Banking and Trading. February 18, Abstract. We study the interaction between relationship banking and short-term arm s length -

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1 Banking and Trading Arnoud W.A. Boot University of Amsterdam and CEPR Lev Ratnovski International Monetary Fund February 18, 2012 Abstract We study the interaction between relationship banking and short-term arm s length - nance that we call trading. Relationship banking is not scalable, pro table (with high franchise value), long-term oriented, and relatively not risky. Trading is transactions-based: scalable, with lower margins (capital constrained), short-term, and prone to risk shifting. When a bank engages in trading, it can use its spare capital (the franchise value of traditional banking) to expand the scale of trading. However there are two ine ciencies. A bank may allocate too much capital to trading ex post, compromising the ability to build relationships ex ante. And a bank may use trading for risk-shifting. We argue that nancial innovation made arm s length nance more short-term (i.e. pushed it into the realm of trading) by improving the tradability of previously non-marketable assets. And, nancial development augmented the scalability of trading the size of positions that banks can take. This initially bene ted conglomeration, but beyond some point ine ciencies dominate. The deepening of nancial markets in recent decades has led trading by banks to become increasingly distortive, so that problems in managing and regulating trading by banks will persist for the foreseeable future. The analysis has implications for the desirability of restricting (prohibiting or ring-fencing) banks trading activities. Contact: a.w.a.boot@uva.nl, lratnovski@imf.org. We thank Stijn Claessens, Giovanni Dell Ariccia, Giovanni Favara, George Pennacchi, Joel Shapiro, and participants of the IDEI-TSE conference Risk Management and Financial Markets, Oxford Financial Intermediation Conference, and Swiss Winter Conference on Financial Intermediation, for helpful comments. The views expressed are those of the authors and do not necessarily represent those of the IMF. 1

2 1 Introduction We study the interaction between relationship banking and (private) information extensive arm s length nance that we call trading. Relationship banking involves private information and describes activities based on repeated and long-term interactions with clients. Trading does not rely on repeated interactions, nor does it involve private information. This allows it to be short term in nature as banks can move in and out of it via nancial market transactions, Our de nition of trading thus highlights the absence of private information and the ability to increase and decrease exposure via nancial market transactions. It includes proprietary trading, taking positions in all kinds of debt instruments (e.g. securitized credit), originating standardized loans solely based on hard information (typically mortgages), and in general any other activities that do not rely on relationship-speci c private soft information. Financial innovation, driven in large part by developments in information technology, has pushed arm s length nance into the realm of trading, by improving the tradability of previously nonmarketable assets. Together with the deepening of nancial markets, again an artifact of information technology, this made doing transactions and engaging in trading very prevalent for banks. The interaction between relationship banking and trading is a novel topic and is fundamentally di erent from the distinction between lending and underwriting that was the focus of much existing literature. A key question in that literature was whether a bank s private information about a borrower coming from the lending side compromises (or facilitates) its ability to o er underwriting services for the same borrower (e.g. Puri, 1996). The pros and cons of such interaction are relatively well-understood, and were not at the forefront during the recent crisis. Our paper downplays the distinction between lending and underwriting. For us both could represent examples of long-term, relationship-based banking. 1 We contrast relationship-based banking to transactions-based activities and evaluate the frictions coming from the di erence in horizon: long term versus short term. 1 Underwriting, insofar as it requires hard and codi ed information that is to be transmitted to the markets, may have a lower relationship intensity than commercial bank lending based on soft information. Nevertheless, one could argue that at its core underwriting remains a relationship-based activity. 2

3 The shift towards trading is a very fundamental change a ecting the industry over the last decades going back at least to the (now defunct) UK Barings Bank trading disasters in Singapore around Some indicators of this process for the U.S. nancial sector include an increase in the share of trading assets and securities on bank balance sheets from around 20% in the early 1990s to 30% in 2012, and an increase of non-interest income as a share of bank revenues from 35% to 50% over the same period (NY Fed, 2012). 2 The recent Liikanen report for the EC (Liikanen, 2012) points at similar developments in Europe. In Europe, some large universal banks have become distressed or failed during the crisis due to exposures to collateralized debt. UBS in Switzerland is perhaps the most vivid example, see UBS, 2008), but very similar patterns were present in banks in many other countries. In the United States, investments in securitized debt have back red particularly in investment banks (e.g. Bear Stearns, Lehman Brothers and Merrill Lynch). But also, commercial banks have used their franchise to expand in information-extensive (wholesale) mortgage origination and holdings (e.g. Washington Mutual and Wachovia), exposing themselves to trading and nancial market risks. The sizable losses on trading activities, such as a 2012 loss related to the treasury activities in JP Morgan is another example. The focus on the risks of arm s length activities by banks is supported by emerging empirical evidence. De Jonghe (2010), Demirguc-Kunt and Huizinga (2010), Brunnermeier et al (2012), and DeYoung and Toma (2013) identify that banks non-lending activities are more risky, and within that De Jonghe (2010) and Brunnermeier et al (2012) show that trading is the most risky activity. Fahlenbach et al. (2012) show that banks with more exposure to trading securities were more likely to be distressed during the 1998 and 2008 crises. Loutskina and Strahan (2011) show that arm s length mortgages are riskier than informed ones. While it is quite understandable that the public debate has focused on losses and risks coming from trading, this paper highlights that trading activity may have undermined the relationshiporiented banking franchise in more subtle ways. Trading may have diverted resources away from the more long term relationship banking activity. Notable here is the example of New 2 The two measures are proxies. For example, in balance sheet composition, some loans may be arm s length, while in income some non-interest earnings may come from relationships. But the trend is nevertheless clear. 3

4 York investment banks that, since the early 1980-s have turned the focus from traditional underwriting to short-term market-making and proprietary investments. And there is evidence of trading being a drain on commercial bank activities in newly created universal banks, such as Bank of America-Merrill Lynch. We will highlight the fundamental friction in short-term versus long-term orientation. The diversion of resources is not just a reassessment of priorities in favor of trading, but, as we will argue, an ine cient process that undermines the viability of relationship-oriented activities to the detriment of overall pro tability. Our analysis proceeds as follows. Key to our analysis is the observation that the relationship business has information-based rents and hence generates implicit capital, yet is not readily scalable. The trading activity on the other hand is scalable but can be capital constrained and hence may bene t from the spare capital available in the bank. Accordingly, relationship banks might expand into trading in order to use their spare capital. This funding (liability-side) synergy is akin to the assertions of practitioners that one can take advantage of the balance sheet of the bank. Opening up banking to trading, however, creates frictions. We highlight two of them. One friction is the misallocation of capital from the banking business to the trading activity. The reason for the misallocation is time inconsistency: banks may be tempted to trade too much ex post, which undermines ex ante investments in relationships by bank customers, and damages the bank s franchise. Another friction is risk-shifting: banks may use trading as a way to boost risk to bene t shareholders as residual claimants. As a result of these two frictions, a bank can overexpose itself to trading: trade too much and in too risky a fashion, compared to what is socially optimal, or ex ante optimal for its shareholders. The time inconsistency problem that traditional banking is subjected to in the presence of trading deserves some further elaboration. The type of relationship activity that we model is one where banks provide their customers with funding insurance (i.e. guarantees for the availability of funding), like credit lines and loan commitments. As Kashyap et. al. (2002) show, borrowing under such funding insurance arrangements represents 70% of bank lending. Time inconsistency may come about because the upfront fees paid for these guarantees lead to front-loaded income from banks. As we will discuss, the business of banking involves quite a 4

5 lot of such (implicit and/or explicit) commitments. An important feature is that banks have considerable discretion in whether or not to honor these lending commitments, which may invite time inconsistency problems. In particular, when banks shift risk capital to the trading business they may undermine their ability to honor commitments and the traditional relationship oriented banking business may su er. As we will argue, the extant literature on relationship banking has largely overlooked the importance of this commitment-oriented relationship banking business with its front-loaded income. We also highlight that risk shifting in banks is linked to their arm s length (trading) activities. Such involvement is rather uid, meaning it can be scaled up (or down) rather quickly and opportunistically without information frictions. This does not mean that risk shifting cannot happen with relationship banking, but the problem there is of a much more muted nature. It is the short term focus of trading and its scalability that facilitate (opportunistic) risk taking. Banking is not (or much less) scalable, much more dependent on an enduring presence and interaction with customers which is at odds with opportunistic risk taking. We show that the frictions associated with trading by banks become more acute when nancial markets are deeper, inducing larger trading positions. This not only increases the potential misallocation of capital but also enables gambles of a scale necessary for risk-shifting. The frictions also become more acute when returns on traditional banking activities are lower. Both factors deeper markets and less pro table relationship banking have been in play in the last years, both driven in large part by changes in information technology and increased availability and role of hard information. Consequently, the economic costs of trading by banks may have started to outweigh its bene ts. Trading by banks, while possibly benign and bene cial historically, might have recently become destructive. And, the distortions are likely to persist in the future, so a regulatory response might be necessary. We include several policy recommendations, which we discuss in the context of recent legislative proposals. The Volcker Rule as contained in the Dodd-Frank Act in the U.S., the Report of the Independent Commission on Banking (the so-called Vickers Report) in the UK, and the Liikanen Report to the European Commission all propose some prohibitions or segregation of 5

6 trading-like activities (see also Haldane, 2012). Interestingly, the three proposals are di erent in many respects (types of activities targeted, and whether to segregate or prohibit). This highlights the need for a framework to understand the underlying risks and market failures that we seek to develop in this paper. The paper is organized as follows. Section 2 discusses the literature. Section 3 outlines the features of banking and trading, and sets up the model. Section 4 demonstrates the bene ts of combining banking and trading (conglomeration). Section 5 identi es the rst friction of conglomeration the misallocation of capital. Section 6 deals with the other friction of conglomeration the risk-shifting problem, and the interaction between the two frictions. Section 7 discusses modeling features, including our characterization of relationship banking, and policy implications. Section 8 concludes. 2 Related Literature Our paper complements a number of strands in the literature on banking and internal capital markets. There is a vast literature on the costs and bene ts of combining commercial and investment banking, in particular whether underwriting that follows prior lending relationships has biased standards (see Puri, 1996, Krosner and Rajan, 1994, and Fang et al., 2010) or bene ts from synergies (Schenone, 2004). While this literature focuses on how borrower speci c information is used across lending and underwriting activities, our analysis focuses on combining private information intensive banking activities (either lending or underwriting) with trading activities that do not depend on private (borrower speci c) information. In studying the problems of conglomeration, we focus on shareholder incentives. An alternative approach would have been to consider the incentive problems of managers (e.g. as in Acharya et al., 2011). While incentive issues in banks are undoubtedly important, banks are subject to pressures from nancial markets to maximize shareholder returns. So understanding the distortions that can be caused by shareholder value maximization alone remains important, particularly when such distortions may have worsened in the recent past because of external factors, such as information technology linked increases in nancial development. Some papers 6

7 have linked the distortions in bank trading activities to the abuse of the safety net, including deposit insurance (Hoenig and Morris, 2011). Our results are not driven by government guarantees, o ering more general implications. There is also a literature that studies how the expansion of markets a ects the nature of bank relationships (Boot and Thakor, 2000), and how links with nancial markets might make banking more procyclical (Shleifer and Vishny, 2010). We do not consider such aspects. Instead we analyze how the presence of relationship banking and trading within one organization may su er from di erences in time frame: respectively their long term versus short term orientation. More generally, our paper relates to the literature on internal capital markets (Williamson, 1975, Danielson, 1984). Conglomeration may help relax the rm s overall credit constraint (Stein, 1997) but also impose costs, primarily related to divisional rent-seeking (Rajan et. al., 2000). Our model is similar in describing the bene ts of conglomeration as relaxing credit constraints, but points to a di erent set of costs: headquarters may misallocate capital due to time inconsistency and risk shifting problems, which arise in combining banking and trading. By analyzing a particular case of the misallocation of resources, we can analyze the evolution of bank business models and draw implications for the future. 3 Model We model two activities. One is a relationship-based business that we call banking. Another is a transaction-based (short-term and arm s length) business that we call trading. Banking relies on a xed endowment of information about existing customers; trading does not. We argue that this distinction alone su ces to highlight a range of synergies and con icts between the two. The xed endowment of information makes banking pro table (hence, we assume, not credit constrained), yet not easily scalable. High franchise value makes banking relatively safe. And when securing the value of information requires non-contractible ex ante investments that pay o over time, banking becomes long-term in nature. In contrast, since it does not rely on any endowment, trading is scalable, less pro table per unit (and hence, we assume, credit 7

8 constrained), short-term oriented, and possibly risky. 3 We use these observations to study the interaction between banking and trading in a universal bank. The synergies between the two activities are driven by di erences in pro t and scalability. Banking activity has extra borrowing capacity but is not scalable, while trading is scalable but credit constrained. Through conglomeration, banks can use their borrowing capacity to pro tably expand the scale of trading. The con icts between banking and trading are driven by di erences in horizon and risk. The rst con ict is capital misallocation. Banks may over-allocate capital to trading ex post, because when considering short-term returns to trading they disregard the negative e ects of such misallocation on ex ante investments in relationships. Put di erently, due to time inconsistency, trading may drain funds from banking and hence destroy its pro table long-term relationship franchise. The second con ict is the use of trading for risk-shifting. Banks may over-allocate capital to trading and choose risky trading strategies, because unlike relatively safe banking, trading gives opportunities for risk-shifting. Overall, banks may trade too much and in too risky a fashion, compared to what is socially optimal. The analysis proceeds in steps. We start with a benchmark model of synergies abstracting from the sources of con icts. We then introduce time-inconsistency in capital allocation by making returns on banking dependent on ex ante decisions of customers. Subsequently we introduce risk-shifting by considering risky trading. We also demonstrate the potential for mutual ampli cation between the capital misallocation and the risk-shifting problems. 3.1 Credit Constraints A key feature of our model is the presence of credit constraints. We build on Holmstrom and Tirole s (1997) formulation that limits leverage based on the owner-manager s incentives to engage in moral hazard. Assume that the owner-manager can choose to run the bank normally, 3 One could characterize the banking activity as a high-margin-low-volume operation and trading as a lowmargin-high-volume operation. Carry trade is perhaps the most notable example of low-margin-high-volume trading by banks. Some trading activities might have high margin (e.g. private equity investments), but these are relatively scarce. 8

9 or engage in moral hazard. She will run the bank normally when: ba, (1) where is the shareholder return when assets are employed for normal business, and ba is the shareholder return to moral hazard: initial investment A multiplied by the conversion factor b > 0 of assets into private bene ts. When the incentive compatibility (IC) constraint (1) is not satis ed, the bank s owner-manager engages in moral hazard, and a bank becomes worthless for creditors. Anticipating that, creditors would not provide funding. Thus, (1) can be seen as describing a leverage-related credit constraint for a bank. 4 We now describe the banking and trading businesses. 3.2 Banking Relationship banking is based on an endowment of information about a xed set of customers, which allows the bank to obtain pro ts from serving them. The key properties of banking are: Not scalable. It is prohibitively costly to expand the customer base. Pro table and not credit constrained. The bank s information on customers is valuable, making pro ts relatively high. Accordingly, we assume that the bank is not credit constrained. 5 Long-term. The return to relationship banking is distributed over time and depends on customers ex ante investment in relationships. We capture this by assuming that a part of the return is obtained in the form of ex ante credit line fees paid by customers. If 4 There are many ways to interpret the payo to moral hazard ba. It can represent savings on exerting the owner-manager s e ort (without which the relationship banking projects do not repay, and trading strategies lose money), limits on the pledgeability of revenues (Holmstrom and Tirole, 1998), or the possibility of absconding (Calomiris and Kahn, 2001). We let the form of moral hazard be identical for standalone banking, trading, and the conglomerated bank. We do not consider outside equity. For now assume that it is very costly. See Section 7.2 for more discussion. 5 The rents imply some informational monopoly on the part of the bank; it may be related to past investments by the bank and its customers into their relationships, and/or to advantages of proximity or specialization in local markets. Note that the time and proximity elements involved in building relationships provide a natural explanation for the lack of scalability. 9

10 there are doubts about the bank s ability to make good on funding commitments, the fees that customers are willing to pay (their investment in relationships) decline. We abstract from this intertemporal feature in the benchmark model of Section 4, and introduce it in Section 5 as a source of con ict between banking and trading. Relatively low risk. Traditional banking has relatively predictable returns and is not prone to risk-shifting (in the model, certain returns and no risk-shifting). Risk-shifting requires probabilistic returns. But a traditional bank that funds a portfolio of small loans with independently distributed returns has minimal idiosyncratic risk thanks to the law of large numbers. A bank could of course take on aggregate risk (for example, interest rate risk), yet incentives to do so may be o set by a high franchise value. To put it di erently, we think of a case when shareholders of a bank with high franchise value and little idiosyncratic risk fully internalize the losses associated with choosing a low monitoring e ort or excess aggregate risk. We contrast this with more risk-prone trading activities in Section 6. Setup The bank operates in a risk-neutral economy with no discounting. It has no explicit equity and has to borrow in order to invest. Creditors require a zero expected return. In the base model the bank is risk-free, so the interest rate on bank borrowing is zero. There are three dates: 0, 1, 2. Relationship franchise. At date 0 the bank is endowed with private information on a mass R of customers. We let information produce a return for the bank in two ways. First, it gives the bank an initial franchise value R 0, coming from existing loans that the bank has outstanding at date 0 with a repayment at date 2. 6 Second, the bank has an opportunity to serve its customers future funding needs. Each customer is expected to have a liquidity need of size 1 at date 1 (with certainty). 7 When 6 For example, assume that at date 0 the bank has lent X to customers with a repayment of X (1 + b) + R 0 at date 2, hence obtaining pro ts Xb + R 0. Substituting this and the private bene ts Xb into the IC constraint (1) gives a wedge between pro ts and private bene ts of R 0. Since R 0 plays a passive role in the model, we can streamline the exposition by setting X = 0: implicit equity is produced from a minimal initial investment. 7 For simplicity, we set the probability that the credit line will be used equal to one. We could envision 10

11 covering it, the bank can collect informational rents r per customer, up to a total of r R, from the repayment at date 2. Spare borrowing capacity. We denote the amount that the bank borrows to cover the customers liquidity needs at date 1 as R R. Then, the IC (leverage) constraint (1) takes the form: R 0 + rr br, (2) where the left hand side is the bank s market value of equity in normal operations: the franchise value R 0 and the information rent on covering its customers liquidity needs rr. We assume that this constraint is satis ed, including at R = R, implying spare borrowing capacity in banking: R 0 + r R > b R. (3) 3.3 Trading The trading business is not based on an endowment of information. Consequently, it has di erent properties: Scalable, with decreasing returns to scale. We think of decreasing returns to scale in the context of a Kyle (1985) framework where the average return of an informed trader falls in the size of her trade because the price impact increases in size. The price impact is smaller when the mass of liquidity traders is larger. Thus, trading is more scalable in deeper nancial markets (or, at higher nancial development). Less pro table, credit constrained. The per-unit return to trading is lower than the return to banking because trading does not bene t from an endowment of private information. Consequently, trading, while scalable, can be credit constrained. Short-term. Unlike banking, trading is transactional in nature. Returns occur at one point in time and do not rely on ex ante investments. a probability less than one. For example, consider uncertainty about future market circumstances, with the credit line only being used when external circumstances make it optimal because spot markets have become too expensive (cf. Boot et al., 1993, Acharya et al., 2007). 11

12 Possibly risky. A bank can choose between two trading strategies. One generates safe but low returns. Another generates somewhat higher returns most of the time, but can lead to catastrophic losses with a small probability. 8 We assume that the risky trading strategy has a lower NPV, yet may be used by a bank as a means of risk-shifting. We introduce risky trading in Section 6. Setup All trading activity is short-term. For T units invested at date 1, trading produces at date 2 net returns of tt for T S and 0 for T > S. The parameter S captures the scalability of trading. It is natural to relate it to nancial development, i.e. S is increasing in the depth of the market. Trading is less pro table per unit than banking since it does not bene t from the informational endowment: t < r. (4) And the low pro tability of trading makes it credit constrained: t < b, (5) implying that the IC constraint (1) does not hold when trading is a standalone activity. We thus, for simplicity, assume that standalone trading is not possible due to credit constraints, despite the opportunity to pro tably invest up to S units. 9 The timeline for the benchmark model is summarized in Figure 1. For now it abstracts from the long-term nature of banking, which can lead to a misallocation of capital (Section 5) and risk-shifting (introduced in Section 6). 8 This is reminiscent of banks taking on tail risk to generate fake alpha (see for example Acharya et al., 2010). 9 The fact that, in our analysis, trading cannot exist as a stand-alone business should not be taken literally. What is meant is that the viability of trading requires a substantial equity commitment. This is what we often observe in practice, as many independent trading houses are partnerships with substantial recourse. 12

13 4 Bene ts of Conglomeration Our model implies a natural bene t to the conglomeration of banking and trading: it links a business with borrowing capacity but no investment opportunities (the relationship bank) with a business that has investment opportunities but is subject to credit constraints (trading). Under conglomeration, at date 1, the bank maximizes pro t: C = R 0 + rr + tt, (6) subject to the joint leverage constraint (1): R 0 + rr + tt b(r + T ), (7) where T S. Comparing this to (3) and (5) shows that conglomeration allows using the borrowing of the relationship bank to fund some trading. The bank allocates the date 1 borrowing capacity between relationship banking R and trading T. Since r > t, the bank will choose to serve all banking customers (R = R) before allocating any remaining capacity to trading. The maximum amount of trading that a universal bank can support, T max (assuming T max S) is given by (7) set to equality, with R = R: T max = R 0 + R(r b). (8) b t Since it is never optimal to trade at a scale that exceeds S, T = min fs; T max g. This means that when S is low the scalability of trading is small the bank covers all pro table opportunities in trading. When S is high trading is more scalable the bank covers trading opportunities T max < S and abstains from the rest. Proposition 1 (Conglomeration without frictions) The conglomeration of banking and trading enables expanding the scale of trading, which is otherwise credit-constrained. In equilibrium, the bank serves all relationship banking customers, R = R, and allocates the rest of its borrowing capacity to trading, as long as trading is pro table, T = min fs; T max g. 13

14 Proposition 1 is a benchmark that provides a rationale for why banks choose to engage in trading, and speci es the rst-best allocation of borrowing capacity between the two activities. Next we study ine ciencies that may arise in combining banking and trading. 5 Capital Misallocation 5.1 The Long-Term Nature of Relationship Banking The previous section has outlined the bene t of combining banking and trading the use of spare capital of the relationship bank to expand trading. We now turn to the costs of conglomeration. This section deals with the rst ine ciency: the misallocation of capital induced by the time inconsistency problem between long-term banking and short-term trading. Banking is long-term because it involves repeated interactions with customers, which produce returns that are distributed over time. We model the intertemporal nature by letting a bank o er funding commitments to customers. The commitments take form of credit lines that cover future funding needs in return for ex ante fees that customers pay to the bank. A rationale for credit lines is that customers may be constrained in how much they can pay to the bank ex post, due to moral hazard at the borrower level (Holmstrom and Tirole, 1998; Boyd and De Nicolo, 2005). By making some payments ex ante, customers reduce the amount that they owe the bank ex post. As a result, returns to banking, although higher than returns to trading, might ex post be lower. This may distort ex post capital allocation: once credit line fees have been collected, a bank might have incentives to allocate too much capital to trading, leaving itself with insu cient borrowing capacity to fully serve the credit lines. Anticipating that, customers may decide to reduce the credit line fees that they are willing to pay ex ante, lowering the bank s overall pro t and borrowing capacity. While a bank can generate return r on covering customers future funding needs, it can only capture r through interest rates charged on the actual lending between dates 1 and 2. The remaining (r ) can be captured at date 0 as a credit line fee. Importantly, in our setup, a 14

15 bank cannot commit to cover the future liquidity needs of customers. That is, we let the bank have discretion to refuse lending in the future if it has no borrowing capacity left to lend under the credit line. (The lack of enforceability in our model is similar to the real-life contractual features of credit lines.) The emphasis on the uncommitted funding insurance role of relationship banks is a key assumption of out model. It contrasts with another common view on relationship banking that focuses on the informational capture e ects. See Section 7.1 for a full discussion of our approach, and of why it captures an important feature of relationship banking. The timeline incorporating the credit line arrangement is shown in Figure Time Inconsistency of Capital Allocation At date 1, the bank chooses R and T to maximize its pro t: C = R 0 + (r )R ex ante + R + tt, (9) where R ex ante is the borrowing that customers expect to get under a credit line and (r )R ex ante is the total credit line fee. R is the actual borrowing under a credit line. The bank maximizes (9) subject to the IC constraint: R 0 + (r )R ex ante + R + tt b (R + T ). (10) Note that in equilibrium, R ex ante = R: This follows since customers correctly anticipate the bank s ability and willingness to lend under the commitment. 10 Recall that in the benchmark case in Section 4, the bank always covered the customers liquidity needs, because the return on the banking activity was higher than that on trading (r > t). However when a part of return to banking is obtained ex ante to deal with potential moral hazard at the borrower level, a time inconsistency problem may distort the allocation 10 As will become apparent, the bank will always charge the maximum possible amount ex-post. That is, is set at the highest level such that the moral hazard problem at the borrower level is not triggered. This minimizes the time inconsistency problem. 15

16 of capital. As long as the ex post return to banking is su ciently high, > t, the rst best allocation persists. Yet when < t, the bank has an incentive to divert borrowing capacity. In maximizing its ex post pro t, the bank chooses to rst allocate the borrowing capacity to trading up to its maximum pro table scale S, and only then to give the remainder to banking. Whether this change in the allocation rule results in a misallocation of capital depends on the scalability of trading. When the scalability is low, S T max, the bank can cover all liquidity needs of customers even after allocating S to trading. That is, the allocation fr; Sj STmax g satis es the leverage constraint (7). Hence, R = R and relationship banking does not su er. However when scalability is high, S > T max, banking is credit constrained ex post: the allocation fr; Sj S>Tmax g no longer satis es (7). The borrowing capacity that remains after the bank has allocated S to trading is insu cient to cover all liquidity needs of customers, hence R < R. Anticipating that the relationship business will be credit constrained, bank customers will prorate the credit line fee which they are willing to pay ex ante: (r )R ex ante < (r ) R. The misallocation of borrowing capacity as a result of the time inconsistency problem thus undermines the ability of a bank to maintain its relationship banking franchise. The bank loses pro table ex ante investments in relationships by customers (in this model, credit line fees). 5.3 The Consequences of Time Inconsistency Under time inconsistency ( < t and S > T max ), the bank chooses to allocate its borrowing capacity to trading even when this means that it cannot deliver on the more pro table banking activity. The severity of the consequences depends on the relationship between the pro tability of banking r and the private bene ts b. Observe that cutting back on banking conserves capital at a rate b (see IC constraint (1)) and undermines bank pro tability at a rate r. There are two cases. Case 1: r < b. When r is small, such that r < b, cutting down on banking frees up more capital than is lost in pro ts (the leverage constraint becomes slack), hence trading can be expanded. This is the case when some banking may be preserved under time inconsistency 16

17 under the intermediate scalability of trading. For: T max < S R 0 b t, (11) we solve (10) as equality to get the equilibrium allocation: R = R 0 S(b t), (12) b r T = S. In this region of the intermediate scalability of trading, a diversion of borrowing capacity from banking to trading is limited (the di erence between S and T max ). This misallocation is less severe at higher levels of banking pro tability r: in (12) R is increasing in r, thus R is closer to the optimal allocation R for higher r. The reason is that a higher r increases the franchise value of the banking unit and allows it to o er more spare capital to trading. We can see this from (8); at higher r, more trading can be accommodated (T max is higher), and this reduces the the ex post diversion to trading (i.e. the di erence between S and T max ). A higher scalability of trading: S > R 0 b t (13) leads to all resources being allocated to the trading activity, so that relationship banking is wiped out. That is: R = 0, (14) T = R 0 b t. Banking cannot be maintained now because the highly scalable trading can now accommodate all resources. Case 2: r b. When r is high, r b, it follows immediately from (8) that T max > R 0 =(b t). Given that as is assumed the time inconsistency problem is present (S > T max ), we now, contrary to Case 1, only have the higher range of scalability in trading, S > R 0 =(b t). From 17

18 Case 1 we know that trading will wipe out all banking activity in that range. An alternative way to see this is to note that for r > b cutting down on banking leads to a loss in pro ts that is more than the capital freed up. This makes the leverage constraint (10) more instead of less binding, reducing the capital available to trading. No smooth reduction in the banking activity can help; in equilibrium, relationship banking totally disappears. The time inconsistency problem is so severe that only trading remains at a modest scale, based on the franchise value R 0 : R = 0, (15) T = R 0 b t. To sum up. Highly pro table relationship banking (r b) allows for a substantial trading activity (i.e. T max > R 0 =(b t), see (8)) without a detrimental e ect on the banking activity. If nevertheless the scalability of trading exceeds this elevated level (S > T max ), the time inconsistency problem in combining trading and banking will very rapidly destroy the relationship banking franchise fully. Hence we have a bang-bang solution. At lower levels of bank pro tability (r < b), the trading volume T max that can be accommodated is smaller. Time inconsistency sets in earlier, and from this point on smoothly starts reducing the level of the banking activity. Note, however, that overall the banking activity su ers more from trading in the case r < b than in the case r b. Figure 3 summarizes the dynamics of relationship banking under time inconsistency as a function of trading opportunities. Figure 3 can help interpret some fundamental changes in the nancial sector. Over the last decades, the deepening of nancial markets has expanded trading opportunities. With modest scalability of trading, banking did not su er: time inconsistency was not binding since the implicit capital of relationship banks could accommodate all trading. Trading elevated overall bank pro tability. Yet more recently two developments may have undermined banks that engage in trading. (i) The scalability S of trading may have become too high, and (ii) developments in information technology (possibly the same that have made trading more scalable) and deregulation may have reduced the pro tability r of relationship banking. So trading has become more 18

19 scalable, while banking became less pro table and less able to support even the same levels of trading without triggering detrimental time inconsistency. The former corresponds to the move to the right on the axes of Figure 3, while the latter points to a shift from case 2 to case 1 in the gure (with lower T max ; note from (8) that T max shrinks for lower values of r). This migration provides some important lessons for the industry structure of banking. With limited trading opportunities and relatively pro table banking activities, there is substantial scope for combining banking and trading. However, more scalable trading coupled with less pro table banking can undermine banking severely. Combining the activities then becomes very costly. The dynamics of R and T for cases r < b and r b, without (as in Section 4) and with time inconsistency (this section), are summarized in Figure 4, panels A and B. Proposition 2 (Time inconsistency of capital allocation) When t >, then for S > T max, the bank will allocate insu cient capital to serving the future funding needs of its customers: R < R. Anticipating this, ex ante investments of customers in bank relationships su er: they pay lower credit line fees; and the bank s relationship franchise deteriorates. 5.4 Costs of Conglomeration under Time Inconsistency We can now derive bank pro ts. Recall that the cumulative pro t of banking and trading as standalone activities is: S = R 0 + r R + 0 = R 0 + r R, (16) where R 0 + rr is the pro t of a standalone relationship bank (see (3)), and zero is the pro t of standalone trading (which is not viable). The pro t of a bank that engages in trading depends on the scalability of trading, S. For S T max, time inconsistency is not present, and the pro t is increasing in S: C = R 0 + r R + ts. (17) 19

20 For higher S, S > T max, C is decreasing in S as time inconsistency distorts capital allocation. Following the two cases in Section 5.2: for r < b a bank substitutes trading for banking, and its pro t decreases smoothly (use (12)) until the maximum feasible scale of trading S = R 0 =(r b) is reached: C = R 0 + rr 0 Sb(r t), for T max < S R 0 =(b t), (18) b r R 0 C = R 0 + t (b t), for S > R 0=(b t). (19) For r b, cutting down on banking does not create borrowing capacity for trading. Hence, the banking activity collapses for S > T max, leading to a discrete drop in pro t at S = T max, to the level given in (19). The pro ts of a conglomerated bank depending on the scalability of trading are summarized in Figure 4, panels C and D. Overall, from ((17)-(19)), we observe that, in comparison to stand-alone banking, trading increases pro tability initially (for low S) but can lead to a loss of pro tability for higher S. Speci cally, when a bank fully substitutes trading for relationship banking (R = 0; T = R 0 =(b t)) its pro t C as given in (19) is less than the standalone pro t S (see (16)) when relationship banking rents r R are su ciently high: R 0 rr > t (b t). (20) The results can be summarized as follows: Proposition 3 (Pro ts under time inconsistency) The e ect of conglomeration on bank pro ts is inverse U-shaped in trading opportunities S. For low trading opportunities (S < T max ), time inconsistency is not present, and pro ts increase in trading opportunities as a bank can better use its spare capital. For large opportunities (S > T max ), pro ts fall with additional trading as the time inconsistency problem intensi es. There exist parameter values such that beyond a certain scale of trading opportunities, banks that do not engage in trading generate higher pro ts than banks that combine relationship banking and trading. 20

21 6 Trading as Risk-Shifting 6.1 Risky Trading The previous section has identi ed an important ine ciency that may arise when banks engage in trading: a misallocation of capital due to time inconsistency, which can damage the relationship banking franchise. This section discusses a related ine ciency: the use of trading for risk-shifting. We also study how the two ine ciencies interact. Shareholders of a leveraged rm have incentives for risk-shifting when the risk is not fully priced at the margin in the rm s cost of funding (Jensen and Meckling, 1978). The latter is a standard feature of corporate nance, and arises when funds are attracted before an investment decision is made, to which shareholders cannot commit. Such lack of commitment, and hence risk not being priced at the margin, is present in banks. 11 Yet, generating risk-shifting in traditional relationship banking is di cult. Risk-shifting requires probabilistic returns: an upside that accrues to shareholders and a downside that exceeds the franchise value and imposes losses on creditors. But a traditional bank that funds a portfolio of small loans with independently distributed returns has minimal idiosyncratic risk thanks to the law of large numbers. A bank could of course take on aggregate risk (such as interest rate risk). But when aggregate risk is relatively small, its negative realizations would be fully internalized by shareholders if a bank has a high charter value. Therefore, opportunities to generate risk-shifting in a traditional relationship bank with a high charter value may be limited (in the model, absent). In contrast, trading allows the bank to generate highly skewed returns, for example, from large undiversi ed positions. Then, for a bank, trading becomes not just a pro t opportunity, but a means to perform risk-shifting. 11 The pricing of risk might be more distorted in banks than in non- nancial companies. One reason is the safety net (for insured deposits or too big to fail banks) that e ectively subsidizes risk taking. Another reason are the e ects of seniority, when newly attracted funding is senior to existing debt due to the use of collateral (Gorton and Metrick, 2011), short maturities (Brunnermeier and Oehmke, 2011), or higher sophistication (Huang and Ratnovski, 2011). Then, new funding is e ectively subsidized by existing creditors (although the latter may anticipate such risk transfer and charge higher interest rates ex ante). In addition to these, a possibly higher liquidity of bank assets compared to industrial rms may make it easier for banks to opportunistically change their risk pro le (see Myers and Rajan, 1998). We do not need these additional e ects in our model. But if present, they would strengthen our results. In particular, while we proceed to assume a positive NPV of risky trading, having risk subsidized may give the bank incentives to engage in risky trading even if it has a negative NPV. 21

22 To model risk-shifting, we introduce risky trading. Assume that a bank can choose between the safe trading strategy considered before and a risky trading strategy, which for T units invested generates a gross return (1 + t + ) T with probability p, and 0 with probability 1 p, up to the maximum scale of trading S. The binary return is a simpli cation, representing a highly skewed trading strategy. The notion is that banks use trading to generate extra return alpha by taking bets that are safe in most states of the world, but occasionally lead to signi cant losses. Such behavior is supported by anecdotal accounts of the strategies employed in the run-up to the nancial crisis (Acharya et al., 2010). We assume that risky trading has an NPV that is lower than in safe trading, yet positive: 0 < p (1 + t + ) 1 < t, (21) so that a bank would only choose risky trading for risk-shifting purposes and, as long as there is spare borrowing capacity, would always choose to trade instead of leaving that capacity unused. And, holding the cost of debt xed, risky trading o ers a higher return to shareholders than safe trading (creating incentives to use it for risk-shifting), yet not as high as to make the IC constraint (1) not binding: t < p(t + ) < b. (22) The choice of the trading strategy is not veri able. In the base model the bank was risk-free, so the interest rate on bank on bank borrowing was zero. Now, under risky trading, a bank may be unable to repay its creditors in full. Shareholders then surrender available cash ows to creditors. Creditors ex ante set the interest rate i based on their expectations of the bank s future trading strategy to achieve zero expected return. For simplicity, we assume that if multiple equilibria are possible, the creditors set the lower rate. The bank chooses safe trading when indi erent. We focus on the richest case that combines time inconsistency ( < t) and a smooth contraction of banking (b > r). 22

23 6.2 Risk-Shifting We rst derive conditions under which the bank would choose risky trading when charged a low interest rate i = 0. This allows us to de ne a threshold T Risky such that for T T Risky the bank chooses safe trading (because shareholders su ciently internalize the lower NPV of risky trading), while for T > T Risky the bank chooses risky trading. We then characterize the risky trading equilibrium interest rates, capital allocation, and pro ts. Assume that i = 0 and consider the payo to risky trading. When a bank invests R in relationship banking and T in risky trading, it obtains at date 2 from relationship banking R 0 +(1+r)R; and from trading (1 + t + ) T with probability p and 0 otherwise. The bank has to repay creditors R +T. It can do so in full when trading succeeds. Yet when trading produces a zero return, the bank has su cient income to repay in full only if R 0 + (1 + r)r R + T, corresponding to an upper bound on the volume of trading: T R 0 + rr. (23) When (23) holds, the bank s debt is safe, and shareholders internalize the losses from risky trading. Their payo is: Risky j T R0 +rr = R 0 + rr + p (1 + t + ) T T. (24) This is lower than the payo with safe trading: Risky j T R0 +rr < C ; where C is given in (6), since risky trading has a lower NPV than safe trading. Hence, bank shareholders will never choose risky trading if they fully internalize possible losses. We thus focus on the case T > R 0 + rr, where a bank cannot repay creditors in full when the risky trading strategy produces zero. Here, the shareholders return when the bank engages in risky trading is: Risky = p (R 0 + rr + (t + ) T ). (25) The bank chooses risky trading when Risky > C. From (6) and (25), this holds when the 23

24 scale of trading exceeds a threshold T Risky such that: T > T Risky = (R 0 + rr) (1 p). (26) p(t + ) t To express T Risky in exogenous variables, note that when a bank allocates T to trading, the borrowing capacity left to banking (from (10)) is: R = R 0 T (b t). (27) b r Substituting this into (26) gives: T Risky = R 0 (1 p) r (p b(1 p)) =b + (p t(1 p)). (28) We can verify the following: Lemma 1 Risky =@ < 0 Risky =@p < 0: when risky trading has a higher upside and a lower risk, the switch to risky trading occurs at a lower scale; Risky =@R 0 > 0 Risky =@r > 0: when the relationship franchise value is higher, the switch to risky trading occurs at a higher scale. Proof. All are obtained by di erentiation and considering that: (i) The denominator in (28) is positive: r (p b(1 p)) =b + (p t(1 p)) = [(b r)p + (1 p)b(r t)] =b > 0, since b > r and r > t: (ii) The expression (p b(1 p)) in the denominator of (28) is positive. To see that, use (22) to obtain: p b(1 p) > p p(t + )(1 p) = p (p(t + ) t) > 0. 24