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

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.

ETF / Futures Arbitrage: FXE and EUR Futures

This is the arbitrage constructed from trading the CME-listed EUR/USD Futures contract (6E) against the CurrencyShares Euro Trust ETF (FXE).  Similar posts can be found discussing the IWM/TF and FXB/6B spreads.  The synthetic spread between the two products can be bought or sold, depending on which trades you make in the underlying legs (6E, FXE).  Due to the nature of both Globex and the many electronic markets providing liquidity for FXE, this particular trade is once again relegated to the realm of microsecond and co-located trading.

3:00am - 3:00pm CST, April 8, 2011

6:09am - 3:00pm CST, April 8, 2011

6:48am - 3:00pm CST, April 8, 2011

Opening 5 Minutes, 8:30am - 8:35am CST, April 8, 2011

Opening Hour, 8:30am - 9:30am CST, April 8, 2011

Full Open Market, 8:30am - 3:00pm CST, April 8, 2011

Closing Hour, 2:00pm - 3:00pm CST, April 8, 2011

Further Reading:

Why We Have a Correlation Bubble (pdf) (JP Morgan's Global Equity Derivatives & Delta One Strategy)

Liquidity Dynamics and Cross-Autocorrelations (pdf)

ETF / Futures Arbitrage: FXB and GBP Futures

This post is a follow up to the recent interview with Allston Trading's Peter Nabicht, in which Mr. Nabicht alluded to putting "on a trade at the CME and we want to hedge it with an ETF." The following is a deconstruction of just such a trade.

Below is the spread constructed from trading a block of FXB shares against 1 CME-listed GBP futures (6B) contract.  Not surprisingly, all of the opportunities to trade this (profitably) are securely tethered to the millisecond level.  In addition to the technological arms needed to execute this trade, proper facilitation also requires extensive order-book and inventory management [pdfs]. 

The Outrights.

The two securities are not meant to be purely fungible, so it is not a pure arbitrage.   They can however be traded against one another and used as pricing mechanisms for each other.  Relationships like this were very involved in the "Flash Crash" [pdf] of May 6, 2010.  As liquidity dried up in one product, the pricing mechanism lost integrity and caused the pricing of other assets to suffer in conjunction.


As Andrew Haldane notes, "HFT liquidity, evident in sharply lower peacetime bid-ask spreads, may be illusory.  In wartime, it disappears."

Pre and Open Market Spread

    

Pre-Market

Opening Hour

Entire Open Market

Closing Hour

This is the strength of the relationship Mr. Nabicht described before and the playing ground of low-latency traders.  More examples to follow.

Further Reading:

Interlisted Trading: Impact of Interlisted Arbitrage Volumes on the Canadian Marketplace [pdf]

Exchange Traded Funds: Consequences of Expansion [pdf]

Forthcoming Posts

For any new readers from Jeff Watson, ResearchPuzzle, or StromMacro, I am currently working on:

Rebate Captures and Choice Markets: A look at intraday TAQ data on SPY and possibly others to discover how often the bid/ask spread is choice/locked (the same) or inverted (higher bid than the current ask).  If you would like me to discuss any stocks or futures in particular in this regard, please email me with their symbol(s). 

ETF/Futures Arbitrage Series: FXB and 6B: An exciting analysis of what has previously been touched on here, and a topic I hope will be a regular here on Front-Run the Delta.

How Knight Makes a Market: Knight Capital (KCG) is an active participant in OTC and Pink sheet markets.  This post will deconstruct how exactly Knight and it's competitors are able to make a market in certain stocks around the world. 

Please keep me accountable.

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