. These times fit well with key events 09:30 London (UK data releases), 13:15 (ECB fix), 15:00 (Options expiries) and 16:00 (WM Fix) We can factor these spikes into a stylised estimate of the flow rate of the FX market by currency pair, per day, per hour, per minute, per millisecond.
Estimating market impact requires a proxy for market volume. The most widely used model to predict market impact for equities is the Square Root Model described by Grinold and Kahn (1994) and commercialised as the Barra Market Impact Model (1997). If participants have all day to trade, the model does a very good job (Gatheral 2016). Unfortunately, the model is not sensitive to the aggressiveness or passiveness of trading. The decision to trade passively or aggressively is largely driven by risk tolerance, and it is risk tolerance which determines strategy.
The Almgren Chriss Model offers a more flexible approach, and frames that question of execution quality in terms that investors are more familiar with, a trade off between performance (lower costs) and risk. Lower costs come at the expense of higher risks. This is possible because the Almgren Chriss framework (explored in depth by Kissel and Glantz) identifies risk tolerance (l) as a utility function.
The utility function introduces convexity into the trade-off between cost and risk. This is the framework of Modern Portfolio Theory. The utility function identifies the efficient trajectory. All other trajectories are sub optimal, they either incur too much cost, or they take too much risk.
Although beyond the scope of the Almgren Chriss framework the efficient trading frontier opens up the possibility of identifying the expected price, or target price we should achieve at a given time horizon. Different trajectories, such as trading faster or slower will generate different market impact, but the optimal trajectory is unique.
How good is a particular trading strategy? Was the target price achieved above or below the efficient price? Furthermore, in an ex-ante framework, the efficient frontier can determine the best trajectory to achieve the target price, given liquidity conditions, market drift and market volatility at the time the decision to trade is taken.
The premise of TCA is that it is hard to manage what you cannot measure. Independent mid-rates, optimised participation strategies for FX, such as SIREN methodology for Benchmark Fixings and the NCFX FX Efficient Frontier are new tools that are products of the effort to identify FX costs. These are powerful tools to measure and manage FX. By identifying alpha and beta of FX markets these tools can deliver on the promise of better FX outcomes for market participants. This is after all what TCA is meant for.
SIREN Benchmarks, Walton 2018
Optimal Execution of Portfolio Transactions, Almgren, Chriss, 2000
Price Discovery in Currency Markets, Osler, Mende, Menkhoff, 2006
Three Market Impact Models, Gatheral, 2016
Transaction Cost Analysis A-Z, D’hondt, Giraud, 2008
The WMR Fix and its impact on currency markets Marsh, Panagiotou and Payne (2017)