Triangular Arbitrage & The Introduction of Liquidity to the Interbank Currency Markets: Evidence from GBP/MXN, JPY/MXN, and GBP/JPY Exchange Rates

Working through some archives, came across some old recordings that I never got a chance to sift through.  Below are the GBP/MXN, JPY/MXN, and GBP/JPY exchange rates recorded from the currency open on Sunday, October 2, 2011 through October 3, 2011.  Following the outright prices below are the spreads constructed from finding the synthetic exchange rates via triangular arbitrage and spreading them to their live equivalents.  

Because of the ease of this arbitrage and the automated nature of these trades, this relationship is a popular topic on this blog.  The market opening and subsequent introduction of liquidity into the interbank market has been particularly interesting to study. 

The Outrights.

  

 

 

These are the aforementioned spreads between the synthetic and live exchange rates.   Despite the volatility of the underlying rates, the spreads unsurprisingly remain remarkably consistent.  More detail on this type of trade can be found in the links below.

The Spreads.

  

 

Previous studies have touched on the following relationships:
CHF, JPY, and NZD
USD, SEK, and NOK
KRW, JPY, and HKD
USD, AUD, and HKD

Further Reading:
Heterogeneous Market-Making in Foreign Exchange Markets: Evidence from Individual Bank Responses to Central Bank Interventions (pdf)
Spread Components and Dealer Profits in the Interbank Foreign Exchange Market (pdf)

Triangular Arbitrage of CHF/JPY using NZD as a Medium

Full Trading Period

The CHF/NZD and JPY/NZD currencies were used to build a live synthetic CHF/JPY which was then spread to the live real CHF/JPY available on Idealpro (left axis).  The corresponding spread (right axis) is given by the orange/green combo hovering around parity (= 0). Prices were recorded Sunday, 2 October through Monday, 3 October, 2011.

The Opening.

Sunday Evening Opening: 4:06PM - Midnight CST

Sunday Evening Opening: 4:06PM - 7:00PM CST

A curious widening of the spread occurs right around 9:00am CST. Seconds after this loss of liquidity, a slight break occurs in the synthetic/real relationship (Figures 1 and 1.A), leading to the first visible arbitrage in the recorded series.  A 2nd break occurs just over an hour later (Figures 2 and 2.A). 

Liquidity Gap

Arbitrage 1.

In the first occurrence, the bid of the synthetic (Dark Blue) rises above the offered price available through the live CHF/JPY (Purple).  The synthetic could have been sold while the live CHF/JPY was purchased for an offsetting amount, resulting in a perceived profit subject to the minimum liquidity available across all the necessary legs of the trade.  Prices broke again in the opposite direction (Red below Green) a fraction of a second later.  After which, they quickly reverted to their "no-arbitrage" relationship. 

Figure 1

Figure 1.A

Arbitrage 2.

In the second (or third) finding, the opposite break in the relationship occurs.  The offered price of the synthetic (Red) falls below the bid price of the live CHF/JPY (Green) allowing the high-frequency trader to take advantage of the arbitrage, purchasing the synthetic and selling the live market.  Again, the availability of the trade is subject to the minimum quantity available on every leg of the trade. 

Figure 2

Figure 2.A

Some Papers on Physical Arbitrage & Route Choice

I apologize for my lack of posting lately.  I am studying for an exam which has and will continue to monopolize my time for the next ~30 days.  Posts should resume "normally" after November 19.

In the coming weeks, I hope to post more research on triangular arbitrage, expanding on a post earlier detailing the introduction of liquidity to the interbank market during the Sunday evening open each week.  This research utilizes new triangles that I hope others will find as interesting as I do.

I have also recorded prices on the SI / SLV relationship and hope to bring this forward in the next few days if time allows. Expanding on the principle of futures vs equity, I recorded prices on the FCX / HG pair and hope to bring this forward as well.  A preliminary look at the prices seems to provide some support for the development of strategies built around this relationship. 

In lieu of new posts, here are a few papers I hope similar minded readers will find interesting.  As mentioned previously, I have a love for physical commodity trading and found each of these to be very illuminating in their own way.

The Papers.

The Nature of LNG Arbitrage, and an Analysis of the Main Barriers for the Growth of the Global LNG Market [pdf] by Polina Zhuravleva, Oxford, June, 2009.

Abstract: Due to its gaseous form, and therefore low energy density, pipeline natural gas has traditionally supplied nearby regional markets which have been historically isolated from each other. Regional markets have traditionally had their own supply-demand balances, contractual structures and gas price formation mechanisms. This model is now under threat. With the growth of liquefied natural gas (LNG) supply which is increasingly flexible in terms of destination, regional markets are becoming progressively more connected.  A decade ago, when the LNG industry was based exclusively on long-term take-or-pay contracts and the number of market players was limited, the impact of price signals, if any, was weak. The liquidity of the "flexible" LNG market has increased in tandem with the growth in the number of LNG producing and consuming countries, the appearance of some uncommitted volumes of LNG and development of arbitrage activity. LNG arbitrage is a new pattern of gas trade still in an embryonic stage of development. Few outside the LNG industry or even outside LNG trading circles understand the term "LNG arbitrage" let alone the specific mechanisms. One of the goals of this paper is to establish a clear definition of LNG arbitrage and distinguish it from other trading activities which superficially appear similar.

Historical gas price data for different markets suggests that price differentials have created opportunities for LNG arbitrage to take place. However, the scale of this type of trading has been constrained to date and has not led to demonstrable gas price convergence between markets. The second aim of the paper is an analysis of the main barriers to the growth of the LNG arbitrage market.

Research for this paper has enabled a framework of barriers and conditions for LNG arbitrage to be developed. According to this framework there are four necessary conditions for an arbitrage transaction to take place.  Barriers, which deter arbitrage, can be divided into four groups. Analysis of the barriers has shown that some constrain arbitrage on the global level while others are more locally focussed (sic). Some barriers strongly preclude arbitrage activity while others merely make it more challenging.

Basic Human Decision Making: An Analysis of Route Choice Decisions by Long-Haul Truckers [pdf] by John H. Knorring, Princeton University, April 2003.  Knorring currently trades natural gas derivatives for Goldman Sachs' commodity arm, J. Aron. 

"Option A is you receive $20.  Option B is you die."

The World's Greatest Coal Arbitrage: China's Coal Import Behavior and Implications for the Global Coal Market [pdf] by Richard K. Morse and Gang He. 

Abstract: In 2009 the global coal market witnessed one of the most dramatic realignments it has ever seen - China, long a net exporter of coal, suddenly imported a record-smashing 126 Mt tons (103 Mt net). This inversion of China's role in global coal markets meant that Chinese imports accounted for nearly 15% of all globally traded coal, and China became the focal point of global demand as traditional import markets like Europe and Japan stagnated in the wake of the financial crisis.  The middle kingdom's appetite for imported coal seems insatiable, and the "China Factor" appears to have ushered in a new paradigm for the global coal market.

But China doesn't "need" the coal.  The world's largest coal producer cranked out 2.96 Bt of production in 2009, backed up by 114.5 Bt of reserves.  While the world's other fastest growing importer, India, is plagued by a growing gap between coal supply and power demand that it is unable to fill domestically, this is not the case in China.  The spike in Chinese demand for imported coal is therefore a more complex (and less easily predictable) phenomenon that requires careful examination if the world is to understand what impact China might have on global energy markets in the coming decade.

Triangular Arbitrage during the Interbank Open: USD, SEK, and NOK

4:06pm - 6:27pm, Sept. 25, 2011

This is the opening of the interbank currency market just after 4pm CST, Sunday, September 25, 2011.  This is a brief preview of another forthcoming post on triangular arbitrage in the currency markets.  This study looks at the USD/SEK, USD/NOK, and NOK/SEK pairs.  To the right is the opening of the real USD/SEK rate spread against the synthetic USD/SEK rate developed from the other two pairs.  Notice how the synthetic rate (red/blue) keys off the movements of the live rate (orange/light blue), narrowing with each passing minute.

This is the first time I have captured the Sunday opening of the FX markets. 

More on Triangular Arbitrage: Korean Won, Japanese Yen, and the Hong Kong Dollar

Triangular arbitrage has been touched on once before using the HKD, USD, and AUD currencies. The strength of this relationship within the currency markets was an early research topic.  As one of the most active and liquid markets in the world, relationships were found to show very infrequent breaks from parity.

This is a follow up to the previous post.  The following are the spreads built from high-frequency trade-and-quote date recorded on August 29, 2011.  Once again utilizing the HKD as a medium, this study includes the KRW/HKD, HKD/JPY, and KRW/JPY pairs.

The Outrights.

KRW/HKD.

HKD/JPY.

KRW/JPY.

Both pairs connected to the KRW suffer from significant increases in the bid/ask spread once the primary Asian markets close.  These increases qualify as making it irresponsible from an asset-management point of view to even transact in the KRW rates unless absolutely necessary.  The cost of doing so is counter productive.

Finding the implied values within the triangle yields a series of spreads as follows.  These are constructed from trading the synthetic values from the live, executable values.

The Spreads.

Implied KRW/HKD spread to the live KRW/HKD.

Implied HKD/JPY spread to the live HKD/JPY.

Implied KRW/JPY spread to the live KRW/JPY.

Triangular Arbitrage using high-frequency TAQ data on USD/HKD, AUD/USD, and AUD/HKD

Please note before reading: the watermarks (if you can call them that) on each picture in this post were from the original URL and authorship (a pseudonym) of this blog.  They have not been taken from another source and reposted - they are original works of this blog and this author.

Triangular arbitrage can be defined as the "price of a second currency expressed in terms of a third or an exchange rate calculated from two other rates." For instance, one can imply the synthetic AUD/HKD rate if one has the live USD/HKD and AUD/USD exchange rates.  The arbitrage relationship is inherent between the synthetic AUD/HKD traded against the live, executable AUD/HKD.

Fenn, Howison, McDonald, Williams, and Johnson (2009) note that "Triangular arbitrage represents one of the simplest arbitrage opportunities. However, there is, to our knowledge, no truly rigorous and robust study of triangular arbitrage in the finance literature.  We believe the main reason for this to be the lack of availability of datasets with prices which are sufficiently high-frequency and which are also executable."

Asynchronous data is a problem when trying to study any arbitrage relationship.  Be it stock to stock, stock to future, future to future, physical to cash, or speaking ubiquitously, any arbitrage relationship.  Studies using end-of-period (days, minutes, seconds) data recordings suffer from this issue whereby one variable may be said to have "this" price at the last known recorded interval, while the second variable similarly has "this" price at the last known recorded interval.  The problem arises because the two recorded prices, while they may be the last known price, cannot reliably be used due to their differences in time period.  This problem can only be eliminated using synchronized data in the most granular form available.

The Data.

The following data set was collected using a proprietary program developed by my IT team.  The software is connected to the interbank foreign exchange market via a direct access API.  In this case, the time and sales for the three pairs were recorded simultaneously and synchronously: any time a single variable changed, the entire data set was recorded as a whole.  The high frequency and synchronicity of the recording alleviates the problem that Fenn et al. (2009) discovered in their research of TriArb.

Below is the spread between the synthetic AUD/HKD and the live AUD/HKD.  As you can see, the arbitrage is remarkably consistent and very robust.  "Although some opportunities appear to exist for in excess of 100s," writes Fenn et al. (2009) in their study, "for both currency groups 95% last for 5 seconds of less and 60% for 1 second of less."

   (Click to enlarge)

There is a significant loss of liquidity beginning around 11:00 AM CST as evidenced by the increase in bid/ask spread of the three pairs, most notably the AUD/HKD.  The increase in bid/ask spread becomes evident in the construction of the synthetic/real arbitrage as referenced previously.

Bid/Ask Spreads
USD/HKD : Blue

AUD/USD : Red

AUD/HKD : Green

(Click to enlarge)

Trading the Opportunity.

At 1:33:55 AM on January 24, 2011, a small break occurs in the AUD/HKD synthetic and live relationship.  The break from parity is caused by an increase in the bid of the live AUD/USD from 0.98945 to 0.9897, an increase of .00052.  This bid-up caused an increase in the bid price of the synthetic AUD/HKD to 7.7154, while the live AUD/HKD rate was then offered at 7.7143, an arbitrage difference of .0011 AUD/HKD.

(Click to enlarge)

Notice: This break lasted only a single second.  While the opportunity undoubtedly lasted much less than a full second, the beta software version we were using to collect this data was not recording at the millisecond level, a problem that has since been eliminated.

The short duration of this break is an obvious barrier to entry.  Fenn et. al. (2009) cite "wider use of electronic trading platforms and trading algorithms" from 2003 to 2005 as the main cause of the opportunity's brevity.  They go on to note that, "From 2003-2005, the proportion of opportunities lasting less than 1 second increased from 40% to 62% for the JPY transactions and from 41% to 64% for the CHF transactions and the proportion of opportunities lasting in excess of 5 seconds halved for both sets of transactions."

Further Reading

Collective Dynamics of Small-World Networks
Hedging Currency Risk in International Investment and Trade
High Frequency Trading and the New-Market Makers