Masaryk University Faculty of Economics and Administration Major: Finance ARBITRAGE OPPORTUNITIES IN SELECTED FINANCIAL MARKETS OF EAST ASIA Arbitrážní příležitosti na vybraných finančních trzích Východní Asie Diploma thesis Advisor: Author: Ing. Boris Šturc, CSc. Pavel WERL Brno, 2014 Masarykova univerzita Ekonomicko-správní fakulta Katedra financí Akademický rok 2013/2014 ZADÁNÍ DIPLOMOVÉ PRÁCE Pro: WERL Pavel Obor: Finance Název tématu: ARBITRÁŽNÍ PŘÍLEŽITOSTI NA VYBRANÝCH FINANČNÍCH TRZÍCH VÝCHODNÍ ASIE Arbitrage opportunities in selected financial markets of East Asia Zá s a dy pro vy pra co vá ní : Cíl práce: Hlavním cílem práce je retrospektivně posoudit arbitrážní příležitosti vybraných investičních instrumentů, obchodovaných na finančních trzích ve Východní Asii. Dílčím cílem je pak navrhnout vhodný algoritmus pro identifikaci a měření arbitrážních příležitostí z burzovních dat. Dalším dílčím cílem je aplikovat zvolený algoritmus na reálná data z finančních trhů Východní Asie a vyhodnotit zjištěné souvislosti. Postup a použité metody:  sběr dat,  analýza dat,  navržení algoritmu pro identifikaci dat,  syntéza a dedukce. Rozsah grafických prací: dle pokynů vedoucího práce Rozsah práce bez příloh: 60 – 80 stran Seznam odborné literatury: REJNUŠ, Oldřich. Finanční trhy. Třetí rozšířené. Ostrava: Key Publishing, 2011. 690 s. Ekonomie. ISBN 978-80-7418-128-3. JÍLEK, Josef. Finanční trhy a investování. 1. vyd. Praha: Grada, 2009. 648 s. ISBN 978-80- 247-1653. SHARPE, William F. a Gordon J. ALEXANDER. Investice. Translated by Zdeněk Šlehofr. 4. vyd. Praha: Victoria Publishing, 1994. 810 s. ISBN 80-85605-47-3. POLOUČEK, Stanislav. Peníze, banky, finanční trhy. Vyd. 1. Praha: C.H. Beck, 2009. xvii, 415. ISBN 978-80-7400-152. PLUMMER, Tony. Prognóza finančních trhů :psychologie úspěšného investování. Vyd. 1. Brno: Computer Press, 2008. xvi, 373 s. ISBN 978-80-251-1592. Vedoucí diplomové práce: Ing. Boris Šturc, CSc. Datum zadání diplomové práce: 5. 3. 2013 Termín odevzdání diplomové práce a vložení do IS je uveden v platném harmonogramu akademického roku. …………………………………… ………………………………………… vedoucí katedry děkan V Brně dne 5. 3. 2013 Author’s full name: Pavel Werl Topic: Arbitrage opportunities in selected financial markets of East Asia Název diplomové práce: Arbitrážní příležitosti na vybraných finančních trzích Východní Asie Department: Finance Advisor: Ing. Boris Šturc, CSc. Year of thesis defense: 2014 Annotation The goal of this paper is to develop algorithms to detect and evaluate arbitrage opportunities on financial data from East Asia. The first part is concentrated on thorough literature research on most types of arbitrage strategies, including the development of methods to exploit the arbitrage opportunities. Among those strategies are triangular arbitrage, cash-and-carry arbitrage, volatility arbitrage, convertible arbitrage, fixed-income arbitrage, and others. In the second part, after describing acquired data from East Asian forex markets, I propose a software algorithm to detect multilateral arbitrage opportunities on foreign exchange markets, and another algorithm to generate all combinations of foreign exchange arbitrage loops. Subsequently, I develop a custom computer program to analyze the market data in automated fashion, including the computerized generation of Excel reports and charts. Finally, I evaluate and interpret the results of the analysis, and conclude. Anotace Cílem této práce je vyvinout algoritmy na detekci a vyhodnocení arbitrážních příležitostí na finančních datech z Východní Asie. První část se zaměřuje na podrobný výzkum literatury o většině typů arbitrážních strategií, včetně navrhnutí metod pro využití arbitrážních příležitostí. Mezi zmíněnými strategiemi je triangulární arbitráž, cash-and-carry arbitráž, arbitráž volatility, konvertibilní arbitráž, arbitráž instrumentů s fixními příjmy, a další. V druhé části, po popisu získaných dat z východoasijských měnových trhů, navrhnu softwarový algoritmus na detekci multilaterálních arbitrážních příležitostí na měnových trzích, a další algoritmus na generování všech kombinací arbitrážních měnových smyček. Poté vyvinu vlastní počítačový program k automatizované analýze tržních dat, a to včetně následného komputerizovaného generování výstupu v Excelu včetně grafů. Nakonec vyhodnotím a interpretuji výsledky analýzy a vyvodím závěr. Keywords Arbitrage, triangular arbitrage, multilateral arbitrage, East Asia, statistical arbitrage, pricing model, risk, algorithm, programming, implementation, forex Klíčová slova Arbitráž, triangulární arbitráž, multilaterální arbitráž, Východní Asie, statistická arbitráž, oceňovací model, riziko, algoritmus, programování, implementace, forex Prohlášení Prohlašuji, že jsem diplomovou práci Arbitrážní příležitosti na vybraných finančních trzích Východní Asie vypracoval samostatně pod vedením Ing. Boris Šturc, CSc. a uvedl v ní všechny použité literární a jiné odborné zdroje v souladu s právními předpisy, vnitřními předpisy Masarykovy univerzity a vnitřními akty řízení Masarykovy univerzity a Ekonomicko-správní fakulty MU. Proclamation I declare that the diploma thesis titled Arbitrage opportunities in selected financial markets of East Asia was written by me and only me, under the supervision of Ing. Boris Šturc, CSc. Furthermore, I declare that I have referenced and properly cited all sources used in this paper, in accordance to the contemporary law, Masaryk University regulations, and internal acts of both Masaryk University and Faculty of Business and Administration MU. V Brně dne 16. května 2014 In Brno on May 16th, 2014 vlastnoruční podpis autora | signature TABLE OF CONTENTS INTRODUCTION ................................................................................................................................................. 1 GOALS.................................................................................................................................................................. 1 METHODOLOGY ................................................................................................................................................... 1 NOTATIONS AND PRELIMINARIES .............................................................................................................. 2 TRADE PAIRS NOTATION ....................................................................................................................................... 2 FOREIGN EXCHANGE (CURRENCY) NOTATIONS..................................................................................................... 3 Currency codes ................................................................................................................................................ 3 Quotations ....................................................................................................................................................... 3 1 DEFINITION OF ARBITRAGE ................................................................................................................. 5 2 GENERAL IDEA BEHIND ARBITRAGE ................................................................................................ 6 2.1 INTEREST RATES ....................................................................................................................................... 7 2.2 OTHER ASPECTS ....................................................................................................................................... 7 3 RISKS OF ARBITRAGE ............................................................................................................................. 8 3.1 LIQUIDITY RISK ........................................................................................................................................ 8 3.2 COUNTERPARTY RISK ............................................................................................................................... 9 3.3 TECHNICAL AND EXECUTION RISK ............................................................................................................ 9 3.3.1 Processor speed ............................................................................................................................. 10 3.3.2 Network latency ............................................................................................................................. 10 3.3.3 Software or hardware malfunction ................................................................................................ 11 3.3.4 Other hardware limitations ........................................................................................................... 11 3.4 IMPLICIT RISK ......................................................................................................................................... 12 4 DETERMINISTIC ARBITRAGE ............................................................................................................. 13 4.1 BILATERAL ARBITRAGE .......................................................................................................................... 13 4.2 TRILATERAL ARBITRAGE ........................................................................................................................ 14 4.3 MULTILATERAL ARBITRAGE ................................................................................................................... 14 4.4 CASH-AND-CARRY ARBITRAGE .............................................................................................................. 16 4.4.1 Generic futures (reverse) cash-and-carry arbitrage ..................................................................... 16 4.4.2 Foreign exchange futures cash-and-carry arbitrage ..................................................................... 20 4.4.3 Options cash-and-carry arbitrage ................................................................................................. 23 4.4.4 Futures-options cash-and-carry arbitrage .................................................................................... 26 4.4.5 Fixed-income cash-and-carry arbitrage........................................................................................ 27 4.5 TAX ARBITRAGE ..................................................................................................................................... 27 4.6 REGULATORY ARBITRAGE ...................................................................................................................... 27 5 STATISTICAL ARBITRAGE ................................................................................................................... 28 5.1 SCALPING (MARKET MAKING) ................................................................................................................ 29 5.2 RELATIVE VALUE ARBITRAGE ................................................................................................................ 32 5.2.1 Convertible arbitrage .................................................................................................................... 33 5.2.2 Fixed-income arbitrage ................................................................................................................. 34 5.2.3 Capital structure arbitrage ............................................................................................................ 35 5.2.4 Pairs trading.................................................................................................................................. 36 5.2.5 Merger arbitrage ........................................................................................................................... 44 5.3 VOLATILITY ARBITRAGE ........................................................................................................................ 45 5.3.1 Directional volatility bet ................................................................................................................ 46 5.3.2 Relative value volatility arbitrage ................................................................................................. 48 5.4 LIQUIDATION ARBITRAGE....................................................................................................................... 51 6 MULTILATERAL ARBITRAGE ALGORITHM STUDY .................................................................... 53 6.1 DATA ..................................................................................................................................................... 53 6.2 METHODOLOGY ..................................................................................................................................... 54 6.2.1 Detecting arbitrage for single set of quotes .................................................................................. 54 6.2.2 Detecting arbitrage for all sets of quotes ....................................................................................... 55 6.2.3 Detecting arbitrage for all variants of arbitrage loops ................................................................. 56 6.2.4 Putting it all together ..................................................................................................................... 56 6.3 RESULTS ................................................................................................................................................. 58 6.3.1 Preliminary datasets analysis ........................................................................................................ 58 6.3.2 Number of variations analysis ....................................................................................................... 60 6.3.3 Arbitrage analysis .......................................................................................................................... 60 CONCLUSION .................................................................................................................................................... 65 BIBLIOGRAPHY ................................................................................................................................................ 67 LIST OF TABLES ............................................................................................................................................... 76 LIST OF FIGURES ............................................................................................................................................. 76 LIST OF EQUATIONS ....................................................................................................................................... 76 APPENDIX A: EAST ASIAN EXCHANGES ................................................................................................... 78 Introduction 1 INTRODUCTION Arbitrage is an exciting field of study in finance, because the premise of riskless profit is so tempting. Apart from that, arbitrage is a paramount principle in pricing financial instruments, and some believe that arbitrage is the omnipresent principle that drives markets into equilibrium. My personal interest in both finance and programming made me choose this exciting topic, which gave me the opportunity to delve deeper into this thrilling area, expand my knowledge greatly, and learn a great deal about automated analysis. Among others, this paper also puts most types of arbitrages into a clear hierarchy, so anyone interested in the field can quickly get into it. 1st. chapter deals with the definition of arbitrage for the purposes of this paper. 2nd. chapter explains the general idea behind arbitrage and some not-so-known nuances 3rd. chapter examines risks in arbitrage, because arbitrage is actually a risky endeavor 4th. chapter takes a look at deterministic (a.k.a. riskless) arbitrage and its kinds 5th. chapter explores the area of statistical arbitrage, a different approach to trading 6th. chapter presents arbitrage algorithms, conducted analysis and interpreted results Goals The main goal of this paper is to evaluate arbitrage opportunities of selected financial instruments on historical data from East Asian financial markets. This main goal can be decomposed into these partial goals:  Develop appropriate algorithm to identify and measure arbitrage opportunities from market data  Apply that algorithm to real market data from East Asian markets and evaluate the results Methodology The exact methodology of how the actual algorithm works and the nuances of my approach to arbitrage measurement are all part of the chapter “6 Multilateral arbitrage algorithm ”. It involves:  Thorough literature research  Collection of historical data from reliable source, which was deemed to be Bloomberg terminal  Design of required algorithms to detect arbitrage opportunities and to generate foreign exchange arbitrage loops  Development of custom software to make use of the algorithms and to automate data analysis  Final evaluation and interpretation of the results 2 Notations and preliminaries NOTATIONS AND PRELIMINARIES For the purposes of this paper, the following notations will be used. These are meant to improve clarity and correctness of the text. Trade pairs notation Each trade requires at least 2 assets. When more than 2 assets are involved, then such trade can be substituted to a mathematical equivalent by using a set of trades each using exactly 2 assets (called trade pair). This can be best explained by an example: If someone wants to buy a car (asset 1 – car), he pays with money (asset 2 – currency). Sometimes, the trade can be more complex and may involve many more assets – such as buying bicycle (asset 1), helmet (asset 2) and clothes (asset 3) and then paying for the whole basket once with cash (asset 4). This trade can be decomposed into 3 elementary trades – buying bicycle with cash, then buying helmet with cash, and lastly buying clothes with cash. Trade pair will be denoted as “A/B”, where “A” stands for one asset, and “B” stands for the other. The first asset “A” is always called base asset, and “B” is the counter asset. When it is said that the trade pair “A/B” is bought, it means that “B” is exchanged for “A”, “B” is called input asset, and “A” is called output asset. When the trade pair “A/B” is sold, “A” is exchanged for “B”. In this case, “A” is the input asset, and “B” is the output asset. Price and sometimes volume are associated with each trade pair. Price is quoted as the number of counter assets required to buy single base asset. When selling the base asset, it represents the number of counter assets received for each unit of base asset sold. Volume is quoted as the number of base assets available at that price (for purchase or sale). To give you an idea of all these notations in action, let’s take a look at the following example. Suppose you are given the following quotation: KRW/CZK Price: 60 Volume: 1000 In this case, KRW is the base currency, CZK is the counter currency. 1 KRW costs 60 CZK, and there are 1 000 KRW available at that price. When you buy this currency pair, CZK is called the input currency, and KRW the output currency. When the currency pair is sold, CZK is called the output currency, and KRW the input currency. Sometimes, trades can be chained one after another. Such as buying KRW/CZK, then buying JPY/KRW, and then selling JPY/CZK. These are called trade chains. When the first input assets matches the last output asset, we can call it a trade loop. Also, please be very aware whether the text talks about KRW/CZK, or CZK/KRW. Although both involve the same assets, it’s important to keep in mind which asset is the base asset, counter asset, input asset, output asset, and also what do both the price and volume relate to. And last but not least, both base and counter assets do not have to be currencies. There can be Car/CZK as well as Car/Bicycle trade pairs, although the latter is not very common in the real world.