An Intervention Analysis Model Examining the Effects of the Capital Purchase & Targeted Investment Programs on the Stock Prices of U.S. Banking Institutions by Alexander Charles Ruth A thesis submited to the Graduate Faculty of Auburn University in partial fulfilment of the requirements for the Degree of Master of Science in Economics Auburn, Alabama May 7, 2012 Keywords: intervention, analysis, bank, bailout, stock, prices Copyright 2011 by Alexander Charles Ruth Approved by Dr. John D. Jackson, Chair, Profesor of Economics Dr. T. Randolph Beard, Profesor of Economics Dr. Hyeongwoo Kim, Asociate Profesor of Economics ii Abstract This thesis uses an Intervention Analysis as an econometric procedure to determine what efect, if any, government capital injection had on stock prices. More specificaly, we look at the efect that the initiation of the Capital Purchase Program and the Targeted Investment Program had on the share prices of U.S. banking institutions. The Intervention Analysis wil suggest whether or not these bailouts had a significant efect on these stock prices. If there does sem to be a significant efect, the analysis wil suggest the magnitude of the shock as wel as the length of this shock?s persistence. We can then look at how these results may give some insight into the U.S. economy as a whole. This thesis evaluates a wide variety of diferent banks so that we can try and make generalizations towards the bailout?s efect on share prices of the banking industry as a whole. As it turns out, the Intervention Analysis involving these many banks suggests that the introduction of the Capital Purchase Program as wel as the Targeted Investment Program did cause a significant drop in the share prices of U.S. banking institutions. This model also suggests that the efected stocks wil take an extremely long time to recover from this specific shock. iii Table of Contents Abstract...............................................................................................................................ii List of Tables.......................................................................................................................v List of Illustrations.............................................................................................................vi List of Abbreviations........................................................................................................vii I. Introduction.....................................................................................................................1 1.1 An Overview of the U.S. Banking Bailout.......................................................1 1.2 Thesis Objective: Market Response to Capital Injections...............................4 1.3 Difering Views of the Bailout.........................................................................5 1.4 Spectrum of Banking Institutions Selected for Analysis..................................6 II. Data..............................................................................................................................13 2.1 Fundamental Data Required to Acount for Market Behavior.......................13 2.2 Share Price Data Procurement, Formulation, and Adjustments.....................15 2.3 Creation of Dummy Variables........................................................................19 III. Model..........................................................................................................................22 3.1 Overview of the Intervention Analysis Model................................................22 3.2 Filtration of U.S. Banking Share Prices..........................................................26 3.3 Regresing the Intervention Model.................................................................29 iv IV. Results.........................................................................................................................31 4.1 Overview of the Results..................................................................................31 4.2 Testing for Estimation of Correct Time Series Proces..................................34 4.3 Interpretation of Bailout Dummy Coeficients...............................................37 4.4 Interpretation of the Lagged and Filtered Share Price Coeficients...............44 V. Comparing Capital Injection Shocks to Other Events.................................................49 5.1 Multi-Dummy Model Formulation.................................................................49 5.2 Multi-Dummy Model Results.........................................................................51 VI. Conclusion..................................................................................................................54 6.1 The Efect of Government Sponsored Capital Injections on Share Prices.....54 6.2 Extensions of the Intervention Analysis Results............................................55 References ........................................................................................................................57 Appendix I ? Individual Filtered LN Bank Share Price Illustrations ..............................58 Appendix II ? Diferencing of the Neded Filtered Bank Share Price Variables ............70 Appendix III ? The Bank Specific Bailout Dummy Intervention Analysis .....................72 v List of Tables Table 1.1 ? Banking Payback Responses to CPP and TIP Capital .....................................3 Table 1.2 ? CPP and TIP Repayment Status of Individual U.S. Banking Institutions .......9 Table 1.3 ? Capital Injection Schedule (In U.S. Dollars) .................................................11 Table 2.1 ? Markov Chain Probabilities for Market Movement Before and After the Capital Injections.........................................................14 Table 3.1 ? Filtered Mean Values of Individual Banking Institutions Before and After the Bailout .........................................................................27 Table 4.1 ? Intervention Model Regresion Results .........................................................32 Table 4.2 ? Significant Share Price Reactions ..................................................................39 Table 4.3 ? Insignificant Share Price Reactions ...............................................................40 Table 4.4 ? Bailout Ratio Correlation with Bailout Dummy Significance .......................41 Table 4.5 ? Estimated Recovery Periods...........................................................................47 Table 5.1 ? Multi-Dummy Intervention Model Regresion Results..................................51 Table A2.1 ? Diferenced Intervention Model Regresion Results...................................71 Table A2.2 ? Bank Specific Dummy Intervention Model Regresion Results.................73 vi List of Equations & Illustrations Equation 2.1 ? Bank Share Price Formulation ..................................................................17 Equation 3.1 ? Intervention Analysis Regresion Equation .............................................23 Equation 3.2 ? Long-Run Pre-Intervention Mean ............................................................23 Equation 3.3 ? Immediate Intercept ..................................................................................23 Equation 3.4 ? Long-Run Mean ........................................................................................24 Equation 3.5 ? Long-Run Efect of Intervention ..............................................................25 Equation 3.6 ? Transitional Efects...................................................................................25 Equation 3.7 ? Long-Run Efect of Intervention ..............................................................25 Equation 3.8 ? Filtration Regresion Equation .................................................................26 Equation 3.9 ? Model Specific Intervention Analysis Regresion Equation ....................29 Equation 4.1 ? Theoretical Shock Level............................................................................46 Equation 4.2 ? Adapted Model Specific Shock Level ......................................................46 Equation 5.1 ? Multi-Dummy Regresion Equation..........................................................49 Illustration A1.1 ? Individual Filtered LN Bank Share Price Illustrations........................58 Equation A2.1 ? Diferenced Variable Formulation..........................................................70 Equation A2.2 ? Diferenced Regresion Equation...........................................................70 Equation A2.3 ? Bank Specific Bailout Dummy Regresion Equation.............................73 vii List of Abbreviations $ U.S. Dollars 911 September 11 th , 2001 AR Auto-Regresive B Bilions Corp Corporation CPP Capital Purchase Program CRA Community Reinvestment Act GLBA Gram-Leach-Bliley Act Inc Incorporated IPO Initial Public Ofering LN Natural Logarithm M Milions NASDAQ National Asociation of Securities Dealers Automated Quotations NYSE New York Stock Exchange S&P Standard and Poor?s STAT Test Statistic TIP Targeted Investment Program U.S. United States 1 I. INTRODUCTION 1.1 An Overview of the U.S. Banking Bailout In 2008, the United States government injected capital into many U.S. companies, including entities in the financial sector, in an atempt to aid them at a time in which the United States was facing one of the worst economic downturns since the Great Depresion. The Capital Purchase Program (CPP) was the name asigned to the government program that began injecting capital into many U.S. banks in October 2008. This initiative marked the beginning of what would be more commonly known as the ?Bailout? of the U.S. banking industry. Soon following the initiation of the Capital Purchase Program also came further government aid in the form of the Targeted Investment Program (TIP). Banks of many diferent types, locations, and sizes received federal funds from these programs. The CPP was pased by congres and began injecting masive amounts of capital into many U.S. firms on October 28, 2008. Some firms would later receive a second instalment of funds from the CPP. The TIP served as another capital supplement to the CPP and in general was only given to a couple of the larger U.S. banks. The TIP began injecting capital into U.S. banking institutions on December 31, 2008. Funds from the CPP as wel as the TIP can be thought of as ?free money with strings atached?. In an atempt to prevent even more economic instability in the United States, the government was using the CPP and the TIP to try and prevent the failure of as wel as runs on many U.S. banks. It is obvious that Henry Paulson, the U.S. Secretary of Treasury, Ben Bernanke, Chairman of the U.S. Federal Reserve, and other members of the U.S. government believed that a healthy banking system played a vital role in the wel being of the U.S. economy as a whole. Thus, during the recesion of 2008, they initiated the CPP and the TIP in an atempt to achieve these desired results. 2 The CPP and the TIP worked in the following manner: The government would give the banks masive amounts of capital in exchange for shares (some degree of partial ownership) of the participating institutions. The banks that received these funds were alowed to pay the government back for these funds by repurchasing the shares. However, like a loan, these funds were to acumulate smal amounts of interest so that when the banks returned the government capital, the government would indeed be profiting from the exchange. The government also gave instructions on the desired use of the extra capital given to the banks. The hope was that institutions would continue making loans at a time in which they normaly would not. The term ?bailout? began to be used to describe this proces and these programs. Currently, the 758 banks and credit unions that received bailout (CPP or TIP) funds have done one of three things. They have either paid back al of the capital, paid back some of the capital, or paid back none of the capital. Of the banks that have paid back al of their bailout money, some did this as soon as they were alowed to and others waited a litle bit longer. Of the smal amount of banks that have not fully repaid the bailout money, some have made promises or given a timetable in which they intend to do so. A portion of these banks may never repay the capital given to them through the CPP or the TIP. This includes some banks that have already or wil fail. It is important to remember that most U.S. financial institutions (including many smaler banks) did not receive any bailout funds. Table 1.1 breaks down the U.S. banks that received bailout capital and their corresponding response to the injection of that capital: 3 TABLE 1.1: BANKING PAYBACK RESPONSES TO CP AND TIP CAPITAL Number of U.S. Banks Percentage of U.S. Banks Fully Repaid al Bailout Funds 266 35.09 Partialy Repaid al Bailout Funds 24 3.17 Have Repaid No Bailout Funds 468 61.74 ProPublica.org, a non-profit journalism site, provides an easily interpretable list of firms that received bailout monies. From this site it is easy to derive tables detailing the full list of banks that received funds from the CPP and TIP and their payback status. We wil tailor this list to fit our specific needs by consolidating it as wel as adding to it in order to form the bulk of tables found in the following portions of Chapter I in this thesis. 4 1.2 Thesis Objective: Market Response to Capital Injections Though the government gave masive financial aid to many diferent types of entities, this thesis wil focus on the aid given to U.S. banking institutions. Specificaly, this thesis wil look at the efect the bailout had on the share (common stock) prices, and hence the market?s evaluation of the riskines, of U.S. banks. This thesis wil also focus on how long the efects on the share prices of U.S. banks resulting from the bailout wil persist. One would expect that the act of a firm receiving large amounts of semingly free capital would be interpreted by market participants in a positive light. However, given the circumstances that these banks were receiving bailout money under, the lender of this capital was not sen as a benign source. It is for this reason that we expect the bailout to cause a negative shock to the share prices of participating banks. We also expect that the bailout proces of selected banks may negatively shock the share prices of the whole U.S. banking industry. If indeed it can be determined that a significant shock did occur, we would like to se how quickly the stock prices of these banks recovered, or if they have recovered at al. If traces of this bailout shock are stil present in the share prices of these banks, this thesis wil use specific econometric techniques to determine a timetable for recovery. It may be the case that the shock to the share prices under evaluation never recover. These are the aspects of the bailout in which this thesis wil concern itself with. It wil also be of note to evaluate just how influential the banking system is to the U.S. economy as a whole. If we believe that the evaluation of the bailout shock on the share prices of U.S. banks may give us some perspective on the recovery status of the entire banking sector, we may be able to make some inferences about the duration of the recovery proces for the entire U.S. economy. 5 1.3 Differing Views of the Bailout There is much debate about the efectivenes of the bailout as it pertains to the prosperity of the U.S. economy. Because the bailout is one of the fundamental aspects of this thesis, it is important to note that the question of whether or not the bailout was a good idea does not mater in this case. Many difering opinions have been formed on whether or not the bailout of U.S. banking institutions was a smart move by the U.S. government. However, this paper wil only concern itself with the results of the bailout on equity prices of U.S. banks rather than trying to answer that question regarding the legitimacy of the bailout. Even if we desired to formulate an opinion on whether or not to support or reject the appropriatenes of the bailout, it may stil be too early to make an informed decision on the mater. Additionaly, searching for an absolute opinion on this isue may also cause one to arrive at the wrong conclusion with regards to the bailout. What this means is that many firms difering in influence and economic health were included in these bailout programs. Hence, it may be the case that the bailout of some firms was a good idea or necesity while the bailout of others was not. Again, this thesis wil not concern itself with answering these questions. However, the results that wil come forth in evaluating the bailout?s efect on U.S. banking entities? equity prices may shed some light on these broader questions and isues. If the conclusions we draw in this analysis are predicated on our opinion about the bailout, then the interpretation of our results wil be clouded and possibly misconstrued. Hence, we eschew judgment on its legitimacy; it simply happened. 6 1.4 Spectrum of Banking Institutions Selected for Analysis In our analysis we desire to look at the efects of the bailout on the equity prices of U.S. banks in general. In order to do this, we must carefully consider which banks wil adequately provide insight into our analysis. As mentioned earlier, most banks that received bailout funds have either paid back the bailout amount in full or have not paid back any of the alotted bailout funds. Also, there exists a handful of banks that have paid back a portion, but not al, of their bailout capital. It wil be necesary to include banks from al three of these situations in this model. In order to properly take a broad look at the response of the share prices of U.S. banks to the shock caused by the introduction of the bailout, this model must also include banks that did not receive federal bailout capital. Most of these banks tend to be smaler banks and tend to be followers in the banking sector as opposed to some larger firms that tend to act as dominant firms or market leaders. The implications of this wil be discussed later. From these aforementioned categories belong banks which we can se are publicly traded companies. We are especialy interested in looking at the firms that received the largest portions of bailout funds. We favor including more banks who received significantly large amounts of capital from the Capital Purchase Program, as wel as the Targeted Investment Program in our analysis. We do this because we are interested in the efects of the bailout. Therefore, it makes sense to look at the banks that received the most federaly injected capital. Also, another reason that these larger bailout recipients warrant inclusion in this model is because they are the entities that would later be the subjects of a financial stres test performed by U.S. government. As results of these stres tests are revealed, it may be interesting to examine whether or not there is any 7 correlation betwen the results of these tests and the results found from using this Intervention Analysis. If we desire to place an added emphasis on evaluating these larger recipients, it may slightly afect which of the smaler banks we choose to select and include in the analysis. When we look at the banks that received significantly larger amounts of bailout capital, we se that almost al of these banks have common stock listings on the New York Stock Exchange (NYSE). Therefore, al of the banks included in this model wil have shares listed on the NYSE. One may be concerned with selection bias occurring in the model because of not being able to properly evaluate the smaler banks or any banks that did not receive capital injections. Incidentaly, many of these smaler banks, as wel as banks the received no bailout money, are also publicly traded firms listed on the NYSE. Thus, we can include share price data from these banks in our analysis as wel. However, only 2 banks that have partialy repaid their bailout funding are listed on the NYSE. Most of the banks in this position are listed on the NASDAQ or Pink Sheets. This may sem like a problem but we must remember that only 24 banks (3.17% of total banks receiving bailout funds) have partialy repaid their bailout capital anyway. We must also leave out banks from our analysis that do not have a sufficient amount of data. Our data for these banks wil consist of monthly stock price data (this wil be covered in detail later). We desire the data to be present around the month of December 1989 until the present period. For this reason, some other banks that were key participants in the bailout saga may be excluded from this model. For instance, Goldman Sachs, a firm that received $10 bilion in bailout funds wil be excluded because we only have monthly share price data for the firm dating back to their IPO in May 1999. 8 Also, within al these diferent factions there are entities which some suspect were esentialy forced to participate in bailout programs. There is much evidence to support this, including documents and public statements from high ranking bank officials of bailout participating banks. We must also include banks that were semingly stable at the time of the bailout, as wel as some that were perceived as unhealthy. Taking al these aspects into consideration, the banks we wil use in our model include the following 24 banking institutions which are listed in order of the amount of bailout funds they received: Bank of America, Citigroup, JP Morgan Chase, Wels Fargo, Morgan Stanley, PNC Financial, US Bancorp, Suntrust, Capital One Financial Corporation, Regions Financial Corporation, Fifth Third Bancorp, BB&T, Bank of New York Melon Corporation, Keycorp, State Street, Synovus Financial Corporation, M&T Bancorp, TCF Financial Corporation, Central Pacific Financial, Auburn Bank, BancFirst Corporation, Bank of Hawai, Community Bank System Incorporated, and BancorpSouth. Al of these banks have corresponding common stock that is sold on the NYSE. Table 1.2 ilustrates the diferent bailout characteristics exhibited by these individual banks. 9 TABLE 1.2: CP AND TIP REPAYMENT STATUS OF INDIVIDUAL U.S. BANKING INSTITUTIONS Fuly Repaid all Bailout Funds Bank of America Citigroup JP Morgan Chase Wels Fargo Morgan Stanley PNC Financial US Bancorp Suntrust Capital One Financial Corp. Fifth Third Bancorp. BB&T Bank of New York Melon Keycorp State Street TCF Financial Corp. Partially Repaid Bailout Funds M&T Bancorp Central Pacific Financial Have Repaid No Bailout Funds Regions Financial Corp. Synovus Financial Corp. Have Not Received Any Bailout Funds Auburn Bank BancFirst Corporation Bank of Hawai Community Bank System Inc. BancorpSouth Though obvious, one must remember that many banks who would have been considered in this thesis either failed or were absorbed during the time period which we are looking at. For instance, a month before the bailout, Bank of America bought up Merril Lynch. Whether or not this institution would have received bailout funds is a 10 mater of speculation but it is certain that Merril Lynch would have been worthy of evaluating in this analysis. This model is looking at the efect the bailout had on the stock prices of these banks in a general sense. What is meant by this is that we have chosen a wide spectrum of banks to include in the analysis and we are looking at the efect of one event which is the initiation of capital injection programs to these banks. Therefore, we are generalizing many injections that occurred in diferent amounts and at difering times into one event. As we have mentioned, these injections began on October 28, 2008 (there were no bank bailout funds alotted before this time) but not al the banks we are analyzing received injections at this time. Because of this, I believe it is worthy of also looking at the bailout schedule of the banks in question so that we can have a beter understanding of how the bailout as a whole was structured. Table 1.3 details the capital injection schedule of these banks. 11 TABLE 1.3: CAPITAL INJECTION SCHEDULE (IN U.S. DOLLARS) BANKING INSTITUTION 10/28/ 2008 CPP 11/14/ 2008 CPP 12/19/ 2008 CPP 12/23/ 2008 CPP 12/31/ 2008 CPP 12/31/ 2008 TIP 1/9/ 2009 CPP 1/16/ 2009 TIP Bank of America 15B 10B 20B Citigroup 25B 20B JP Morgan Chase 25B Wels Fargo 25B Morgan Stanley 10B PNC Financial 7.58B US Bancorp 6.60B Suntrust 3.5B 1.35B Capital One Financial Corp. 3.56B Regions Financial Corp. 3.5B Fifth Third Bancorp 3.41B BB&T 3.13B Bank of New York Melon Corp. 3B KeyCorp 2.5B State Street 2B Synovus Financial Corporation 968M M&T Bank Corporation 600M TCF Financial Corporation 361M Central Pacific Financial 135M Values are rounded for clarity 12 As we can se, most of the bailout capital was isued on October 28, 2008 with remaining capital injections coming later. It should be noted that the banks in our model that did not receive bailout funds are not included in the above table for obvious reasons. This capital injection schedule wil prove to be useful information later in our analysis. 13 I. DATA 2.1 Fundamental Data Required to Acount for Market Behavior As mentioned throughout the introduction of this thesis, we wil use the share price data of diferent U.S. banks to evaluate the general efect of the U.S. government?s bailout on banking stock prices. Before we do this, we know that in order to develop a succesful intervention model, we wil have to acount for the efect that the market as a whole has on U.S. bank stock prices. We wil use monthly stock price data on the individual banks, and to represent the market as a whole, we wil use monthly data from the S&P 500 Index. The S&P 500 serves as a good indicator of the U.S. economy by indexing the fluctuations of some the U.S.?s largest publicly traded companies listed on the NYSE and the NASDAQ. We can find the desired historical monthly S&P 500 data from many various sources including Yahoo Finance (the site which was used to procure most share pricing data found in this thesis). This monthly data comes in the form of monthly closing data as wel as monthly adjusted data. Because the S&P 500 is an index and not an actual firm that pays dividends or performs stock splits, both the monthly closing price data and the monthly adjusted data for the S&P 500 index is the same. We retained the monthly S&P 500 Index data in both of these forms so that we could use the most suitable form later. It is also useful to examine what the U.S. market was doing before and after the bailout. We know that the S&P 500 index wil decrease around the time of the bailout which also coincides with a masive economic downturn. However, we may want to look at other things like the volatility and behavior of the market before and after the bailout. We can do this by examining the S&P 500 data with a Markov Chain for periods before and after the bailout. Table 2.1 shows the results of the Markov Chain proces. 14 TABLE 2.1: MARKOV CHAIN PROBABILITIES FOR MARKET MOVEMENT BEFORE AND AFTER THE CAPITAL INJECTIONS Recesion, Recesion Recesion, Boom Boom, Recesion Boom, Boom Before Bailout 14.0969163 23.78854626 24.22907489 37.88546256 After Bailout 17.14285714 25.71428571 22.85714286 34.28571429 The above table shows the probabilities of the S&P 500 index declining when it experienced a decline in the previous period (Recesion, Recesion), increasing when experiencing a decline in the previous period (Recesion, Boom), declining when experiencing an increase in the previous period (Boom, Recesion), and increasing when an increase was observed in the previous period (Boom, Boom) respectively. Surprisingly, the post-bailout market sems to be behaving similarly to how it was behaving before the bailout; hence after the masive decline of the U.S. economy. This is good to know before we do our analysis because we can se that the market is not in constant decline, but rather just took a large hit and then leveled off again. This Markov Proces can also serve as an indicator of just how random the stock market (evidenced by the S&P 500 index) can behave. 15 2.2 Share Price Data Procurement, Formulation, and Adjustments We can easily gather historical monthly stock price data for the banks in question. The S&P 500 data shares many characteristics with the share price data we have retrieved for each of the banks being evaluated. That is, we can quickly find and record historical monthly stock price data in the form of monthly closing price data and monthly adjusted price data. It is not quite clear how the adjusted monthly data is formulated. I speculate that it is adjusted for splits, dividends, and possibly for volume as wel as inflation. If we were to use this data, we would need to know exactly how it was formulated. This information is not readily available. Recal that for the S&P 500 monthly data (which is from the same source) the closing price data was exactly the same as the adjusted price data. This is why I believe the adjusted monthly share price data is formulated the way it sems to be. Since we need the S&P 500 data and the share price data for the individual banks to be formulated in the same manner, this model wil concern itself with the monthly closing price stock data. It should be noted that al of the tests and analysis performed in this model were performed using both the adjusted monthly data and the closing price monthly data. These results were esentialy the same. Thus, we fel strongly that using the closing price data instead of the adjusted price data is the correct choice. However, the individual monthly closing prices for these banks are not adjusted for stock splits. For instance, a stock price may jump from $40 a share to $20 a share in the data. This is not because the share price fundamentaly decreased but because there was a stock split. This, coupled with the fact that the historicaly adjusted data does not fit the desired form, causes the need to introduce a ?split multiplier? to achieve the appropriate measures of stock prices. This adjustment wil give us the same results 16 shown on pricing charts from sites like Yahoo Finance and wil also fit the same form as the S&P 500 data. The ?split multiplier? wil be an integer that the aforementioned monthly closing share price data wil be divided by in order to achieve adequate pricing data that coincides with the form of the monthly S&P 500 data. Thus, if no splits occurred in the time period of December 1989 to October 2011 for a bank, the multiplier would be 1 in al periods for that bank. Obviously, this would mean that the monthly closing price data for this bank with no splits would already be in the desired form. If there were, for instance, a 2 for 3 split, the multiplier would be 2 / 3 and would be applied to stock prices in the relevant periods. The relevant periods in this case would be the period that the split occurred in and al periods before this split. Remember that if this was the only split, al of the following periods would incur a ?split multiplier? of 1. Most of these banks? share prices involve more than one stock split. So, starting with the most recent period, the multiplier is 1 and wil stay 1 going back periods until we encounter a split. We wil then multiply the type of split that we encounter next while counting back periods by the amount of the ?split multiplier? in the period imediately following the split, which in this case is 1. So, if the split was a 5 for 3 split, the new split multiplier would be 1 x 5/3 or 1.66666 until we encounter the next split counting backwards. The proces is then repeated for further stock splits. For example, if we next encounter a 2 for 1 stock split, the new multiplier would become 1 x 5/3 x 2/1 or 3.33333 for the period the split occurred in as wel as the preceding periods. We continue formulating this multiplier al the way back to December of 1989 for each bank that we are evaluating. Then, we divide the corresponding month?s closing price by the relevant split multiplier to get the 17 appropriate stock price values for each bank. Equation 2.1 shows how each observation for the BANK SHARE PRICE variable is formulated for each bank: (2.1) BANK SHARE PRICE = _______________BANK MONTHLY CLOSING PRICE_______________ (XN / YN) ? (XN-1 / YN-1) ? (XN-2 / YN-2) ? (XN-3 / YN-3) ? (XN-T / YN-T) where X and Y denote a X for Y or X:Y split, N denotes the Nth stock split, T denotes the total number of stock splits It can also be sen that dividends are generaly too smal and too random to systematicaly afect the final share prices we have formulated. Therefore, we do not bother with incorporating dividends into this formulation. In addition to the formulation of this BANK SHARE PRICE variable, we can later compare results achieved through using this newly formulated data as opposed to results obtained from using the adjusted data. We can do this as a precautionary measure to ensure that the transformation of this monthly share price data does not yield conflicting results when compared to the results yielded from using the adjusted monthly share price data. Once we have obtained the desired monthly stock price data for each bank included in this analysis as wel as the monthly S&P 500 observations, we wil convert al of this data to its natural logarithmic form. We need do this because we are using financial data, and thus there is a need to correct for potential trends in variance. Once we have done this, we can use common statistical methods to create new filtered variables, and run the required tests on this data. It should be noted that even though the BANK SHARE PRICE and S&P 500 variables have now been converted to their natural logarithmic form, they wil retain the same variable name throughout the rest of this thesis so that we 18 can expres the proces of this Intervention Analysis clearly without being repeatedly reminded that al data included in this model is of the natural log variety. This should not pose any isues as long as one remembers that al further price variables and results expresed are in the form of natural logs. 19 2.3 Creation of Dummy Variables For our analysis we also need to create some other variables. The introduction section of this thesis covered the events atributed to what is now more commonly referred to as the bailout. First and foremost, we create a dummy variable which we wil cal the BAILOUT DUMY. This BAILOUT DUMY variable wil correspond to the capital injection programs, or bailout, that took place in many U.S. banking institutions. The BAILOUT DUMY variable wil be in binary form with 0?s before the bailout and 1?s after the bailout. Because the bailout occurred at the very end of October 2008, we wil use 0?s up until this period starting in December 1989. We wil use 1?s starting in November 2008 al the way up until the current period which is October 2011 in the case of this analysis. Thus, the BAILOUT DUMY variable wil contain 0?s for the first 228 observations and 1?s for the following 36 observations. This dummy variable wil play an instrumental role in this analysis. Additionaly, we wil want to compare the efects of the bailout to other significant events that could also possibly have an efect on the stock prices of U.S. banks. This wil ensure that if we do se a shock that appears to stem from the government?s capital injection programs, that this shock is not random. It wil also alow us to se how intense the efect of the bailout was on the share prices of U.S. banks compared to other significant events that transpired during the time periods for which we have collected data. The addition of these extra dummy variables wil alow the conclusions we draw from our results to be more robust. For this model, three more supplementary dummy variables wil be added. We wil add dummy variables that correspond to the unanticipated terrorist atacks that occurred in the U.S. on September 20 11, 2001, the amending and major overhauling of the Community Reinvestment Act on May 4, 1995, and the erosion of the Glas-Stegal Act by the enacting of the Gram? Leach?Bliley (or Financial Services Modernization) Act on November 12, 1999. The September 11 th terrorist atacks in the United States shocked the entire world. This was an atack of an unprecedented magnitude. For this reason it may be interesting to se if there was any shock to U.S. banking stock prices as wel as to compare these results with that of the bailout. Similar to the BAILOUT DUMY variable, the dummy variable we create for these terrorist atacks wil also be in binary form and wil be caled the 911 DUMY. The 911 DUMY variable wil contain 0?s before the atacks and 1?s after the atacks. Therefore, the first 141 for the 911 DUMY variable wil be al 0?s and the following 122 observations wil contain al 1?s. The Community Reinvestment Act is a federal law which forces lending institutions such as banks to make housing loans to citizens that might otherwise not be approved for such loans. On May 4, 1995, President Clinton signed into afect significant changes to this law which made it more prevalent and broadened the Act?s scope. This amendment also included provisions that alowed the federal government to check for and punish banks that were not making these loans. This may have some efect on the share prices of U.S. banks but we would stil not expect these efects to be larger than ones caused by the bailout or the events of September 11 th . This dummy variable wil be denoted as the CRA DUMY variable and wil also contain 0?s before the amending of the Community Reinvestment Act and 1?s after congres amended this act. As one would imagine, the CRA DUMY variable wil contain al 0?s for the first 62 observations and 1?s for the remaining 201 observations. 21 The fourth dummy variable which wil be created for this analysis wil be labeled as the GLBA DUMY. The GLBA DUMY variable wil correspond to enactment of the Gram-Leach-Bliley Act on November 12, 1999. This act is more commonly referred to as the Financial Services Modernization Act. This act alowed banking institutions in the U.S. to engage in many diferent types of financial busines. Previously, banks could not involve themselves with many diferent aspects of commercial banking, insurance, and many other types of financial instruments due to the Glass-Stegal Act of 1933. This Financial Services Modernization Act eroded many aspects of the Glas-Stegal Act of 1933. In general, most view this as the beginning of bank deregulation in the United States. We can se that this is another event that we would like to consider using in our analysis. This GLBA DUMY variable wil also be another binary variable with 0?s for the first 119 observations and 1?s for the following 144 observations. Now that we have procured the necesary data, we can begin to look at how we wil perform this Intervention Analysis. 22 II. Model 3.1 Overview of the Intervention Analysis Model We can evaluate the efect of masive capital injections given to banks by the U.S. government such as the Capital Purchase Program and the Targeted Investment Program through the use of an Intervention Analysis as used by Box and Tiao in their 1975 paper ?Intervention Analysis with applications to Economic and Environmental Problems?. However, this thesis wil follow the Intervention Analysis as detailed by Walter Enders (Enders 1995). This analysis can show the short and long run efects that this capital infusion had on the common stock share prices of the corresponding U.S. banking institutions. In Enders? 1995 book, Applied Econometric Time Series, Walter Enders details a proces he cals an ?Intervention Analysis? in the first section of the books? chapter on Multi-Equation Time-Series Models. Enders explains that an Intervention Analysis can be used to generalize the univariate (Box-Jenkins) methodology by alowing the time path of the relevant variable to be influenced by its past values and possibly other exogenous variables. Enders also explains that most isues encountered from using this Intervention Analysis can be dealt with later by using a vector autoregresive proces. Enders uses an example that describes the efect that the introduction of metal detectors (the intervention) had on skyjackings (the time series variable in question). The intervention in our case wil be the initiation of the government bailout of U.S. banks and the time series variable that we are concerned with wil be the share prices of those U.S. banks that received federal bailout capital as wel as some that did not. Enders explains that we must do more than just take the mean value of our dependent variable (bank?s stock prices) before and after the intervention and compare 23 them. However, this is not to say that the mean comparison may not serve as a decent preliminary measure to undertake. It is for this reason that we wil briefly examine the pre and post-intervention means of the time series in question. However, we must go beyond this simple comparison because we are dealing with a time series proces and the share price data is serialy correlated with itself. Thus, we do not want to only compare the mean values of this data before and after the bailout because observations after the bailout could be afected by observations occurring before the bailout. For the intervention analysis we can look at regresion equation 3.1: (3.1) Y t = A o + A 1 Y t-1 + C o Z t + ? t In this equation, Z t represents a binary dummy variable, which we wil cal for our purposes BAILOUT DUMY. Remember that the BAILOUT DUMY variable wil contain 0?s before the bailout and 1?s after the bailout. Y t and Y t-1 refer to the time series in question, which is the individual share prices of the U.S. banks included in our model. ? t represents a white noise disturbance term in this case. Enders details that because Z t wil be zero before the bailout, the intercept given by A o wil clearly reveal the mean of the bank?s share price before the bailout. Thus, the long-run (Y t = Y t-1 ) pre-intervention mean of the series wil be given by equation 3.2: (3.2) A o / (1-A 1 ) Subsequently, Z t wil become 1 after the bailout and so the new imediate intercept or mean of the equation wil be given by equation 3.3: (3.3) A o + C o 24 Thus, we can se that the long-run mean wil be represented by equation 3.4 in the following manner: (3.4) (A o + C o ) / (1-A 1 ) Walter Enders describes using the initial jump, or difering mean if you wil, as the ?impact efect? of the intervention. In our case this intervention wil be the government bailout. It can be sen that the size of C o wil detail the magnitude of the impact efect that the government?s capital infusion to U.S. banks had on the equity prices of individual U.S. banks. We can test C o for being statisticaly significantly diferent from zero. We could conclude that the bailout caused an increase in share prices if C o is positive and statisticaly significant and the opposite could consequently be said if C o is negative as wel as significant. In our case, C o is caled the BAILOUT DUMY COEFFECIENT. It should be duly noted at this point that, in terms of his hijacking example, Enders is making an asumption that the introduction of metal detectors plays a very large role in decreasing the number of skyjackings when holding al else constant. However, in the case of the U.S. banking industry share prices, there was a large drop in values around the same time as the government?s intervention or ?bailout?. We might atribute this to the recesion and significant economic downturn that the U.S. markets were encountering at the time of the bailouts, rather than the bailout itself per se. Thus, if we do not adjust, or take into acount, the efect of the market as a whole on the share prices of these banks, we might risk incorrectly suggesting that the bailouts were solely the cause of this masive decrease in bank?s share prices. Therefore, we wil have to take into acount the efect of the market on bank share prices when performing this analysis. 25 The manner in which we use the previously discussed S&P 500 variable to correct for these variations in the market and the state of the economy wil be described later. After testing C o for significance, Enders shows that the ?long-run efect of the intervention is equal to the new long run mean minus the value of the original long-run mean? which is shown here by equation 3.5: (3.5) [C o / (1 ? A 1 )] = [(A o + C o ) / (1 ? A 1 )] ? [A o / (1 ? A 1 )] From this, Enders shows that we can use lag operators to rewrite our original regresion equation in order to obtain an impulse response function, which can be used to analyze other transitional efects: (3.6) Y t = A o + A 1 Y t-1 + C o Z t + ? t (impact efect) (1 ? A 1 L)Y t = A o + C o Z t + ? t (final ? long run efect) Y t = A o / (1 ? A 1 ) + C o ?A 1 Z t-i + ? A 1 ? t ?i (interim efect) The final equation is the impulse response function. We can continualy diferentiate this function as wel as limit the series to infinity to reveal the entire impact of the government bailout to U.S. banks on the share prices of those banks as wel as others. Enders does indeed do this and shows that the long-run efect of the bailout wil be given by: (3.7) C o / (1 ? A 1 ) 26 3.2 Filtration of U.S. Banking Share Prices We are now ready to use statistical methods to create a couple more variables as wel as run some tests. As mentioned throughout this thesis, we need to filter the BANK SHARE PRICE variable for each bank in order to acount for the efect of the market as a whole before we can move forward with this Intervention Analysis. For each bank we regres the following: (3.8) BANK SHARE PRICE t = ? 1 (ONE) + ? 2 (S&P 500 PRICE) t + ? t This regresion results in a residual or filtered share price which factors out the efect of the overal market and economy as a whole on the individual bank?s share price. Recal that prior to this regresion the BANK SHARE PRICE and the S&P 500 PRICE variables have taken on a natural logarithmic form. Thus, the residual given by this regresion wil yield a new variable, the FILTERED BANK SHARE PRICE variable, that is also in the form desired for the remainder of the analysis. A graphical representation of these filtered variables can be sen in Appendix I. As was aluded to earlier, we can now take a preliminary look at the pre and post-intervention means of the time series. Table 3.1 ilustrates the pre and post-intervention (or pre and post-bailout) means of the newly created FILTERED BANK SHARE PRICE variables: 27 TABLE 3.1: FILTERED MEAN VALUES OF INDIVIDUAL BANKING INSITUTIONS BEFORE AND AFTER THE INTERVENTION BANKING INSTITUTION PRE- BAILOUT MEAN POST- BAILOUT MEAN DIFERENCE Bank of America 0.128322 -0.835927 0.964249 Citigroup 0.27095 -1.76505 2.036 JP Morgan Chase -0.00372834 0.0242875 -0.02801584 Wels Fargo -0.0226268 0.147397 -0.1700238 Morgan Stanley 0.0808296 -0.438789 0.5196186 PNC Financial 0.00162679 -0.0105974 0.01222419 US Bancorp 0.00638381 -0.041586 0.04796981 Suntrust 0.124284 -0.809621 0.933905 Capital One Financial Corp. 0.0211619 -0.102182 0.1233439 Regions Financial Corp. 0.208335 -1.3393 1.547635 Fifth Third Bancorp 0.166524 -1.07051 1.237034 BB&T 0.0243422 -0.156485 0.1808272 Bank of New York Melon Corp. 0.0184356 -0.120095 0.1385306 KeyCorp 0.160061 -1.04268 1.202741 State Street -0.00343407 0.0223705 -0.02580457 Synovus Financial Corporation 0.255683464 -1.6582899 1.913256 M&T Bank Corporation -0.0163143 0.0960215 -0.1123358 TCF Financial Corporation 0.0239499 -0.156016 0.1799659 Central Pacific Financial 0.292276 -1.87892 2.171196 Auburn Bank -0.0548403 0.249131 -0.3039713 BancFirst Corporation -0.0668009 0.429434 -0.4962349 BancorpSouth Incorporated 0.00741309 -0.048291 0.05570409 Bank of Hawai -0.0502851 0.327571 -0.3778561 Community Bank System Inc. -0.0403416 0.262797 -0.3031386 Mean values are in natural logarithmic form As you can se from Table 3.1, it sems that the mean values of most of these time series sems to be of leser value after the intervention or bailout. This is our first piece of evidence suggesting a decrease in the share prices of U.S. banking institutions resulting from the bailout although some of them sem to have risen. The reason why some of these means have actualy risen is atributable to the growth of these share prices. The pre-intervention mean values contain prices dating back to 1989 when prices were a lot lower. These earlier low values can cause the mean of a bank?s pre-intervention share 28 price to sem quite lower than the post-intervention mean prices because al share price observations are weighted the same in this comparison. As we have mentioned throughout, this is why only looking at these mean values alone is not enough to adequately addres the isues we are looking at. After looking at these mean values, we are now ready to use the FILTERED BANK SHARE PRICE variable in replace of the original BANK SHARE PRICE variable because we have taken out the afect of the market as a whole. 29 3.3 Regresing the Intervention Model Now that the market efect has been filtered out, we can then lag this new FILTERED BANK SHARE PRICE variable by one period in order to obtain a new variable, which we cal the FILTERED BANK SHARE PRICE [t-1]. We do this because we believe an AR(1) proces can adequately describe the time series proces of share price data. We wil later examine this asumption. Once this lagged variable has been created, another regresion equation can be estimated that wil now incorporate the binary BAILOUT DUMY variable. Equation 3.9 shows the Intervention Analysis regresion formula used for this model: (3.9) FILTERED BANK SHARE PRICE t = ? 1 (ONE) + ? 2 (FILTERED BANK SHARE PRICE) t-1 + ? 3 (BAILOUT DUMY) t + ? t This regresion can yield some important results. First, it can yield a coeficient asociated with the FILTERED BANK SHARE PRICEt-1. If this coeficient is statisticaly significant, it wil be suggesting the decay rate of the impulse response function resulting from the bailout. The regresion can also result in a negative coeficient asociated with the BAILOUT DUMY variable, indicating an instantaneous drop in bank share prices asociated with the bailout. The subsequent empirical analysis indicates that in some cases, this coeficient is indeed statisticaly significant and in other cases it is not. Finaly, we wil also analyze the residual arising from this model, which can be thought of as a variable that we can cal the PROCESS RESIDUAL. We must check the PROCESS RESIDUAL to make sure it resembles white noise so that we know that we have estimated the correct time series proces. We wil do this by looking at the significance level of the Box-Pierce and Box-Ljung Q Test Statistics relating to this 30 PROCESS RESIDUAL. We wil use 36 periods when we perform the identification of this residual. A white noise proces on the PROCESS RESIDUAL variable for each bank wil suggest that there is nothing left out of the intervention equation and that we have used the appropriate model specification when estimating time or t. 31 IV. RESULTS 4.1 Overview of the Results We can compile the results achieved by executing the previously mentioned regresion into the following table which is ilustrated below. With the banks listed in order of the total bailout amount they received individualy, the table includes coeficients on ? 2 and ? 3 as wel as the significance level of the Q-Statistics for each bank?s corresponding PROCESS RESIDUAL. Recal from the previous outline of Enders? intervention example that the ? 2 coeficient represents an AR(1) term that wil serve as a decay rate steming from the shock of the intervention, or bailout in this case. ? 3 , which is the coeficient asociated with the BAILOUT DUMY variable for each bank, wil describe the imediate reaction of banking share prices to the enactment of the capital injection programs. Additionaly, the significance level of the Box-Pierce and Box-Ljung Q-Statistics wil suggest whether or not we have modeled the correct time series proces. These important aspects of our results are detailed in the following table: 32 TABLE 4.1: INTERVENTION MODEL REGRESSION RESULTS BANKING INSTITUTION TOTAL BAILOUT AMOUNT ($) DECAY RATE (? 2 ) STOCK PRICE RESULT (? 3 ) BOX-PIERCE / BOX-LJUNG Q-STAT SIGNIFICANCE Bank of America 45,000,000,000 .92046502* (38.658) -.1142315* (-4.079) .2392 / .1861 Citigroup 45,000,000,000 .93877416* (58.1) -.17190284* (-4.823) .3545 / .2953 JP Morgan Chase 25,000,000,000 .89660684* (31.662) -.01052947 (-.741) .935 / .9157 Wels Fargo 1 25,000,000,000 .94715726* (43.43) -.01093432 (-.737) .0296 / .0184 Morgan Stanley 10,000,000,000 .96795239* (39.954) -.02546545 (-1.304) .7425 / .6688 PNC Financial 7,579,200,000 .90966699* (35.086) -.01500747 (-1.179) .6741 / .5889 US Bancorp 6,599,000,000 .94172101* (45.378) -.01610425 (-1.165) .2049 / .1507 Suntrust 2 4,850,000,000 .91581803* (40.357) -.10280503* (-4.047) 0 / 0 Capital One Financial Corp. 3,555,199,000 .94145065* (39.927) -.01994538 (-.958) .1263 / .0695 Regions Financial Corp. 1 3,500,000,000 .94911395* (48.677) -.10807022* (-3.203) .0005 / .0002 Fifth Third Bancorp 3,408,000,000 .96517236* (53.523) -.04835266 (-1.616) .175 / .1328 BB&T 3,133,640,000 .93298059* (42.184) -.03353213* (-2.316) .1382 / .1035 33 TABLE 4.1 (Continued): INTERVENTION MODEL REGRESSION RESULTS BANKING INSTITUTION TOTAL BAILOUT AMOUNT ($) DECAY RATE (? 2 ) STOCK PRICE RESULT (? 3 ) BOX-PIERCE / BOX-LJUNG Q-STAT SIGNIFICANCE Bank of New York Melon 3,000,000,000 .94776781* (44.762) -.03213922* (-2.36) .8122 / .7701 KeyCorp 2,500,000,000 .94762867* (48.118) -.08056086* (-2.893) .0774 / .0524 State Street 2,000,000,000 .94504624* (44.981) -.01342033 (-.982) 6929 / .6354 Synovus Financial Corp. 1 967,870,000 .94599251* (59.762) -.16104261* (-4.798) .0206 / .0089 M&T Bank Corporation 600,000,000 .97254006* (62.623) -.01308955 (-.943) .4307 / .3374 TCF Financial Corporation 361,172,000 .97073546* (62.549) -.03304947 (-1.882) .9781 / .9674 Central Pacific Financial 1 135,000,000 .95503310* (70.984) -.18713818* (-5.401) .0019 / .001 Auburn Bank 0 .97174535* (48.802) -.0070981 (-.461) .6868 / .5692 BancFirst Corporation 0 .98353505* (64.154) -.01379618 (-.839) .6599 / .5981 BancorpSouth Incorporated 0 .96879679* (50.285) -.0338268* (-2.619) .7858 / .7195 Bank of Hawai 1 0 .98398629* (73.551) -.00896991 (-.655) .0344 / .0196 Community Bank System Inc. 0 .96492386* (54.075) .00069147 (.044) .7819 / .73 * Statisticaly significant 1 BANK SHARE PRICE RESIDUAL variable can be differenced before runing the second regresion in order for the PROCESS RESIDUAL to exhibit a white noise proces. This is exhibited in the next section as wel as Apendix I. 2 Could not obtain a white noise proces on the PROCESS RESIDUAL through differencing the BANK SHARE PRICE RESIDUAL (ie Box-Pierce and Box-Ljung significance levels always remain les than .05). 34 4.2 Testing for Estimation of the Correct Time Series Proces As mentioned earlier, the previous regresion yields a new residual, which we are caling the PROCESS RESIDUAL. I have given the variable this name because we can use it to check and be sure we have estimated the correct time series proces needed for this intervention model. In this case, we would expect this residual to exhibit a white noise proces if we have modeled the time series proces correctly. We can check for this by looking at the significance level of the Box-Pierce and Box-Ljung test statistics asociated with the PROCESS RESIDUAL. We wil use a significance level of at least .05 in order to claim that the PROCESS RESIDUAL follows the desired white noise proces. The reported Box-Pierce and Box-Ljung test statistics reported in the above table are P-values which are computed using 36 lags can tel us if this residual exhibits a white noise proces. If this is the case, we can fel confident that we have indeed estimated the correct proces. In this model, we have asumed that these banks follow an AR(1) proces. This asumption sems legitimate for most of the banks analyzed. However, the PROCESS RESIDUAL asociated with the banks Wels Fargo, Regions Financial, Synovus Financial Corporation, Central Pacific Financial, and Bank of Hawai did yield marginaly significant Box-Pierce and Box-Ljung test statistics. Nevertheles, the decay rate and coeficient on the dummy variables for these banks are very similar in magnitude to the results given from the other banks whose PROCESS RESIDUAL did reveal white noise when identified. For these banks (Wels Fargo, Regions Financial, Synovus Financial Corporation, Central Pacific Financial, and Bank of Hawai), we can try to further diference the data in order to achieve significant white noise on the PROCESS RESIDUAL. Indeed, further diferencing the FILTERED BANK SHARE 35 PRICE variable for these institutions did yield a white noise proces on the PROCESS RESIDUAL for the corresponding banks. More specificaly, Wels Fargo, Regions Financial, Synovus Financial Corporation, Central Pacific Financial, and Bank of Hawai can be 4 th , 5 th , 3 rd , 2 nd , and 3 rd diferenced, respectively, to produce a white noise proces with regards to identifying the PROCESS RESIDUAL. The other results steming from further diferencing these banks does mimic the original results from when we asumed that Wels Fargo, Regions Financial, Synovus Financial Corporation, Central Pacific Financial, and Bank of Hawai al followed an AR(1) proces. Furthermore, the BAILOUT DUMY COEFFICIENT did become les significant in some cases but in some instances (i.e. Bank of Hawai) the BAILOUT DUMY COEFFICIENT actualy became more significant. This proces of diferencing as wel as the results from doing so are further expounded upon in Appendix II of this thesis. In the case of Suntrust however, we could not achieve a white noise proces on the PROCESS RESIDUAL through diferencing. In al likelihood, this is because the share price data for Suntrust follows a more complicated time series proces. Though other results given by this model for Suntrust sem to be in-line with the results from the other banks, the results this model has yielded for Suntrust should be viewed with caution. We can se that the PROCESS RESIDUAL on the overwhelming majority of the banks analyzed looks like white noise when we asume the time series follows an AR(1) proces. We have also examined validity of the notion that we can diference the FILTERED BANK SHARE PRICE by the desired number of time periods for the few remaining banks whose PROCESS RESIDUAL did not met the previously stated 36 criteria for revealing a white noise proces. This can be done without significantly changing the results given by the BAILOUT DUMY COEFFICIENT as wel as the FILTERED BANK SHARE PRICE COEFFICIENT. Taking both of these observations into acount, we can fel confident that we have correctly identified the time series for al of these banks. Because of this, in what follows, we wil analyze the results given from the original non-diferenced model even if the time series needed to be further diferenced for some to achieve significant Box-Pierce and Box-Ljung test statistics on the PROCESS RESIDUAL. Now that we have substantial evidence that this model is using the correct time series proces, we can begin to realy look at the efect that the Capital Purchase Program and the Targeted Investment Program had on the share prices of U.S. banking institutions. 37 4.3 Interpretation of Bailout Dummy Coefficients We can se that al but one of the coeficients the bailout dummies in Table 4.1 are negative, though they are not al significant. This sems to suggest that the capital infusion to these banks by the government did not help the equity prices of these banks when we adjust for the market and hold everything else constant. As mentioned earlier, this does not mean the bailout, as a whole, was a bad idea necesarily, but that it may have put some downward presure on the share prices of U.S. banking institutions. This is interesting because you would normaly expect to se a positive afect on an aset?s value when it is receiving masive amounts of semingly free capital. However, given the circumstances and reasons that the capital was given to the banks, it sems that this was not the case. Also, the fact that the lender of this capital was the government most likely sent a bad signal to the market which in turn caused a decline in share prices. This decline does not sem to discriminate betwen the amount of bailout funds these individual banks received (or if they received any at al). We cannot say for sure that we are 100% certain that the capital infusion by the government had a negative efect on al of these bank?s stock prices because al of the BAILOUT DUMY COEFFICIENTS are not significant. However, we do fel confident in saying that the data suggests that it most certainly did not have a positive influence on the share prices of these financial institutions. In fact, asuming independence among regresions, we can use the binomial distribution to check what the probability is of our results actualy being insignificant when they sem to be significant. The probability of finding as many as 9 out of 24 significant BAILOUT DUMY COEFFICIENTS by chance (when the probability of finding one significant by chance is 0.05) is 0.00018131155% or .0000018131155. 38 Given this extremely low probability it is not unreasonable to alege, based on these results, that the bailout resulted in a system wise drop in the stock prices of U.S. banks. This is evident because al of the signs on these coeficients are negative. But again, only a litle over 1/3 rd of them are significant. As we have stated throughout this thesis, the data and thus the results which we are interpreting through the use of this intervention model are in the natural logarithmic form. It is because of this that when the BAILOUT DUMY COEFFICIENT is interpreted as the amount of a decline in share prices, it should be viewed as a percentage drop in the filtered share price of the asociated financial institution atributable strictly to the bailout. This is true even though we are dealing with the filtered price, since the filtering proces only removed the market efect on stock prices alone. Hence the change in the filtered price atributable to the bailout is the change in the market price atributable to the bailout. When we take this into acount, you can se that some of stock prices of these banks took negative hits after the capital injections began in late October of 2008. It may be desirable to look at the impact efect of the bailout on banking share prices in a way other than percentage decreases. Kep in mind that we are looking at the efect of the filtered share price of these banks so these drops represent the minimal amount that the share price dropped due to the bailout. Table 4.2 ilustrates the minimal dollar amount of the decrease in equity prices on U.S. banks that have a statisticaly significant BAILOUT DUMY COEFFICIENT: 39 TABLE 4.2: SIGNIFICANT SHARE PRICE REACTIONS BANKING INSTITUTION IMEDIATE STOCK PRICE REACTION (? 3 ) OCTOBER 2008 SHARE PRICE ($) IMEDIATE STOCK PRICE REACTION ($) Bank of America -0.1142315 24.17 -2.76 Citigroup -0.17190284 136.5 -23.46 Suntrust -0.10280503 40.14 -4.13 Regions Financial Corp. -0.10807022 11.09 -1.20 BB&T -0.03353213 35.85 -1.20 Bank of New York Melon Corp. -0.03213922 32.99 -1.06 KeyCorp -0.08056086 12.41 -1.00 Synovus Financial Corporation -0.16092731 10.33 -1.66 Central Pacific Financial -0.18713818 312 -58.39 BancorpSouth Incorporated -0.0338268 24.27 -.082 Table 4.2 ilustrates the minimal dollar amount of the decrease in equity prices on U.S. banks that have did not have a statisticaly significant BAILOUT DUMY COEFFICIENT: 40 TABLE 4.3: INSIGNIFICANT SHARE PRICE REACTIONS BANKING INSTITUTION IMEDIATE STOCK PRICE REACTION (? 3 ) OCTOBER 2008 SHARE PRICE ($) IMEDIATE STOCK PRICE REACTION ($) JP Morgan Chase -0.01052947 41.25 -0.43 Wels Fargo -0.01093432 34.05 -0.37 Morgan Stanley -0.02546545 17.47 -0.44 PNC Financial -0.01500747 66.67 -1.00 US Bancorp -0.01610425 29.81 -0.48 Capital One Financial Corp. -0.01994538 39.12 -0.78 Fifth Third Bancorp -0.04835266 10.85 -0.52 State Street -0.01342033 43.35 -0.58 M&T Bank Corporation -0.01308955 81.1 -1.06 TCF Financial Corporation -0.03304947 17.74 -0.59 Auburn Bank -0.0070981 22.41 -0.16 BancFirst Corporation -0.01379618 50.4 -0.70 Bank of Hawai -0.00896991 50.71 -0.45 Community Bank System Inc. 0.00069147 24.95 0.02 As one would expect, the financial institutions which have a significant BAILOUT DUMY COEFFICIENT sem to have experienced larger negative shocks to their share prices percentage wise as wel as dollar wise. The results sem to suggest that al imediate minimal shocks of more than one dollar are being interpreted as statisticaly significant drops. We can se that there sems to be no correlation betwen a bank?s total bailout amount received and the corresponding significance level of the bank?s BAILOUT DUMY COEFFICIENT. However, we must realize that the total bailout amounts given in this analysis do not take into acount the size of the banking institution. Hence, we need to also check to se if there is any correlation betwen a bank?s bailout amount relative to the size of the bank and the significance level of the BAILOUT DUMY COEFFICIENT. The Bank Holding Company Act as wel as Regulation Y both require 41 bank holding companies to file quarterly Y-9LP forms to the U.S. Federal Reserve. We can use these financial statements to determine the total amount of asets these banks had as of June 2008 (the nearest quarterly report preceding the bailout). Once we have retrieved June 2008 total aset information for these banks, we can divide this amount by the total amount of bailout capital the corresponding bank received. This wil give us a ?bailout ratio? that we can check for correlation with the significance level of the BAILOUT DUMY COEFFICIENTS. Table 4.4 shows that there sems to be no correlation betwen the significance of a bank?s BAILOUT DUMY COEFFICIENT and this newly formulated ?bailout ratio? for that same bank. TABLE 4.4: BAILOUT RATIO CORELATION WITH BAILOUT DUMY SIGNIFICANCE BANKING INSTITUTION TOTAL BAILOUT AMOUNT JUNE 2008 TOTAL ASETS BAILOUT RATIO SIGNIFICANT BAILOUT DUMMY Morgan Stanley 10,000,000,000 283,140,000,000* 28.31 No Bank of New York Melon Corp. 3,000,000,000 44,931,000,000 14.98 Yes JP Morgan Chase 25,000,000,000 345,646,000,000 13.823 No M&T Bank Corporation 600,000,000 8,068,542,000 13.45 No State Street 2,000,000,000 23,309,081,000 11.65 No Capital One Financial Corp. 3,555,199,000 33,429,104,000 9.40 No Bank of America 45,000,000,000 368,684,845,000 8.19 Yes Citigroup 45,000,000,000 339,703,000,000 7.55 Yes 42 TABLE 4.4 (Continued): BAILOUT RATIO CORELATION WITH BAILOUT DUMY SIGNIFICANCE BANKING INSTITUTION TOTAL BAILOUT AMOUNT JUNE 2008 TOTAL ASETS BAILOUT RATIO SIGNIFICANT BAILOUT DUMMY Regions Financial Corp. 3,500,000,000 25,737,490,000 7.35 Yes BB&T 3,133,640,000 19,978,622,000 6.38 Yes Wels Fargo 25,000,000,000 156,493,000,000 6.256 No KeyCorp 2,500,000,000 14,183,611,000 5.67 Yes Fifth Third Bancorp 3,408,000,000 18,382,392,000 5.39 No Suntrust 4,850,000,000 26,005,949,000 5.36 Yes US Bancorp 6,599,000,000 35,008,728,000 5.31 No Central Pacific Financial 135,000,000 617,175,000 4.57 Yes Synovus Financial Corp. 967,870,000 4,279,576,000 4.42 Yes TCF Financial Corporation 361,172,000 1,102,413,000 3.05 No PNC Financial 7,579,200,000 18,271,731,000 2.41 No Auburn Bank 0 61,365,000 0 No BancFirst Corp. 0 417,870,000 0 No BancorpSouth Inc. 0 1,396,194,000 0 Yes Bank of Hawai 0 806,938,000 0 No Community Bank System Inc. 0 593,989,000 0 No * June 2008 Y-9LP not available so March 2009 Y-9LP was used 43 We can se that there sems to be no correlation betwen the ?bailout ratio? which we have just created and the BAILOUT DUMY COEFFICIENTS. It may also be wise to regres the banks with an insignificant BAILOUT DUMY COEFFICIENT in a model which includes a BAILOUT DUMY which corresponds to that bank only. Recal from the earlier table detailing the capital injection schedule that diferent banks were given bailouts at diferent times. For the banks that did not initialy return a significant BAILOUT DUMY COEFFICIENT, we can se that some of them received bailout capital later than October 28, 2008. It is for these few banks that the earlier steps for this model are repeated but this time the BAILOUT DUMY variable corresponds only to the time of that bank?s bailout. Hence, we wil need to create three more BAILOUT DUMY variables with 0?s on al observations before the bailout and 1?s on al observations after the bailout. Once this has been completed and the earlier model steps are performed on these select banks, we stil find the same results. Even after running the model including the creation of these bank specific BAILOUT DUMY variables, the BAILOUT DUMY COEFFICIENTS for these specific banks stil remains insignificant. 44 4.4 Interpretation of the Lagged and Filtered Share Price Coefficients The most interesting results given are the extremely high coeficients on the FILTERED BANK SHARE PRICE [t-1] variables, which are labeled as Decay Rates on the above table. The closer to 1 these coeficients are, the longer it wil take the share prices of these banks to recover or return to normal. Thus, the closer the coeficient is to 1, the longer it wil take the shock on share prices from the bailout to die out. If the coeficients would have been 1, this would have meant that the shock would have resulted in a permanent and constant change in the share prices and we would have a random walk occurring from this point on in the time series. If these coeficients would have been greater than 1, we could se that the bailout would have resulted in causing the share prices of these banks to be exploding and never reverting back to their position before the bailout. However, since these coeficients are so close to 1, we can look at the shock from the government bailout on share prices of U.S. banks as having a very long lasting (but not quite permanent) efect. We can se that the AR(1) terms are so large due to an autonomous increase in riskines, that it wil take an extremely long time for the efect of the bailout to die out on the corresponding share prices of these banks. We might have expected to se banks that had les to do with the government?s capital infusion have a smaler decay rate. However, we can se that banks like Bank of America and Citigroup were some of the largest recipients of government funds and yet these banks have some of the fastest decay rates of al 24 banks analyzed. Meanwhile, banks like BancorpSouth Incorporated and others that received no bailout funds face some of the longest recovery periods out of al the banks analyzed. Thus, it is easy to se that the bailout of a couple hundred banks caused a long lasting shock throughout the 45 entire banking industry with respect to the common stock share prices of U.S. banks. Again, the market participants did not sem to diferentiate betwen who took government funds and who did not, as wel as how much the individual banks took. This is quite interesting when we consider that some banks did not particularly desire a capital injection from the government and that most banks did not even receive one. It appears the efect of the bailout on banking share prices is here for a very long time. These coeficients are so high on some of these banking entities that we may even view this a semi-permanent efect or shock. The reason these decay rates are so high may be due to the nature of the banking industry. Banks in general have dramaticaly changed the way that they operate following the recent financial collapse. Even though the bailout was an atempt by the U.S. government to stabilize the banking industry by giving capital to banks specificaly for loaning purposes, there is stil a shortage of available capital in U.S. loan markets. Until the behavior and perception of these banks change, it appears the recovery periods wil be very long. This is not to say that these decay rates must remain this high forever. If we continue to keep updating the banking data in the future and there are significant financial developments (like an influx of loan market capital) in the future, these decay rates may begin to decrease. However, until something of this nature occurs, the recovery period of U.S. banking share prices resulting from government capital injections wil take a very long time. It is of interest for us to ask just how long this analysis is suggesting that it wil take the stock prices of these banks to recover. James Hamilton shows (though he did not introduce) in his text Time Series Analysis (1994) that the FILTERED BANK SHARE 46 PRICE [t-1] COEFFICIENT from this intervention model wil determine the rate of decay of the shock due to the intervention, which in this case is the bailout. The efect of the shock can be expresed by the following: (4.1) ? T = 0 where ? denotes ? 2, where T denotes number of time periods We can se that a larger value of ? wil require a larger number of recovery periods in order for the left hand side of the equation to equal zero. Thus, the larger the value is on the FILTERED BANK SHARE PRICE [t-1] COEFFICIENT or ? 2 , the longer it wil take for the efect of the shock to die out. It can also be sen that any value of ? that is les than 1 in absolute value (which is what we encounter in this model) wil require limiting T to infinity in order for the efect or above equation to reach absolute zero. For practical purposes, we may want to rewrite the equation as follows: (4.2) ? T = 0.004999999?. If we concede for our purposes that .004999999 is close enough to esentialy being zero, we can solve for T (which in our case is denominated in months) for each of the 24 banks we have included in this analysis. The following table shows the results from doing this for each bank and their following estimated recovery periods: 47 TABLE 4.5: ESTIMATED RECOVERY PERIODS BANKING INSTITUTION DECAY RATE (? 2 ) ESTIMATED RECOVERY PERIOD (MONTHS) JP Morgan Chase 0.89660684 49 PNC Financial 0.90966699 56 Suntrust 0.91581803 60 Bank of America 0.92046502 64 BB&T 0.93298059 76 Citigroup 0.93877416 84 Capital One Financial Corp. 0.94145065 88 US Bancorp 0.94172101 88 State Street 0.94504624 94 Synovus Financial Corporation 0.94599251 96 Wels Fargo 0.94715726 98 KeyCorp 0.94762867 99 Bank of New York Melon Corp. 0.94776781 99 Regions Financial Corp. 0.94911395 102 Central Pacific Financial 0.9550331 115 Community Bank System Inc. 0.96492386 148 Fifth Third Bancorp 0.96517236 150 Morgan Stanley 0.96795239 163 BancorpSouth Incorporated 0.96879679 167 TCF Financial Corporation 0.97073546 178 Auburn Bank 0.97174535 185 M&T Bank Corporation 0.97254006 190 BancFirst Corporation 0.98353505 319 Bank of Hawai 0.98398629 328 48 As we can se in Table 4.5, a smal movement in the FILTERED BANK SHARE PRICE [t-1] COEFFICIENT or ? 2 can lead to a very dramatic change in the estimated monthly recovery period. We can also se that this recovery period is very long with the average recovery period being about 10.75 years. We can also se from the earlier table that the smaler banks (including ones that received no bailout funds) face longer recovery periods. This is perhaps because the larger banks have aces to many more financial tools and are more diversified in many aspects. These larger firms tend to act as leaders or first movers in the banking industry while the smaler firms (comprised mostly of banks that did not receive any bailout capital) tend to act as followers or second movers. Hence, the recovery period of the share prices of the smaler banks may be lengthier and occur after the recovery of the share prices of the larger entities. Again, it appears that the share prices of the industry as a whole face a long recovery period resulting from the capital injection shocks. 49 V. COMPARING CAPITAL INJECTION SHOCKS TO OTHER EVENTS 5.1 Multi-Dummy Model Formulation We have succesfully looked at the efect of the bailout alone on U.S. banking share prices but it is important that we compare these results to other results obtained from also looking at the efect that other significant events may have had on these same stock prices. This is important because we want to make sure our significant results are indeed just that when compared to other interventions or shocks. Recal that in addition to the creation of the BAILOUT DUMY variable, we also created three other binary dummy variables which are the 911 DUMY, CRA DUMY, and the GLBA DUMY variables. The reasoning behind including these additional dummy variables as wel as descriptions of the events which they represent has been covered earlier in this thesis; thus there is no need to re hash this aspect of the model. Because we have already created the FILTERED BANK SHARE PRICE variable for each bank, which acounts for market movement, we can append the three new dummy variables to the previous intervention model regresion. The following equation shows the new regresion model: (5.1) FILTERED BANK SHARE PRICE t = ? 1 (ONE) + ? 2 (FILTERED BANK SHARE PRICE) t-1 + ? 3 (BAILOUT DUMY) t + ? 4 (GLBA DUMY) t + ? 5 (CRA DUMY) t + ? 3 (911 DUMY) t + ? t This model wil give us coeficient estimates which wil suggest the level of significance of these four events on U.S. bank?s stock prices as wel as the level of impact efect that these difering events had on these same share prices. From these results we can analyze the validity of our earlier discoveries with regards to the bailout?s efect on 50 U.S. banks? share prices. If these results are in agreement with our findings from the single dummy intervention model, it wil reasure our previously stated inferences. 51 5.2 Multi-Dummy Model Results The resulting dummy variable coeficients and their corresponding significance level from running the previous regresion equation 5.1 with four binary dummy variables are ilustrated on Table 5.1 which includes asociated t-statistics in parenthesis. TABLE 5.1: MULTI-DUMY INTERVENTION MODEL REGRESSION RESULTS BANKING INSTITUTION BAILOUT EFFECT (? 3 ) GBLA EFFECT (? 4 ) CRA EFFECT (? 5 ) 9/11 EFFECT (? 6 ) Bank of America 1 -0.20147694* (-4.925) -0.05418105 (-1.938) 0.02623079 (1.396) 0.07855831* (2.602) Citigroup -0.21797384* (-4.687) 0.03432627 (1.477) 0.01578846 (0.906) -0.02210562 (-1.005) JP Morgan Chase 0.00157341 (0.097) -0.03362359 (-1.638) 0.03129882 (1.955) -0.00174601 (-0.092) Wels Fargo 1 -0.02245859 (-1.443) -0.00315467 (-0.154) -0.01662031 (-1.135) 0.04316454 (1.861) Morgan Stanley -0.02904106 (-1.178) 0.02913847 (1.25) -0.00905399 (-0.432) -0.02523601 (-1.28) PNC Financial -0.01978283 (-1.396) 0.0075218 (0.415) -0.00555585 (-0.424) 0.00385498 (0.218) US Bancorp -0.02713483 (-1.765) -0.06199001* (-2.358) 0.02224565 (1.395) 0.05866792* (2.494) Suntrust 2 -0.13656965* (-4.231) -0.03149289 (-1.33) 0.03098092 (1.712) 0.02371172 (1.07) Capital One Financial Corp. -0.04568248 (-1.874) 0.03095891 (1.108) 0.02260027 (0.751) Regions Financial 1 -0.11473504* (-2.793) -0.02008115 (-0.816) 0.01723202 (0.873) 0.00183969 (0.08) 52 TABLE 5.1 (Continued): MULTI-DUMY INTERVENTION MODEL REGRESSION RESULTS BANKING INSTITUTION BAILOUT EFFECT (? 3 ) GBLA EFFECT (? 4 ) CRA EFFECT (? 5 ) 9/11 EFFECT (? 6 ) Fifth Third Bancorp -0.03333175 (-0.977) 0.0196031 (0.696) 0.00111906 (0.053) -0.03488936 (-1.303) BB&T -0.0481056* (-2.811) -0.00802152 (-0.38) 0.0052457 (0.352) 0.02376213 (1.104) Bank of New York Melon -0.03213285* (-2.125) 0.01744933 (0.923) 0.00381071 (0.267) -0.0170677 (-0.945) KeyCorp 1 -0.09444555* (-2.828) -0.02011577 (-0.877) 0.01822747 (1.072) 0.01110335 (0.508) State Street -0.02875576 (-1.889) 0.03961966* (2.095) -0.03110665 (-2.008) 0.00918313 (0.456) Synovus Financial 1 -0.18181173* (-4.32) 0.02035745 (0.837) 0.02181231 (1.134) -0.02240914 (-0.953) M&T Bank Corporation -0.02725589 (-1.765) 0.02264463 (1.118) -0.02420859 (-1.489) 0.02226477 (0.819) TCF Financial Corporation -0.03849613 (-1.885) 0.03790742 (1.485) -0.01289238 (-0.715) -0.01719113 (-0.657) Central Pacific Financial 1 -0.29902445* (-5.779) 0.03221628 (1.079) -0.0071703 (-0.323) 0.03982539 (1.255) 53 TABLE 5.1 (Continued): MULTI-DUMMY INTERVENTION MODEL REGRESSION RESULTS BANKING INSTITUTION BAILOUT EFFECT (? 3 ) GBLA EFFECT (? 4 ) CRA EFFECT (? 5 ) 9/11 EFFECT (? 6 ) Auburn Bank -0.00853315 (-0.552) -0.02267152 (-1.048) 0.05650561* (2.221) BancFirst Corporation -0.01776441 (-1.043) 0.01239081 (0.547) -0.02479669 (-1.621) 0.0321798 (1.172) BancorpSouth Incorporated -0.04580858* (-3.113) -0.01232715 (-0.6) -0.00095103 (-0.071) 0.02982157 (1.392) Bank of Hawai 1 -0.01446675 (-1.027) -0.00743808 (-0.353) -0.02157511 (-1.545) 0.05618853 (1.95) Community Bank System -0.00765655 (-0.467) -0.00534304 (-0.233) -0.01420269 (-0.96) 0.03705651 (1.497) * Statistically significant coeficient 1 As in the earlier single dumy regresion, this bank?s share price data must and can be differenced to achieve a white noise proces on the associated bank?s PROCES RESIDUAL 2 Could not achieve a white noise proces on the PROCES RESIDUAL through differencing As indicated by the results of this multi-dummy regresion, the previous observation that the bailout caused a systematic decrease in stock prices of U.S. banks holds. As wel as substantiating earlier claims, this new regresion actualy yields even beter results. We can se that the model now suggests 10 (instead of 9) out of 24 banks received a significant drop in share prices due to the bailout. Furthermore, every single BAILOUT DUMY COEFFICIENT for every bank is negatively signed. Thus, we stil fel quite confident that the capital injections to U.S. banks put downward presure on U.S. banking share prices as this multi-dummy analysis has reinforced those beliefs. 54 VI. CONCLUSION 6.1 The Effect of Government Sponsored Capital Injections on Share Prices The results from this intervention analysis sem to strongly suggest that the U.S. government?s injection of masive amounts of capital into U.S. banking institutions through the Capital Purchase Program as wel as the Targeted Investment Program caused an imediate drop in the stock prices of the U.S. banking industry and that traces of this shock wil be found in the share prices of U.S. banks for a long time. The negative shock to share prices sems to have been an industry wide occurrence that afected banks of al sizes, regardles of how much bailout money was received by that institution. However, it does sem to be the case that the stock prices of the larger banks (who typicaly received more bailout capital) look like they wil recover from this bailout shock somewhat faster than smaler banking institutions (who typicaly received les bailout capital). As mentioned earlier, this makes sense because of the structure of these diferent types of banks as wel as the difering roles they play in the U.S. banking market. Although these masive capital injections did sem to cause a drop in stock prices for these banks, it is important to remember that some of these banks may have gone the route that many other financial institutions did at the time and failed without this capital injection. Whether or not the government should have alowed these banks to fail or not is up for much debate. However, we sem to have a beter understanding of what happened in relation to banking share prices as a result of the bailout. Although this is just one aspect of the bailout which we have examined, our results can help serve as a piece to the puzzle of understanding the efect that the Capital Purchase Program and the Targeted Investment Program had on the U.S. economy as a whole. 55 6.2 Extensions of the Intervention Analysis Results Though this model only deals with the stock prices of U.S. banking institutions which is only one aspect of the U.S. economy as a whole, we may be able to make some inferences about the economy in its entirety based on the results as wel as the conclusions we have drawn from this thesis. By granting the following premises, it sems plausible that we can make inferences on the state of the economy as a whole by drawing from the results outlined in this thesis. First, this model suggests that the stock prices of U.S. banks took a hit around October 2008 when al these capital injections began and that the banks are recovering from this extremely slowly. Second, it may be reasonable to asume that the share price of a bank is an indication of how it is performing based on the fact that the market is eficiently valuating these banks individualy. Last, it is also natural to acept the general notion that the performance of the banking industry plays an integral and fundamental role in the health of an economy as a whole. Thus, it is plausible that the evidence uncovered through this intervention analysis may shed some light on a timetable for the recovery of the U.S. economy as a whole when holding al other exogenous influences constant. This may sem like a conclusion that is reaching for validity, but it is definitely something worth considering. If we go by the recovery rates previously mentioned in this model, it sems the average timetable for al banks is a litle les than 11 years. However, the larger banks have a mean recovery period of about 8 years. This would put share prices of these banks recovering around the years 2016-2019 ceteris paribus. We asume that at this later point in time, the share prices have recovered because the banks are being perceived as les risky, healthy, and more stable. At this point the prosperity of the banking industry may 56 reflect or influence the state of the U.S. economy and financial markets as a whole in a positive manner. If we are asuming the positive perception of the banking industry by the market is a fundamental catalyst for growth in al sectors of the market, then we must acount for a period in which the prosperity of the banking industry translates into economic growth through the entire economy. How long it would take for one to efect the other is a mater of debate and beyond the scope of this paper but even if this time frame was relatively short, we would stil be looking at a long recovery period for the U.S. economy. However, recal that we earlier stated that a change in the market or shift in the behavior of larger banking institutions (such as the un-freezing of credit) could lead to a faster recovery. A faster recovery by the larger banking firms is then followed by a swifter recovery by the smal U.S. banks. This could possibly render or produce a faster return to prosperity for the U.S. economy. There is much hope that something of this nature wil occur sooner rather than later. Nonetheles, if the decay periods of U.S. banking equity prices as portrayed in this intervention model serve as any indication to the recovery speed of the U.S. economy from the recent financial downturn, it appears that it may take a few years at best before we se a progresing banking industry intertwined with a positively functioning U.S. economy. 57 REFRENCES Box, G. E. P. and Tiao, G. C. (1975). Intervention Analysis with Applications to Economic and Environmental Problems. Journal of American Statistical Asociation. 70(349):70-79. Enders, W. (1995). Applied Econometric Time Series. John Wiley & Sons, New York, NY. Greene, W.H. (2008). Econometric Analysis (6 th Ed.). Pearson-Prentice Hal, Upper Saddle River, NJ. Hamilton, J.D. (1994). Time Series Analysis. Princeton University Pres, Princeton, NJ. National Information Center. (2011). A Repository of Financial Data and Institution Characteristics Collected by the Federal Reserve System. http:/ww.ffiec.gov/nicpubweb/nicweb/NicHome.aspx. Acesed on 8/27/2011. Pro Publica Inc. (2011). Eye on the Bailout. http:/ww.propublica.org/ion/bailout. Acesed on 8/27/2011. Skinner, S.J. (2006). Estimating the Real Efects of Blockbuster Art Exhibits: A Time Series Approach. Journal of Cultural Economics 30(2):109-125. Yahoo Finance. (2011). Historical Prices. http:/finance.yahoo.com. Acesed on 8/27/2011. 58 APENDIX I Individual Filtered LN Bank Share Price Ilustrations (A1.1) 59 60 61 62 63 64 65 66 67 68 69 70 Apendix II Differencing of the Neded Filtered Bank Share Price Variables After running the regresion from equation 3.9, most of the PROCESS RESIDUALS from the individual banks analyzed reveals a white noise proces (i.e. Box- Pierce and Box-Ljung Q-Statistics significance levels greater than .05). This is because we correctly modeled the time series proces as an AR(1) proces. However, the FILTERED BANK SHARE PRICE variable for Wels Fargo, Regions Financial, Synovus Financial Corporation, Central Pacific Financial, and Bank of Hawai must be diferenced in order to find white noise on the PROCESS RESIDUALS of these banks. The first step in this proces is creating a diferenced variable by lagging the necesary filtered variables for each of the needed banks by one period. This variable is formulated in the following manner: (A2.1) DIFFERENCED BANK SHARE PRICE = FILTERED BANK SHARE PRICE t - FILTERED BANK SHARE PRICE t-1 As you can se, this new variable is the FILTERED BANK SHARE PRICE lagged by one period. Using this new variable, the DIFFERENCED BANK SHARE PRICE, we can run the same intervention model regresion from equation 3.9 only this time we wil diference the DIFFERENCED BANK SHARE PRICE variable by the appropriate number of periods instead of just one period: 71 (A2.2) DIFFERENCED BANK SHARE PRICE t = ? 1 (ONE) + ? 2 (DIFFERENCED BANK SHARE PRICE) t-n + ? 3 (BAILOUT DUMY) t + ? t where n denotes the desired number of lags As we can se, the time series wil take on the shape on an ARI(1,N) proces instead of the previously asumed AR(1) proces where N represents the number of periods that the time series is diferenced. As mentioned in section 4.2, Wels Fargo, Regions Financial, Synovus Financial Corporation, Central Pacific Financial, and Bank of Hawai can be 4 th , 5 th , 3 rd , 2 nd , and 3 rd diferenced, respectively, to produce a white noise proces with regards to identifying the PROCESS RESIDUAL. Table A2.1 shows the results from executing this diferenced regresion on these banks. TABLE A2.1: DIFERENCED INTERVENTION MODEL REGRESSION RESULTS BANKING INSTITUTION ESTIMATED TIME SERIES PROCESS DECAY RATE (? 2 ) STOCK PRICE RESULT (? 3 ) BOX-PIERCE / BOX-LJUNG Q-STAT SIGNIFICANCE Wels Fargo ARI(1,4) -.22345474* (-3.691) -.02253673 (-1.645) .2774 / .2162 Regions Financial Corp. ARI(1,5) .154414* (2.391) -.02699863* (-1.598) ..0607 / .0363 Synovus Financial Corporation ARI(1,3) -.16394939* (-2.673) -.07044727* (-4.019) .1512/ .0879 Central Pacific Financial ARI(1,2) -.24218875* (-4.015) -.116418* (-5.295) .1804 / .1249 Bank of Hawai ARI(1,3) -.18589595* (-3.052) -.01763083 (-1.434) .3799/ .2902 * Statisticaly significant We can se that the results ilustrated in Table A2.1 are not that diferent from the results of the earlier non-diferenced model. 72 Apendix II The Bank Specific Bailout Dummy Intervention Analysis Model As evidenced in Table 4.1, some of the BAILOUT DUMY COEFFICIENTS on some of the bank analyzed are not significant. We can also se from the capital injection schedule on Table 3.1 that some U.S. banking institutions received funds at diferent times. We need to make sure that the reason why some of the BAILOUT DUMY COEFFICIENTS resulting from our model are not significant is not because the individual bailouts of these banks occurred at a diferent time. Throughout this thesis, we have analyzed what the general efect that the initiation of the bailout had on U.S. banking share prices as a whole. Therefore, the BAILOUT DUMY variable we earlier created was designed to represent this intervention in the general case for al banking institutions included in the model. Now, we wil test to se if any banks whose BAILOUT DUMY COEFFICIENT was not significant in the original model become significant when we tailor the BAILOUT DUMY variable to the specific bailout timeframe of these corresponding banks. To do this, we must first create new BAILOUT DUMMY variables for each banking institution included in this extension. We wil cal these new dummy variables the BANK SPECIFIC BAILOUT DUMY. The BANK SPECIFIC BAILOUT DUMY wil contain 0?s before the bailout and 1?s after the bailout of the individual bank currently being analyzed in the model. Equation A2.3 shows this new intervention analysis regresion equation. 73 (A2.3) FILTERED BANK SHARE PRICE i,t = ? 1 (ONE) + ? 2 (FILTERED BANK SHARE PRICE) t-1 + ? 3 (BANK SPECIFIC BAILOUT DUMY) i,t + ? t where i denotes the banking institution; where t denotes the time period The results from this regresion are detailed in table A2.2. TABLE A2.2: BANK SPECIFIC DUMY INTERVENTION MODEL REGRESSION RESULTS BANKING INSTITUTION DECAY RATE (? 2 ) STOCK PRICE RESULT (? 3 ) BOX-PIERCE / BOX-LJUNG Q-STAT SIGNIFICANCE U.S. Bancorp .94172101* (45.378) -.01610425 (-1.165) .2049 / .1507 Capital One .94145065* (39.927) -.01994538 (-.958) .1263 / .0695 TCF Financial .97073546* (62.549) -.03304947 (-1.882) .9781/ .9674 M&T Bancorp -.97118443* (62.67) -.00631959 (-.446) .4372 / .3437 PNC Financial .90850306* (34.995) -.01019394 (-.781) .656/ .5695 Fifth Third Bancorp .97183422* (54.975) -.03005401 (-1.162) .1447/ .1083 * Statisticaly significant We can se that adding this BANK SPECIFIC BAILOUT DUMY did not significantly change our results from the original model.