ADJUSTING FOR SIZE.

Liquidity and risk effects in foreign exchange trading

By Jim Cochrane, Director, ITG TCA^® for FX, Ian Domowitz, Managing Director, Head of ITG Analytics, Milan Borkovec, Managing Director, Head of Financial Engineering and Sandor Ferencz, Vice President, ITG Analytics.

As the next advance in FX TCA reporting, our clients in the investment community have requested size-adjusted spread (SAS) benchmarks that account for risk and liquidity on a pre-trade and a post-trade basis. However, one of the more frustrating aspects of over-the-counter trading is the lack of transparency around these spreads. An accurate size-adjusted spread based on aggregated electronic foreign exchange quotes would replace the old method of supplying expected spreads: manually-filled matrices for each trading region with spreads for given currency pairs and sizes. Buyside traders depended on this information to both hold banks accountable for their agreed spreads as well as manage their own expectations for costs. Now that buyside firms are more responsible for currency risk, they need a system that will digitally re-create those matrices and give them a benchmark that will show that they add value to the investment process.

While every benchmark is a useful tool for the analyst, the lack of a benchmark that measures the impact of their trading skill and discretion in FX has been sorely missed over the past several years. Most traders feel that they add value to the funds for which they trade. A true accounting for that currency risk management will not only provide them with a skill measure, but it will also provide valuable information to every constituent group at a buyside firm regarding portfolio performance, implementation shortfall and process improvement.

As a provider of foreign exchange transaction cost analysis (FX TCA) ITG created FX cost curves from our tradable quote database that provide insights into expected costs for any size trade at any time of day for liquid, deliverable currency pairs. Our curves were split up into four distinct categories from our quote sources: all sources, the best bank quotes, the average bank quotes and ECN-only quotes. Each cost curve had a different expectation for SAS, which would be expected for FX trading. While each have their uses for pre-trade analysis and trading strategy, which is the “best” curve? Which curve produces the most accurate cost estimate?

Since ITG also has access to executed transactions in our database, we tested our cost curves for accuracy. The result of this examination was a modified cost curve that can be used to adjust for the size of currency transactions during times of differing liquidity and risk profiles. This cost curve can then be used to create a SAS benchmark rate that will account for trader skill as well as provide a more precise pre-trade measurement of expected trading costs. The result can then be a source for decision-making and research at firms that seek to outperform their peers.

First we will review FX market structure and our methodology for managing both opacity and aggregation. Then we will detail the first results of our study in size-adjusted spreads and the creation of our cost curves. Lastly, we will review our test of those curves against actual transactions to see which curve is the best fit for SAS.

The lack of a central exchange in the FX market has challenged analysts pursuing accurate cost measurement and useful benchmarks. In a market that has literally dozens of bid/offer spreads at any single point in time (see Figure 1), it is difficult to discover correct pricing even under normal market conditions. Transparency in foreign exchange has become a house of mirrors where the real rate is difficult to find, let alone define, among the dozens of false images. One way to instill clarity among the chaos is to capture and organize as many of these quotes as possible into a limit order book.

The development of a consolidated limit-order book using aggregated FX price streams was once reserved for the interbank market. That changed with the advent of electronic trading, but the rates became separated and sub-divided as the market became fragmented. Aggregators with different feeds would produce different results for any study. One way to increase transparency is to build a comprehensive data set and create cost curves with that data and test them against actual executions.

At ITG, we aggregate pricing data for 38 liquid, deliverable currency pairs from 12 global FX banks and five major electronic communication networks (ECNs). This data is then culled for duplicate and stale quotes. We then review the cumulative depth of each currency pair to ensure that enough trade data is available for in-depth analysis. The resulting empirical order book permits the construction of size-adjusted spreads for any time of day. Intuitively, the spread should depend on the notional amount of liquidity available at any given price. The order book quantifies this notion, based on the cost of climbing, or sweeping, the book for any given deal size.

We apply the following model to create daily FX size-adjusted cost curves:

SizeAdjCost_t,i = SizeAdjCost_b,i • (ImpvolSurprise_t-1,i)^b (1)

where:

• t is the day index,
• i specifies the currency pair (38 pairs currently),
• SizeAdjCost_t,i is size-adjusted cost for date t and currency pair i for a specific size depending on the currency pair,
• SizeAdjCost_b,i is the median size-adjusted cost during the benchmark period,
• ImpvolSurprise_t-1,i = Impvol_t-1,i
  Impvol_b,i
• Impvol_t-1,i is the implied volatility of the currency pair i at as of 8pm Eastern Time on date t-1,
• Impvol_b,i is median implied volatility during the benchmark period.

The model produces results that estimate costs by time and size and provider.

One of our initial observations was that our SAS did not match earlier research (Borkovec, Cochrane, Domowitz and Escobar [2014]). These observations were based solely on sweeping the book of liquidity using all sources, and produced spreads that were lower than other studies. Our own experience led us to believe that SAS reported in earlier research was too generous. True spreads, while wider than the bid/offer spread in the market, were not as wide as estimated in other papers and articles. That same insight also led us to believe that sweeping the book was not a popular method for achieving low costs and our results were too extreme due to the microstructure of the aggregated market. Even after culling our data, our size-adjusted spreads were probably not achievable.

The above insights prompted us to alter our methodology in order to account for venue performance and last-look liquidity. It is very unlikely that sweeping the book would be successful if the banks have the ability to take one last look before accepting the trade, especially if the top of book has already been triggered. And, in cases where an investor was successful in sweeping the book for a large trade, then the last banks holding the now toxic position would either stop quoting to the successful investor or widen the quotes to that investor in order to account for the increased risk in her trading style. In response to our observations and understanding of the FX market, we created a variety of cost curves that would match a trader’s execution style.

While keeping the swept book concept in our “ALL” size-adjusted spreads, we also derived three other cost curves: Avg Bank, ECN and Best Bank. As you can observe in Figure 2, “Cost by Provider,” in sizes above 50m USDCAD at the end of the NY trading day, Best Bank outperforms Avg Bank, which outperforms the ECN curve. The Best Bank cost curve is based on the best dealer quotes for each size at this point in time. The Avg Bank curve is calculated from the average cost of all dealer banks for each size at this point in time. Lastly, the ECN line is the average of the consolidated ECN tradable quotes. We discovered that our wider costs matched earlier research more closely than the ALL or Best Bank curves.

It is interesting to note that the ECN cost curve significantly outperforms in relatively smaller sizes, even beating the finest quotes of the Best Bank curve. Clearly this is an indication that in sizes up to 25 million U.S. dollars, the banks would prefer clients to use electronic trading platforms for this currency pair. Similarly, the inflection point between the Avg Bank curve and ECN curve at about 60 million US dollars reveals a desire to have clients pick up the phone and deal directly. Now we have four curves that could represent normal operating procedures for dissimilar trading desks: one that relies solely on ECNs, one that calls up a bank randomly (Avg Bank), one that knows the best broker-dealer for each currency pair (Best Bank), especially in large size transactions and one that sweeps the book (ALL). While each provides a cost expectation that fits a unique scenario, we still do not know which curve is the closest to actual experiences of FX traders in the market. We will discuss which of the four curves is the best curve in the next section of the article.

The table in Figure 3 below represents the first step of our inquiry into which cost curve is the best to use to create a SAS benchmark. It contains the results of comparing our test SAS benchmark rates against actual executions. The “Quoted Mid bps” column is the difference between the execution rate of a transaction subtracted by the mid rate prevailing in the market at the time of the transaction (if selling the base currency) expressed as a percentage of the same mid rate in basis points. That difference between the two rates is then compared to our four SAS benchmark rates. The results in the “SAS” columns are the expected SAS minus the “Quoted Mid bps”. A result of zero indicates that the expected SAS benchmark matched the actual transaction rate. A positive result indicates that the actual trade was a “gain” against this benchmark. A negative result indicates that the execution was outside, or worse, than the expected spread. “We did not differentiate for size. All trades are between 5 and 100 million base currency units. In total, 82,705 trades were analyzed for this study.

The observations do not create a clear picture of which SAS curve should prevail. In other words, there is no clear winner using this analysis. The cells outlined in white are the closest to a zero in comparing the total cost of the transaction against the predicted cost using the SAS benchmark rate. The cost curve that produces differentials closest to zero changes by currency pair. Further tests made in this fashion revealed that the SAS_Avg cost curve came closer to the actual trades more often than the others, but not enough to say it is the best choice. The next test was to create a simple regression between the total cost of the actual executions against the cost curves and produce scatter plots. The results of this phase of the test were more conclusive and striking.

The analysis in Figure 4 compares the actual spread (Total Cost) on the y-axis to the expected SAS Benchmark spread on the x-axis for each of the cost curves. As seen by the R2 values for the various charts above, the best-fit line corresponded to the All Providers setting and not the Avg Bank setting. That is not to say that the ALL cost curve, which sweeps the book, is closer to zero across all trades. It is the cost curve with the best fit (R2=0.8497).

This insight provided the focus for the last phase; modeling the ALL cost curve against actual transactions and deal size. As seen in Equation 1, the model attempts to explain the relationship between actual transaction cost using the top-of-book quoted mid rate as a benchmark, and ITG’s size-adjusted spread, taking deal size into consideration.

Equation 1:
Total Cost = B₀ + SAS_[P]b + Deal Sizeg

where:

• Total Cost is the difference between the mid rate of the best bid and offer in the market and the execution rate of the transaction expressed in basis points,
• B₀ is the intercept for the model,
• SAS_[P] is the expected cost of the SAS benchmark expressed in basis points, and
• Deal Size is size of the trade.

The multiple regression analysis results are shown above in Figure 5.

As seen in Figure 5, the model was able to explain 83.7% of the variation in the actual Total Costs against the all-venue based size-adjusted spread (SAS_All). The model shows a positive relationship between total costs and the size adjusted spread benchmark. Moreover, for every basis point increase in the size-adjusted spread, total costs, on average, will increase by 1.0075 basis points. It is important to note that the p-value stochastically approaches zero as the sample size increases. Significance was tested by seeing if the lower and upper bounds crossed zero. If the lower and upper limits contain 0, then the independent variables are not considered to be a significant predictor of total cost. Based upon the results found in Figure 5, the following model was created:

Total Cost _Prediction =
-0.344 + 1.0075(SAS_All) + -2.50E-09(Deal Size)

After re-running the actual costs against the modified size-adjusted spread benchmark, the results fell within ±0.5bps of the actual top of book quoted mid benchmark values 90% of the time, and within ±0.25bps of the actual top of book quoted mid benchmark values 69% of the time. To state this differently, of the 82,705 initial observations, 74,117 fell within ±0.5bps of the actual total cost and 56,682 fell within ±0.25bps. Based on the findings of this high-level study, the next logical step would be to investigate estimated total costs given different scenarios and real time market inputs, such as deal size and market volatility, as well as individual currencies.

In an OTC market such as foreign exchange, an overload of prices can lead to not only a lack of transparency, but also a debate on which price is best or which mid rate is correct. By comparing actual trades against our estimates of costs, it is clear that in the multitude of prices in an aggregated limited order book, an accurate size-adjusted spread prediction can be achieved. Additionally, contrary to earlier research results, lower costs in foreign exchange transactions should be expected. Attention to these details and matching trading strategy to execute in the market at the times of lower volatility and tighter spreads will certainly improve performance and increase competitiveness.

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