PhD Program in Economics PhD dissertation Vilmos Fliszár Budapest interbank offered rate in the shadow of London interbank offered rate Abstract Supervisor: Tamás Solymosi PhD Budapest, 2015 Operations Research and Actuarial Sciences Department PhD dissertation Vilmos Fliszár Budapest interbank offered rate in the shadow of London interbank offered rate Abstract Supervisor: Tamás Solymosi PhD © Fliszár Vilmos 2 Contents Contents ................................................................................................................................................... 3 1. Introduction ................................................................................................................................... 4 2. Methodology background ............................................................................................................. 6 2.1. Game Theory ............................................................................................................................. 6 2.2. Statistics ...................................................................................................................................... 7 3. London interbank offered rate ................................................................................................... 10 3.1. Early signs in the press .............................................................................................................. 10 3.2. Definition of London interbank offered rate ............................................................................. 10 3.2.1. Incentives arise from the LIBOR definition in connection of game theory .......................... 12 3.3. Results of the investigation of regulators .................................................................................. 16 3.4. The effect of the scandal to other benchmarks .......................................................................... 18 4. Budapest interbank offered rate ................................................................................................ 19 4.1. History of Budapest interbank offered rate ............................................................................... 19 4.2. The definition of BUBOR ......................................................................................................... 20 4.3. Main differences between the LIBOR and BUBOR ................................................................. 22 4.4. BUBOR in the Hungarian law process ...................................................................................... 23 5. Statistical analysis of BUBOR-based transactions and fixed values ....................................... 23 5.1. BUBOR related studies before the LIBOR scandal .................................................................. 24 5.2. BUBOR based transactions ....................................................................................................... 25 5.2.1. BUBOR based deposit and loan portfolio ............................................................................. 25 5.3. Calculation method of BUBOR and individual fixing .............................................................. 26 5.3.1. Calculation method of BUBOR ............................................................................................. 26 5.3.2. Standard deviation of the daily BUBOR fixing..................................................................... 26 5.3.3. Individual fixings .................................................................................................................. 27 5.4. Tenors and possible benchmarks ............................................................................................... 28 5.4.1. Tenors .................................................................................................................................... 28 5.4.2. Benchmarks (base rate, DKJ, swap and FRA) ...................................................................... 31 5.4.3. The single active tenor........................................................................................................... 32 5.4.4. Counterparty risk in BUBOR values ..................................................................................... 34 5.5. Statistical modeling of possibility anomalies in the fixings of contributor banks ..................... 35 5.5.1. Actual data and behavior ....................................................................................................... 37 5.5.2. Individual data – fact versus estimation ................................................................................ 37 5.5.3. Comparison of the estimated results ...................................................................................... 38 5.6. Summary of the statistical analysis ........................................................................................... 38 5.7. Connection between BUBOR and the internal banking process ............................................... 39 5.8. Possible ways in the further research ........................................................................................ 39 6. Conclusion .................................................................................................................................... 41 7. Main references ........................................................................................................................... 43 8. Own publications ......................................................................................................................... 45 8.1. In the topic of the dissertation ................................................................................................... 45 8.2. In the topic of the used methodologies ...................................................................................... 45 3 1. Introduction1 The interbank reference rates play a crucial role in the everyday financial processes. The reference values defined by the main players of the interbank market appear in the most banking products. Beyond the interbank deals the retail and corporate loan and deposit products also reprice according to a given reference rate. Only in case of the US dollar LIBOR more than 300 trillion US dollar transactions belong to the fixed interbank reference rate in the whole world. The Budapest interbank offered rate is the basis of more than 3000 billion Hungarian forint retail and corporate transactions. These huge numbers also show the importance of the interbank reference rates and the fact that these would be an integral part of the economic processes. Their analyses are very important because based on such studies give much information about the market and the behavior of the contributor banks. Therefore the results can be useful for the financial institutions, the consumers and the regulators. With an accurate knowledge about the reference rate’s market can result more operating profit for a financial institution or the supervisory authority is able to identify the distortion of the market. However a study about the reference rate is able to strengthen the social acceptance. These reasons confirm that the interbank reference rates are key players in the economic world and the relevant studies can send very important messages for the market players. Coming into the view of interbank reference rates was the inspiration of my thesis. In summer 2012 it turned out the biggest contributor institutions manipulated the fixing process in London. The result of the manipulation was the level of LIBOR didn’t show the real market whereas it showed better the interest of some contributor institution. Therefore the English regulator took into counter with tight control against the referred contributor institutions (Barclays, UBS, Royal Bank of Scotland), set up huge punishments and in some cases it waited the replacement of the referred chief officers. In the study I describe the background of the chosen methodology, the fixing process of the LIBOR, the incentives for manipulation, the history of the scandal and the main regulatory responses. I also use the elements of the game theory to show the weak points and the manipulative incentives of the definition and the fixing process. The regulatory responses is 1 The views in this study are those of the author and do not necessarily reflect those of Hungarian Financial Supervisory Authority or the Central Bank Hungary. 4 an important part of the topic because under short time many guidelines, analysis were published by regulators. These documents showed the former studies about reference rates missed a very important aspect which is the accurate data. Thus a new area came into focus where there weren’t benchmark studies for the researchers. The focus point of my thesis is the fixing of Budapest interbank offered rate (BUBOR). Beyond the description of history of BUBOR I show the connected rules and point out the differences from the LIBOR. Near that I analyze the fixed values of forint reference rate and the behavior of the market and the contributor institutions. In the study I would like to find the answer to the following questions:  Can be founded manipulation incentives in the LIBOR definition?  Are the founded weaknesses in the LIBOR fixing relevant for the BUBOR? How much the level of similarity between the BUBOR and LIBOR?  Is the BUBOR replaceable with any other benchmark?  What kind of attribute does the fixing process of BUBOR show? Can we found any information about the market of the unsecured lending market?  Can define any behavior structure in the whole fixing process or in the individual fixing of a contributor bank? First I show with the help of the game theory there are manipulation incentives in the LIBOR definition. After this to answer the further questions I use descriptive statistic and cluster analysis. In the study I show that an old definition from a new aspect has got in the centre of interest and the former used time series methods are hardly applicable. My goal is to show how can an analyst handle this situation and find the most information which can be an important source for future research. 5 2. Methodology background In this study before the statistical analysis I detailed show the definition of the London interbank offered rate and it’s fixing process between the description of the LIBOR scandal and the regulatory reactions. In the LIBOR definition chapter in a simple fixing market with the tool of game theory I emphasize the weaknesses of the definition and the fixing process. In a simple example I show the fact even if one injured condition the truthfulness can be a dominated strategy. Therefore in a non-cooperative simultaneous game for the gamer (contributor institution) in the equilibrium it is better if he deviates from the truthfulness strategy. It is easily foreseeable if every contributor institutions hurt the same condition the result of their simultaneous decision will be such a dominant Nash-equilibria in that everybody is lying. It is very important to emphasize there is differences between the LIBOR and the BUBOR definition. In case of BUBOR there is much less incentives for lying. In the statistical analysis I also will examine these incentives and the weaknesses/strengths of the fixing process and definition. 2.1. Game Theory I use only non-cooperative models in this study therefore I give the definition based on the normal form of non-cooperative games. This models has got three main elements:  list of players  strategies’ list of each players  the payments’ list of each players for each joint strategy which contains only one strategy from each player. The G = {S1,…, Sn; f ,…, f } structure is (n-players) game, where the S is the ith player’s 1 n i non-empty strategy set, the f : S → R is its payment function where S = S ×…×S . i 1 n I use only simultaneous games in my models which mean that the players make the decisions at the same time and they are not able to choose mixed strategies. The dominance is an important definition in these analyses. Let G is an n-players game in normal form and s; t are i i the ith player clear strategies:  s is strictly dominated t if f(s; s ) > f(t; s ) for each s S ; i i i i -i i i -i -i -i  s is weakly dominated t if f(s; s ) ≥ f(t; s ) for each s S and there is a (t; s ) that i i i i -i i i -i -i -i i -i the inequality is strict, where S is the set of those strategy profiles which do not contain the strategies of the ith -i player. 6 The best response function gives those strategies of the ith player which result the highest payment for the player assume the others do it according to a given strategy profile. It is formally the following B : S → S function: i i B(s) ={t S | f(t; s ) ≥ f(r; s ) for each r S. i i i i i -i i i -i i i Through Nash the conception of the selection of a game’s equilibrium would be the stability (Nash [1950]). A solution of a game is stable if any player is not able to raise its payment if the others do not change their strategy. It means that the player gives its best response for the expected strategy of the other players. The definition of the Nash-equilibrium gives back this attribution: Let G is an n-players game in normal form. The s* strategy profile (which only contains clear strategies) is a Nash-equilibrium if the following inequality is true fi(s*; s* ) ≥ f(s; s* ) i -i i i -i for each s S and i = 1, … , n. Expressed: each players give their best response for the i i action of the others. If each players choose a dominant strategy in the equilibrium it results a dominant Nash-equilibrium. 2.2. Statistics In the statistical analysis I focus on the identified manipulation incentives and the attribution of the fixing process. My goal is to show the useful of description statistic in such a problems. The distributional parameters of the fixed rates of contributor institutions contain much information for the analysts. The examination of central values, outliers, percentiles or standard deviation results important statements. Beyond these I also examine the difference time series of an individual bank. It is very important to emphasize that these methods are easily applicable. In the possible benchmarks chapter I examine the difference between BUBOR and base rate. Next to this I mention the behavior of correlation between Budapest forint reference rate and the possible benchmark rates under disjunct periods. Erhart, Ligeti and Molnár pointed to the fact the 3 months BUBOR time series is very strong autocorrelated and it can be describe as an AR(1) process (Erhart-Ligeti-Molnár [2013]). Their – above 0.99 – coefficient urged me to avoid the OLS estimation methods or the other time series methodology and show the applicable of descriptive statistic. In the analysis I also will examine the fixing behavior of contributor institution. With help of descriptive statistic I point to that it is difficult question because we need to find behavior 7 structure not only a break event. I support it could not define any manipulation event in Hungarian data. Because the fixing time series is highly autocorrelated my target is to show is there any variables with them we can conclude from the individual fixed values to the fixing of the other contributors. For this reason I rescaled to ordinal scale my target variable and I will use the clustering methods. To validate the choosed methodology I cluster the fact data next to the estimated variables and compare the results. Cluster analysis My analysis is based on a “two-steps” clustering. First I clustered with K-means algorithm the trading days in case of every contributor institution into three categories taking into consideration both the external (other benchmarks) and the internal (the derivative position of the institution) effects. Because the units of the used variables were different I standardized them. This estimation is result an alternative variable which will be challengeable with the from the real fixing rates rescaled ordinal target variable. The K-means cluster algorithm is based on an iteration process which contains three main steps:  Choosing the initial cluster centers  Updating the cluster centers  Classifying the observations into the nearest cluster This iteration process stops if the number of iteration reaches the given maximum value or the change of the cluster centers remains under a predetermined ε between two steps. After that I will cluster separately by institutions the estimated (with K-means algorithm) and the rescaled fact variables with hierarchical method. The hierarchical clustering is such a classifying methodology which is based on similarity or dissimilarity measure. Denote S the initial similarity matrix and S the similarity measure between the i-th and j-th cluster. ij Because the variables measure are ordinal I will use the chi-square method for define the distances. 8 The massing process of hierarchical clustering is based on the following general steps assuming N clusters:  For starting to assume each variable is a separate cluster.  Define the S similarity matrix (NxN dimension) of variables.  To find the most similar clusters (p and q) where p is greater than q. Denote S their pq similarity measure. Note if we use dissimilarity measure the higher value shows less similarity (as in the case of chi-square).  To reduce the number of clusters by merging p and q cluster. Denote t the merged cluster.  Updating the similarity matrix between the new cluster groups. Iterate this process while only one cluster remains. From the possible agglomeration methods I use the further neighbor algorithm where In this algorithm the agglomeration is based on the distance of the furthest clusters therefore this method is particularly sensitive for the outliers. 9 3. London interbank offered rate 3.1. Early signs in the press In the press there were articles in connection the sign of problems in LIBOR fixing before in the 2012 started scandal. In Wall Street Journal (WSJ) many articles were published by Carrick Mollenkamp about the credibility of the LIBOR fixing (Mollenkamp [2008] and Mollenkamp – Enrich [2011]). In 2008 he called the attention to the risk which arises from the LIBOR definition. This comes from that the contributor institutions were able to modify their own pictures on the market with fixing false reference rates. Thus they can even hide they bad liquidity situation with these false signals. Mollenkamp’s article also contained a detailed description about the definition of LIBOR, its role in the market (from the interbank deals to the mortgage loans) and the list of potential benchmarks. In 2011 Mollenkamp and Enrich wrote the world manipulation. In the article they stated that there is very low probability that the regulators would refer the founded failures in the LIBOR fixing process only simple incorrect mistakes. To confirm this statement they referred the study of Snider and Youle (Snider – Youle [2010]). Snider and Youle examined how the LIBOR is able to meet its own definition. Did the contributor banks fix that interest rate level on which they can get unsecured liabilities from the market? In professional journals the reader could meet the word manipulation even in 2008 but at that time Mollenkamp was not so brave to declare it in the much more popular WSJ. Abrantes- Metz and his colleagues has already questioned it in the title: LIBOR manipulation? (Abrantes-Metz et al. [2008]). The authors identified many signs (for example the move of CDS spreads and LIBOR) which could imply anti-competitive manipulative behavior but they had not got any concrete evidence to proof the manipulation. In the conclusion further examinations were urged. 3.2. Definition of London interbank offered rate The London interbank offered rate is the most used reference rate in the world which is the base of more than 300 trillion US dollar valued transactions. The LIBOR fixing process was taken place in 10 different currencies for 15 tenors (till one year) in 2012 by the contributor banks which are defined annually by the British Bankers’ Association (for example in GBP 10