The Effects of Issuing Subordinated Debt on the Banking Industry

The Effects of Issuing Subordinated Debt on the Banking Industry Justin Svec Honors Thesis Advisor: Susan Athey Economics Advisor: Edward Vytlacil May 13, 2003 Department of Economics Stanford University Abstract: Using both a theoretical and empirical model, this paper examines the relationship between subordinated debt and risk in the banking industry. Analyzing quarterly data from March 1997 to December 2000, I use asset variance as a proxy for bank risk. I discover that the beta on subordinated debt is negative and insignificant. Therefore, my empirical work suggests the potential presence of market discipline. Government risk measures, the size of the bank, and its operating income are other measures that are highly correlated to asset variance. Acknowledgments: I would like to thank Professor Susan Athey for her commitment to helping me. Without her, this thesis would not have been completed. I would also like to thank Professor Geoffrey Rothwell for his dedication to my project. 1. Introduction: The banking industry is one of the most regulated industries in the United States. The government, in its effort to ensure financial stability, creates both beneficial and harmful incentives for banks. To correct for the negative incentives, supervisors monitor both the asset and liability side of a bank’s balance sheet. Loans are heavily scrutinized for their potential of spiraling out of control as a depository institution becomes unhealthy. Emergency funds are provided by the Federal Reserve’s Discount Window. Rather than being an industry guided by the invisible hand of the market, the banking industry is enticed and goaded into good behavior by the government. There are many reasons for the intense government regulation of banks. First, and most important, the failure of one bank can accelerate the failure of other banks. This contagion can spread throughout the industry, causing a bank panic. With the ensuing disruption of the financial system, the whole economy would feel the disastrous repercussions. Therefore, regulation ensures the stability of our financial system. Second, the government regulates the banking industry in order to correct for the riskinducing incentives imposed by bank regulators. In trying to save investors from the full impact of the contagion effect, the government provides a safety net. This net induces banks to take on additional risk through both moral hazard and adverse selection1 . Third, the government could think that, although the market is able to constrain the behavior of non-bank firms, the market is not able to limit the amount of risk a bank undertakes. Thus, the government must step in to restrain the risk banks undertake. 1 Moral hazard arises because banks can take on a higher level of risk, knowing that their depositors are protected by the government’s safety net. Adverse selection arises because risky entrepreneurs would enter the banking industry because they understand that they would be able to increase bank risk since a safety net protects them. 2 Why would the government think that the market is incapable of regulating the behavior of banks? Morgan (1997) analyzed this question. He explains that, among other reasons, the opacity of banks clouds the market’s perception. This blurred perception leads to financial crisis. Depositors understand that their deposits are actually loans to the bank. They understand that the bank, in turn, loans out this money to others for a profit. However, the risk levels of these loans remain unclear to investors. Investors do not know the borrower of the loans, nor do they know the project for which the loans were made. This lack of perfect information exposes the entire financial system to systemic risk. Bank runs and contagion could turn a small insolvency problem into a banking crisis that threatens the health of the whole economy. If investors could measure risk accurately, then regulation would be unnecessary. Investors would then judge each bank for its own risk level and so withdraw their money only from those banks that are unhealthy. Thus, bank runs would not occur. However, because investors find it difficult to monitor banks effectively, contagion is possible. Thus, the underlying reason the government must regulate the banking industry is that perfect information does not exist. The difficulty of monitoring banks is compounded by the problem that private investors do not have the incentive to calculate a bank’s risk level. Government insurance dulls the motivation of depositors to examine the risk undertaken by banks. Regardless of the behavior of the bank, depositors know that the Federal government will refund up to $100,000 of their money in times of crisis. Therefore, they do not have the incentive to actively monitor bank risk. In response, the bank assumes a higher level of risk than is socially beneficial because it knows that private depositors are insured. Consequently, with the system of incentives in place today, the market does not attempt 3 to control a bank’s risk level. The fact that the market cannot (due to opacity) and will not (due to the incentive problem) monitor the banking industry creates the need for government regulation. The government must ensure that banks do not take on excessive risk at the cost of taxpayers. Yet, government regulators are having difficulty in correctly assessing a bank’s risk level. Forcing the government alone to be responsible for managing the risk of banks assumes that the government can correctly asses a bank’s risk level. This ability to regulate banks requires 1.) an accurate assessment of bank health by regulators and 2.) the ability to exert influence over the bank’s management. If either of these conditions is not met, then regulation is impractical. For example, if the government cannot correctly measure the risk level of a bank, then it cannot make informed decisions about the bank’s future. This risk assessment is not easy or costless. In fact, it requires expensive monitoring for regulators to even make vague approximations about the health of a bank. The second prerequisite is just as important as the first. Assuming that the government can monitor banks effectively, regulation also requires that the regulators are able to affect the decisions of bank managers. There must be a feedback mechanism that allows regulators to influence the actions of the bank. Recently, the ability of the government to meet these necessary conditions has been questioned. As banks are becoming more complex2 , regulators are having increasing trouble in effectively monitoring the actions of banks. American banks have extended both the scope of their products and the size of their market. As recent amendments to the law allow banks to expand into many new products, banks are quickly 2 The Riegle-Neal Interstate Banking and Branching and Efficiency Act of 1994 and the Gramm-LeachBliley Financial Services Modernization Act of 1999 increased the size and scope of bank activities. 4 expanding into high growth markets. As Portfolio Theory suggests, these high growth markets are very risky. Depository institutions have overwhelmingly crossed into the realm of both securities and insurance firms. Also, they now offer these products to more people, as they have stretched into international markets. This fact has been recognized in a recent study by the Federal Reserve Board and the Treasury, “The erosion of legal and regulatory barriers has permitted depository institutions and their holding companies to expand the scope of their activities” (Board and Treasury 13). The expansion has made it almost impossible for regulators alone to monitor accurately the risk levels of banks. The increased difficulty of monitoring leads regulators to suggest other methods of obtaining information on banks. However, as discussed earlier, neither the market nor the government alone can control the risk levels of banks. What, then, can help monitor and constrain banks? Within the last few years, the government is turning towards the market for assistance. The combination of both market intervention and government regulation, it is hoped, will restrain the risky behavior of banks. This proposal, on first glance, seems perplexing. The government and the market, in principle, have access to the same information. If anything, the government could obtain better information than the market because it could force banks to disclose key information. Therefore, the market seemingly could not provide any better regulation than the government. However, even though the market does not have more information than the government, the market is still valuable in monitoring the banking industry. This is because, in some situations, the private markets might either have higher-powered incentives or greater expertise than regulators. Another possible benefit of having the 5 market monitor risk is that bank contagion is partially a function of market confidence. Therefore, the addition of the market will allow for a better determination of risk levels because the market can judge its own confidence. Knowing that the market does not presently have the incentive to monitor the actions of banks, regulators hope to modify the system of incentives so that it aligns the objectives of the market with those of the government. These new incentives would encourage the market to help the government constrain the amount of risk a bank undertakes. Regulators would achieve this by creating a class of investors who are held responsible monetarily if the bank fails. This potential for loss would give investors the incentive to monitor the risk levels of banks. With this information, the market would then discipline banks when they become excessively risky. This idea is known as market discipline. One proposal that is widely discussed among both policymakers and economists for encouraging market discipline is to force banks to issue subordinated debt. This policy would mandate that banks issue a specified percentage of their assets as subordinated debt. The Federal Reserve Board and Treasury report (2000) on subordinated debt goes on to say that “The Board and the Secretary believe that existing evidence supports efforts to use subordinated debt as a way to encourage market discipline” (6). The defining characteristic of subordinated debt is that it is unsecured by the government. This means that if a bank becomes insolvent, the subordinated debt holders will lose their investment. The government will not refund the initial investments of the 6 unsecured debt holders, like they do with most types of debt. In the order of repayment during insolvency, subordinated debt claimants are just above shareholders3 . Because subordinated debt is unsecured by the government, investors demand a premium on this debt to compensate for the greater downside risk. This premium is reflected by the yield spread, which is the difference between the yield to maturity of a subordinated debt bond and a risk free government bond of similar maturity. This yield spread contains more information than just the default risk of the bank. The spread also contains the liquidity and credit risk. Thus, the yield spread reflects all public information about a bank. If this were not the case, arbitrage would occur. For example, investors who realize that the return on an unsecured bond was higher than the risk level would suggest, would invest heavily in this bond. This increased demand would raise the price of the bond which lowers its yield to maturity. The yield to maturity falls until the risk / return ratio is in equilibrium again. Thus, the yield spread fully incorporates the market’s knowledge about the bank’s risk level. It is important that the yield spread reflects the public’s full knowledge because the government can then use this spread to aid in their regulation of the banking industry. To give an example of the sizes of the yield spread, banks that issued subordinated debt in 1990 had spreads from 0.92% to 32.53%. This means that some banks were so risk free that they could obtain funds at similar rates to the national government. Other banks were so risky that investors demanded extraordinarily high rates to loan the banks money. 3 Shareholders, like investors who hold subordinated debt, are not protected by the government. However, shareholders do not have the incentive to regulate the risk banks take. This is because, as I will show later in the paper, shareholders have the incentive to increase the risk of banks. 7 To align the incentives of the market and the government, many economists have proposed a mandatory subordinated debt policy. This policy has many advantages. Most importantly, it creates a well-informed group of investors who privately monitor the risks taken by banks. Potential investors realize that subordinated debt is unsecured by the government. The fear of losing their investment due to excessive risk-taking by the bank gives these investors the incentive to monitor the bank. They would guard their investment to ensure that their money is safe. One caveat of this is that the mandatory subordinated debt policy does not create the highest powered incentives. Some investors would free-ride upon the actions of others. Those who invest less will follow the behavior of those have invest more without assuming the costs of monitoring. Regardless of this qualification, though, the subordinated debt policy will create a group of investors who will actively scrutinize the banking industry. A result of this monitoring is that potential investors would affect the yield spread of the subordinated debt. If a potential investor learns that the bank is increasing its risk (possibly by learning that the bank is expanding into securities underwriting, insurance, or real estate), the investor would demand a higher rate of return on the bond to compensate for the higher uncertainty. Therefore, the yield spread would be sensitive to the changing risk level of a bank. This has two effects. First, it constrains the actions of the bank because the managers realize that for every increase in risk, their cost of funds also increases. As we assume that banks try to minimize their cost of funds, managers have the incentive to maintain acceptable levels of risk. This eases the job for the regulators because the bank helps to regulate its own uncertainty. Second, because the yield spread changes due to variations in the risk levels of banks, government regulators can use the spreads as an 8 indicator of the bank’s health. If yield spreads are relatively high, then the regulators would be warned that the bank is taking on increasing risk. This could be a sign of an unsound bank. Thus, the changing premiums on subordinated debt could lead regulators to discipline banks. The premium, however, does not need to act as a trigger for regulation: if the yield spread reaches a pre-determined level, supervisors must act. Instead, the proposed policy offers the premium as yet another indicator of bank health. Supervisors still retain the flexibility to discipline banks even if yield spreads are high. This discretion would serve to insulate banks after shocks that are unrelated to the banks’ health. For example, even though the yield spread on subordinated debt increased sharply after September 11th , 2001, the government could choose not to discipline banks. As regulation was not the optimal response to the shock, it is best not to have the spread act as a trigger. The subordinated debt policy, therefore, allows the regulators some discretion to react to unique conditions. Another advantage of mandating banks to issue subordinated debt is that it would improve the transparency of the banking industry. Banks that take on a relatively low amount of risk would seek to take advantage of this situation by obtaining funds cheaply. To do this, these banks would disclose their low level of risk to the public. They would not want investors to misinterpret their risk levels and so charge them higher rates for funding than the banks deserve. Therefore, low risk banks would advertise their low levels of uncertainty to obtain low cost funds from subordinated debt. Banks that take on a relatively high amount of risk would initially think that it is in their best interest to remain vague about their risk levels. However, the public would quickly learn that the 9 banks that remain vague in their disclosures take on highly risky projects. Similar to the lemons problem, this would lead investors to demand abnormally high returns for investing in these banks. Therefore, even the risky banks would want to become more transparent in order to limit the cost of their funds. A third advantage of having a mandatory subordinated debt policy is that the market can react much more quickly to additional information about a bank than government regulators can. This implies that during volatile times, the market can regulate banks’ decisions more accurately than regulators. The government supervisors would have to go through layers of bureaucracy before making a decision, while the additional information would immediately be reflected in the market-determined yield spread. During times of crisis, there is an incentive for bank regulators to forbear closing insolvent depository institutions. Closing a bank would mean that the regulators did not catch and correct a problem at an early enough stage. Because this would reflect poorly on the regulators, they would rather wait out the financial crisis in case the bank miraculously becomes solvent once again. Mandating subordinated debt helps to limit forbearance by creating a class of investors who are owed money, not by the government, but by the bank. This group of investors would like to limit their loss by resolving the bank quickly and so possibly get back some of their money. The longer the insolvent bank remains open, the smaller chance that subordinated debt holders will get their money back. Therefore, these investors would encourage the regulators to close the bank promptly. This additional prompting from investors would decrease the likelihood of forbearance. 10 One last advantage of a subordinated debt policy is that the unsecured debt would act as a cushion for the Federal Deposit Insurance Corporation. If a bank that has no subordinated debt fails, then the FDIC must assume responsibility for all the losses accrued by debt holders. However, if the bank had issued subordinated debt, then the FDIC would not need to pay back this group of investors. This is because subordinated debt holders are only paid back after the deposit insurer has been fully compensated for its losses. The FDIC would consequently be spared from using some of its resources. A mandatory subordinated debt policy is not a panacea for the entire banking industry, though. This is because the policy is not feasible for every bank. The policy would only be applicable to large banks. Small banks cannot maintain a liquid secondary market for their subordinated debt, so the risk premium would not provide an accurate, timely depiction of the bank’s risk level. The importance of a liquid secondary market is seen in which banks voluntarily hold subordinated debt. In 1990, 45 out of the 50 largest US banks held subordinated debt, while only 61 out of 8,159 small banks held subordinated debt. Thus, because large banks voluntarily hold unsecured debt, the policy can be applied to them without trouble. For my analysis, I plan on examining the relationship between the amount of subordinated debt a bank issues and the risk levels of that bank. This information is crucial for the Federal Reserve to know before it implements the mandatory subordinated debt policy because it affects the optimal amount of subordinated debt a bank should be forced to issue. I further analyze which variables have an impact on bank asset variance. Theoretically, subordinated debt could both increase and decrease bank risk. Since the cost of issuing unsecured debt is higher than issuing other forms of debt, banks 11 must enter more risky projects to repay these costly liabilities. This leads the bank to raise its level of risk. Conversely, for the reasons mentioned earlier, subordinated debt would decrease the level of risk a bank would undertake. Thus, the goal of my study is to analyze the effects of subordinated debt on the bank’s risk level. 12 Literature Review: Research on this topic has generally focused on whether subordinated debt encourages market discipline. If market discipline occurs, then the relationship between the risk of banks and the yield on subordinated debt would be positive. As the risk level of a bank increases, potential investors would demand a higher rate of return on the unsecured debt. If economists could prove that the market does discipline banks, then regulators could rely on the market to help control the risk levels of banks. The regulation of the banking industry would no longer be the sole responsibility of the government. Instead, government regulators could rely on the market to provide indicators of when a bank becomes unhealthy. Initial studies on the impact of subordinated debt showed mixed results. Hannan and Hanweck (1988) hypothesized that bank risk is correlated to the yields on unsecured certificates of deposit. To test this hypothesis, they surveyed 300 banks for information on the rates of return on large, unsecured CDs for 5 different maturities. All the data gathered falls within the first quarter of 1985. With this information, they calculated the probability of default for each of these 300 banks. To do this, they assumed that a bank fails when the current losses exhaust all capital. The actual equation they used for the probability of default is p = (1/2) ? 2 [E (p / A) + K / A] 2 . Given each bank’s level of assets, capital, E (p / A), and ?, the authors could calculate the probabilities of default for all 300 banks. This measure, though, was criticized for being inaccurate. Calculating the probability that a bank will fail within a given time can be, at best, a vague estimate. 13 Formally, the authors tested whether the rate of return on the unsecured CDs was positively related to the probability that the bank will default before the subordinated debt matures. Their structural model is shown below. (1+i ) –t = (1- p) t (1 + r f ) –t + [1- (1 - p) t ] (1 - L) (1 + r f ) –t (1) where i is the one-period unsecured CD yield, t is the number of periods until maturity, r f is risk-free rate, p is the probability of default, and L is the expected loss per dollar in case of bank insolvency. Thus, this model shows that the present value of one dollar invested in a CD is equal (given risk neutrality) to the discounted value of that dollar in the two cases of solvency and insolvency at the end of the CD’s maturity. After controlling for the structural characteristics of banks, the two authors found that their measure of the probability of default was positively correlated to the rates of return on the CDs. For four out of the five maturities, the conclusion that increased bank risk leads to higher CD yields was significant at the 5% level. The fifth maturity was significant at the 10% level. Even though these results showed strong support for market discipline, there are many limitations to their analysis. First, as stated earlier, their measure of bank risk is questionable. Calculating the probability that a bank will become insolvent within a period of time is more based on statistical speculation than reality. Second, their study looked at only the first quarter of 1985 for their data. As this time could have been exceptional, their results are not necessarily applicable to other time periods. Third, the authors have simplified their theoretical model by assuming that the unsecured CDs can only be redeemed at maturity. In reality, the CDs can be recalled at any time by accepting a penalty. Last, their estimates have been called into question because they did 14 not successfully isolate the effect of default risk. Liquidity differences were inevitably linked to their yield spreads, and so the results showed the impact of both credit risk and liquidity variations. In spite of the criticisms, this study provides evidence for the existence of market discipline. Avery, Belton, and Goldberg (1988) expand previous results by making a distinction between public and private measures of risk. They find that the risk premium on unsecured debt is “virtually unrelated” to public measures of risk and only weakly correlated to private measures (608). As their public measure of risk, the authors use the FDIC Index of bank risk. As their private measure, they use both Moody’s and Standard and Poor’s risk rating system. (Their study is much closer to my analysis than that of Hannan and Hanweck because these three authors use subordinated debt instead of large, unsecured CDs.) Analyzing the average yield spread on the subordinated debt issued by each of the largest 100 banks, Avery, Belton, and Goldberg test for a correlation between the return and both measures of risk. This study is unique in that it tests whether the government measures bank risk more accurately than the market. In their analysis, they loosen the assumptions of Hannan and Hanweck by allowing the holders of the subordinated debt to recall their investment before maturity. By thinking of subordinated debt as call options with specific exercise prices4 , they are able to make their results more robust than previous studies. After running a two-step modified GLS regression, they find that the risk premiums are weakly correlated to Moody’s and Standard and Poor’s rating systems and robustly negatively correlated to the FDIC Index of bank risk. In fact, the public measures of risk become significant at 4 Subordinated debt has the same payoff function as one held call option with exercise price = DT and one written call option with exercise price = DT + BT 15 the 5% level when the bond goes from A to BC. These are very odd results. One would expect that the rating systems would imply similar correlations. However, the FDIC Index gave the opposite result and the negative correlation was statistically significant. This implies that either market discipline does not occur at all or the Index was very inaccurate. Avery, Belton, and Goldberg gave possible explanations for this unusual result. One of the reasons they cited was that the rating system was based on how regulators viewed the bank. Subordinated debt holders do not necessarily view the risk levels of the bank in the same way that regulators do and so would not think the same characteristics are important. With these results, the authors came to the conclusion that the market did not discipline the banks. Specifically, the authors found that “Risk premiums on bank-related long-term debt are virtually unrelated to traditional accounting measures of bank performance and the index proposed by the FDIC for assessing risk-related insurance premiums. Even more surprisingly, the risk premiums are only weakly related to private-sector bond ratings…Given the range of specifications examined, it seems unlikely that these fundamental conclusions would change with adjustments.” (608) Gorton and Santomero (1990) find no evidence of market discipline in the subordinated debt market. The two economists criticized previous research for being inexact because the other papers did not have a specific, detailed economic model as the base of their research. Instead, Gorton and Santomero believed previous studies used vague models that offered nebulous dependent variables to test. Their analysis, on the other hand, is more theoretically rigorous than previous studies. They apply the BlackScholes (1973) contingent claims valuation model to subordinated debt. This model leads Gorton and Santomero to discover that the yield spread on subordinated debt is a 16 convex function when the value of senior debt is lower than the value of the firm and is concave when the value of senior debt is greater than the value of the firm. Gorton and Santomero first test whether the measures of bank risk used by previous economists (balance sheet ratios) were good proxies for credit risk. The authors find that credit risk is not correlated to balance sheet measures of risk. This implies that previous studies used inaccurate proxies for risk. Their next regression depended on a critical insight inspired by their economic model. Gorton and Santomero regressed the yield spread of subordinated debt issued by banks from 1983 to 1984 on their measure of asset volatility. They found that the balance sheet risk measures and asset volatilities only marginally predict the yield spreads on subordinated debt. Gorton and Santomero conclude, “taken as a whole these results offer little support for the presence of market discipline in the subordinated debt market” (127). Therefore, this paper provides little support for that idea that the actions of the bank are controlled by the pricing of debt by the market. Flannery and Sorescu (1996) discussed the possibility that the earlier mixed results were a product of the “too-big-to-fail” (TBTF) belief. This belief posits that if one of the top banks fails, then the FDIC would bail out all the creditors, including the subordinated debt holders. This allows investors who hold unsecured debt to refrain from monitoring the bank, since they know their investment is safe even in times of crisis. Beginning in 1988, the FDIC made it clear that it would not bail out subordinated debt holders. Then, in 1993, the National Depositor Preference Act was passed. This amendment to the FDIC completely rejected the idea of “too-big-to-fail.” The new policies served, among other things, to make subordinated debt holders aware that they 17 would absorb the losses if a bank fails. Flannery and Sorescu hypothesized that the risk sensitivity on subordinated debt yields would depend on these changing government policies. Flannery and Sorescu collected data from 1983-1991 to test this hypothesis. By studying the change in subordinated debt yield spreads before and after the TBTF belief, they were able to analyze whether the strength of market discipline changed over time. They looked at all fixed rate, nonconvertible subordinated debt yields from 1983-1991. During this period 422 issues from 83 banks fit their criteria. They then subtracted the yield to maturity of a similar maturity Treasury bond, which created their variable for yield spread. To run their regressions, they used a fixed effects panel model with dummy variables for each calendar year and an ordinary least squares regression. They concluded that investors rationally reflect changes in the government’s policy toward the private sector absorbing losses in case of bank failure. Their results indicate “bank investors clearly impounded the value of conjectural government guarantees into debentures prices” (1373). When the implicit government guarantees stopped, then the risk sensitivity of the spread increased. Previous mixed results could therefore be explained because of tacit government protection on unsecured debt. Further, Flannery and Sorescu showed that the market disciplined banks that take on additional risk after the TBTF belief was rejected. Morgan and Stiroh (1999) studied the data on market discipline after the amendments to the FDIC. They extended the analysis of market discipline by testing the strength of the market in controlling the behavior of banks. They questioned whether the 18 market alone is enough to discipline banks. Morgan and Stiroh analyzed the yield spread on 4100 fixed-rate bonds issued by banks between 1993 and 1998. They compared the yield spread on these bonds with the risk rating given by Moody’s or Standard and Poor’s. In their first test, they evaluated whether the market only uses public measures of risk as an indicator of a bank’s overall level of risk. They find that public measures of risk are correlated to the yield spreads of subordinated debt. Further, they analyzed whether market discipline is effective enough alone that it can control a bank’s risk. They find that, even though market discipline is highly effective, it cannot completely regulate the actions of the bank. They cite two reasons for this finding: investors still partially believe in the too-big-to-fail hypothesis and investors cannot accurately determine a bank’s level of risk. Another significant paper on market discipline through subordinated debt is that of Bliss and Flannery (2000). The authors divided the idea of market discipline into two categories. First, the market must be able to evaluate accurately the bank’s level of risk. Second, the market’s assessment must influence managers’ decisions. They indicate that the first category is well studied and supported in the literature. The second category, note Bliss and Flannery, rests upon shaky ground. The authors explain that one possible reason for their finding that managers are not influenced by the market is that the claimants could potentially have differing incentives. Equity holders (equity is also unsecured by the government) often have the incentive to increase growth dramatically at the cost of increased risk. Subordinated debt holders, though, would want to maintain a low level of risk to assure their repayment. 19 In their paper, Bliss and Flannery concentrate on the second assumption: whether the market influences managers’ decisions. Using information from bank holding companies, their analysis shows that if there is market feedback, then it is weak and mixed. Only a few relationships between returns and managerial actions were statistically significant. The parametric models showed that it is possible that the market has influence over managers, but that this influence is unsubstantiated. Covitz, Hancock, and Kwast (2000) expand the work of previous studies to allow more robust conclusions to be drawn from the subordinated debt data. The authors first solve why risk measures are apparently unrelated to yield spreads of subordinated debt before the amendments to the FDIC. Their novel idea is that previous measures of risk can be both understated and overstated when “liquidity premiums on the risk-sensitive managerial decision to issue debt is ignored” (1). Yield spreads are not just a function of the credit risk of a bank but are also determined by the liquidity of the debt. As the liquidity of a bank’s subordinated debt market increases, the yield spread also increases. This is because investors are paying for the ability to buy and sell the debt quickly. Accounting for the liquidity premium, the authors go back and update previous research. They find that both before and after the modifications to the FDIC, risk measures are correlated to yield spreads. Thus, previous research that found that risk is uncorrelated to yield spreads simply failed to account for the liquidity of the subordinated debt markets. This paper goes further, though, by testing Bliss and Flannery’s conclusion. The authors examine whether bank issuance decisions by the largest 50 banks are risk sensitive. They find that the market’s effect on the number of subordinated debt issues depends on the health of the economy. During times of prosperity, market discipline has 20 a smaller effect than during the times of crisis. Market discipline is most potent when the economy is facing a downturn. Thus, Bliss and Flannery’s result occurred because of the years they chose for their dataset. If they would have chosen an earlier dataset, then they would have gotten different results. More generally, though, Covitz, Hancock, and Kwast’s results strengthened the evidence for the second requirement for market discipline. They showed that the market is able to influence the decisions of managers. In addition, they add a nuanced view of market discipline and the impact of subordinated debt on bank risk. No longer does the market react in a similar fashion when banks increase their risk level regardless of the health of the economy. Instead, the impact varies depending on the economic conditions of the nation. Subsequent research by Goyal (2001) tested the market’s ability to assess accurately a bank’s level of risk. Instead of looking at public risk measures of a bank’s bonds, Goyal took a unique approach and studied the number of covenants on a debt contract. The covenants act as a protection for the holder of the debt against bank moral hazard. Fewer covenants imply that the bank can undertake a wider variety of ventures, including more risky projects. Investors understand this and so would demand greater yields on debt with fewer restrictions. Goyal then showed that market discipline does occur because “banks with greater risk taking incentives include more restrictive covenants in their debt contracts” (21). Therefore, banks that are relatively risky are forced to assure the market that they are limiting their level of risk. This evidence of market discipline leads many economists to propose that the government should enact a mandatory subordinated debt policy. This policy would force banks to issue and maintain a specified amount of unsecured debt. The Federal Reserve 21 Board and Treasury (2000) examined whether a mandatory subordinated debt policy would be feasible and useful. In their research, they examined some possible parts of the policy. They suggested that only the largest banks would have to issue subordinated debt. The reason behind this is that the market for small banks is too small to be liquid. They also suggested that the level of debt required would most probably be a specific percentage of total assets. After looking at the potential costs and benefits of these proposals, the Board and Treasury paper concluded that they could not advocate a specific policy at this time because of lack of ancillary evidence. Instead, they suggested that more work be done on this topic. Thus, much of the early work on the topic of subordinated debt focused on whether the market was able to discipline banks. After many papers showed a variety of contradictory results, later research determined that government policies have an effect on how thoroughly investors monitor their investments. The next step in the research was to make the previous conclusions more robust. Studies expanded and qualified the implications drawn earlier. Each paper, though, connected its conclusions to possible options for the Federal Reserve. Many economists are in favor of instituting a mandatory subordinated debt policy, which will generally serve to increase the transparency of banks while reducing the incentive for banks to increase their risk. 22 3. Economic Model: To fully understand the implications of a mandatory subordinated debt policy, an economic model must be created. I quickly realized that modeling subordinated debt is difficult because banks do not necessarily act like most firms. Unlike the typical firm, a bank’s profit function is unclear. Government regulation affects the function, while the variety of the products complicates the equation. To describe how subordinated debt functions in the market, I split up my model into 1.) How individuals view subordinated debt and 2.) How banks view subordinated debt. Each of these models offers significant contributions to the theoretical foundations of my analysis. 3.1 The Individual’s View of Subordinated Debt: This theoretical model is largely taken from Levonian (2001) and Gorton and Santomero (1990). However, I extend their models by adding in the realistic qualification that the holder of debt receives both coupon payments and one final payment. A second addition I make to Gorton and Santomero’s model is that I do not assume that the bank operates until time T, but rather assume the bank must be closed whenever liabilities are less than assets. If the bank is closed, it must liquidate all its assets and pay off its creditors. Lastly, I do not assume continuously compounded interest. The model begins with the hypothesis that there is a bank whose assets are valued at A t by the market. The value of these assets is random. There are three sources of funds for the bank: senior debt, subordinated debt, and equity5 . Senior debt holders will receive coupon payments of D, while subordinated debt holders will receive coupon 5 In this model, I have not included deposits as a source of funds for banks. This is because it complicates the equation and so hides how subordinated debt interacts with senior debt, equity, and the value of assets. 23 payments of C. At time T, the senior debt holders are still owed DT by the bank and subordinated debt holders are owed BT . Thus, the present value of the senior debt is Dt = S T t=1 C t / (1 + r ) t + D T / (1+ r ) T (2) Where T is the total number of periods and r is the interest rate. And the present value of subordinated debt is Bt= S T t=1 C ’ t / (1 + r ) t + B T / (1+ r ) T (3) Lastly, the present value of equity is E t = A t – (D t + B t ) = A t – [S T t=1 C t / (1 + r ) t + D T / (1+ r ) T ] T – [S T t=1 C ’ t / (1 + r ) t + B T / (1+ r ) ] (4) The investors, before investing their money, realize that subordinated debt and equity are risky assets. This is because all the claims against the bank are paid out of its assets, which are randomly valued in this model. At time, t, there are three possibilities for the claimants. If the bank remains solvent, then the bank can pay back both types of debt holders and give the residual to the equity holders. If the value of the assets at time t is less than the total value of the debt and greater than D t , then shareholders get nothing in return. The subordinated debt holders then become the residual claimants. They receive A t – D t . The senior debt holders, therefore, get their full payment, D t . If the value of assets is less than the payment owed to senior debt holders, then neither shareholders nor subordinated debt holders get anything. Senior debt holders, though, get A t . This discussion is summarized in Table 1. 24 Table 1 At >D t +B t Senior Debt Subordinated Debt Equity Dt Bt A t – (D t + B t ) Dt + B t > At > Dt Dt A t – Dt 0 Dt > A t At 0 0 The next part of this economic model was first described by Black and Cox (1976). Their model is an extension on the classic Capital Asset Pricing Model (CAPM). Black and Cox realized that subordinated debt has a similar payoff structure to two call options, one written and one held. To be more exact, subordinated debt is equivalent to one held call option with exercise price equal to DT and one written call option with exercise price equal to DT + BT . 6 The graph of this payoff structure is shown in Figure 1. 6 This is assuming no cost for the options. 25 Figure 1: Payoff Structure of One Written Call Option (Exercise Price = DT + BT ) + One Held Call Option (Exercise Price = DT ) The rest of this theoretical model follows Levonian (2001) without exception. Following the assumptions of the CAPM, this model assumes that the value of this bank’s assets is random and normally distributed. One can then derive the present value of subordinated debt and equity at t = 0. Subordinated Debt: S = A N (z) – D N (z – s) – A N (x) + (B + D) N (x – s), Equity: E = A N (x) – (B + D) N (x – s), (6) (5) where N ( ) is a normal distribution and s is asset volatility. X and z are defined as x = (s / 2) + ( ln (A / (B+D) ) / s ) z = (s / 2) + ( ln (A / (D) ) / s ) (7) (8) 26 Here I follow the standard in the literature when I assume that x and z are equal to the given functions. The amount of disturbance in the functions can vary, but I follow the assumptions of the literature to maintain continuity. At this point, the implications change based on whether market discipline occurs. I will examine both conditions. For the first part of this analysis, I will assume the more stringent condition: market discipline does not occur. This implies that the cost of issuing subordinated debt, B, does not change with different levels of risk. Equity holders, as usual, maximize the value of their shares subject to the risk level. (dE / d?) = (B + D) N’ (x – s ) (9) As equation 9 suggests, equity always increases in value with an increase in bank risk. There is no cost to shareholders for continually increasing risk. This fact is the reason that moral hazard exists. Equity holders, in order to maximize their profits, have the incentive to increase the bank’s asset volatility. Regulators, therefore, want to curb this desire by imposing a cost for increasing risk. However, as market discipline is assumed not to occur, regulators cannot rely on the market to help. Analyzing the validity of the equation, though, shows that the expression has a fault: there is no optimal level of risk. The owners of the bank would always strive to take on more risk because the only term in the equation is positive7 . Therefore, this equation can only be trusted to show part of the true relationship between risk and return. The derivative of the present value of subordinated debt with respect to asset volatility is shown in equation 10. (dS / d?) = D N’ (z – s) – (B + D) N’ (x – s) 7 (10) The reason behind this unintuitive result is that the model assumes that an increase in risk does not affect the costs of the bank. Thus, there are no costs to equity holders to increase risk, while the benefits still remain. 27 With a small change in risk, two distinct effects can be seen in the value of subordinated debt. The main impact of an increase in volatility on junior debt is the increased probability that the bank will default on its claims. The negative term of equation 10 shows this effect: when risk rises, the value of subordinated debt decreases. The positive term, though, signifies that increased asset volatility will make it more likely that the subordinated debt will be paid. This is because the bank will potentially make larger returns with the increased risk. Thus, the price of subordinated debt to potential investors does not change because I have assumed market discipline does not occur. However, the value of subordinated debt to current holders of subordinated debt changes based on variations in bank risk. Overall, it can be shown that the value of subordinated debt falls when risk increases, given that the bank remains solvent. Thus, the basic model shows that shareholders and subordinated debt holders are in conflict about the bank’s ideal level of risk. Equity holders have the incentive to increase the risk of the bank, while subordinated debt holders prefer a decrease in risk. As shareholders choose what level of risk the bank undertakes, subordinated debt holders must protect themselves against the actions of the shareholders. In reality, potential subordinated debt holders will demand different prices on subordinated debt depending on the risk level of the bank. As I have assumed that market discipline does not occur, investors will choose alternate ways of discouraging banks from taking risks. For example, potential investors will force risky banks to add many covenants to the debt contracts. These covenants restrict the amount of risk the bank can undertake. Therefore, when market discipline is assumed not to exist, subordinated debt holders force the banks to limit their risky behavior by signing contracts. 28 This basic model can become more realistic if the assumption is made that the market does discipline the bank. As the literature on subordinated debt has suggested, this is not a very dubious assumption to make. This extended model can show specifically how market discipline works. In our imaginary bank, the value of the subordinated debt at time t, assuming continuously compounding interest, is St = BT e ( - y (T – t) ) , (11) where y is the continuously compounding interest rate yield. Debt holders would like to maintain the value of their subordinated debt, so they would aim to keep St constant. Because debt holders cannot affect the interest rate or the time to maturity, they can only change the final payment, BT . Thus, investors see the level of risk that the bank undertakes and then vary BT to maintain the value of their debt. BT cannot be immediately affected, though. Realistically, BT changes with the following issuance of junior debt. Thus, market discipline works by increasing the bank’s cost of funds. It cannot change its risk level, while maintaining the same cost of funds. A bank will continue to raise its risk level until the cost of additional risk (from an increase in the cost of funds) is greater than the benefit (the extra gain in profits). It is at this point that the bank will be deterred from undertaking any additional risk. 3.2 The Bank’s View of Subordinated Debt: To describe how banks view subordinated debt, I will make many assumptions that are common in the literature. First, banks face the same marginal revenue curve for loans, which will be called RL. This curve is downward sloping because banks exert some market influence on the price of loans. Banks generally have market influence over 29 loans because they sell these loans mainly to local customers. Because the market is local, it is not so competitive and so the bank has the power to vary the price. Second, bank funds are obtained through both insured deposits and uninsured bonds. The marginal cost of deposits slope upward, which I will denote RI. This is because the deposit market is local, and so the bank can influence the price of deposits. At every rate of return, a number of investors would deposit their money at a bank. To obtain more deposits, the bank must increase the interest paid on the demand deposits. The marginal cost curve for uninsured bonds is flat, though. This is because this market is national or international in scope. This makes the market highly competitive. Because the bonds are uninsured, potential investors will demand different rates of return depending on the risk level of the bank. Therefore, risky banks will pay more to sell their bonds than less risky banks, RUH > RUL. RUH is the rate of return (marginal cost) on the bonds of high risk banks, while RUL is the rate of return on the bonds of low risky banks. Initially, banks would prefer to obtain funds through insured deposits because they are cheaper than bonds. However, as more people have deposited money in the bank, the cost rises beyond that of bonds. At this point, the bank would prefer to issue bonds to obtain funds. The equilibrium of this market depends on the risk level of the bank. If the bank assumes low levels of risk, then the equilibrium amount of loans for the bank will be at the intersection of RL and RUL. This is called L*. Therefore, the bank must obtain this amount of funds from insured deposits and uninsured bonds. The equilibrium for deposits occurs at I*, which is the intersection of RUL and RI. The equilibrium for bonds is the remaining amount of funds needed: L* - I*. 30 The amount of loans a risky bank makes in equilibrium is L* - ? L8 , which is the intersection between the marginal revenue and cost of loans. The risky bank obtains I* + ?I worth of deposits, which is the intersection of RUH and RI. The remaining amount of funds needed is filled by unsecured bonds: (L* - ?L) – (I* + ?I). The graph of these curves is shown below in Figure 2. Figure 2: A Bank’s Loaning and funding Decisions The model shows that the risky bank would obtain a larger share of its funds from insured deposits. The average investor, being risk averse, would want his money to be safe so would invest in deposits, which are guaranteed by the national government. The risky bank would obtain a smaller share of its funds through unsecured bonds because their marginal cost is high. This model supports the idea of market discipline. The market charges a premium on the unsecured debt of risky banks which consequently forces the bank to substitute away from unsecured debt. 8 I use ?L to denote that this amount is less than that of less risky banks. 31 Therefore, the structural model shows how the market disciplines banks. Potential subordinated debt holders change their final payment, BT , to reflect changes in bank risk. Banks, seeing that their funds are sensitive to their risk levels, choose optimal amounts of risk to undertake. Risky banks choose to issue less subordinated debt, while less risky banks rely more on subordinated debt. Thus, the market disciplines risky banks into changing both their risk level and their source of funds. 32 4. Research Design: As noted in my literature review, the majority of studies have used the yield spread on subordinated debt issues as data. The sizes of the yield spreads were then used to test whether market discipline occurs. The market is said to discipline banks when public measures of the risk of individual bonds are correlated to the yield spread on that specific bond. Some studies then creatively extend the literature by analyzing different public measures of risk. The number of covenants on debt contracts, for example, was used as a proxy for risk. Each of these studies, though, has limited its analysis to the level of the individual bond. None have looked at the effect of issuing subordinated debt on the bank itself. None have determined whether the amount of subordinated debt issued is correlated to the overall risk level of that bank. In my analysis of subordinated debt, therefore, I examine how subordinated debt impacts the future risk level of the bank. This impact is especially important since the Federal Reserve is considering enacting a law that forces all banks of a certain size to issue a specified amount of subordinated debt. Using a panel data set that includes aggregate data on 74 banks, I will test whether the amount of subordinated debt that a bank issues is correlated with that bank’s future risk level. More specifically, I will run a generalized least squares regression with fixed effects. The use of this method is common in the literature. Using the GLS model is important because it accounts for the heteroskedasticity in the errors that is often present in panel datasets. The fixed effects variant allows for the unobserved heterogeneity that is fixed over time. Idiosyncratic error on the firm level has thus been accounted for in my dataset. The general equation that I will use is shown in Equation 12. 33 Asset Variance it = ß0 + ß1 Balance Sheet Measures it + ß2 Bank Profit Measures it + ß3 Risk Measures it + a i + u it (12) Additionally, I will take the log of each of my variables, so that my results can be interpreted as a percentage change in variance due to a percentage change in an independent variable. There are three possible relationships between subordinated debt and bank risk. If my results show that there is a positive correlation between the two, then this paper would provide evidence against market discipline. This means that when the level of subordinated debt increases, then the bank’s risk level also increases. Just as important, the Federal Reserve will have to make sure that its potential policy of forcing banks to issue subordinated debt will not greatly increase the risk levels of the banking industry. This increased risk could be more detrimental to the banking industry than the positive effects of having the market discipline the industry. My results could also show that there is no correlation between the level of subordinated debt a bank issues and the risk of the bank. This would mean that subordinated debt has no impact on bank risk and so the point of enacting a mandatory policy would be moot. Lastly, my results could determine that the level of subordinated debt at time t is negatively correlated to bank risk. This would signify the presence of market discipline. As this quarter’s subordinated debt increases, then the market will become more involved in the bank’s decisions, constraining the actions of the bank in future quarters. If this were the case, the Federal Reserve would want to mandate that banks hold a large amount of subordinated debt. If increased subordinated debt decreases bank risk, the Federal Reserve would want banks to issue large percentages of subordinated debt. 34 5. Data: The data used for my empirical analysis is derived from the Call Data of the Federal Reserve Bank of Chicago. This quarterly data contains structural and balance sheet information on all banks in the United States. To form my dataset, I gathered 16 quarters of data from banks that hold subordinated debt. This restriction could potentially bias my results because my sample population is no longer random. However, 45 out of the largest 50 commercial banks in the US hold subordinate debt. Consequently, I believe that my results will remain representative of large banks. My dataset includes information on 18 variables collected for 74 banks followed over 16 quarters from March 1997 to December 2000. The data I collected was then deflated by the GDP Deflator. Unless otherwise stated, the figures are measured in the thousands. The variables I chose to include in my dataset are basic balance sheet variables (total assets, total loans, total liabilities, amount of subordinated debt, total equity capital, and demand deposits), variables related to bank profit (operating income and net income), and risk variables (net risk-weighted assets, assets of off-balance sheet assigned to the 0%, 20%, 50%, and 100% risk categories). These variables need explanation to understand the nuances in their definitions. The variable TotAsset is the sum of all asset items for a bank. This must be equal to the variable TotLiab because, by definition, the bank’s assets are equal to the bank’s liabilities. The variable TotLoans is the value of all of a bank’s loans and leases at a given time. The crucial independent variable in this analysis is SubDebt, which includes the amount of outstanding subordinated notes and debentures for each bank. This measure denotes the total amount of unsecured debt that a bank is liable for in the current 35 quarter. It does not take into account the maturity of the debt. This variable also does not take into account the risk level of the bond. TotEq is the amount of common stock a bank issues. In general, banks obtain their funds through equity, subordinated debt, deposits, and other forms of debt. The variable Deposits measures the amount of demand deposits a bank receives through local depositors. The variable NetInc offers my first measure of bank profitability. The variable OpInc offers another measure of the size of the bank. A large bank will have high operating costs because it has expanded into many products and many markets. Because risk is central to my analysis, I have included many government measures of bank risk. The variable NetRisk is the amount of capital that the Federal Reserve requires the bank to have, which is based on its level of risk. The greater the risk level, the more capital the Fed requires the bank to hold. The next four variables, _0risk, _20risk, _50risk, and _100risk, measure the amount of assets assigned to the federally constructed 0%, 20%, 50%, and 100% risk categories. These variables are related to each other. Each measures how many assets on the off-balance sheet are assigned to particular risk categories. The variable _0risk measures the book value of all the assets that the Fed deems to be risk free. This includes claims from central banks. The variable _20risk includes high quality claims from other banks. The variable _50risk measures the value of loans that are supported by collateral. Lastly, the variable _100risk computes all the loans made to corporations. 36 Table 2: Variable Definitions Variable TotAsset TotLoans SubDebt TotEq Deposits OpInc NetInc NetRisk _0risk _20risk _50risk _100risk Interpretation Total Assets Total Loans Subordinated Debentures and Notes Total Equity Issued Total Demand Deposits Operating Income Net Income Required Capital Based on Risk Off-Balance Sheet Claims Against Central Banks9 Off-Balance Sheet Claims Against Banks Off-Balance Sheet Collateralized Loans Off-Balance Sheet Loans to Corporations For my dependent variable, I follow the conventions of Portfolio Theory and use asset variance as my proxy for bank risk. With this measure, I connect my empirical results to economic theory relating to bank risk and subordinated debt. My results can therefore be analyzed to determine whether they fit the predictions of my economic model. The bank’s asset variance will be calculated over one year time periods. The greater the variance per period, the greater the risk level of that bank. This risk measure takes out the mean bank growth rate and uses only the deviations around the mean. As this asset variance is measured once a year, the variable allows the risk tolerance of a 9 Both _0risk and _20risk are guaranteed by the United States government. 37 bank to change on a yearly basis. Depending on the opportunities with which a bank is presented or the management, a bank can become increasingly risk averse or risk tolerant over time. Therefore, I believe my variable serves as a good proxy for bank risk. To match the timing of my dependent variable, I use the yearly mean of each of my independent variables as my data points. Consequently, my regression will test whether the yearly average of an independent variable is correlated to the bank’s asset variance during that year. Before describing my empirical model, I analyze the variables individually and jointly. The results will provide insight on how to best specify the model and to interpret the results. My initial examination of this information looked at the means of the data. The quarterly averages of many independent variables are shown below in Table 3. Table 3: Quarterly Averages Averages over Time: Mar-97 Jun-97 Sep-97 Dec-97 Mar-98 Jun-98 Sep-98 Dec-98 Mar-99 Jun-99 Sep-99 Dec-99 Mar-00 Jun-00 Sep-00 Dec-00 Total Asset (Billions) 19.43 21.18 21.76 22.31 22.66 23.35 23.46 23.55 23.40 23.30 21.89 22.97 24.07 24.62 25.20 26.54 Subordinated Debt (Millions) 361 384 390 418 435 438 448 462 458 460 438 441 454 460 481 504 Total Equity (Billions) 1.46 1.59 1.63 1.65 1.69 1.75 1.79 1.83 1.84 1.84 1.69 1.70 1.80 1.87 1.95 2.02 Deposits (Billions) 1.80 2.02 1.84 2.03 1.95 2.03 1.84 1.91 1.80 1.80 1.54 1.50 1.57 1.60 1.45 1.73 Net Income (Millions) 55.12 11.43 16.89 23.06 57 12.21 17.65 22.02 72.80 12.39 19.25 27.26 87.39 16.10 24.42 33.38 38 This table shows that most of the balance sheet variables in my dataset generally increased over time, even after being deflated. Oddly enough, many of the variables dipped dramatically in late 1999. This is unusual because one would have expected the dip to occur simultaneously with the stock market drop in mid 2000. Only NetInc fell when the stock market dropped. This was expected because the value of the bank’s assets would fall with the market. The change in the dependent variable, asset variance, over time is shown in Figure 3. The mean asset variance peaked in 1999, while the peak of the median of asset variance occurred in 1998. As the economy heated up and the banking industry was given license to expand into new markets, banks rapidly increased their risk levels. As time passed, both the number of profitable ventures decreased and the industry became skeptical about the sustainability of the market success. Banks therefore became more cautious with their funds. This led to a decrease in mean asset variance from 1999-2000 and in median asset variance from 1998-2000. 39 Figure 3 Asset Variance over Time 6E+13 5E+13 Median Asset Variance 1.8E+11 1.6E+11 1.4E+11 Mean Asset Variance 4E+13 3E+13 1.2E+11 1E+11 8E+10 Mean Asset Variance Median Asset Variance 2E+13 1E+13 6E+10 4E+10 2E+10 0 1 2 Time 3 4 0 Because this is such an important variable in my regression, a more detailed look at asset variance would be telling. Table 4 shows the mean, maximum, and minimum of asset variance. Table 4: Mean, Maximum, and Minimum of Asset Variance Asset Variance 1997 1998 1999 2000 Mean 1.46951E+13 4.87E+12 4.81E+13 1.96E+13 Maximum 3.84544E+14 1.29E+14 2.3E+15 8.63E+14 Minimum 18580.54422 3874.249 142952.7 106696.6 The trends over time in both total assets and subordinated debt are shown in Figure 4. Each increased from March 1998 until August 1999. After a one quarter dip, both variables increase in value. The trends in these two variables show remarkable 40 similarity. However, this can be explained because the banks in my dataset have grown over time. Correspondingly, this leads to an increase in most categories of a bank’s balance sheet. Thus, the observed trends in the variables are generally expected when banks grow in size. Figure 4 Average Total Assets and Subordinated Debt Millions Subordinated Debt Billions 28 27 26 25 24 23 22 21 20 19 18 Mar- Jun- Sep-Dec-Mar- Jun- Sep-Dec-Mar- Jun- Sep-Dec98 98 98 98 99 99 99 99 00 00 00 00 Date 350 400 450 500 550 Total Assets Average Total Assets Average Subordinated Debt More interesting, though, is how the percentage of subordinated debt a bank issues changes over time. This would indicate whether banks rely more on subordinated debt as a source of funds when the market is growing. Figure 5 shows this relationship. The graph shows that, when the market was expanding, the percentage of subordinated debt issued increases. During times of prosperity, the market perceives that banks have a smaller likelihood of failure. This implies that the fact that the debt is unsecured by the government would not be a key consideration for investors. Therefore, the market would demand a lower rate of return during prosperous times. Banks, trying to minimize their cost of funds, would increase their use of subordinated debt. Conversely, as the market 41 moved towards the downturn, the percentage of subordinated debt issued fell. This is because during times of crisis, the public would demand high rates of return on the unsecured debt because the risk of bank failure increases. As this would increase the cost of issuance, banks would issue less subordinated debt during times of crisis. Banks therefore relied more on deposits, their traditional source of funds. Figure 5 Average Percentage Subordinated Debt over Time 1.98 Percentage of Subordinated Debt over Total Assets 1.96 1.94 1.92 1.9 1.88 1.86 1.84 1.82 1.8 Jan-98 Jul-98 Feb-99 Aug-99 Date Mar-00 Oct-00 Apr-01 Figure 6 shows how the percentage of common stock issued by banks rises and falls within the 16 quarter time period. 42 Figure 6: How Bank Size Affects Equity Percentage of Total Equity Capital over Assets 9.2 Percentage of Total Equity Capital over Assets 9.15 9.1 9.05 9 8.95 8.9 8.85 8.8 8.75 Jan-98 Jul-98 Feb-99 Aug-99 Date Mar-00 Oct-00 Apr-01 Even though this betrays no overarching pattern, some conclusions can still be drawn. A bank would issue equity when the cost for funds in other areas was too high. In times of crisis, for example, the rate of return demanded by investors to hold subordinated debt is high because the bank has a higher probability of failing. Instead of resorting to this high cost for funds, the bank would instead issue stock during times of economic crisis. This trend is shown in Figure 6 because the percentage of equity a bank issues after the stock market crash. Table 5 shows a more detailed look at the data. 43 Table 5 Variable Observations Mean Standard Deviation Ln (VAsset) Ln (TotAsset) Ln (Loans) Ln (SubDebt) Ln (TotEq) Ln (Deposit) Ln (OpInc) Ln (NetInc) Ln (NetRisk) Ln (_0Risk) Ln (_20Risk) Ln (_50Risk) Ln (_100Risk) 296 296 296 296 296 296 296 296 296 296 296 296 296 23.95168 15.11576 14.62546 10.93954 12.64829 12.73211 12.25417 10.25599 14.85629 12.45112 13.74482 12.74655 14.97158 5.018195 2.233565 2.241138 2.445445 2.223749 2.189473 2.27551 2.306713 2.342467 2.35089 2.112125 2.614373 2.089247 8.262107 9.493984 8.961349 5.920669 7.319912 6.883254 6.883254 4.185732 9.148146 6.604134 7.862977 2.169054 7.46308 35.37096 19.70008 19.27015 15.86005 17.04292 16.96299 16.98298 14.997 19.43344 18.10833 18.14549 17.38692 19.03754 Minimum Maximum 44 Empirical Results: The foundation of this analysis depends on the ability of asset variance to proxy for bank risk. Asset variance seems to be a good choice because it is often used in economic theory to represent risk. However, this does not necessarily imply that it is a good measure. The ideal proxy for bank risk would be the expected variance in assets. This measure, though, would be full of problems because finding the true expected variance is impractical. Consequently, I strove to find a variable that is a good proxy for the government’s measure of bank risk. As the government has much invested in determining true bank risk, their numerous risk measures would be an accurate gauge of bank risk. Therefore, to ensure the validity of asset variance as my dependent variable, I must test whether asset variance is highly correlated to the government’s risk measures. A correlation matrix is shown in Table 6. Table 6 Ln (VAsset) 1 .8984 .7865 .8444 .6670 .8916 Ln (NetRisk) Ln (_0Risk) Ln (_20Risk) Ln (_50Risk) Ln (_100Risk) Ln (VAsset) Ln (NetRisk) Ln (_0Risk) Ln (_20Risk) Ln (_50Risk) Ln (_100Risk) 1 .8500 .9132 .7805 .9884 1 .9905 .7318 .9884 1 .7801 .9001 1 .7777 1 The matrix shows that asset variance is very closely related to all the government measures of bank risk. My dependent variable is correlated to both on-balance sheet risk 45 levels, as measured by ln (NetRisk), and off-balance sheet risk levels, as measured by the other four variables. Thus, this variable captures much of the pertinent information obtained by the government about bank risk. Assuming the government measures are accurate proxies for bank risk, this implies that my dependent variable is a good proxy for bank risk. I have chosen to use asset variance rather than some amalgam of government risk measures because asset variance has the additional benefit of being well integrated into theory. This allows my results to be interpreted through the lens of an economic model. Knowing that asset variance is an accurate representation of bank risk, I can test which variables are correlated to asset variance. The results from the fixed-effects GLS regression are shown in Table 7. The most striking result is how few coefficients are statistically significant. Out of the balance sheet variables, only TotAsset was significant at the 5% level. This surprising result hints at the opaque nature of banks. Investors, trying to calculate the expected asset variance of banks, would look to the balance sheet for their inputs. However, in my analysis, these variables are largely insignificant predictors of bank risk. Investors, just looking at the bank’s balance sheet, would not be able to calculate bank risk accurately. Out of the bank profitability measures, OpInc was the only significant variable, and it was significant only in one of the regressions. The coefficients on the risk variables were different, though. Log (_0risk) and Log (_20risk) were statistically significant in all 3 of the regressions at the 5% level. This result is understandable in that my dependent variable has already been shown to be highly correlated to the government’s measures of bank risk. 46 Table 7: Determinants of Bank Risk – Dependent Variable: Log (Asset Variance) - March 1997- December 2001 Fixed-Effects GLS Regression Variables 1 2 Balance Sheet 3 Risk Variables 4 Profitability Variables 11.22 ** (5.13) -.17 (.45) 5 Balance and Risk -3.62 (7.30) -.43 (.44) 1.13 (1.91) -1.00 (1.92) .40 (.96) .040 (.24) 1.2 *** (.47) -.019 (.21) 6 Balance and Income -6.04 (8.05) -.60 (.48) 5.24 *** (1.73) -1.41 (1.36) -.65 (.94) -.052 (.22) -1.10 (1.05) .053 (.24) 7 Total Constant Log (SubDebt) Log (TotAsset) Log (TotLoans) Log (TotEq) Log (Deposits) Log (OpInc) Log (NetInc) -3.29 (5.65) -.42 (.40) 2.11 *** (.52) -5.18 (6.05) -.35 (.41) 3.57** (1.44) -1.10 (1.29) -.43 (.86) .044 (.19) -.38 (5.15) -.26 (.37) -4.27 (9.46) -.88 * (.52) 3.55 (2.38) -1.10 (2.07) -.089 (1.04) -.066 (.26) -1.95 (1.23) -.11 (.29) Log .73 ** (_0risk) (.29) Log 1.06 *** (_20risk) (.40) Log -.25 (_50risk) (.25) Log .51 (_100risk) (.51) * indicates coefficient is statistically significant at the 10% level ** indicates coefficient is statistically significant at the 5% level *** indicates coefficient is statistically significant at the 1% level .72 ** (.31) .93 ** (.45) -.31 (.28) .50 (.83) .70 ** (.31) .99 ** (.47) -.15 (.30) .39 (.86) 48 After controlling for balance sheet, bank profitability, and risk variables, my results show that there is a negative correlation between subordinated debt and asset variance. The betas, though, on subordinated debt are statistically insignificant in all 7 regressions. The fact that the coefficients on SubDebt are always negative is highly suggestive of the presence of market discipline between March 1997 and December 2001. An increase in the level of subordinated debt issued this quarter is correlated to a decrease in a bank’s asset variance. The market, through its pricing of subordinated debt issues, was able to limit the risk that banks could assume. The coefficient for subordinated debt remains relatively similar across all 7 regressions, ranging from -0.17 to -0.88. This fact suggests that as banks issue 1% more subordinated debt, the bank’s asset variance will decrease by around 0.5%. This is a substantial decrease in asset variance. Thus, by allowing the market to exert some influence over the bank’s cost of funds, the bank becomes more stable. Even though the betas are statistically insignificant and so this analysis cannot conclusively support the presence of market discipline, the results suggest the presence of market discipline. As shown earlier, the literature on subordinated debt has had many conflicting results about whether this unsecured debt induces market discipline. There are many reasons that this analysis cannot conclusively support the idea of market discipline. First, theory suggests that subordinated debt reduces expected bank risk. However, my dependent variable measures observed asset variance. Theory predicts nothing about the relationship between subordinated debt and actual asset variance. This would tend to disrupt any correlation between subordinated debt and bank risk. Second, as Covitz, Hancock, and Kwast (2000) discover, during times of prosperity, market discipline has a 49 smaller impact than during the times of crisis. Conversely, market discipline is most effective when the economy is facing hard times. As my data depicted the information from March 1997 to December 2000, I have chosen a period in which the United States’ economy was unusually successful. This would tend to hide or confuse the true impact of subordinated debt on bank’s asset value. The empirical results show that TotAsset is positively correlated with asset variance. In fact, this relationship is statistically significant at the 5% level whenever government risk measures are not included in the regression. Therefore, as a bank increases its assets, the amount of risk the bank undertakes also increases. This result is reasonable because as the size of the bank increase, the bank can expand into newer products and markets. These areas are often highly risky. Consequently, assets are positively correlated to asset variance. The size of the coefficients on TotAsset is interesting. The statistically significant betas range from 2.11 to 5.24. Thus, if a bank’s assets increase by 1%, its asset variance increases by at least 2%. The impact of assets on asset variance seems unusually large. However, the average amount of assets a bank in my dataset holds is $23 billion. This means a 1% increase in assets would require an asset increase of $230 million. As this is a huge rise, it would necessarily lead to a correspondingly large rise in asset variance. The relationship between asset variance and TotLoans is negative and insignificant in all my regressions. Even though the betas are insignificant, it is suggestive that they are always negative. As the number of loans increases, the bank’s asset variance decreases. One theoretical argument belies the sign of these coefficients. Each of the regressions I run with TotLoans holds constant the deposits of the bank. 50 Therefore, as the inflow remains constant, the number of loans increases. An increase in the bank’s outflow would put pressure on the capital stock of the bank. The bank consequently has a greater chance of becoming insolvent. This would imply that the sign of TotLoans should be positive. A more likely theoretical argument, though, supports the sign on TotLoans. As a bank increases its loans, it diversifies its assets. Diversification leads to a decrease in bank risk, so asset variance should fall. Thus, it is reasonable that the sign on TotLoans is negative. The betas on both TotEq and Deposits are statistically insignificant. The coefficients are never statistically distinct from 0. In fact, the signs on both variables change as the regressions vary. These are surprising results. I expected the betas on both variables would be positive. TotEq should be positively correlated to asset variance because shareholders have the incentive to increase risk. As a larger percentage of ownership of the bank goes to shareholders, the pressure for managers to increase risk becomes greater. This additional pressure would translate into higher asset variance, which would make the beta positive. My economic model suggests that the beta on Deposits should also be positive. As banks become more risky, they rely more on deposits as their source of funds because they are cheaper than issuing bonds. Thus, it is unusual that the betas of both TotEq and Deposits change signs and are insignificant. Again, one reason that could explain this odd result is that my dependent variable reflects observed rather than expected asset variance. My theoretical model suggests relationships only with expected asset variance, and so makes no predictions about actual asset variance. Therefore, unless actual and expected bank risk are highly correlated, the betas do not have to follow the predictions of the economic model. 51 The coefficient on OpInc is significantly positive when regressed on only profitability variables, but becomes negative and insignificant when regressed with any other group of variables. When regressed alone, the coefficient could be positive because it is correlated to assets, an omitted variable. The omitted variable would create an upward bias. When regressed with other variables, operating income becomes negative and insignificant. This is the more expected sign, as there is an opportunity cost for this money. Instead of using these funds as loans, the bank is using the money to run the bank. As the amount devoted to operating income increases, asset variance should decrease because the bank is not putting the money into risky projects. NetInc was left in the regressions with OpInc because it was jointly significant with OpInc at the 5% level. However, the coefficients on NetInc are statistically insignificant in all 3 regressions. Even though this seems like a surprising result, it supports the idea that relationship between risk and return only works in one direction. Portfolio Theory suggests that risk and return are related. As expected risk increases, then the expected return also increases. The converse does not hold, though. More related to this result, Portfolio Theory does not suggest a relationship between observed return and observed risk. Therefore, the result that the beta on NetInc changes signs and is insignificant is reasonable. The risk variables are the most significant in my empirical analysis. _0risk and _20risk are significant at the 5% level in every regression they are included. Jointly, the 4 government measures of risk (_0risk, _20risk, _50risk, and _100risk) were highly significant. In the regression with all groups of variables, the 4 risk measures were jointly significant at the 1% level. The high F-Value bolsters the validity of my analysis. 52 My dependent variable is an accurate gauge of the government’s risk calculations, which we assume approximates true bank risk. Therefore, the regressions remain valid indicators of which variables impact asset variance. The betas of both _0risk and _20risk are positive and significant, whereas the other two coefficients remain insignificant. I did not expect that only _0risk and _20risk would be individually significant. These two variables measure the off-balance sheet loans to central banks and commercial banks, respectively. Intuitively, these two categories do not seem like they would add much variance to a bank’s assets. However, they are both highly significant. In fact, the sizes of the betas remain relatively constant over each regression. If the average bank increased its loans to central banks by 1%, then its asset variance would increase by around 0.7%. Likewise, if the average bank increased its loans to other commercial banks by 1%, its asset variance would increase by nearly 1%. Interestingly, both categories are guaranteed by the United States government. For reasons cited earlier, this guarantee encourages the bank to undertake higher risk levels than are socially optimal. Thus, it is not surprising that the risk levels are so significant in their relation to asset variance. 53 Conclusions: I began this paper knowing very little about the risk-taking behavior of banks. Delving into the literature, I realized that this is not uncommon. Banks, cloaked behind their veil of complexity, have free reign over the risk level of their ventures. Neither the market through lack of incentive nor the government through lack of ability can effectively constrain banks alone. These facts lead policymakers to consider a policy that would align the incentives of the market and the government. The hope is that the combination of governmental and market monitoring can set limitations to bank behavior. Ideally, banks would begin to act more like firms. They would maximize their profits subject to the pricing decisions of investors. Equally important, banks’ profit maximization function would become known to both the regulators and the market. Therefore, a mandatory subordinated debt policy has been offered as a panacea to the many inherent problems within the banking industry. Before this policy could be implemented as the universal remedy for many bank ailments, many long-standing debates had to be solved. The first question was whether the market could effectively discipline banks, given the right system of incentives. After years of empirical studies, many economists have come to the conclusion that the market can both evaluate banks’ risk levels and affect the decisions of bank managers. The regulators can then use the signals offered by the market to help protect against bank runs. The next important line of research that must be explored before policy implementation is to analyze the effect subordinated debt has on the banking industry. This policy could potentially have harmful side effects that cause more damage than it prevents. For example, if issuing this unsecured debt greatly increases the risk of banks, 54 then regulators would have made their job harder, rather than easier. Conversely, the mandatory subordinated debt policy could reduce bank risk. This would lead policymakers to accept and implement the current proposals. My study of subordinated debt focused on this second line of research. Whereas previous research had concentrated on the level of the bond, I extended the literature by studying the impact of subordinated debt on the bank as a whole. Before I could test how subordinated debt affects the banking industry, I had to ensure that my proxy for bank risk was accurate. I did this by testing the similarity between my measure of bank risk and the government’s measure of bank risk. Using a correlation matrix, I saw that my proxy was up to 90% correlated with both on- and off-balance sheet risk. Assuming that the government can measure bank risk reasonably well, my variable became a good approximation of bank risk. As my dependent variable was now legitimate, I obtained aggregate data on banks from March 1997 to December 2000. The goal of this paper was to analyze which variables impacted bank asset variance. My results from a generalized least square model with fixed effects indicate that the total amount of assets a bank holds is positively correlated to that bank’s asset variance. Thus, as a bank grows, its risk level also increases. Other balance sheet variables have the expected sign, but remain insignificant. Bank profitability measures largely remain insignificant, also. The government risk measures, however, are highly correlated to asset variance, which indicates that the government accurately monitors the risk level of banks. _0risk and _20risk are especially significant in their positive correlation to asset variance. 55 The main conclusion from this study is to find the relation between subordinated debt and asset variance. This paper finds that the beta on subordinated debt is negative but insignificant. This is highly suggestive of the presence of market discipline. Issuing subordinated debt would effectively give the market the motivation to monitor and constrain the behavior of banks. Subordinated debt would create a class of investors who have similar incentives to the FDIC. Even though this analysis cannot conclusively support the existence of market discipline, this paper does provide evidence that subordinated debt has the potential to constrain the risk-taking behavior of the banking industry. 56 Bibliography Avery, Robert, Terrence Belton, and Michael Goldberg. "Market Discipline in Regulating Bank Risk: New Evidence from the Capital Markets." Journal of Money, Credit and Banking, 20 (1988): 597-610. Black, Fischer and John Cox. “Valuing Corporate Securities: Some Effects of Bond Indentures.” Journal of Finance 31 (1976): 351-367. Black, Fishcer and Myron Scholes. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973). 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