SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS ...
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS Abstract. This paper introduces a theoretical liquidity risk model to explain how the fire-sale price happens by banks’ portfolio composition and the liquidity shocks. The model illustrates that the derivatives can serves as ArrowDebreu securities for banks to share and eliminate the liquidity risks. The shadow banking system serves as the external funds aids banks to absorb the liquidity shocks, and re-enforce their advantage in borrow-short-and-lend-long. The results are helpful to understanding how bank runs among financial institutions occurred during the subprime crisis, and why the $500B subprime mortgage losses could not be fixed by more than $2T government aids, and crashed the prices and led to a frozen market.
Keywords: liquidity risk, derivatives, origination-and-distribution model, interbank market, bank run, subprime crisis JEL Classifications: D12, G12, G21
Contents 1. Introduction
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2. Model to Bank’s Asset Management
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2.1. Benchmark:
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2.2. ABCP Eliminates Deposit Shocks:
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2.3. MBS Creates Liquidity.
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2.4. ABCP and MBS as Arrow-Debreu Securities:
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Received by the editors July 2010. 1
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
3. Model to Market Limit
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3.1. Idiosyncratic and Systematic Liquidity Risk
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3.2. The limit of the Shadow Banking System:
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3.3. The Path to Overloaded Market
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4.
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Evidences
4.1. Banks Represent the Financial Industry:
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4.2. The Shadow Banking System:
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4.3. The Deposit Shocks:
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4.4. Other Evidence:
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5. Summary
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References
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
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1. Introduction It’s not the things you don’t know that cause disasters; it’s the things you do know, but are’t true. Mark Twain This paper introduces a liquidity risk model to understand how shadow banking system changes commercial banks’ operation, and the benefits as well as the risks of the system. The term ’shadow banking system’ was used by Freidrich Hayek in 1935, referring to the credit growth by unregulated institutions. In the book ’Prices and Production’, Hayek pointed out that shadow banking system was ’other forms of media of exchange which occasionally or permanently do the service of money’. As the system was not ’subject to any central control’, a collapse of credit was to be unavoidable when the credit originated from shadow banking system was converted into other forms of money. After the financial deregulation in the late 1980s, financial innovations expanded the shadow banking system rapidly. The over-the-counter(OTC) trading of structured investment vehicles, including CDOs, CDS’s and other derivatives, expanded from zero in 1980s to a over $20T before the subprime crisis. The shadow banking system competed with commercial banks in channeling the investors and borrowers, and was supposed to bear the similar risks to the banking system. Gorton ([30], [31], [32], [33], [34] and [35]) repeatedly compared the shadow banking system with the banking industry and concluded that the subprime crisis was caused by improper regulation, and the essential of the subprime crisis was a bank run among financial institutions.
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The failure of the derivatives market indicated the imperfection of credit risk models. Even without central regulation, financial institutions have a long tradition of expertise in analyzing the amount of capital necessary to support its risk portfolios. Mature credit risk management techniques have been systematic used, including information collection by credit scoring systems and bureau scores (FICO, NextGen, VantageScore, Equifax, Experian, TransUnion, etc), data analyses techniques (portfolio aging and vintage analyses, deliquiency/roll rates/flow rates analyses, internal rating-based approaches, external rating agencies’ models, classified accounts), and credit risk models (Basel II models, CreditMetrics, Credit Protfolio View, CreditRisk+, Merton OPM/KMV Moody’s model, VaR, and so on)(Ivo [50]). However, credit risk models cannot fully explain the risks to the financial institutions, as the asset prices could dramatically deviate from their fundamentals, especially during the crisis. In 2008, ABX index lost more than 45% of their value, and subprime-mortgage-backed-securities alone lost over $1T market value. Such losses did not reflect the underlying asset’s losses at all. Based on loanlevel data, David ([37]) estimated that even housing prices declined 20% more in 2009, all underwater mortgages led to the total losses of $500B, which was only 50% to subprime-mortgage-backed-securities losses. As of 2010, the average subprime default rate was around 19%, which was 65% less than the losses of subprimemortgage-backed-securities. Meanwhile, the market saw the similar losses of other subprime unrelated assets, such as primary mortgage backed securities, student loan backed securities, credit card backed securities etc. Gorton ([35]) described the credit risk models failure as ”slapped in the face by the invisible hand”.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
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The industry has acknowledged the existence of other risks beside credit risk. Mark and Rene ([15]) pointed out that credit risk only counted about 53% of banks risks before 2007. Basle committee has chosen a confidence level of 99% and a 10-day horizon to compute VAR, and the resulting VAR is multiplied by a factor of THREE to determine the minimum capital1. The assumption that total risk was capped by three times credit risk may works in normal time, but the total risk can easily exceed the cap during the crisis. For instance, Jorion ([38]) estimated that LTCM’s losses ’would occurs once every 800 trillion years, or 40,000 times the age of the universe, according to standard credit risk model. The cause of LTCM’s losses was not the credit risk of its portfolio, but the fire-sale of its assets. Surely, credit risk model was not sufficient, and the chosen of arbitrage factor of THREE by Basel II was not enough, especially during the crisis. As individual financial institutions are aware of the credit risk model’s limit, the market was cursed by the prisoner’s dilemma during the crisis. Every one was willing to sell, but refused to buy even the price was much lower than the rational price. The subprime crisis evidences that the market may be as irrational as it was before World War II, as John Keynes described that ’market can remain irrational longer than you remain solvent’. We introduce a liquidity model to answer market’s call for a new theory to explain how market remains solvent. Even the model has its insight for both banking industry and shadow banking system, this paper applies the model to the banking industry for good reasons. First, the shadow banking system as whole carries out the similar function and bears the similar risks as the banking industry (Garton [32], [33] and [35]). It is easier to deliver 1
These capital adequacy requirements are detailed in the Basle Committee on Banking Super-
vision 1995.
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the essential ideas based on the understanding to banking than to jump into the shadow banking system with opaque information. Secondly, the most restrictive regulation did not keep banks stay away from the shadow banking system. Banks’ liquidity preference honestly reflects the risks from the derivatives market. Last, banks’ balance sheet has been regularly released by the Federal Reserve System, FDIC and other government agencies, which make it possible to verify the model. The liquidity model focuses on market depth and the earlier warning indicators to remain solvent, which is independent from credit risk models, who attempt to predict the losses. In banks’s view, liquidity risk is about the quantity of sustainable long term loans, and credit risk is about loans’ return until mature. Bank run does not occurs, because of bad assets; it occurs because the bank has not enough time to liquidate its assets (Diamond and Dybvig [21] Diamond [20]). Liquidity risk model and credit risk model explain the causes of the crisis from different origination of the shocks. All credit risk models can be derived from random discount model (Cochrane [17]). The prices reflect the present value of future cash flow: P rice = E(mX), where m is random discount factor and X is the future cash flow. The model suggests that the origination to the market volatility is exogenous shocks 4E{mX}. Price changes reflect exogenous information 4E(mX) ⇒ 4P rice. Market is efficient in recognizing the exogenous information(Fama [27]). During the crisis, the losses in asset value reflect either the falling return of individual project X or the bad macro-economy enviornment m or both. The safety is depends on the amount of capital to absorb such possible losses. Bank run occurs when the losses exceed the capital. The credit risk model explains the process of bank panic by the following chain reaction:
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(OriginalShocks) 4 E{mX} ⇒ 4AssetP rice ⇒ 4BankAssetV alue ⇒ 4DepositsW ithdrawals ⇒ BankRuns If a efficient market fails to recognize the signals to predict a crisis, the crisis is unavoidable and there is nothing to do to stop it in advance. Solvent problem concerns whether an existing long term investment can be rolled over on short term financing, and fire-sale due to insolvency may not relate to the fundamentals at all(Acharya and Yorulmazer [1], Brunnermeier etc [14]). For instance, LTCM lost more than $150 million when forced to liquidate its positions in Royal Dutch Shell trade. Under ’convergence-arbitrage’ trade strategy, LTCM established an arbitrage position in the dual-listed company Royal Dutch Shell in the summer of 1997, when Royal Dutch traded at an 8-10% premium relative to Shell. The investment in Shell was financed by ’short’ in Royal Dutch. In the view of cash flow, the portfolio was credit risk free. The only risk is whether LTCM could hold the portfolio until Royal Dutch and Shell converge. It is obviously, LTCM’s trade partners did not have the same faith to the rational market price as LTCM. LTCM could not sustain its long position under an unexpected margin call of its short position. In August 2008, LTCM was forced to close both its long and short positions. The fire-sale enlarged the spread to 30%, and costed LTCM $200M. Beside Royal Dutch Shell trade, LTCM liquidated more than $15B assets in August 2008. Fang shows that the market conspire against the falling LTCM was the causes to the deterioration of LTCM’s asset value, and the aggregate engaged in front running against LTCM explains most of LTCM’s losses. During LTCM lost more than $2T of its capital, each of its 437 active trading parterres yielded $5M
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abnormal return on average, and such abnormal return disappeared after LTCM bailout; LTCM’s portfolio did not bring further losses to Chase, Goldman Sachs, Merrill Lynch, and other bailout creditors. LTCM’s losses show that the key to stay away from the crisis is to avoid fire-sale due to short-term financing shocks. In bank’s view, it is to protect their long term loans from the deposit shocks. Tobin ([56]) pointed in 1982 that ’The volume of deposits in a bank is partly within and partly outside its control’. And the key to prevent the crisis is not to predict the asset prices, as ”(they) are in the short run either illiquid or unpredictable in value”, but to ”hold a certain quantity of defensive (liquid) assets”. Banks’ asset allocation is determined by current and future deposit shocks. Banks stop issuing new loans and liquidate some assets when facing net withdrawals, and vise verse. Secondly, solvent problem does not treat price change as a consequence to exogenous shocks alone. Banks’ operation in the interbank market has directly impact on the asset demand-and-supply and fire-sale price is too wild to be predictable. The most important difference between credit risks and liquidity risks is that raising adequate equity is the only solution to prepare the losses due to the credit risk, while banks can depend on both internal funds and external resources to control the liquidity risk. The liquidity risk model is illustrated by the following chain action: (OriginalShocks) 4 Deposits ⇒ 4BankAssetP ostion ⇒ 4Share × P rice + Share × 4P rice ⇒ M arketCollapse where 4Share is banks’ operation to re-balance their portfolio, and 4P rice is the externality of 4Share on prices. In the case of LTCM, liquidating the pairs trading of Royal Dutch Shell amplified the gap to over 30%. The fire sale created
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
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extra losses to LTCM. The correlation between price change and banks’ operation is determined by asset’s liquidity characteristic. The correlation is ignorable for liquid assets, such as Treasure bond, and it could be substance for illiquid assets. An example is helpful to illustrate the essential idea of the impact of credit supply on banks’ asset value. Bank could choose either refinancing or foreclosure when the homeowner faces financial distress, which is not rare as refinance accounts more than 60% of mortgage origination. Bank’s choice is determined by not only the borrower’s financial characteristic, but also the available funds. With plenty credits, refinancing is easy to be granted, and the shock from borrowers’ financial distress was reduced; under tight credit, it is more likely banks prefer foreclosure, which amplifies the shocks and brings considerable losses. Based on loan-level data, Demyanyk and Hemertthe ([18]) show that the average subprime borrowers’ FICO score raised from 601.2 in 2001 to the peak of 620.9 in 2005 and stays above 613.2 in 2007. And the new issuance of subprime mortgage was unrelated to the FICO scores. When the credit was tighten in 2008, refinance was more difficult, which contributes to the wave of foreclosure. One contribution of this paper is to show that banks can depend on both internal funds and external resources to absorb the liquidity shocks. The shadow banking system reduces banks’ liquidity risk in two ways. First, banks can dramatically reduce their deposit shocks through the interbank market. Even individual banks face significant deposit uncertainties, the currency seldom leaves the financial system. One bank’s withdrawal is another banks’ deposit. In 1960s, when cash played more important role in the economy, few ned to keep more than fifteen days’ income in money (Ashok [8]). Through overnight borrowing, repo, ABCP and other
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derivatives, banks with net withdrawals borrow from those with deposit surplus. Derivatives serves as the Arrow-Debreu securities for banks to reduce the deposit shocks. Secondly, the shadow banking system creates the liquidity among banks. Mortgage was illiquid assets due to its long mature term and MBS is very liquid asset in the secondary OTC market. Gorton (Gorton [35]) named such phenomena ’informationally-insensitive’ debt, which reduces the transaction cost and creates the liquidity. Then, banks could re-balance their portfolio according to their deposit shocks in a timely manner. The change of the liquidity creation could explain the crisis (Berger and Bouwman [11]). The most important contribution of this paper is to draw the line of the shadow banking system’s limit. Liquidity risk is different from credit risk, which could be measured by the trade off between volatility and returns continually. There are only two states in the view of liquidity risk model: a safe market and a collapse market. Under a safe market, the created liquidity can improve the returns (Shawky Ding and Tian [52]); there was not trade off between liquidity risks and returns as its credit risk counterpart dose. The earlier attempts to measure market liquidity include Berger and Bouwman’s preferred liquidity creation measure (Berger and Bouwman [11]). But the application of such measurement on the data from 1984 to 2008 failed to give a constant pattern of liquidity creation change pre-crisis, during-crisis and post-crisis. Berger and Bouwan’s preferred liquidity creation also failed to explain the successful survivals of American banking industry during Loanand-Saving crisis, 1997 Asian financial crisis, LTCM and Russian crisis, Dot-Com bubble, Latin and South American currency crisis without major scratch, and the unexpected failure of the subprime mortgage crisis (Berger and Bouwman [11]).
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Predicted by the three period model, the market limit counts on both banks’ liquid and illiquid components in their assets as well as the idiosyncratic shocks and systematic shocks on their liability. The financial industry is safe when the derivatives are less than the idiosyncratic risks, and there is enough liquidity assets to absorb the systematic shocks. Then there is enough credit supply in the market to consume the derivatives. The shadow banking system is overloaded when all financial institutions falsely believe the market has unlimited depth and depend on it to absorb both idiosyncratic shocks and systematic shocks. The reset of the paper is organized as follows:
• Chapter 2 introduces a three period model to analyze banks’ liquidity preference with/without the shadow banking system. In the rest of the paper, interbank operations, interbank market and shadow banking system are exchangeable, as the model use ABCP and MBS as the representative to both interbank operations among interbank market and the investment vehicles in the shadow banking system. Banks’ liquidity safety margin is determined by their ability to shield illiquid assets from fire-sale. The model shows that the shadow banking system serves as Arrow-Debreu securities to help banks to share and eliminate deposit shocks and to create liquidity. Naturally, banks take the advantage to issue more long-term-loan for higher margin. • Chapter 3 investigates the limit of interbank market. When market breakthroughs its limit, the banking industry holds too less liquidity assets to
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
absorb liquidity shocks. Any small shocks can break down balance of the interbank market supply-and-demand, and may cause considerable irrational price change. • Chapter 4 lists the evidences to the liquidity risk model. and the last Chapter is the summary.
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2. Model to Bank’s Asset Management All financial implosions stem from the same cause: borrowing short and lending long without enough equity to weather periodic storms in the gap between. Vernon L. Smith2, WSJ, Dec. 18, 2007 Smith correctly noticed that financial crisis was rooted in banks’ long lasting business model: borrowing short and lending long. However, equity is not the only measurement to buffer the gap between financing and investment. This chapter introduces a three-period-model to illustrate that the shadow banking system provides a flexible solution to meet the gap and helps banks to control the liquidity shocks and issue more long term loans. There are three periods, t = 0, 1 or 2. Bank’s long term and short term investments {Lt , St } are financed by its equity m and deposits {Dt }. Deposits and short term loans are to be repayed at the end of each period. Long term loans are to be repayed at the end of the next period. Let εt be the deposit shock at time t. Bank’s future deposits can be rewritten as Dt = D0 + εt , which are random variable. Liquidity is used in two senses here: first, liquid investment matures shorter period. In the model, short term loans represent liquid assets and long term loans represent illiquid assets. Secondly, liquid investments have less transaction cost and are easier to be traded at high frequency. In the model, we use loan demand as a proxy to transaction cost. It takes uncertain time and cost to find new long term projects, and the long term loan demand {BLt }(t=0,1) is uncertain. For instance, credit card is liquid, compared to commercial & industry loans, because it matures one month 2Smith is 2002 Nobel Laureate,
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
and requires less information to grant the loans. Changing customers’ credit line to stimulate loans costs less than issuing new commercial & industry loans. Similar to deposit shocks, define ξ1 = BL1 − BL0 to measure the BLt ’s illiquid nature. To present the liquid/illiuqid investment demand in a consistent way, we define liquid asset demand as BSt . {V Ct }(t=1,2) and {V Mt }(t=1,2) are the banks’ operation in ABCP and MBS market, representing the shadow banking system. To focus on liquidity risk, assume all assets are credit risk free. Deposit-interestrate, short-term-loan-rate and long-term-loan-rate are constants i, (i+α), (i+α+β). α indicates deposit-loan spread, and β indicates term-spread. Realized profit is distributed among shareholders immediately. Relaxing these assumptions does not change the main results. At each period t, bank’s liquid preference is given by its liquid/illquid assets allocation {St , Lt }(t=0,1,2) , for current deposit {Dt }t=0,1,2 . Bank’s action set is A = {Lt , St , V Ct , V Mt }t . Bank has to roll over current long term loans Lt on the next period short-term deposits Dt+1 , and a bank run occurs when future deposits Dt+1 can not support current long term loans Lt . Assume that the penalty to bank run is infinite. A bank’s problem is given by the following optimal problem:
maxA
(i + α)(S0 + S1 + S2 + V C0 + V C1 + V C2 )
(short-term-loan revenue)
+(i + α + β)(2L0 + 2L1 + V M0 + V M1 + V M2 )
(long-term-loan revenue)
−i(D0 + D1 + D2 )
(short-term-deposit cost)
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
S.T : L0 + S0 + V C0 + V M0 ≤ D0
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(BRR0 )
L0 + L1 + S1 + V C1 + V M1 ≤ D1
(BRR1 )
L1 + S2 + V C2 + V M2 ≤ D2
(BRR2 )
0 ≤ St ≤ BSt
for t = 0, 1, 2
(LDRS )
0 ≤ Lt ≤ BLt
for t = 0, 1
(LDRL )
where BRRt indicates bank run restriction at time t, and LDRt indicates loan demand restriction. Bank maximize its profit with BRRt and LDRt restrictions under any deposit shocks {Dt }. 2.1. Benchmark: The benchmark is individual bank’s liquid/illquid asset allocation without the shadow banking system. The interbank operations are zero {V Ct = V Mt = 0}t=1,2,3 , and banks address deposit shocks alone. The benchmark represents banks’ liquidity preference and the liquidity risk before financial deregulation, when banks served depositors and borrowers from non-financial sectors without complex derivatives. A bank’s problem can now be rewrote as: maxA (i + α)(S0 + S1 + S2 ) + 2(i + α + β)(L0 + L1 ) − i(D0 + D1 + D2 ) S.T : L0 + S0 ≤ D0
(BRR0 )
L0 + L1 + S1 ≤ D1
(BRR1 )
L1 + S2 ≤ D2
(BRR2 )
0 ≤ St ≤ BSt
for t = 0, 1, 2
(LDRS )
0 ≤ Lt ≤ BLt
for t = 0, 1
(LDRL )
Assume random variable {εt }t=1,2 has the lower boundary {εt }t=1,2 , which indicates the severity of deposit shocks. The solution to bank’s problem is given by Property 2.1.1 without prove.
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Proposition 2.1.1. When banks serve ultimate depositors and borrowers from non-financial sectors without derivatives, the optimal loan issuance is:
L∗0 = min{D0 + ε1 , BL0 } L∗1 = min{D1 − L0 , D0 + ε2 , BL1 } S0∗ = D0 − L0 S1∗ = D1 − L0 − L1 S2∗ = D2 − L1
Visualize that bank A receives deposit D0 = 1 at time 0, the worst deposit shock in the future is {εt }t=1,2 = −0.5, and loan demands are BLt = BSt = ∞. Bank’s safety is determined by whether bank successfully protects long term loan from the worst shocks. A’s optimal loan allocation is L∗0 = 0.5 at time 0. When A issues more long term loans and L0 > L∗0 , bank run occurs when the net withdrawal at time 1 is ε1 = −0.5; when A issues more short term loans and L0 < L∗0 , A can improve its profit margin by reallocating some fund from short term loans to long term loans without increasing the risk of bank run. At time 1 and 2, the amount of loan issuance is subject to bank’s current deposits shocks ε1 and ε2 . Under the worst deposit shocks, ε1 = ε2 = −0.5, loan issuance is L0 = 0.5, S0 = 0.5, L1 = 0, S1 = 0 and S2 = 0.5, and total profit is (2α + β). A better economic condition can improves bank’s returns. For instance, if ε1 = 0.1, ε2 = −0.1, bank A can issue more long term loan at time 1: L1 = 0.5, S1 = 0.1. The total profit is (3α + 2β). Proposition 2.1.1 shows that banks’ safety depends on holding adequate liquid assets, which could be liquidated to absorb both the current and future deposit shocks. As figure 1 shows that banks depend on their
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
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Figure 1. Absorbing Deposit Shock: Autarky
internal fund to absorb the deposit shocks. If banks do not hold sufficient liquidity assets, banks may fail to hold the long term loans until mature. Proposition 2.1.1 derives other results. The liquid assets benefit banks’ stability (Wagner [57]). As large banks serves more diversified customers pool, and they face less deposit shocks than small banks. Then large banks are required to hold less liquidity assets and have more ability to issue long term loans. Carletti, Hartmann and Spagnolo ([16]) documented banks’ liquidity preference change after mergers, and shows that ”a merger creates an internal money market that induces financial cost advantages”.
2.2. ABCP Eliminates Deposit Shocks: This chapter shows that banks can reduce the deposit shocks from non-financial sectors through ABCP market, then banks can issue more long term loans for higher margin without worrying about a bank run.
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
ABCP represents the external funds to absorb the deposit shocks, because ”Before the financial crisis of 2007, ABCP was the largest short-term debt instrument witho more than $1.2T outstanding” (Acharya etc [1]). There are other forms of interbank instruments, such as Treasury Bill, securities lending, which play the similar role with relative small outstanding. When banks can buy/sell ABCP in the interbank market, bank’s problem is written as
maxA
(i + α)(S0 + S1 + S2 + V C1 + V C2 ) (short term loan revenue) +(i + α + β)(2L0 + 2L1 )
(long term loan revenue)
−i(D0 + D1 + D2 )
(short term deposit cost)
S.T : L0 + S0 ≤ D0
(BRR0 )
L0 + L1 + S1 + V C1 ≤ D1
(BRR1 )
L1 + S2 + V C2 ≤ D2
(BRR2 )
0 ≤ St ≤ BSt
for t = 0, 1, 2
(LDRS )
0 ≤ Lt ≤ BLt
for t = 0, 1
(LDRL )
V Ct > −Lt−1
for t = 1, 2
(ABSR)
The solution to the bank’s problem with ABCP is given by Proposition 2.2.1 without prove.
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Proposition 2.2.1. ABCP operation reduces the impact of the deposit shocks on banks’ long term loan issuance, and the optimal loan issuance is: L∗0 = min{D0 , BL0 } L∗1 = min{D1 , BL1 } S0∗ = min{D0 − L0 , BS0 } {0, D1 − L0 − L1 } ∗ ∗ {V C1 , S1 } = {D1 − BL1 − L0 , 0} {−L0 , 0} {0, D2 − L1 } if D2 ∗ ∗ {V C2 , S2 } = {D2 − L1 , 0} if D2
if D1 > BL1 + L0 if BL1 + L0 ≥ D1 > BL1 if D1 ≤ BL1 > L1 ≤ L1
Figure 2. Absorbing Deposit Shock: with ABCP
Proposition 2.2.1 can be also illustrated by figure 2. The existence of ABCP market provides external funds for banks to absorb the deposit shocks. By buying/selling ABCP, banks shield the directly impact of the deposit shocks on their
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
assets. Then banks cut off liquidity assets holding and allocated more resource on long term loans, comparing to Proposition 2.1.1. The ABCP market helps banks to earn higher return without extra liquidity risk. For instance, even the deposit shock at time 1 could be as bad as −0.5, at time 0, bank A can invest all its deposits on long term loans L0 = 1(= D0 ). If εt < 0, bank A can roll over its long term loan by selling the same amount of ABCP. Banks avoid bank runs without holding any liquid assets.
2.3. MBS Creates Liquidity. This section shows that MBS creates liquidity of long term loans among banks. With MBS market, bank’s problem is written as
maxA
(i + α)(S0 + S1 + S2 ) +(i + α + β)(2L0 + 2L1 + V M0 + V M1 + V M2 ) −i(D0 + D1 + D2 )
S.T : L0 + S0 + V M0 ≤ D0
(BRR0 )
L0 + L1 + S1 + V M1 ≤ D1
(BRR1 )
L1 + S2 + V M2 ≤ D2
(BRR2 )
0 ≤ St ≤ BSt
for t = 0, 1, 2
(LDRS )
0 ≤ Lt ≤ BLt
for t = 0, 1
(LDRL )
V Mt ≥ −Lt−1
for t = 1, 2
(M BSR)
Banks gain more freedom to invest long term loans. They sell MBS to address the net withdrawals, and buy MBS when they run out local long term investment opportunities. The solution is given by Proposition 2.3.1 without prove.
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Proposition 2.3.1. When banks can adjust long term loan position through MBS, the optimal loan issuance is: L∗0 = min{D0 , BL0 } V M0∗ = max{D0 − BL0 , 0} {0, D1 − L0 } {L∗1 , V M1∗ } = {D1 − L0 , 0} {BL1 , D1 − L0 − L1 }
if D1 < L0 if L0 ≤ D1 < L0 + BL1 if D1 ≥ L0 + BL1
V M2∗ = D2 − L1 S0∗ = S1∗ = S2∗ = 0 With MBS, banks do not invest in liquid assets at all, but invest all their deposit in illiquid assets directly or indirectly for higher margin, and expect to buffer the deposit shocks through external funds from MBS market. Proposition 2.3.1 can also be illustrated by Figure 3. Facing the deposit shocks εt , loan origination bank does Figure 3. Absorbing Deposit Shock: with MBS
not recall the loan from borrower, and the long term project yields the return of
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
i + α + β. The gap between the deposit and the long term loan is met by the selling of MBS to other banks. Note that selling/buying MBS involves only transactions among banks. Such operation has no direct impact on the underlying asset value, or housing prices. The trade of MBS, comparing to deny refinancing and other directly measurement to cut back mortgage outstanding, reduces foreclosure rate, stabilizes housing market, and improves banks’ return. Table 1 compares banks’ liquid/illiuqid asset allocation under different market environment: without the shadow banking system, with ABCP, and with MBS. Without any kind of interbank operation, banks only depend on their internal funds to absorb deposit shocks, and they have to hold adequate liquid assets. Therefor, their ability to issue long term loan is a function of both both the deposit shocks εt and the investment opportunities BLt . ABCP provides external funds for banks to reduce their deposit shocks exposure. As banks depend less on internal funds to absorb the deposit shocks, they issue more long term loans. MBS creates mortgage’s liquidity among banks. Banks absorb all deposit shocks by selling MBS, and remove the restriction imposed by the local long term investment opportunities.
2.4. ABCP and MBS as Arrow-Debreu Securities: There is another way to understand the benefit of the shadow banking system. ABCP and MBS serves as Arrow-Debreu securities to pool banks liquidity shocks together and eliminate part of banks’ uncertainties. A simple example illustrates the idea. There are two banks, A and B, in one island serving the residents. All residents put their money into either of the two banks as well as borrows from either of them. Initially, bank A and bank B receive $1B deposits each. Residents may transfer their money among two banks, which
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
23
Table 1. Liquid and Illiquid Asset Allocation Benchmark
ABCP
MBS
t=0
D0
D0
D0
t=1
D1
min{max{D1 , BL1 + L0 }, D1 + L0 }
D1
t=2
D2
max{D2 , L1 }
D2
L0
min{D0 + ε1 , BL0 }
min{D0 , BL0 }
min{D0 , BL0 }
L1
min{D1 − L0 , D0 + ε2 , BL1 }
min{D1 , BL1 }
max{min{BL1 , D1 − L0 }, 0}
Liabilities
Illiquid Asset
Liquid Asset S0
min{D0 − L0 , BS0 }
D0 − L0 ,
0
S1
D1 − L0 − L1
max{D1 − L0 − L1 , 0}
0
S2
D2 − L1
max{D2 − L1 , 0}
0
generates deposit shocks to both banks. At state 1, $100M is transferred from bank B to A; at state 2, $100M is transferred from bank A to B. The chance of state 1 and 2 is 50%. Loans yield a constant margin r, and the cost to recall loans is $c(> 2r). Without a interbank market, both banks hold $100M cash in hands for the deposit shocks. Even the total available credit is $2B,total loan outstanding is $1.8B. The banking industry is not efficient and total profit is $r · 1.8B. Arrow-Debreu security improves efficiency. There are two Arrow-Debreu securities: security I pays off $1 at state 1, and security II pays off $1 at state 2. The price of securities I and II are PI = PII = $0.50. A lends $1B out, and hedge the deposit shocks by buying r · 100M shares of security I. Under state 1, with the payment of $r · 100M from security I, bank A can offer the interest to borrow $100M
24
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
from B. The portfolio, $1B loan plus $r · 100M security 1, yield identical return $r · 1B under both state 1 and 2. Similarly, bank B buys security II and issues $1B loans. The total loan outstanding is $2B, equaling to the total available credit. Arrow-Debreu securities improves banks’ efficiency and total revenue is improved to $r · 2B. Both ABCP and MBS can achieve the same improvement as Arrow-Debreu securities. With ABCP, bank A and B lend $1B initially. At state 1, bank A sells $100M ABCP to bank B, and bank B is ready to buy $100M ABCP with the same amount of deposit surplus. At state 2, bank B sells $100M ABCP to bank A. Hence both bank A and B eliminate deposit shocks exposure. Total loan outstanding is $2B, and total revenue is $r · 2B. ABCP and MBS are more flexible and practicable than Arrow-Debreu securities, as bank A and B do not need to decide the amount of Arrow-Debreu securities they have to buy before the deposit shock occurs. In the real world, such flexibility is crucial. There are more than 8000 banks in U.S., and an infinite number of possible shocks. The requirement of common knowledge of the distribution of possible shocks is unpracticable. However, the trade of ABCP and MBS are based on current shocks. Bank A and B can decide the trade volume after they observe the shocks. Figure 4 summaries how banks depend on both internal funds and the shadow banking system to to absorb the deposit shocks. ABCP is a practical Arrow-Debreu securities to pool the banks’ deposit shocks together and reduces the directly impact of deposit shocks’ on banks’ assets. Then banks liquidate their assets to absorb the rest of the deposit shocks. Liquidity creation on mortgage yields higher return on
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
25
the underlying assets, and facilitate the trade among banks. Compare to figure 1, banks gain more ability to control deposit shocks, and can issue more illiquid loans.
Figure 4. Absorbing Deposit Shock: with ABCP and MBS
26
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
3. Model to Market Limit Chapter 2 shows that the shadow banking system helps individual banks to improve profit margin without taking more liquidity risks, as the liquidity shocks are shared and eliminated through interbank operations. This chapter focuses on the mechanism that the shadow banking system damage the safety cushion, in the view of the banking industry as whole. The key is interbank market’s limit. The market is about to collapse when neither banks nor the regulators are aware that the shadow banking system maybe overloaded. Market’s limits is determined by the nature of deposit shocks originated from the non-financial sectors. Distinguish idiosyncratic risk and systematic risk is crucial to understand market limit, because derivatives can only eliminate idiosyncratic shocks. At least some banks expect that the market has unlimited depth, and keep not sufficient liquid assets. The market becomes overloaded and the banking industry has no enough buffer to absorb the deposit shocks.
3.1. Idiosyncratic and Systematic Liquidity Risk. Deposit shocks are decomposed into systematic shock and idiosyncratic shock. Systematic shock is the aggregate deposit shock to the banking industry, and idiosyncratic shock is the unexpected transfer among banks. Imagine a depositor who has accounts in two banks. His future income is uncertain and his preference to any bank is also random. The income uncertainty is systematic risk, as it changes the net deposits to the banking industry. The depositor’s uncertain preference is idiosyncratic risk. When the depositor transfers money from unfavored bank to favored one, the deposit shocks effect two banks but not the banking industry.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
27
The formal definition of the systematic and the idiosyncratic deposit shock is given in the following manner. There are N banks and bank j’s deposits at time t is Dj,t . Dj,t = Dj,· + εj,t , where Dj,· is bank j’s average deposits, and εj,t is bank j’s total deposit shocks. Let the aggregate deposits Dt = where D is the average aggregate deposits, and ωt = deposit shocks. Bank j bears the share αj (=
P j
D(j,·) ) D
P j
Dj,t = D +
P j
εj,t ,
εj,t measures the aggregate
of systematic risk, and the
remaining is bank j’s idiosyncratic shock νj,t = εj,t − αj ωt . The most important proposition to the idiosyncratic shocks is that
P j
νj,t = 0.
P j
νj,t has no net
effect on systematic shocks. Similarly, the long term investment opportunities is decomposed into the systematic risk uncertainty and the idiosyncratic risk: ξj,t = αj $t + σj,t , where $t is systematic risk and σj,t is idiosyncratic risk. The systematic deposit shock |ωt | is less than the sum of individual banks’ deposit shock
P j
P
|εj,t |. There is not accurate estimation to the ratio
it is expected to be very large.
P j
|εj,t | |ωt | ,
j
but
|εj,t | reflects the dynamical economy. In 2007,
there were more than 20 million Americans changing jobs (about 20% of American non-farm private sector workers), over 647,000 new small business opened, over 568,000 small business closed, and more than 33,000 bankrupted 3. Such a dynamical economy environment created considerable uncertainties to individual banks, especially the reginal ones. Moving from one place to another creates noticeable deposit shocks and loan demand uncertainty. People close bank accounts, pre-pay the mortgage, sell house, cars and other properties, then take the money to a new
3Data is released by U.S. Dept.
of Commerce, Bureau of the Census; Administrative Of-
fice of the U.S. Courts; U.S. Dept.
of Labor, Employment and Training Administration.
www.sba.gov/advo/research/rs258tot.pdf
28
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
place. Opening and closing business also bring considerable uncertainties to banks. However, the systematic shocks are much smaller, as most shocks are canceled out. 3.2. The limit of the Shadow Banking System: The clue of interbank market limit lies in the difference between ωt and
P j
εj,t . The limit of the shadow banking
system is determined by the size of idiosyncratic shocks. The essential idea is illustrated by a similar example. There are two banks, bank A and B, in one island serving the residents. Initially, bank A and bank B receive $1B deposit each. Beside the idiosyncratic shocks - $150M transfer among two banks, there is ±$100M systematic shock caused by residents’ future uncertain income. Table 2 shows the possible deposit shocks to bank A and B. Table 2. Possible Deposits under All States State
Systematic
Idiosyncratic
A’s deposits
B’s deposits
Aggregate Deposits
1
Good (+$100M )
A→B
$0.9B
$1.2B
$2.1B
2
Good (+$100M )
A←B
$1.2B
$0.9B
$2.1B
3
Bad (−$100M )
A→B
$0.8B
$1.1B
$1.9B
4
Bad (−$100M )
A←B
$1.1B
$0.8B
$1.9B
Without the shadow banking system, bank A and B hold $0.2B cash to prepare the deposit shocks. If bank A attempts to issue more illiquid loans, according to Proposition 2.1.1, A suffers bank run under state 3. Similarly, B can issue $0.8B long term loans at most. Then the aggregate long term loan outstanding is $1.6B, less than the minimum aggregate deposits of $1.9B. When ABCP market exists and the size of the market is limited to idiosyncratic risk of $150M , bank A and B need to hold only $50M in cash to absorb the deposit shocks. Under state 1, A sells $50M ABCP to meet the gap between its $0.9B
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
29
deposit and $0.95B loan; bank B has $250M cash in hand to buy all ABCP in the market. Under state 2, B sells $50M ABCP to A. Under state 3, A sells $150M ABCP; and bank B has the exactly same amount of cash in hand to buy ABCP in the market. At state 4, bank B can successfully sell $150M ABCP to A. Bank A and B eliminate idiosyncratic risk to improves their profit margin, and the aggregate loan outstanding is $1.9B, the revenue is $r · 1.9B. when A and B have the illusion that derivatives market has unlimit depth, banks hold no cash in hand as proportion 2.2.1 predicts. A and B lend $1B at current period. During good economics times, bank A buys(sells) $100M ABCP, and B sells(buys) the same amount. Both banks depend on ABCP market to absorb the deposit shock and enjoy the high profit margin. At state 3, bank A needs to sell $200M ABCP, as its deposit is only $800M and its loan outstanding is $1B. But B has only $100M in cash on hand, not enough to purchase all ABCP in the market. Bank A faces a bank run. Similarly, at state 4, bank B faces a bank run. The market may be crashed by few banks’ aggressive investment on illiquid assets. Assume that A recognizes the market limit of $150M , but B does not. A holds $50M in cash and B lends $1B. Both banks survive at state 1 and 2, but not at state 3 and 4. At state 4, bank B needs to sell $200M ABCP, but A has only $150M in cash on hand. At state 3, bank A needs to sell $150M ABCP, but B has only $100M in cash on hand. There is not enough purchase power in the market. Bank run is unavoidable, as bank A has no way to raise necessary fund through the market, no matter what price A asks for.
30
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
The market limit is set up by the derivative demand-and-supply balance under the worst liquidity shocks. Proposition3.2.1 predicts the factors determine interbank market supply and demand. For given deposit shocks, the demand-and-supply is determined by banks’ liquid/illiquid asset allocation. When banks hold more liquid assets, they can depend on their internal funds to absorb the deposit shocks. Hence banks demand less external funds from the derivatives market.
Proposition 3.2.1. The supply/demand of derivatives is a increasing/decreasing function to illiquid asset outstanding, and the supply/demand of derivatives is a decreasing/increasing function to system shocks.
Proof: A bank sells ABCP when its deposit Dj,t is insufficient to support long term loan Lj,t−1 . Let V CSj,t = − min{Dj,t − Lj,t−1 , 0} be ABCP supply for bank j. It is easy to see, the higher illiquid asset position, the higher supply of ABCP. Similarly, the larger systematic liquidity shock is, the smaller ω is, the higher ABCP supply V CSj,t is. Market clearing price is not the first concern of the shadow banking system safety. Pricing mechanism only determines the choice over internal funds and external funds. Banks prefers externals funds when the interest rate is low, and vice verse. And market safety concerns wether the industry as whole has enough liquid assets to liquidate in order to address the deposit shocks. If the banking industry has no enough liquidity assets, no matter what the derivative price is, the interbank market can not provide enough external funds to those who need cash. In another words, the limit of the market is that the derivative supply equals to the derivatives demand under the worst deposit shocks.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
31
Proposition 3.2.2. The shadow banking system’s limit is that banks hedge idiosyncratic risk through derivatives market, and depends on the internal funds to absorb systematic risk. Under the worst deposit shocks, the derivative supply and demand equal to each other, and credit supply can always support existing illiquid loans.
Proof: According to Proposition 3.2.1, the demand is a decreasing function to illiquid asset outstanding, and the supply is a increasing function to illiquid asset outstanding. There exist an unique market equilibrium. When bank absorbs systematic risk by liquidating its liquid asset, long term loan is limited to Lj,t−1 = Dj,0 − αj · ω. And the demand/suppply of commercial paper at time t is max{νj,t , 0}/−(min{νj,t , 0}). Note Σj νj,t = 0, the aggregate commercial paper demand equals to aggregate supply. Proposition 3.2.2 does deny price mechanism and other frictions. Proposition 3.2.2 concerns the existing of the market. Price mechanism works as long as the market exists. For instance, a comparatively low ABCP yield rate encourages banks depends more on external funds and liquidate less assets to absorb the deposit shocks. Price determines the choice over external and internal funds, and price works only when the market exists, and there are enough liquid assets covering the deposit shocks. There is another way to understand Proposition 3.2.2. Banks depend on either external funds or internal funds to answer the deposit shocks. For each bank j, 4Assetj,liquid + 4ABCPj = εj = νj + αj ω For the banking industry as whole Σj 4 Assetj,liquid + Σj 4 ABCPj = Σj νj + Σj αj ω
32
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
As Σj νj = 0 and Σj αj = 1, we have Σj 4 Assetj,liquid + Σj 4 ABCPj = ω. The necessary condition to the interbank market clearing Σj 4 ABCPj = 0 under any shock is that Σj 4 Assetj,liquid = ω for any ω. Then Σj Assetj,liquid ≥ ω, or the banking industry has to depends on liquid assets to absorb the systematic shocks.
3.3. The Path to Overloaded Market. ”The well-known adage that ’one cannot manage what one cannot measure’ is particularly timely with respect to the notion of systemic risk”(Andrew W. Lo [6]). The liquidity risk is determined by the gap between the amount of liquidity assets and the size of deposit shocks. The liquidity risk is accumulated when individual banks reduce their liquid assets and depend on the shadow banking system to to absorb deposit shocks. When individual banks have no enough information to distinguish idiosyncratic shocks and systematic shocks, banks have no way to estimate the market limit. Then the market is about to be overloaded soon or later.
Proposition 3.3.1. When some banks attempt to hedge both idiosyncratic risk and systematic risk through derivatives market, the derivatives market is overloaded. When the systematic shocks are negative, the ABCP supply exceeds the demand, and the credit supply is less than credit demand. Banks can not meet net withdrawals by borrowing from interbank market. Bank run occurs.
The explanation is based on the fact that individual banks are not able to distinguish between idiosyncratic deposit shocks and systematic shocks. Banks just observe cash flow in and out εj,t , and have no clue on the size of idiosyncratic shocks νj,t and systematic shocks ω. For instance, a distributor purchases GUCCI purses from Chinese manufactory and requires his bank transferred $100M out of
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
33
America, $40M after the contract and $60M in three months. Consequently, Chinese manufactory has to import alligator skin from Florida, which leads to $60M cash flow into another American bank. The systematic shock is −$40M after the contract, then +$20M , and −$40M in the end. However, there is no way for both banks to tell their share of systematic shocks by observing their own cash flows. Without the information of systematic shocks, banks estimated the market limit by their own experience, especially the successful experience during the crises: S&L crisis, Asian financial crisis, LTCM and Russian financial crisis, Dot-Com bubble, 911 and South American currency crisis, etc. As the market never failed banks’ demand for short term credit, bank built up the confidence on the market, and never bothered to think about the market limit any more. The market expanded quickly. On one hand, more banks accepted the idea to share and eliminate liquidity risk through the interbank market. The more banks joined the market, the deeper was the market, and the more idiosyncratic shocks were eliminated. On the other hand, the successful banks took over the market share from the less profitable banks, who held more liquid assets and depended on their own internal fund to absorb the shocks. Optimism dominated the industry. Banks assumed that the market had unlimited depth, and felt safe to reduce their liquid assets. The market was overloaded after all banks issued more long term loans. The banking industry as whole did not have enough liquid assets to absorb systematic deposit shocks. A small negative shock crashed the market. During the crash of subprime crisis, $500B bad loans or less than 5% loss of total mortgage outstanding, triggered the worst recession ever since the great depression.
34
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
After the interbank market collapsed, banks did not only write off the subprime mortgages losses, but had to fire sale long term loans. Because banks needed more liquid assets to answer the deposit shocks. The simultaneous fire-sale of long term loans, both subprime and other subprime unrelated long term loans, pushed the price down. As the fire-sale price was far below its fundamental, it required far more capital to cover the ’losses’, than the actually underlying assets losses. The estimated losses in subprime mortgages of between $400 and $500B are relatively modest in terms of wealth destruction, which are roughly correspond to a non-souncommon drop of between 2 and 3 percent of the U.S. stock market (Markus [47]). The model explains why Fed and Treasury spent more than $2T , but still did not fix the problem caused by a moderate shocks. Meanwhile, banks stopped issue new loans, cut back re-financing, and froze other credit supply to the real economy. The economy was in recession.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
35
4. Evidences This chapter provides some evidences that the shadow banking system plays more important role in sharing and eliminating deposit shocks among banks. Actually, some puzzle under the credit risk models turn out to be evidence to the liquidity risk model, for instance, ’securitization without risk transfer’ (Acharya etc [1]). 4.1. Banks Represent the Financial Industry: The earliest known deposit bank, Banco di San Giorgio, was founded in 1407. Today, banks still play a important role in channeling investors and borrowers, and keep the essential of the business model - borrowing-short-and-lending-long. The developing of market did not slow the developing of banking industry. On the contrary, depending on the shadow banking system as the external resources to address deposit shocks, banks are more robust and more efficient. Table 3 shows significant reduction in bank failures. Banks’ successful survival of numerous crises makes banks’ asset management a good represent to the operations in the shadow banking system. And the wisdom of banks operation in the shadow banking system is helpful to understand how the system as whole works. Table 3. Bank Failures: 1982-2007 Year # of failures Year # of failures
82
83
84
85
86
87
88
119
99
106
180
204
262
470
89
90
91
92
93
94
95 ∼ 07
534
382
271
181
50
15
58 total
More evidences are listed in three aspects: first, banks did not depend on interbank market to shift credit risks; secondly, banks’ operation is similar to other
36
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
financial institutions in the shadow banking system; last, banks were serious investors in the interbank market. • Banks did not depend on the shadow banking system to shift credit risks. It is a puzzle in the view of credit risk models that banks ’securities’ mortgages and hold MBS. Banks did not buy credit risk insurance from market either. When Collateralized debt obligations (CDOs) and other derivatives, which were designed to hedge the credit risk, expanded to $24T at 2008. Less than 1.5% of MBS held by banks is covered by CDOs4. The buying and selling of CDS by large U.S. banks were similar. Before the crisis, large U.S. banks bought $4.165T CDS and sold $4.094T CDS, and the net CDS position was $71B, which counted 2.1% of their loans (Duffie [23]). The phenomenon indicates that banks had the confidence to manage both credit risk and other types of risks. Meanwhile, banks expanded their market share as other financial institutions in the shadow banking system. Eichengreen ([25]) showed that banks typically outsource mortgage issuance and paid fee to independent mortgage brokers. • Commercial banks investment strategy was not significantly different from other financial intuitions. Table 4 compares Bank of America’s balance sheet with Bank of America Secularities, an investment bank, before the subprime crisis. Both the commercial bank and the investment banks borrowed from and lent to REOP simultaneously. Both the borrowing and the lending were significant large than the direct investment on securities.
4S&P Industry Report: Investment and Diversified 2009.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
37
Table 4. BOA Securities and BOA Balance Sheet, Dec 2006 (in B$) BOA
BOA Securities
Lending to REPO
288
80.5
Directly Securities Holding
192
69
Borrowing from REPO
285.1
136
Net Borrowing from REPO
-2.9
55.5
Asset
Liabilities
Source: BOA and BOA Securities Annual Report, 2006.
Table 5 compares the breakdown of CDS buyers and that of CDS sellers in 2007, which indicates that banks’ operations in the shadow banking system is similar to hedge funds and mutual funds. All of them were actively buyers and sellers in the market, and their net position was relatively small.
Table 5. The Breakdown of CDS Buyers and Sellers, Dec 2006 (in %) Breakdown of Buyers
Breakdown of Sellers
Net Position
Banks and Dealers
33
39
-6
Hedge Funds
31
28
3
Mutual funds
3
2
1
Insurers
18
6
12
Loan Portfolios
7
20
-13
Pension Funds
5
2
3
corps
2
2
-
Mics
1
1
-
Source: Bank of America, March 2007.
38
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
The large amount of buying-and-selling operation indicates that the shadow banking system served the banks for other objects rather than financing and shifting credit risks.
• Table 7 and table 6 show banks’ operation in the shadow banking system was consistent. Banks were actively buyer/seller in the market, and were investors in net. Table 6 shows that at the end of 2007, commercial banks mortgage exposure was $2.881T, of which 69.12% was direct held and 32.98% was held in RMBS. Commercial banks’ RMBS to direct holding ratio was higher than the average over all private leveraged institutions. The ratio was way above the necessary inventory required to package and sell MBS, which is less than 1% of MBS outstanding for brokers5. By comparing commercial banks MBS holding with other institutional investors’ Table 6. Home Mortgage Exposure at 2007 (in B$) Home Mortgage Debt
Total
Total
11,028
1,368
5,591
671
US Leveraged Institutions
Direct
MBS
subprime
M BS Direct
Commercial banks
2,881
1,935
946
250
48.9%
Savings Institutions
1,148
895
253
-
28.3%
Credit Unions
361
300
61
-
20.3%
Brokers and Dealers
213
0
213
-
-
GSE
987
457
530
112
116.0%
Source: Federal Reserve Board, FDIC, calculated by Greenlaw etc, 2008.
from 2004 to 2006, table 7 shows similar result. Banks held 20% more MBS 5Estimated by Bank of America.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
39
Table 7. MBS Investors at 2005 and 2006($ Billions) Investor type
2006
2005
%
% Since
All MBS
Non-agency
All MBS
Non-agency
Chg
2004
FDIC banks
876
124
913
158
20
4
FannieMea/FreddieMac
1,261
267
1,192
363
26
-5
Life Insurance
465
N.A.
480
N.A.
10
3
Mutual Fund
318
N.A.
325
N.A.
7
2
Personal Sector
270
N.A.
290
N.A.
6
7
Public Pension
270
N.A.
275
N.A.
6
2
All Thrifts
234
7
228
6
5
-3
Priv. Pension
125
13
128
15
3
2
FHL Banks
113
71
117
71
3
3
REITs
95
50
105
60
2
11
Dealer Inventory
41
15
55
20
1
34
Federal CreditUnion
28
N.A.
29
N.A.
1
2
Finance Companies
85
N.A.
88
N.A.
2
4
Foreign Investors
280
30
400
50
9
43
Others
317
N.A.
474
N.A.
49
N.A.
Total Outstanding
4,779
1,076
5,098
1,289
9.1
N.A.
Source: Inside MBS & ABS, computed by JPMorgan 2006.
from 2005 to 2006; from 2004 to 2006, banks invested 4% more in MBS, which was higher than Fannie Mea and Frediie Mac, insurance companies, pension funds, who were supposed to be at better position to bearing the credit risks. As the top three investors in year 2006, and top five from 2004
40
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
to 2006, banks were most active investors in the shadow banking system, then
4.2. The Shadow Banking System: Previous researches focus on how the shadow banking system directly channels investors and borrowers, and assume that banks’ operation was described by the models. For instance, origination-and-distribution model catches the benefit to agency and the potential risks to the investors, and treats banks as brokers. This section shows evidences that instead of being brokers in the shadow banking system, banks used the interbank market as external sources to share and eliminate the deposit shocks. Financial innovations and the derivative market did not change banks’ business model, but re-enforced their core business - borrowing-short-and-lending-long. The evidences are presented in two aspects: first, we will review banks’ buying-and-selling operations in the interbank market in a long period window; secondly, we will exam the interbank operation’s direct impact on their profit. By comparing banks’ quarterly net change in mortgages and MBS from 2006Q4 to 2008Q4, table 8 shows that banks were potential buyers as well as sellers in the market. Banks were net sellers in three of nine quarters, and net buyers in the rest six weeks. By comparing mortgage new issuance and net MBS change, table 8 also indicates that banks did not depend on MBS to transfer the credit risks to other investors. MBS net change was higher than the the sum of residential mortgage and commercial mortgage net issuance in four of nine quarters; MBS net change was similar to net mortgage issuance in two quarters; and net MBS change was less than net mortgage new issuance in the rest three quarters. By comparing banks’ annual net change in mortgages and MBS from 1999 to 2008, table 9 shows similar
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
41
Table 8. Quarterly Net Change in Mortgages and MBS, 2006Q4-2008Q4 items
2006
2007
Q4
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
4.7
8.04
10.37
3.63
-5.62
-3.93
-8.60
-7.52
-3.73
Commercial Real Estate
11.96
6.14
9.76
9.22
9.49
5.05
5.32
4.628
0.8
MBS
7.36
7.83
-2.58
-7.58
5.36
19.25
15.52
-13.10
15.49
Capital Account
9.48
6.69
3.69
19.4
7.06
5.19
-.90
-4.89
-6.85
Federal Home Loan Bank
1.53
22.09
10.09
92.3
0.38
15.53
8.02
52.85
-56.15
One-to-Four-Family
2008
Source: Federal Reserve Bulletin, June, 2009.
result as table 8. The net MBS change is not necessary positive, neither does it correlated with net mortgage issuance. From 1999 to 2008, banks’ MBS increment Table 9. Net Change in Mortgages and MBS, all U.S. banks, 99-08 Item
99
00
01
02
03
04
05
06
07
08
% Residential Mortgage
12.22
10.74
7.94
14.44
9.75
15.41
13.8
14.49
7.044
4.49
% Commercial Mortgage
15.42
12.16
13.1
6.82
8.99
13.93
16.87
14.91
9.2
6.77
% RMBS
-3.34
3.29
29.05
15.54
10.12
13.45
2.06
10.22
-1.24
11.37
Source: Federal Reserve Bulletin, June, 2009.
was higher than mortgage increment in four of ten years (year 01, 02, 03 and 08); banks bought MBS, but MBS increment was less than mortgage increment in year 04, 05 and 06); banks were net sellers only in two years 99 and 07. Banks buy and sell MBS simultaneously in the second market, even during the crisis. Table 10 reports banks’ revenue and cost from 2000 to 2008. First, interest net income was the only source to banks’ profit over the whole period. Banks did not make any net profit from non-interest business at all. Even worse, the net non-interest expense climbed from $63B in 2000 to $148B in 2008. Banks also
42
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
Table 10. Revenue and Cost of U.S. Banks, 2000-2008, Million$ items
00
01
02
03
04
05
06
07
08
Gross income
423,845
404,251
349,603
329,218
348,667
426,600
551,039
616,995
566,000
Gross expense
222,161
188,746
118,741
94,123
98,541
162,501
263,372
310,412
227,066
Deposits
151,147
132,311
81,701
62,400
63,639
105,922
173,878
212,783
154,812
repurchase
26,860
19,583
9,920
7,590
8,842
19,161
33,775
37,715
19,755
Other
44,155
36,852
27,122
24,133
26,058
37,418
55,720
59,914
52,499
201,684
215,505
230,862
235,095
250,126
264,099
287,667
306,583
338,934
Gross income
153,101
160,902
168,236
183,792
188,999
201,768
222,887
218,554
207,880
Gross expense
216,375
225,979
230,128
243,214
263,304
274,136
294,890
321,406
355,910
Net expense
63,274
65,077
61,892
59,422
74,305
72,368
72,003
102,852
148,030
-2,280
4,630
6,411
5,633
3,393
-220
-1,320
-649
-16,186
Interest
Net income Noninterest
Investment Net income
Source: Federal Reserve Bulletin, June, 2009. lost money on security investment after 2005. In the best year, banks’ investment income accounted for less than 3% of net-interest-income. All the numbers indicate banks do not buy/sell derivatives for profit, but more likely for hedging purposes. The gap of interest expense and interest income provides important information of banks’ portfolio. As the interest spread was relatively stable before the subprime crisis, banks had invest more long term loans and held less liquid assets. Otherwise, banks could not improve their interest gross income by more than 50% and kept their interest gross expense at the same level.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
43
4.3. The Deposit Shocks: The deposit shocks are the origination to liquidity risks. Tobin ([56] ) in 1982 pointed out that the deposit uncertainty could erode banks safety. ’To be sure of realizing their (illiquid assets’) full value, the bank must hold them to maturity. Consequently, these assets can be available for meeting deposit withdrawals only at some risk of loss.’ And banks need to hold a certain quantity of liquid assets to absorb the deposit shocks. Even the shadow banking system created liquidity among banks, Tohin’s definition of liquid assets is still valuable to analysis the industry liquidity safety, which is still account on the aggregate liquid assets to absorb the deposit shocks as it did centuries before. Banking industry safety is determined by whether banks can successfully shield the illiquid assets from deposit shocks. Figure 5 compares weekly deposit change and loan change from 1974 to 2009. Deposit shocks are the weekly deposit change, defined by way
Depositt −Depositt−1 . Depositt−1
Loant −Depositt−1 . Loant−1
And weekly loan change is defined in a similar
In normal times, deposit changes, the blue solid line, is
significantly more volatility than loan changes, the red dot-line. More importantly, the figure also reveals that loans were perfectly covered from deposit shock. Net withdrawals were common as the blue line stays blows zero quite often. But the loan changes were all positive except during recessions in 1973, 1990, 2001 and 2007. Another way to measure deposit shocks and loan adjustments is the standard deviation(STD) of deposit/loan changes, given by Figure 6. Deposit shocks were dominant before the crisis. The difference between loan STD and deposit STD was even bigger before 1985.
44
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
Figure 5. Deposit Change v.s. Loan Change: 1974-2009 (in %)
Ͳ
Ͳ
Ͳ
Source: Federal Reserve Banks
Deposit shocks dominating loan changes is not a recent phenomena. Figure 7 compares Loan/deposit STD before the great depression. Deposit shocks dominated asset change in good time, and the inverse of this relationship predicted the great depression. The long term high frequency observations indicate that deposit shocks are not trivial. The market safety was, and is counting on banks’ ability to shield the assets from the deposit shocks. Otherwise, fire sale will bring extra losses to the banks, which is far beyond losses due to credit risks. AIG bailout is such a case. In September 2008, AIG was downgraded by S&P, Moody and Fitch. AIG was forced to liquidate some of its assets to address $20B in additional collateral
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
45
Figure 6. Deposit STD v.s. Loan STD : 1985-2009
Ͳ
Ͳ
Ͳ
Ͳ
Ͳ
Ͳ
Ͳ
Ͳ
Ͳ
Source: Federal Reserve Banks
calls due to these downgrades. AIG raised $19.8B by a fire sale of residential mortgage-backed-secularities to NY Fed in Oct 2008, and the directly losses of the sale was $19.5B(Sjostrom [53]). The fire-sale price deviated far away from the asset’s fundamental, as most of AIG’s MBS holding was classified to ”Super Senior”, which was safer than AAA bonds. After banks failed to protect their illiquid assets from deposit shocks, the market collapsed. The ABCP outstanding dropped more than 40% from 2007 to 2008, even the the margins reduced more than 1%, from over 5% in 2006 to 4% in 2007 (Brunnermeier and Pedersen [47]). There was significant withdrawn from all inter
46
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
Figure 7. Deposit and Loan Position Change Volatility % (1921-1929)
Source: Federal Reserve Banks
bank market, including the Fed funds market. The number of lenders in the Fed fund market was over 300 before the crisis, and the number reduced to around 100 in 2009 (Afonso etc [4]). After the interbank market was frozen, the external resource to banks were frozen and the liquidity creation was gone. Banks needed to depend on their internal funds to absorb the deposit shocks. By comparing 98 international banks with assets in excess of $50B at 2006, including 19 U.S. banks, Beltratti and Stulz ([9]) show that banks with more loans (less liquidity creation) and more liquid assets performed better after Lehman bankruptcy, banks with more deposits and less ABCP, who depended less on external funds from the shadow banking system, also performance better after Lehman bankruptcy. The financial stress hit the real economy after banks cut back re-financing and new loans issuance to hold more liquid assets. 4.4. Other Evidence: There are other evidences that banks’ operation in the shadow banking system is less credit risk related as ordinate-to-distribute model
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
47
predicts. Comparing the returns and financial characteristics of the loans securitized and sold, securitized and not sold, and not securitized, Berndt etc ([10]) found that borrowers in an active loan market, whose loans were more likely to be securitized, had higher credit rating; and banks were more likely to hold the loans lent to the borrowers with rating lower than BB. Demyanyk and Hemert ([18]) reported the FICO scores of the first-lien subprime loans from 2001, the average FICO scores raised from 601.2 in 2001 to over 618 in 2006. Gorton ([32]) compared quarterly delinquency rate between prime borrowers and subprime borrowers from 2003Q1 to 2007Q4, and the ratio of
P rimeDelinquencyRate SubprimeDelinquencyRate
was stable. David etc ([37])
computed the U.S. investment banks and commercial banks leverage from 1998 to 2008, and show that commercial banks leverage was stable before the crisis, and investment banks leverage increased slightly.
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
5. Summary We are not skilled enough in these areas and we should not be expected to, Alan Greenspan 2007 Two years after the subprime crisis, our knowledge of liquidity risk is still behind the market complexity. Based on the deeply rooted belief of the credit risk model, most researches focus on banks’ potential losses of their risk investments and the amount of adequate equity to write off the bad assets. Crises, in the view of the credit risk model, are unpredictable rare events. This paper introduces a independent liquidity risk model to show that banks’ liquidity safety depends on their ability to protect illiquid assets from exogenous deposit shocks, and the liquidity risk could be absorbed by both banks’ internal funds and external resources from the shadow banking system. • First, liquidity risk is not caused by assets price fluctuation. On the contrary, it is the reason to irrational price. The banks with solid assets can not stay away from the crisis, because the disappear of the interbank market cuts back their external resources to absorb the deposit shocks. All banks have to increase their liquidity assets, and a massive fire-sale of illiquid assets amplifies the deposit shocks and leads to bank panic. • Second, MBS, ABCP and derivatives are practicable Arrow-Debreu securities for banks to share and eliminate the deposit shocks. Banks reduce their exposure to exogenous deposit shocks by buying/selling ABCP. MBS creates mortgages’ liquidity through interbank market. The transfer of MBS among banks has less impact on housing price than restricting refinancing
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
49
and foreclosure. Derivatives help banks to gain more control of their capital flow, then banks issue more long term loans without compromising safety. • However, derivative market has its limits, which are determined by idiosyncratic deposit shocks. Banks lack the knowledge to distinguish between idiosyncratic shocks and systematic shocks, and mistakenly believe that the market has unlimited depth. When banks issue too much long term loan, the market is overloaded and the banking industry as whole does not have enough liquid assets to absorb systematic deposit shocks. A small negative shock in a weak economy can trigger bank runs and crash the industry. The key differences between independent liquidity risk model and credit risk model are listed in the following table.
Table 11. Credit Risk v.s. Liquidity Risk Credit Risk
Liquidities Risk
The Origination to Risk
random future returns
realized deposit shocks
Risk Measurement
Price Fluctuation
Deposit/Loan Volatility
Risk Management
Predict Rare Events
Share and reduce deposit
Appropriate Pricing Model
shocks through Arrow-Debreu
Raise Capital
Securities
Market Collapse
mis-pricing
overloaded market
Crisis Prediction
not-available
Loan volatility Converges to Deposit Volatility.
Under the liquidity risk model, the subprime crisis is divided into three phases according to banks’ liquidity preference and the market evolution.
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
• Before the deregulation, banks were largely absorbing the deposit shocks through their internal funding. Banks had to hold enough liquid assets to prepare unexpected withdrawal. The banking industry as whole required less liquid assets to absorb the systematic deposit shocks. The industry was safe but less efficient. • After the deregulation, banks learned to absorb the deposit shocks through the interbank market. Banks gradually reduced their liquid assets and reallocated the resources on high yield long term investments. The banking industry held less liquid assets, but its liquid assets were still enough to absorb systematic shocks. • At 2007, mortgages alone accounted 65% of banks’ assets, almost doubled their weight before 1995. The interbank market was overloaded and the banking industry as whole held too little liquid assets to prepare the deposit shocks. $500B loss during the subprime mortgage created enough deposit shocks to crash the market. Without the interbank market, all banks suddenly realized that their liquid assets were not enough to buffer the exogenous shocks. The simultaneously selling of mortgages and MBS ends in bank panic.
This paper sets up a framework to analyse bank liquidity risk, and provides supporting evidence from recent date. The results are helpful to the debate among restrictive government regulation and free market. While Alan Greenspan (former Fed Chairmna) disagrees with the idea of rolling back commercial banks to GlassSteagall era, Volcker (former Fed Chairman) and Joseph. Stiglitz, standing with other economists, argue that risky securities ’brought us to where we are today’,
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
51
and ’a cleaner and safer banking system’ requires ’splitting banks from investment banks’. The common knowledge of bank liquidity risk helps the government and the Wall Street to work together to monitor the risks and prevent future banking crisis.
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
References [1] Viral V. Acharya, and S. viswananthan, (2010), ”Leverage, Moral Hazard and Liquidity”, NBER working paper [2] Acharya, Viral V. and Schnabl, Philipp, (2010). ”Do Global Banks Spread Global Imbalances? The Case of Asset-Backed Commercial Paper During the Financial Crisis of 2007-09”. Economic Review, International Monetary Fund, Forthcoming. [3] Viral Acharya and Tanju Yorulmazer, (2007). ”Cash-in-the-market pricing and optimal resolution of bank failures,” Bank of England working papers 328, Bank of England. paper 15837 [4] Gara Afonso, Anna Kovner, Antoinette Schoar (2010). ”Stressed not Frozen: The Fed Funds Market in the Financial Crisis”. NBER Working Paper No. 15806 [5] Allen, Franklin, and Elena Carletti, (2006), ”Credit risk transfer and contagion”, Journal of Monetary Economics 53, 89-111. [6] Lo, Andrew W., (2008). ”Hedge Funds, Systemic Risk, and the Financial Crisis of 2007-2008”. Written Testimony for the House Oversight Committee Hearing on Hedge Funds. [7] Arvind Krishnamurthy, (2009), ”How Debt Market Have Malfunction in the Crisis”, NBER working paper 15542 [8] Ashok V. Desai, (1968). ”Who Keeps His Money in the Bank?”. Economic and Political Weekly, Vol. 3. No3. 197-198 [9] Andrea Beltratti and Ren M. Stulz, (2009). ”Why Did Some Banks Perform Better During the Credit Crisis? A Cross-Country Study of the Impact of Governance and Regulation,” NBER Working Papers 15180, [10] Berndt, Antje and Gupta, Anurag, (2009). ”Moral hazard and adverse selection in the originate-to-distribute model of bank credit,” Journal of Monetary Economics, vol. 56(5), pages 725-743 [11] Berger, Allen N. and Bouwman, Christa H. S. (2008). ”Financial Crises and Bank Liquidity Creation” [12] Berger, Allen N. and Bouwman, Christa H. S.,(2008). ”Bank Liquidity Creation” Revieve of Financial Studies. Vol22: 3779-3837
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[27] Fama, Eugene (1970). ”Efficient Capital Markets: A Review of Theory and Empirical Work”. Journal of Finance 25 (2): 383C417. [28] Cai, Fang, (2002). ”Does the Market Conspire Against the Weak? An Empirical Study of Front Running Behavior During the LTCM Crisis”. EFA 2002 Berlin Meetings Presented Paper. [29] Franklin Allen and Douglas Gale, (2007), ”Understanding Financial Crises (Clarendon Lectures in Finance)”, Oxford University Press, USA. [30] Gary B. Gorton, (2010), ”Questions and Answers about the Financial Crisis”, NBER working paper 15787 [31] Gary B. Gorton and Andrew Winton, (2002), ”Financial Intermediation”, NBER working paper 8928 [32] Gary B. Gorton , (2008), ”The Panic of 2007”, NBER working paper [33] Gary B. Gorton and Ping He, (2007), ”Bank Credit Cycles”, working paper [34] Gary B. Gorton , (2008), ”The suprim Panic”, NBER working paper [35] Gary B. Gorton , (2009), ”Slapped in the Face by the Invisible Hand: Banking and the Panic of 2007”, Federal Reserve Bank of Atlanta’s 2009 Fianancial Markets Conference. [36] Kay Giesecke, Francis A. Longstaff, Stephen Schaefer, and Ilya Strebulaev, (2010), ”Corporate Bond Default Risk: a 150-year Perspective”, NBER working paper 15848 [37] David Greenlaw, Jan Hatzius, Anil K Kashyap, and Hyun Song Shin. (2008), ’Leveraged Losses: Lessons from the Mortgage Market Meltdown’ US Monetary Policy Forum Conference [38] Jorion, Philippe, (1999). ”Risk Management Lessons from Long-Term Capital Management, European Financial Management”, September 2000. [39] Johannes C. Stroebel and John B. Taylor. (2009). ”Estimated Impact of the Fed’s MortgagesBacked Securities Purchase Program”. NBER Working paper 15626. [40] John L. Eatman, and Calvin W. Sealey, Jr. (1977). ”A spectral analysis of aggregate commercial bank liability management and its relationship to short-run earning asset behavior”, Jouranl of Financial and Quantitative Analysis, Vol. 12, No. 5, [41] Joshua Aizenman and Gurnain Kaur Pasricha, (2010), ”On the Ease of Overstating the Fiscal Stimulus in the U.S.”, NBER working paper 15784
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[42] Jan Kregel (2008). ”Minsky’s Cushions of Safety”, Public Policy Brief [43] Jan Kregel (2008). ”Changes in the U.S. Financial System and the Subprime Crisis”. The Levy Economics Institute of Bard College. Working paper No. 530. [44] Leland, Hayne, and David Pyle, (1977), ”Information asymmetries, Financial structure, and Financial intermediation”, Journal of Finance 32, 371-387. [45] Hyman P. Minsky. (1987). ’Securitization’, Policy Note, The Levy Eco nomics Institute of Bard [46] Mark Carey, Rene M. Stulz, (2005), ’The Risks of Financial Institutions’, NBER working paper 11442 College. [47] Markus K. Brunnermeier and Lasse Heje Pedersen, (2007). ”Market Liquidity and Funding Liquidity” NBER Working Paper No. 12939 [48] Markus K. Brunnermeier. (2008). ’Deciphering the 2007-2008 liquidity and credit crunch’ Journal of Economic Perspectives, forthcoming. [49] Parlour Christine and Guillaume Plantin, (2008), ”Loan sales and Relationship Banking”, Journal of Finance 63, 1291-1314. [50] Pezzuto Ivo, (2008). ”Miraculous Financial Engineering or Toxic Financ? The genesis of the U.S. Subprime mortgage loans crisis and its consequences on the global financial markets and real economy”. SMC working paper, [51] Rajan, Raghuram, (2008), ”A View of the Liquidity Crisis”, mimeo, University of Chicago. [52] Ding, Bill, Shawky, Hany A. and Tian, Jianbo (2008). ”Liquidity Shocks, Size and the Relative Performance of Hedge Fund Strategies”. Journal of Banking & Finance, vol. 33(5), pages 883891 [53] Sjostrom, William K.,(2009). ”The AIG Bailout” Washington and Lee Law Review, Vol. 66, p. 943, 2009. [54] Tobias Adrian and Hyun Song Shin, (2007), ”Liquidity and Leverage”, Federal Reserve Bank of New York Staff Reports [55] Tobias Adrian and Hyun Song Shin, (2008), ”Financial Intermediary Leverage and Value-atRisk”, Federal Reserve Bank of New York
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[56] Tobin, James. (1882). ”The Commercial Banking Firm: A Simple Model”. Journal of Economics, 84(4) 495-530 Staff Reports [57] Wagner, Wolf, (2007). ”The liquidity of bank assets and banking stability,” Journal of Banking & Finance, vol. 31(1), pages 121-139. [58] Yoram Landskroner and Jacob Paroush, (2008), ”Liquidity Risk Risk and Competition in Banking”, New York University, working paper.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
Jianbo Tian, 363 Manning Blvd, apt2, Albany, NY 12206, [email protected]
57
Keywords: liquidity risk, derivatives, origination-and-distribution model, interbank market, bank run, subprime crisis JEL Classifications: D12, G12, G21
Contents 1. Introduction
3
2. Model to Bank’s Asset Management
13
2.1. Benchmark:
15
2.2. ABCP Eliminates Deposit Shocks:
17
2.3. MBS Creates Liquidity.
20
2.4. ABCP and MBS as Arrow-Debreu Securities:
22
Received by the editors July 2010. 1
2
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
3. Model to Market Limit
26
3.1. Idiosyncratic and Systematic Liquidity Risk
26
3.2. The limit of the Shadow Banking System:
28
3.3. The Path to Overloaded Market
32
4.
35
Evidences
4.1. Banks Represent the Financial Industry:
35
4.2. The Shadow Banking System:
40
4.3. The Deposit Shocks:
43
4.4. Other Evidence:
46
5. Summary
48
References
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
3
1. Introduction It’s not the things you don’t know that cause disasters; it’s the things you do know, but are’t true. Mark Twain This paper introduces a liquidity risk model to understand how shadow banking system changes commercial banks’ operation, and the benefits as well as the risks of the system. The term ’shadow banking system’ was used by Freidrich Hayek in 1935, referring to the credit growth by unregulated institutions. In the book ’Prices and Production’, Hayek pointed out that shadow banking system was ’other forms of media of exchange which occasionally or permanently do the service of money’. As the system was not ’subject to any central control’, a collapse of credit was to be unavoidable when the credit originated from shadow banking system was converted into other forms of money. After the financial deregulation in the late 1980s, financial innovations expanded the shadow banking system rapidly. The over-the-counter(OTC) trading of structured investment vehicles, including CDOs, CDS’s and other derivatives, expanded from zero in 1980s to a over $20T before the subprime crisis. The shadow banking system competed with commercial banks in channeling the investors and borrowers, and was supposed to bear the similar risks to the banking system. Gorton ([30], [31], [32], [33], [34] and [35]) repeatedly compared the shadow banking system with the banking industry and concluded that the subprime crisis was caused by improper regulation, and the essential of the subprime crisis was a bank run among financial institutions.
4
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
The failure of the derivatives market indicated the imperfection of credit risk models. Even without central regulation, financial institutions have a long tradition of expertise in analyzing the amount of capital necessary to support its risk portfolios. Mature credit risk management techniques have been systematic used, including information collection by credit scoring systems and bureau scores (FICO, NextGen, VantageScore, Equifax, Experian, TransUnion, etc), data analyses techniques (portfolio aging and vintage analyses, deliquiency/roll rates/flow rates analyses, internal rating-based approaches, external rating agencies’ models, classified accounts), and credit risk models (Basel II models, CreditMetrics, Credit Protfolio View, CreditRisk+, Merton OPM/KMV Moody’s model, VaR, and so on)(Ivo [50]). However, credit risk models cannot fully explain the risks to the financial institutions, as the asset prices could dramatically deviate from their fundamentals, especially during the crisis. In 2008, ABX index lost more than 45% of their value, and subprime-mortgage-backed-securities alone lost over $1T market value. Such losses did not reflect the underlying asset’s losses at all. Based on loanlevel data, David ([37]) estimated that even housing prices declined 20% more in 2009, all underwater mortgages led to the total losses of $500B, which was only 50% to subprime-mortgage-backed-securities losses. As of 2010, the average subprime default rate was around 19%, which was 65% less than the losses of subprimemortgage-backed-securities. Meanwhile, the market saw the similar losses of other subprime unrelated assets, such as primary mortgage backed securities, student loan backed securities, credit card backed securities etc. Gorton ([35]) described the credit risk models failure as ”slapped in the face by the invisible hand”.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
5
The industry has acknowledged the existence of other risks beside credit risk. Mark and Rene ([15]) pointed out that credit risk only counted about 53% of banks risks before 2007. Basle committee has chosen a confidence level of 99% and a 10-day horizon to compute VAR, and the resulting VAR is multiplied by a factor of THREE to determine the minimum capital1. The assumption that total risk was capped by three times credit risk may works in normal time, but the total risk can easily exceed the cap during the crisis. For instance, Jorion ([38]) estimated that LTCM’s losses ’would occurs once every 800 trillion years, or 40,000 times the age of the universe, according to standard credit risk model. The cause of LTCM’s losses was not the credit risk of its portfolio, but the fire-sale of its assets. Surely, credit risk model was not sufficient, and the chosen of arbitrage factor of THREE by Basel II was not enough, especially during the crisis. As individual financial institutions are aware of the credit risk model’s limit, the market was cursed by the prisoner’s dilemma during the crisis. Every one was willing to sell, but refused to buy even the price was much lower than the rational price. The subprime crisis evidences that the market may be as irrational as it was before World War II, as John Keynes described that ’market can remain irrational longer than you remain solvent’. We introduce a liquidity model to answer market’s call for a new theory to explain how market remains solvent. Even the model has its insight for both banking industry and shadow banking system, this paper applies the model to the banking industry for good reasons. First, the shadow banking system as whole carries out the similar function and bears the similar risks as the banking industry (Garton [32], [33] and [35]). It is easier to deliver 1
These capital adequacy requirements are detailed in the Basle Committee on Banking Super-
vision 1995.
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
the essential ideas based on the understanding to banking than to jump into the shadow banking system with opaque information. Secondly, the most restrictive regulation did not keep banks stay away from the shadow banking system. Banks’ liquidity preference honestly reflects the risks from the derivatives market. Last, banks’ balance sheet has been regularly released by the Federal Reserve System, FDIC and other government agencies, which make it possible to verify the model. The liquidity model focuses on market depth and the earlier warning indicators to remain solvent, which is independent from credit risk models, who attempt to predict the losses. In banks’s view, liquidity risk is about the quantity of sustainable long term loans, and credit risk is about loans’ return until mature. Bank run does not occurs, because of bad assets; it occurs because the bank has not enough time to liquidate its assets (Diamond and Dybvig [21] Diamond [20]). Liquidity risk model and credit risk model explain the causes of the crisis from different origination of the shocks. All credit risk models can be derived from random discount model (Cochrane [17]). The prices reflect the present value of future cash flow: P rice = E(mX), where m is random discount factor and X is the future cash flow. The model suggests that the origination to the market volatility is exogenous shocks 4E{mX}. Price changes reflect exogenous information 4E(mX) ⇒ 4P rice. Market is efficient in recognizing the exogenous information(Fama [27]). During the crisis, the losses in asset value reflect either the falling return of individual project X or the bad macro-economy enviornment m or both. The safety is depends on the amount of capital to absorb such possible losses. Bank run occurs when the losses exceed the capital. The credit risk model explains the process of bank panic by the following chain reaction:
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
7
(OriginalShocks) 4 E{mX} ⇒ 4AssetP rice ⇒ 4BankAssetV alue ⇒ 4DepositsW ithdrawals ⇒ BankRuns If a efficient market fails to recognize the signals to predict a crisis, the crisis is unavoidable and there is nothing to do to stop it in advance. Solvent problem concerns whether an existing long term investment can be rolled over on short term financing, and fire-sale due to insolvency may not relate to the fundamentals at all(Acharya and Yorulmazer [1], Brunnermeier etc [14]). For instance, LTCM lost more than $150 million when forced to liquidate its positions in Royal Dutch Shell trade. Under ’convergence-arbitrage’ trade strategy, LTCM established an arbitrage position in the dual-listed company Royal Dutch Shell in the summer of 1997, when Royal Dutch traded at an 8-10% premium relative to Shell. The investment in Shell was financed by ’short’ in Royal Dutch. In the view of cash flow, the portfolio was credit risk free. The only risk is whether LTCM could hold the portfolio until Royal Dutch and Shell converge. It is obviously, LTCM’s trade partners did not have the same faith to the rational market price as LTCM. LTCM could not sustain its long position under an unexpected margin call of its short position. In August 2008, LTCM was forced to close both its long and short positions. The fire-sale enlarged the spread to 30%, and costed LTCM $200M. Beside Royal Dutch Shell trade, LTCM liquidated more than $15B assets in August 2008. Fang shows that the market conspire against the falling LTCM was the causes to the deterioration of LTCM’s asset value, and the aggregate engaged in front running against LTCM explains most of LTCM’s losses. During LTCM lost more than $2T of its capital, each of its 437 active trading parterres yielded $5M
8
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
abnormal return on average, and such abnormal return disappeared after LTCM bailout; LTCM’s portfolio did not bring further losses to Chase, Goldman Sachs, Merrill Lynch, and other bailout creditors. LTCM’s losses show that the key to stay away from the crisis is to avoid fire-sale due to short-term financing shocks. In bank’s view, it is to protect their long term loans from the deposit shocks. Tobin ([56]) pointed in 1982 that ’The volume of deposits in a bank is partly within and partly outside its control’. And the key to prevent the crisis is not to predict the asset prices, as ”(they) are in the short run either illiquid or unpredictable in value”, but to ”hold a certain quantity of defensive (liquid) assets”. Banks’ asset allocation is determined by current and future deposit shocks. Banks stop issuing new loans and liquidate some assets when facing net withdrawals, and vise verse. Secondly, solvent problem does not treat price change as a consequence to exogenous shocks alone. Banks’ operation in the interbank market has directly impact on the asset demand-and-supply and fire-sale price is too wild to be predictable. The most important difference between credit risks and liquidity risks is that raising adequate equity is the only solution to prepare the losses due to the credit risk, while banks can depend on both internal funds and external resources to control the liquidity risk. The liquidity risk model is illustrated by the following chain action: (OriginalShocks) 4 Deposits ⇒ 4BankAssetP ostion ⇒ 4Share × P rice + Share × 4P rice ⇒ M arketCollapse where 4Share is banks’ operation to re-balance their portfolio, and 4P rice is the externality of 4Share on prices. In the case of LTCM, liquidating the pairs trading of Royal Dutch Shell amplified the gap to over 30%. The fire sale created
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
9
extra losses to LTCM. The correlation between price change and banks’ operation is determined by asset’s liquidity characteristic. The correlation is ignorable for liquid assets, such as Treasure bond, and it could be substance for illiquid assets. An example is helpful to illustrate the essential idea of the impact of credit supply on banks’ asset value. Bank could choose either refinancing or foreclosure when the homeowner faces financial distress, which is not rare as refinance accounts more than 60% of mortgage origination. Bank’s choice is determined by not only the borrower’s financial characteristic, but also the available funds. With plenty credits, refinancing is easy to be granted, and the shock from borrowers’ financial distress was reduced; under tight credit, it is more likely banks prefer foreclosure, which amplifies the shocks and brings considerable losses. Based on loan-level data, Demyanyk and Hemertthe ([18]) show that the average subprime borrowers’ FICO score raised from 601.2 in 2001 to the peak of 620.9 in 2005 and stays above 613.2 in 2007. And the new issuance of subprime mortgage was unrelated to the FICO scores. When the credit was tighten in 2008, refinance was more difficult, which contributes to the wave of foreclosure. One contribution of this paper is to show that banks can depend on both internal funds and external resources to absorb the liquidity shocks. The shadow banking system reduces banks’ liquidity risk in two ways. First, banks can dramatically reduce their deposit shocks through the interbank market. Even individual banks face significant deposit uncertainties, the currency seldom leaves the financial system. One bank’s withdrawal is another banks’ deposit. In 1960s, when cash played more important role in the economy, few ned to keep more than fifteen days’ income in money (Ashok [8]). Through overnight borrowing, repo, ABCP and other
10
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
derivatives, banks with net withdrawals borrow from those with deposit surplus. Derivatives serves as the Arrow-Debreu securities for banks to reduce the deposit shocks. Secondly, the shadow banking system creates the liquidity among banks. Mortgage was illiquid assets due to its long mature term and MBS is very liquid asset in the secondary OTC market. Gorton (Gorton [35]) named such phenomena ’informationally-insensitive’ debt, which reduces the transaction cost and creates the liquidity. Then, banks could re-balance their portfolio according to their deposit shocks in a timely manner. The change of the liquidity creation could explain the crisis (Berger and Bouwman [11]). The most important contribution of this paper is to draw the line of the shadow banking system’s limit. Liquidity risk is different from credit risk, which could be measured by the trade off between volatility and returns continually. There are only two states in the view of liquidity risk model: a safe market and a collapse market. Under a safe market, the created liquidity can improve the returns (Shawky Ding and Tian [52]); there was not trade off between liquidity risks and returns as its credit risk counterpart dose. The earlier attempts to measure market liquidity include Berger and Bouwman’s preferred liquidity creation measure (Berger and Bouwman [11]). But the application of such measurement on the data from 1984 to 2008 failed to give a constant pattern of liquidity creation change pre-crisis, during-crisis and post-crisis. Berger and Bouwan’s preferred liquidity creation also failed to explain the successful survivals of American banking industry during Loanand-Saving crisis, 1997 Asian financial crisis, LTCM and Russian crisis, Dot-Com bubble, Latin and South American currency crisis without major scratch, and the unexpected failure of the subprime mortgage crisis (Berger and Bouwman [11]).
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
11
Predicted by the three period model, the market limit counts on both banks’ liquid and illiquid components in their assets as well as the idiosyncratic shocks and systematic shocks on their liability. The financial industry is safe when the derivatives are less than the idiosyncratic risks, and there is enough liquidity assets to absorb the systematic shocks. Then there is enough credit supply in the market to consume the derivatives. The shadow banking system is overloaded when all financial institutions falsely believe the market has unlimited depth and depend on it to absorb both idiosyncratic shocks and systematic shocks. The reset of the paper is organized as follows:
• Chapter 2 introduces a three period model to analyze banks’ liquidity preference with/without the shadow banking system. In the rest of the paper, interbank operations, interbank market and shadow banking system are exchangeable, as the model use ABCP and MBS as the representative to both interbank operations among interbank market and the investment vehicles in the shadow banking system. Banks’ liquidity safety margin is determined by their ability to shield illiquid assets from fire-sale. The model shows that the shadow banking system serves as Arrow-Debreu securities to help banks to share and eliminate deposit shocks and to create liquidity. Naturally, banks take the advantage to issue more long-term-loan for higher margin. • Chapter 3 investigates the limit of interbank market. When market breakthroughs its limit, the banking industry holds too less liquidity assets to
12
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
absorb liquidity shocks. Any small shocks can break down balance of the interbank market supply-and-demand, and may cause considerable irrational price change. • Chapter 4 lists the evidences to the liquidity risk model. and the last Chapter is the summary.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
13
2. Model to Bank’s Asset Management All financial implosions stem from the same cause: borrowing short and lending long without enough equity to weather periodic storms in the gap between. Vernon L. Smith2, WSJ, Dec. 18, 2007 Smith correctly noticed that financial crisis was rooted in banks’ long lasting business model: borrowing short and lending long. However, equity is not the only measurement to buffer the gap between financing and investment. This chapter introduces a three-period-model to illustrate that the shadow banking system provides a flexible solution to meet the gap and helps banks to control the liquidity shocks and issue more long term loans. There are three periods, t = 0, 1 or 2. Bank’s long term and short term investments {Lt , St } are financed by its equity m and deposits {Dt }. Deposits and short term loans are to be repayed at the end of each period. Long term loans are to be repayed at the end of the next period. Let εt be the deposit shock at time t. Bank’s future deposits can be rewritten as Dt = D0 + εt , which are random variable. Liquidity is used in two senses here: first, liquid investment matures shorter period. In the model, short term loans represent liquid assets and long term loans represent illiquid assets. Secondly, liquid investments have less transaction cost and are easier to be traded at high frequency. In the model, we use loan demand as a proxy to transaction cost. It takes uncertain time and cost to find new long term projects, and the long term loan demand {BLt }(t=0,1) is uncertain. For instance, credit card is liquid, compared to commercial & industry loans, because it matures one month 2Smith is 2002 Nobel Laureate,
14
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
and requires less information to grant the loans. Changing customers’ credit line to stimulate loans costs less than issuing new commercial & industry loans. Similar to deposit shocks, define ξ1 = BL1 − BL0 to measure the BLt ’s illiquid nature. To present the liquid/illiuqid investment demand in a consistent way, we define liquid asset demand as BSt . {V Ct }(t=1,2) and {V Mt }(t=1,2) are the banks’ operation in ABCP and MBS market, representing the shadow banking system. To focus on liquidity risk, assume all assets are credit risk free. Deposit-interestrate, short-term-loan-rate and long-term-loan-rate are constants i, (i+α), (i+α+β). α indicates deposit-loan spread, and β indicates term-spread. Realized profit is distributed among shareholders immediately. Relaxing these assumptions does not change the main results. At each period t, bank’s liquid preference is given by its liquid/illquid assets allocation {St , Lt }(t=0,1,2) , for current deposit {Dt }t=0,1,2 . Bank’s action set is A = {Lt , St , V Ct , V Mt }t . Bank has to roll over current long term loans Lt on the next period short-term deposits Dt+1 , and a bank run occurs when future deposits Dt+1 can not support current long term loans Lt . Assume that the penalty to bank run is infinite. A bank’s problem is given by the following optimal problem:
maxA
(i + α)(S0 + S1 + S2 + V C0 + V C1 + V C2 )
(short-term-loan revenue)
+(i + α + β)(2L0 + 2L1 + V M0 + V M1 + V M2 )
(long-term-loan revenue)
−i(D0 + D1 + D2 )
(short-term-deposit cost)
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
S.T : L0 + S0 + V C0 + V M0 ≤ D0
15
(BRR0 )
L0 + L1 + S1 + V C1 + V M1 ≤ D1
(BRR1 )
L1 + S2 + V C2 + V M2 ≤ D2
(BRR2 )
0 ≤ St ≤ BSt
for t = 0, 1, 2
(LDRS )
0 ≤ Lt ≤ BLt
for t = 0, 1
(LDRL )
where BRRt indicates bank run restriction at time t, and LDRt indicates loan demand restriction. Bank maximize its profit with BRRt and LDRt restrictions under any deposit shocks {Dt }. 2.1. Benchmark: The benchmark is individual bank’s liquid/illquid asset allocation without the shadow banking system. The interbank operations are zero {V Ct = V Mt = 0}t=1,2,3 , and banks address deposit shocks alone. The benchmark represents banks’ liquidity preference and the liquidity risk before financial deregulation, when banks served depositors and borrowers from non-financial sectors without complex derivatives. A bank’s problem can now be rewrote as: maxA (i + α)(S0 + S1 + S2 ) + 2(i + α + β)(L0 + L1 ) − i(D0 + D1 + D2 ) S.T : L0 + S0 ≤ D0
(BRR0 )
L0 + L1 + S1 ≤ D1
(BRR1 )
L1 + S2 ≤ D2
(BRR2 )
0 ≤ St ≤ BSt
for t = 0, 1, 2
(LDRS )
0 ≤ Lt ≤ BLt
for t = 0, 1
(LDRL )
Assume random variable {εt }t=1,2 has the lower boundary {εt }t=1,2 , which indicates the severity of deposit shocks. The solution to bank’s problem is given by Property 2.1.1 without prove.
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
Proposition 2.1.1. When banks serve ultimate depositors and borrowers from non-financial sectors without derivatives, the optimal loan issuance is:
L∗0 = min{D0 + ε1 , BL0 } L∗1 = min{D1 − L0 , D0 + ε2 , BL1 } S0∗ = D0 − L0 S1∗ = D1 − L0 − L1 S2∗ = D2 − L1
Visualize that bank A receives deposit D0 = 1 at time 0, the worst deposit shock in the future is {εt }t=1,2 = −0.5, and loan demands are BLt = BSt = ∞. Bank’s safety is determined by whether bank successfully protects long term loan from the worst shocks. A’s optimal loan allocation is L∗0 = 0.5 at time 0. When A issues more long term loans and L0 > L∗0 , bank run occurs when the net withdrawal at time 1 is ε1 = −0.5; when A issues more short term loans and L0 < L∗0 , A can improve its profit margin by reallocating some fund from short term loans to long term loans without increasing the risk of bank run. At time 1 and 2, the amount of loan issuance is subject to bank’s current deposits shocks ε1 and ε2 . Under the worst deposit shocks, ε1 = ε2 = −0.5, loan issuance is L0 = 0.5, S0 = 0.5, L1 = 0, S1 = 0 and S2 = 0.5, and total profit is (2α + β). A better economic condition can improves bank’s returns. For instance, if ε1 = 0.1, ε2 = −0.1, bank A can issue more long term loan at time 1: L1 = 0.5, S1 = 0.1. The total profit is (3α + 2β). Proposition 2.1.1 shows that banks’ safety depends on holding adequate liquid assets, which could be liquidated to absorb both the current and future deposit shocks. As figure 1 shows that banks depend on their
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
17
Figure 1. Absorbing Deposit Shock: Autarky
internal fund to absorb the deposit shocks. If banks do not hold sufficient liquidity assets, banks may fail to hold the long term loans until mature. Proposition 2.1.1 derives other results. The liquid assets benefit banks’ stability (Wagner [57]). As large banks serves more diversified customers pool, and they face less deposit shocks than small banks. Then large banks are required to hold less liquidity assets and have more ability to issue long term loans. Carletti, Hartmann and Spagnolo ([16]) documented banks’ liquidity preference change after mergers, and shows that ”a merger creates an internal money market that induces financial cost advantages”.
2.2. ABCP Eliminates Deposit Shocks: This chapter shows that banks can reduce the deposit shocks from non-financial sectors through ABCP market, then banks can issue more long term loans for higher margin without worrying about a bank run.
18
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
ABCP represents the external funds to absorb the deposit shocks, because ”Before the financial crisis of 2007, ABCP was the largest short-term debt instrument witho more than $1.2T outstanding” (Acharya etc [1]). There are other forms of interbank instruments, such as Treasury Bill, securities lending, which play the similar role with relative small outstanding. When banks can buy/sell ABCP in the interbank market, bank’s problem is written as
maxA
(i + α)(S0 + S1 + S2 + V C1 + V C2 ) (short term loan revenue) +(i + α + β)(2L0 + 2L1 )
(long term loan revenue)
−i(D0 + D1 + D2 )
(short term deposit cost)
S.T : L0 + S0 ≤ D0
(BRR0 )
L0 + L1 + S1 + V C1 ≤ D1
(BRR1 )
L1 + S2 + V C2 ≤ D2
(BRR2 )
0 ≤ St ≤ BSt
for t = 0, 1, 2
(LDRS )
0 ≤ Lt ≤ BLt
for t = 0, 1
(LDRL )
V Ct > −Lt−1
for t = 1, 2
(ABSR)
The solution to the bank’s problem with ABCP is given by Proposition 2.2.1 without prove.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
19
Proposition 2.2.1. ABCP operation reduces the impact of the deposit shocks on banks’ long term loan issuance, and the optimal loan issuance is: L∗0 = min{D0 , BL0 } L∗1 = min{D1 , BL1 } S0∗ = min{D0 − L0 , BS0 } {0, D1 − L0 − L1 } ∗ ∗ {V C1 , S1 } = {D1 − BL1 − L0 , 0} {−L0 , 0} {0, D2 − L1 } if D2 ∗ ∗ {V C2 , S2 } = {D2 − L1 , 0} if D2
if D1 > BL1 + L0 if BL1 + L0 ≥ D1 > BL1 if D1 ≤ BL1 > L1 ≤ L1
Figure 2. Absorbing Deposit Shock: with ABCP
Proposition 2.2.1 can be also illustrated by figure 2. The existence of ABCP market provides external funds for banks to absorb the deposit shocks. By buying/selling ABCP, banks shield the directly impact of the deposit shocks on their
20
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
assets. Then banks cut off liquidity assets holding and allocated more resource on long term loans, comparing to Proposition 2.1.1. The ABCP market helps banks to earn higher return without extra liquidity risk. For instance, even the deposit shock at time 1 could be as bad as −0.5, at time 0, bank A can invest all its deposits on long term loans L0 = 1(= D0 ). If εt < 0, bank A can roll over its long term loan by selling the same amount of ABCP. Banks avoid bank runs without holding any liquid assets.
2.3. MBS Creates Liquidity. This section shows that MBS creates liquidity of long term loans among banks. With MBS market, bank’s problem is written as
maxA
(i + α)(S0 + S1 + S2 ) +(i + α + β)(2L0 + 2L1 + V M0 + V M1 + V M2 ) −i(D0 + D1 + D2 )
S.T : L0 + S0 + V M0 ≤ D0
(BRR0 )
L0 + L1 + S1 + V M1 ≤ D1
(BRR1 )
L1 + S2 + V M2 ≤ D2
(BRR2 )
0 ≤ St ≤ BSt
for t = 0, 1, 2
(LDRS )
0 ≤ Lt ≤ BLt
for t = 0, 1
(LDRL )
V Mt ≥ −Lt−1
for t = 1, 2
(M BSR)
Banks gain more freedom to invest long term loans. They sell MBS to address the net withdrawals, and buy MBS when they run out local long term investment opportunities. The solution is given by Proposition 2.3.1 without prove.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
21
Proposition 2.3.1. When banks can adjust long term loan position through MBS, the optimal loan issuance is: L∗0 = min{D0 , BL0 } V M0∗ = max{D0 − BL0 , 0} {0, D1 − L0 } {L∗1 , V M1∗ } = {D1 − L0 , 0} {BL1 , D1 − L0 − L1 }
if D1 < L0 if L0 ≤ D1 < L0 + BL1 if D1 ≥ L0 + BL1
V M2∗ = D2 − L1 S0∗ = S1∗ = S2∗ = 0 With MBS, banks do not invest in liquid assets at all, but invest all their deposit in illiquid assets directly or indirectly for higher margin, and expect to buffer the deposit shocks through external funds from MBS market. Proposition 2.3.1 can also be illustrated by Figure 3. Facing the deposit shocks εt , loan origination bank does Figure 3. Absorbing Deposit Shock: with MBS
not recall the loan from borrower, and the long term project yields the return of
22
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
i + α + β. The gap between the deposit and the long term loan is met by the selling of MBS to other banks. Note that selling/buying MBS involves only transactions among banks. Such operation has no direct impact on the underlying asset value, or housing prices. The trade of MBS, comparing to deny refinancing and other directly measurement to cut back mortgage outstanding, reduces foreclosure rate, stabilizes housing market, and improves banks’ return. Table 1 compares banks’ liquid/illiuqid asset allocation under different market environment: without the shadow banking system, with ABCP, and with MBS. Without any kind of interbank operation, banks only depend on their internal funds to absorb deposit shocks, and they have to hold adequate liquid assets. Therefor, their ability to issue long term loan is a function of both both the deposit shocks εt and the investment opportunities BLt . ABCP provides external funds for banks to reduce their deposit shocks exposure. As banks depend less on internal funds to absorb the deposit shocks, they issue more long term loans. MBS creates mortgage’s liquidity among banks. Banks absorb all deposit shocks by selling MBS, and remove the restriction imposed by the local long term investment opportunities.
2.4. ABCP and MBS as Arrow-Debreu Securities: There is another way to understand the benefit of the shadow banking system. ABCP and MBS serves as Arrow-Debreu securities to pool banks liquidity shocks together and eliminate part of banks’ uncertainties. A simple example illustrates the idea. There are two banks, A and B, in one island serving the residents. All residents put their money into either of the two banks as well as borrows from either of them. Initially, bank A and bank B receive $1B deposits each. Residents may transfer their money among two banks, which
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
23
Table 1. Liquid and Illiquid Asset Allocation Benchmark
ABCP
MBS
t=0
D0
D0
D0
t=1
D1
min{max{D1 , BL1 + L0 }, D1 + L0 }
D1
t=2
D2
max{D2 , L1 }
D2
L0
min{D0 + ε1 , BL0 }
min{D0 , BL0 }
min{D0 , BL0 }
L1
min{D1 − L0 , D0 + ε2 , BL1 }
min{D1 , BL1 }
max{min{BL1 , D1 − L0 }, 0}
Liabilities
Illiquid Asset
Liquid Asset S0
min{D0 − L0 , BS0 }
D0 − L0 ,
0
S1
D1 − L0 − L1
max{D1 − L0 − L1 , 0}
0
S2
D2 − L1
max{D2 − L1 , 0}
0
generates deposit shocks to both banks. At state 1, $100M is transferred from bank B to A; at state 2, $100M is transferred from bank A to B. The chance of state 1 and 2 is 50%. Loans yield a constant margin r, and the cost to recall loans is $c(> 2r). Without a interbank market, both banks hold $100M cash in hands for the deposit shocks. Even the total available credit is $2B,total loan outstanding is $1.8B. The banking industry is not efficient and total profit is $r · 1.8B. Arrow-Debreu security improves efficiency. There are two Arrow-Debreu securities: security I pays off $1 at state 1, and security II pays off $1 at state 2. The price of securities I and II are PI = PII = $0.50. A lends $1B out, and hedge the deposit shocks by buying r · 100M shares of security I. Under state 1, with the payment of $r · 100M from security I, bank A can offer the interest to borrow $100M
24
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
from B. The portfolio, $1B loan plus $r · 100M security 1, yield identical return $r · 1B under both state 1 and 2. Similarly, bank B buys security II and issues $1B loans. The total loan outstanding is $2B, equaling to the total available credit. Arrow-Debreu securities improves banks’ efficiency and total revenue is improved to $r · 2B. Both ABCP and MBS can achieve the same improvement as Arrow-Debreu securities. With ABCP, bank A and B lend $1B initially. At state 1, bank A sells $100M ABCP to bank B, and bank B is ready to buy $100M ABCP with the same amount of deposit surplus. At state 2, bank B sells $100M ABCP to bank A. Hence both bank A and B eliminate deposit shocks exposure. Total loan outstanding is $2B, and total revenue is $r · 2B. ABCP and MBS are more flexible and practicable than Arrow-Debreu securities, as bank A and B do not need to decide the amount of Arrow-Debreu securities they have to buy before the deposit shock occurs. In the real world, such flexibility is crucial. There are more than 8000 banks in U.S., and an infinite number of possible shocks. The requirement of common knowledge of the distribution of possible shocks is unpracticable. However, the trade of ABCP and MBS are based on current shocks. Bank A and B can decide the trade volume after they observe the shocks. Figure 4 summaries how banks depend on both internal funds and the shadow banking system to to absorb the deposit shocks. ABCP is a practical Arrow-Debreu securities to pool the banks’ deposit shocks together and reduces the directly impact of deposit shocks’ on banks’ assets. Then banks liquidate their assets to absorb the rest of the deposit shocks. Liquidity creation on mortgage yields higher return on
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
25
the underlying assets, and facilitate the trade among banks. Compare to figure 1, banks gain more ability to control deposit shocks, and can issue more illiquid loans.
Figure 4. Absorbing Deposit Shock: with ABCP and MBS
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
3. Model to Market Limit Chapter 2 shows that the shadow banking system helps individual banks to improve profit margin without taking more liquidity risks, as the liquidity shocks are shared and eliminated through interbank operations. This chapter focuses on the mechanism that the shadow banking system damage the safety cushion, in the view of the banking industry as whole. The key is interbank market’s limit. The market is about to collapse when neither banks nor the regulators are aware that the shadow banking system maybe overloaded. Market’s limits is determined by the nature of deposit shocks originated from the non-financial sectors. Distinguish idiosyncratic risk and systematic risk is crucial to understand market limit, because derivatives can only eliminate idiosyncratic shocks. At least some banks expect that the market has unlimited depth, and keep not sufficient liquid assets. The market becomes overloaded and the banking industry has no enough buffer to absorb the deposit shocks.
3.1. Idiosyncratic and Systematic Liquidity Risk. Deposit shocks are decomposed into systematic shock and idiosyncratic shock. Systematic shock is the aggregate deposit shock to the banking industry, and idiosyncratic shock is the unexpected transfer among banks. Imagine a depositor who has accounts in two banks. His future income is uncertain and his preference to any bank is also random. The income uncertainty is systematic risk, as it changes the net deposits to the banking industry. The depositor’s uncertain preference is idiosyncratic risk. When the depositor transfers money from unfavored bank to favored one, the deposit shocks effect two banks but not the banking industry.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
27
The formal definition of the systematic and the idiosyncratic deposit shock is given in the following manner. There are N banks and bank j’s deposits at time t is Dj,t . Dj,t = Dj,· + εj,t , where Dj,· is bank j’s average deposits, and εj,t is bank j’s total deposit shocks. Let the aggregate deposits Dt = where D is the average aggregate deposits, and ωt = deposit shocks. Bank j bears the share αj (=
P j
D(j,·) ) D
P j
Dj,t = D +
P j
εj,t ,
εj,t measures the aggregate
of systematic risk, and the
remaining is bank j’s idiosyncratic shock νj,t = εj,t − αj ωt . The most important proposition to the idiosyncratic shocks is that
P j
νj,t = 0.
P j
νj,t has no net
effect on systematic shocks. Similarly, the long term investment opportunities is decomposed into the systematic risk uncertainty and the idiosyncratic risk: ξj,t = αj $t + σj,t , where $t is systematic risk and σj,t is idiosyncratic risk. The systematic deposit shock |ωt | is less than the sum of individual banks’ deposit shock
P j
P
|εj,t |. There is not accurate estimation to the ratio
it is expected to be very large.
P j
|εj,t | |ωt | ,
j
but
|εj,t | reflects the dynamical economy. In 2007,
there were more than 20 million Americans changing jobs (about 20% of American non-farm private sector workers), over 647,000 new small business opened, over 568,000 small business closed, and more than 33,000 bankrupted 3. Such a dynamical economy environment created considerable uncertainties to individual banks, especially the reginal ones. Moving from one place to another creates noticeable deposit shocks and loan demand uncertainty. People close bank accounts, pre-pay the mortgage, sell house, cars and other properties, then take the money to a new
3Data is released by U.S. Dept.
of Commerce, Bureau of the Census; Administrative Of-
fice of the U.S. Courts; U.S. Dept.
of Labor, Employment and Training Administration.
www.sba.gov/advo/research/rs258tot.pdf
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SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
place. Opening and closing business also bring considerable uncertainties to banks. However, the systematic shocks are much smaller, as most shocks are canceled out. 3.2. The limit of the Shadow Banking System: The clue of interbank market limit lies in the difference between ωt and
P j
εj,t . The limit of the shadow banking
system is determined by the size of idiosyncratic shocks. The essential idea is illustrated by a similar example. There are two banks, bank A and B, in one island serving the residents. Initially, bank A and bank B receive $1B deposit each. Beside the idiosyncratic shocks - $150M transfer among two banks, there is ±$100M systematic shock caused by residents’ future uncertain income. Table 2 shows the possible deposit shocks to bank A and B. Table 2. Possible Deposits under All States State
Systematic
Idiosyncratic
A’s deposits
B’s deposits
Aggregate Deposits
1
Good (+$100M )
A→B
$0.9B
$1.2B
$2.1B
2
Good (+$100M )
A←B
$1.2B
$0.9B
$2.1B
3
Bad (−$100M )
A→B
$0.8B
$1.1B
$1.9B
4
Bad (−$100M )
A←B
$1.1B
$0.8B
$1.9B
Without the shadow banking system, bank A and B hold $0.2B cash to prepare the deposit shocks. If bank A attempts to issue more illiquid loans, according to Proposition 2.1.1, A suffers bank run under state 3. Similarly, B can issue $0.8B long term loans at most. Then the aggregate long term loan outstanding is $1.6B, less than the minimum aggregate deposits of $1.9B. When ABCP market exists and the size of the market is limited to idiosyncratic risk of $150M , bank A and B need to hold only $50M in cash to absorb the deposit shocks. Under state 1, A sells $50M ABCP to meet the gap between its $0.9B
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
29
deposit and $0.95B loan; bank B has $250M cash in hand to buy all ABCP in the market. Under state 2, B sells $50M ABCP to A. Under state 3, A sells $150M ABCP; and bank B has the exactly same amount of cash in hand to buy ABCP in the market. At state 4, bank B can successfully sell $150M ABCP to A. Bank A and B eliminate idiosyncratic risk to improves their profit margin, and the aggregate loan outstanding is $1.9B, the revenue is $r · 1.9B. when A and B have the illusion that derivatives market has unlimit depth, banks hold no cash in hand as proportion 2.2.1 predicts. A and B lend $1B at current period. During good economics times, bank A buys(sells) $100M ABCP, and B sells(buys) the same amount. Both banks depend on ABCP market to absorb the deposit shock and enjoy the high profit margin. At state 3, bank A needs to sell $200M ABCP, as its deposit is only $800M and its loan outstanding is $1B. But B has only $100M in cash on hand, not enough to purchase all ABCP in the market. Bank A faces a bank run. Similarly, at state 4, bank B faces a bank run. The market may be crashed by few banks’ aggressive investment on illiquid assets. Assume that A recognizes the market limit of $150M , but B does not. A holds $50M in cash and B lends $1B. Both banks survive at state 1 and 2, but not at state 3 and 4. At state 4, bank B needs to sell $200M ABCP, but A has only $150M in cash on hand. At state 3, bank A needs to sell $150M ABCP, but B has only $100M in cash on hand. There is not enough purchase power in the market. Bank run is unavoidable, as bank A has no way to raise necessary fund through the market, no matter what price A asks for.
30
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
The market limit is set up by the derivative demand-and-supply balance under the worst liquidity shocks. Proposition3.2.1 predicts the factors determine interbank market supply and demand. For given deposit shocks, the demand-and-supply is determined by banks’ liquid/illiquid asset allocation. When banks hold more liquid assets, they can depend on their internal funds to absorb the deposit shocks. Hence banks demand less external funds from the derivatives market.
Proposition 3.2.1. The supply/demand of derivatives is a increasing/decreasing function to illiquid asset outstanding, and the supply/demand of derivatives is a decreasing/increasing function to system shocks.
Proof: A bank sells ABCP when its deposit Dj,t is insufficient to support long term loan Lj,t−1 . Let V CSj,t = − min{Dj,t − Lj,t−1 , 0} be ABCP supply for bank j. It is easy to see, the higher illiquid asset position, the higher supply of ABCP. Similarly, the larger systematic liquidity shock is, the smaller ω is, the higher ABCP supply V CSj,t is. Market clearing price is not the first concern of the shadow banking system safety. Pricing mechanism only determines the choice over internal funds and external funds. Banks prefers externals funds when the interest rate is low, and vice verse. And market safety concerns wether the industry as whole has enough liquid assets to liquidate in order to address the deposit shocks. If the banking industry has no enough liquidity assets, no matter what the derivative price is, the interbank market can not provide enough external funds to those who need cash. In another words, the limit of the market is that the derivative supply equals to the derivatives demand under the worst deposit shocks.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
31
Proposition 3.2.2. The shadow banking system’s limit is that banks hedge idiosyncratic risk through derivatives market, and depends on the internal funds to absorb systematic risk. Under the worst deposit shocks, the derivative supply and demand equal to each other, and credit supply can always support existing illiquid loans.
Proof: According to Proposition 3.2.1, the demand is a decreasing function to illiquid asset outstanding, and the supply is a increasing function to illiquid asset outstanding. There exist an unique market equilibrium. When bank absorbs systematic risk by liquidating its liquid asset, long term loan is limited to Lj,t−1 = Dj,0 − αj · ω. And the demand/suppply of commercial paper at time t is max{νj,t , 0}/−(min{νj,t , 0}). Note Σj νj,t = 0, the aggregate commercial paper demand equals to aggregate supply. Proposition 3.2.2 does deny price mechanism and other frictions. Proposition 3.2.2 concerns the existing of the market. Price mechanism works as long as the market exists. For instance, a comparatively low ABCP yield rate encourages banks depends more on external funds and liquidate less assets to absorb the deposit shocks. Price determines the choice over external and internal funds, and price works only when the market exists, and there are enough liquid assets covering the deposit shocks. There is another way to understand Proposition 3.2.2. Banks depend on either external funds or internal funds to answer the deposit shocks. For each bank j, 4Assetj,liquid + 4ABCPj = εj = νj + αj ω For the banking industry as whole Σj 4 Assetj,liquid + Σj 4 ABCPj = Σj νj + Σj αj ω
32
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
As Σj νj = 0 and Σj αj = 1, we have Σj 4 Assetj,liquid + Σj 4 ABCPj = ω. The necessary condition to the interbank market clearing Σj 4 ABCPj = 0 under any shock is that Σj 4 Assetj,liquid = ω for any ω. Then Σj Assetj,liquid ≥ ω, or the banking industry has to depends on liquid assets to absorb the systematic shocks.
3.3. The Path to Overloaded Market. ”The well-known adage that ’one cannot manage what one cannot measure’ is particularly timely with respect to the notion of systemic risk”(Andrew W. Lo [6]). The liquidity risk is determined by the gap between the amount of liquidity assets and the size of deposit shocks. The liquidity risk is accumulated when individual banks reduce their liquid assets and depend on the shadow banking system to to absorb deposit shocks. When individual banks have no enough information to distinguish idiosyncratic shocks and systematic shocks, banks have no way to estimate the market limit. Then the market is about to be overloaded soon or later.
Proposition 3.3.1. When some banks attempt to hedge both idiosyncratic risk and systematic risk through derivatives market, the derivatives market is overloaded. When the systematic shocks are negative, the ABCP supply exceeds the demand, and the credit supply is less than credit demand. Banks can not meet net withdrawals by borrowing from interbank market. Bank run occurs.
The explanation is based on the fact that individual banks are not able to distinguish between idiosyncratic deposit shocks and systematic shocks. Banks just observe cash flow in and out εj,t , and have no clue on the size of idiosyncratic shocks νj,t and systematic shocks ω. For instance, a distributor purchases GUCCI purses from Chinese manufactory and requires his bank transferred $100M out of
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
33
America, $40M after the contract and $60M in three months. Consequently, Chinese manufactory has to import alligator skin from Florida, which leads to $60M cash flow into another American bank. The systematic shock is −$40M after the contract, then +$20M , and −$40M in the end. However, there is no way for both banks to tell their share of systematic shocks by observing their own cash flows. Without the information of systematic shocks, banks estimated the market limit by their own experience, especially the successful experience during the crises: S&L crisis, Asian financial crisis, LTCM and Russian financial crisis, Dot-Com bubble, 911 and South American currency crisis, etc. As the market never failed banks’ demand for short term credit, bank built up the confidence on the market, and never bothered to think about the market limit any more. The market expanded quickly. On one hand, more banks accepted the idea to share and eliminate liquidity risk through the interbank market. The more banks joined the market, the deeper was the market, and the more idiosyncratic shocks were eliminated. On the other hand, the successful banks took over the market share from the less profitable banks, who held more liquid assets and depended on their own internal fund to absorb the shocks. Optimism dominated the industry. Banks assumed that the market had unlimited depth, and felt safe to reduce their liquid assets. The market was overloaded after all banks issued more long term loans. The banking industry as whole did not have enough liquid assets to absorb systematic deposit shocks. A small negative shock crashed the market. During the crash of subprime crisis, $500B bad loans or less than 5% loss of total mortgage outstanding, triggered the worst recession ever since the great depression.
34
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
After the interbank market collapsed, banks did not only write off the subprime mortgages losses, but had to fire sale long term loans. Because banks needed more liquid assets to answer the deposit shocks. The simultaneous fire-sale of long term loans, both subprime and other subprime unrelated long term loans, pushed the price down. As the fire-sale price was far below its fundamental, it required far more capital to cover the ’losses’, than the actually underlying assets losses. The estimated losses in subprime mortgages of between $400 and $500B are relatively modest in terms of wealth destruction, which are roughly correspond to a non-souncommon drop of between 2 and 3 percent of the U.S. stock market (Markus [47]). The model explains why Fed and Treasury spent more than $2T , but still did not fix the problem caused by a moderate shocks. Meanwhile, banks stopped issue new loans, cut back re-financing, and froze other credit supply to the real economy. The economy was in recession.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
35
4. Evidences This chapter provides some evidences that the shadow banking system plays more important role in sharing and eliminating deposit shocks among banks. Actually, some puzzle under the credit risk models turn out to be evidence to the liquidity risk model, for instance, ’securitization without risk transfer’ (Acharya etc [1]). 4.1. Banks Represent the Financial Industry: The earliest known deposit bank, Banco di San Giorgio, was founded in 1407. Today, banks still play a important role in channeling investors and borrowers, and keep the essential of the business model - borrowing-short-and-lending-long. The developing of market did not slow the developing of banking industry. On the contrary, depending on the shadow banking system as the external resources to address deposit shocks, banks are more robust and more efficient. Table 3 shows significant reduction in bank failures. Banks’ successful survival of numerous crises makes banks’ asset management a good represent to the operations in the shadow banking system. And the wisdom of banks operation in the shadow banking system is helpful to understand how the system as whole works. Table 3. Bank Failures: 1982-2007 Year # of failures Year # of failures
82
83
84
85
86
87
88
119
99
106
180
204
262
470
89
90
91
92
93
94
95 ∼ 07
534
382
271
181
50
15
58 total
More evidences are listed in three aspects: first, banks did not depend on interbank market to shift credit risks; secondly, banks’ operation is similar to other
36
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
financial institutions in the shadow banking system; last, banks were serious investors in the interbank market. • Banks did not depend on the shadow banking system to shift credit risks. It is a puzzle in the view of credit risk models that banks ’securities’ mortgages and hold MBS. Banks did not buy credit risk insurance from market either. When Collateralized debt obligations (CDOs) and other derivatives, which were designed to hedge the credit risk, expanded to $24T at 2008. Less than 1.5% of MBS held by banks is covered by CDOs4. The buying and selling of CDS by large U.S. banks were similar. Before the crisis, large U.S. banks bought $4.165T CDS and sold $4.094T CDS, and the net CDS position was $71B, which counted 2.1% of their loans (Duffie [23]). The phenomenon indicates that banks had the confidence to manage both credit risk and other types of risks. Meanwhile, banks expanded their market share as other financial institutions in the shadow banking system. Eichengreen ([25]) showed that banks typically outsource mortgage issuance and paid fee to independent mortgage brokers. • Commercial banks investment strategy was not significantly different from other financial intuitions. Table 4 compares Bank of America’s balance sheet with Bank of America Secularities, an investment bank, before the subprime crisis. Both the commercial bank and the investment banks borrowed from and lent to REOP simultaneously. Both the borrowing and the lending were significant large than the direct investment on securities.
4S&P Industry Report: Investment and Diversified 2009.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
37
Table 4. BOA Securities and BOA Balance Sheet, Dec 2006 (in B$) BOA
BOA Securities
Lending to REPO
288
80.5
Directly Securities Holding
192
69
Borrowing from REPO
285.1
136
Net Borrowing from REPO
-2.9
55.5
Asset
Liabilities
Source: BOA and BOA Securities Annual Report, 2006.
Table 5 compares the breakdown of CDS buyers and that of CDS sellers in 2007, which indicates that banks’ operations in the shadow banking system is similar to hedge funds and mutual funds. All of them were actively buyers and sellers in the market, and their net position was relatively small.
Table 5. The Breakdown of CDS Buyers and Sellers, Dec 2006 (in %) Breakdown of Buyers
Breakdown of Sellers
Net Position
Banks and Dealers
33
39
-6
Hedge Funds
31
28
3
Mutual funds
3
2
1
Insurers
18
6
12
Loan Portfolios
7
20
-13
Pension Funds
5
2
3
corps
2
2
-
Mics
1
1
-
Source: Bank of America, March 2007.
38
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
The large amount of buying-and-selling operation indicates that the shadow banking system served the banks for other objects rather than financing and shifting credit risks.
• Table 7 and table 6 show banks’ operation in the shadow banking system was consistent. Banks were actively buyer/seller in the market, and were investors in net. Table 6 shows that at the end of 2007, commercial banks mortgage exposure was $2.881T, of which 69.12% was direct held and 32.98% was held in RMBS. Commercial banks’ RMBS to direct holding ratio was higher than the average over all private leveraged institutions. The ratio was way above the necessary inventory required to package and sell MBS, which is less than 1% of MBS outstanding for brokers5. By comparing commercial banks MBS holding with other institutional investors’ Table 6. Home Mortgage Exposure at 2007 (in B$) Home Mortgage Debt
Total
Total
11,028
1,368
5,591
671
US Leveraged Institutions
Direct
MBS
subprime
M BS Direct
Commercial banks
2,881
1,935
946
250
48.9%
Savings Institutions
1,148
895
253
-
28.3%
Credit Unions
361
300
61
-
20.3%
Brokers and Dealers
213
0
213
-
-
GSE
987
457
530
112
116.0%
Source: Federal Reserve Board, FDIC, calculated by Greenlaw etc, 2008.
from 2004 to 2006, table 7 shows similar result. Banks held 20% more MBS 5Estimated by Bank of America.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
39
Table 7. MBS Investors at 2005 and 2006($ Billions) Investor type
2006
2005
%
% Since
All MBS
Non-agency
All MBS
Non-agency
Chg
2004
FDIC banks
876
124
913
158
20
4
FannieMea/FreddieMac
1,261
267
1,192
363
26
-5
Life Insurance
465
N.A.
480
N.A.
10
3
Mutual Fund
318
N.A.
325
N.A.
7
2
Personal Sector
270
N.A.
290
N.A.
6
7
Public Pension
270
N.A.
275
N.A.
6
2
All Thrifts
234
7
228
6
5
-3
Priv. Pension
125
13
128
15
3
2
FHL Banks
113
71
117
71
3
3
REITs
95
50
105
60
2
11
Dealer Inventory
41
15
55
20
1
34
Federal CreditUnion
28
N.A.
29
N.A.
1
2
Finance Companies
85
N.A.
88
N.A.
2
4
Foreign Investors
280
30
400
50
9
43
Others
317
N.A.
474
N.A.
49
N.A.
Total Outstanding
4,779
1,076
5,098
1,289
9.1
N.A.
Source: Inside MBS & ABS, computed by JPMorgan 2006.
from 2005 to 2006; from 2004 to 2006, banks invested 4% more in MBS, which was higher than Fannie Mea and Frediie Mac, insurance companies, pension funds, who were supposed to be at better position to bearing the credit risks. As the top three investors in year 2006, and top five from 2004
40
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
to 2006, banks were most active investors in the shadow banking system, then
4.2. The Shadow Banking System: Previous researches focus on how the shadow banking system directly channels investors and borrowers, and assume that banks’ operation was described by the models. For instance, origination-and-distribution model catches the benefit to agency and the potential risks to the investors, and treats banks as brokers. This section shows evidences that instead of being brokers in the shadow banking system, banks used the interbank market as external sources to share and eliminate the deposit shocks. Financial innovations and the derivative market did not change banks’ business model, but re-enforced their core business - borrowing-short-and-lending-long. The evidences are presented in two aspects: first, we will review banks’ buying-and-selling operations in the interbank market in a long period window; secondly, we will exam the interbank operation’s direct impact on their profit. By comparing banks’ quarterly net change in mortgages and MBS from 2006Q4 to 2008Q4, table 8 shows that banks were potential buyers as well as sellers in the market. Banks were net sellers in three of nine quarters, and net buyers in the rest six weeks. By comparing mortgage new issuance and net MBS change, table 8 also indicates that banks did not depend on MBS to transfer the credit risks to other investors. MBS net change was higher than the the sum of residential mortgage and commercial mortgage net issuance in four of nine quarters; MBS net change was similar to net mortgage issuance in two quarters; and net MBS change was less than net mortgage new issuance in the rest three quarters. By comparing banks’ annual net change in mortgages and MBS from 1999 to 2008, table 9 shows similar
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
41
Table 8. Quarterly Net Change in Mortgages and MBS, 2006Q4-2008Q4 items
2006
2007
Q4
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
4.7
8.04
10.37
3.63
-5.62
-3.93
-8.60
-7.52
-3.73
Commercial Real Estate
11.96
6.14
9.76
9.22
9.49
5.05
5.32
4.628
0.8
MBS
7.36
7.83
-2.58
-7.58
5.36
19.25
15.52
-13.10
15.49
Capital Account
9.48
6.69
3.69
19.4
7.06
5.19
-.90
-4.89
-6.85
Federal Home Loan Bank
1.53
22.09
10.09
92.3
0.38
15.53
8.02
52.85
-56.15
One-to-Four-Family
2008
Source: Federal Reserve Bulletin, June, 2009.
result as table 8. The net MBS change is not necessary positive, neither does it correlated with net mortgage issuance. From 1999 to 2008, banks’ MBS increment Table 9. Net Change in Mortgages and MBS, all U.S. banks, 99-08 Item
99
00
01
02
03
04
05
06
07
08
% Residential Mortgage
12.22
10.74
7.94
14.44
9.75
15.41
13.8
14.49
7.044
4.49
% Commercial Mortgage
15.42
12.16
13.1
6.82
8.99
13.93
16.87
14.91
9.2
6.77
% RMBS
-3.34
3.29
29.05
15.54
10.12
13.45
2.06
10.22
-1.24
11.37
Source: Federal Reserve Bulletin, June, 2009.
was higher than mortgage increment in four of ten years (year 01, 02, 03 and 08); banks bought MBS, but MBS increment was less than mortgage increment in year 04, 05 and 06); banks were net sellers only in two years 99 and 07. Banks buy and sell MBS simultaneously in the second market, even during the crisis. Table 10 reports banks’ revenue and cost from 2000 to 2008. First, interest net income was the only source to banks’ profit over the whole period. Banks did not make any net profit from non-interest business at all. Even worse, the net non-interest expense climbed from $63B in 2000 to $148B in 2008. Banks also
42
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
Table 10. Revenue and Cost of U.S. Banks, 2000-2008, Million$ items
00
01
02
03
04
05
06
07
08
Gross income
423,845
404,251
349,603
329,218
348,667
426,600
551,039
616,995
566,000
Gross expense
222,161
188,746
118,741
94,123
98,541
162,501
263,372
310,412
227,066
Deposits
151,147
132,311
81,701
62,400
63,639
105,922
173,878
212,783
154,812
repurchase
26,860
19,583
9,920
7,590
8,842
19,161
33,775
37,715
19,755
Other
44,155
36,852
27,122
24,133
26,058
37,418
55,720
59,914
52,499
201,684
215,505
230,862
235,095
250,126
264,099
287,667
306,583
338,934
Gross income
153,101
160,902
168,236
183,792
188,999
201,768
222,887
218,554
207,880
Gross expense
216,375
225,979
230,128
243,214
263,304
274,136
294,890
321,406
355,910
Net expense
63,274
65,077
61,892
59,422
74,305
72,368
72,003
102,852
148,030
-2,280
4,630
6,411
5,633
3,393
-220
-1,320
-649
-16,186
Interest
Net income Noninterest
Investment Net income
Source: Federal Reserve Bulletin, June, 2009. lost money on security investment after 2005. In the best year, banks’ investment income accounted for less than 3% of net-interest-income. All the numbers indicate banks do not buy/sell derivatives for profit, but more likely for hedging purposes. The gap of interest expense and interest income provides important information of banks’ portfolio. As the interest spread was relatively stable before the subprime crisis, banks had invest more long term loans and held less liquid assets. Otherwise, banks could not improve their interest gross income by more than 50% and kept their interest gross expense at the same level.
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
43
4.3. The Deposit Shocks: The deposit shocks are the origination to liquidity risks. Tobin ([56] ) in 1982 pointed out that the deposit uncertainty could erode banks safety. ’To be sure of realizing their (illiquid assets’) full value, the bank must hold them to maturity. Consequently, these assets can be available for meeting deposit withdrawals only at some risk of loss.’ And banks need to hold a certain quantity of liquid assets to absorb the deposit shocks. Even the shadow banking system created liquidity among banks, Tohin’s definition of liquid assets is still valuable to analysis the industry liquidity safety, which is still account on the aggregate liquid assets to absorb the deposit shocks as it did centuries before. Banking industry safety is determined by whether banks can successfully shield the illiquid assets from deposit shocks. Figure 5 compares weekly deposit change and loan change from 1974 to 2009. Deposit shocks are the weekly deposit change, defined by way
Depositt −Depositt−1 . Depositt−1
Loant −Depositt−1 . Loant−1
And weekly loan change is defined in a similar
In normal times, deposit changes, the blue solid line, is
significantly more volatility than loan changes, the red dot-line. More importantly, the figure also reveals that loans were perfectly covered from deposit shock. Net withdrawals were common as the blue line stays blows zero quite often. But the loan changes were all positive except during recessions in 1973, 1990, 2001 and 2007. Another way to measure deposit shocks and loan adjustments is the standard deviation(STD) of deposit/loan changes, given by Figure 6. Deposit shocks were dominant before the crisis. The difference between loan STD and deposit STD was even bigger before 1985.
44
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
Figure 5. Deposit Change v.s. Loan Change: 1974-2009 (in %)
Ͳ
Ͳ
Ͳ
Source: Federal Reserve Banks
Deposit shocks dominating loan changes is not a recent phenomena. Figure 7 compares Loan/deposit STD before the great depression. Deposit shocks dominated asset change in good time, and the inverse of this relationship predicted the great depression. The long term high frequency observations indicate that deposit shocks are not trivial. The market safety was, and is counting on banks’ ability to shield the assets from the deposit shocks. Otherwise, fire sale will bring extra losses to the banks, which is far beyond losses due to credit risks. AIG bailout is such a case. In September 2008, AIG was downgraded by S&P, Moody and Fitch. AIG was forced to liquidate some of its assets to address $20B in additional collateral
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
45
Figure 6. Deposit STD v.s. Loan STD : 1985-2009
Ͳ
Ͳ
Ͳ
Ͳ
Ͳ
Ͳ
Ͳ
Ͳ
Ͳ
Source: Federal Reserve Banks
calls due to these downgrades. AIG raised $19.8B by a fire sale of residential mortgage-backed-secularities to NY Fed in Oct 2008, and the directly losses of the sale was $19.5B(Sjostrom [53]). The fire-sale price deviated far away from the asset’s fundamental, as most of AIG’s MBS holding was classified to ”Super Senior”, which was safer than AAA bonds. After banks failed to protect their illiquid assets from deposit shocks, the market collapsed. The ABCP outstanding dropped more than 40% from 2007 to 2008, even the the margins reduced more than 1%, from over 5% in 2006 to 4% in 2007 (Brunnermeier and Pedersen [47]). There was significant withdrawn from all inter
46
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
Figure 7. Deposit and Loan Position Change Volatility % (1921-1929)
Source: Federal Reserve Banks
bank market, including the Fed funds market. The number of lenders in the Fed fund market was over 300 before the crisis, and the number reduced to around 100 in 2009 (Afonso etc [4]). After the interbank market was frozen, the external resource to banks were frozen and the liquidity creation was gone. Banks needed to depend on their internal funds to absorb the deposit shocks. By comparing 98 international banks with assets in excess of $50B at 2006, including 19 U.S. banks, Beltratti and Stulz ([9]) show that banks with more loans (less liquidity creation) and more liquid assets performed better after Lehman bankruptcy, banks with more deposits and less ABCP, who depended less on external funds from the shadow banking system, also performance better after Lehman bankruptcy. The financial stress hit the real economy after banks cut back re-financing and new loans issuance to hold more liquid assets. 4.4. Other Evidence: There are other evidences that banks’ operation in the shadow banking system is less credit risk related as ordinate-to-distribute model
SHADOW BANKING SYSTEM, DERIVATIVES AND LIQUIDITY RISKS
47
predicts. Comparing the returns and financial characteristics of the loans securitized and sold, securitized and not sold, and not securitized, Berndt etc ([10]) found that borrowers in an active loan market, whose loans were more likely to be securitized, had higher credit rating; and banks were more likely to hold the loans lent to the borrowers with rating lower than BB. Demyanyk and Hemert ([18]) reported the FICO scores of the first-lien subprime loans from 2001, the average FICO scores raised from 601.2 in 2001 to over 618 in 2006. Gorton ([32]) compared quarterly delinquency rate between prime borrowers and subprime borrowers from 2003Q1 to 2007Q4, and the ratio of
P rimeDelinquencyRate SubprimeDelinquencyRate
was stable. David etc ([37])
computed the U.S. investment banks and commercial banks leverage from 1998 to 2008, and show that commercial banks leverage was stable before the crisis, and investment banks leverage increased slightly.
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5. Summary We are not skilled enough in these areas and we should not be expected to, Alan Greenspan 2007 Two years after the subprime crisis, our knowledge of liquidity risk is still behind the market complexity. Based on the deeply rooted belief of the credit risk model, most researches focus on banks’ potential losses of their risk investments and the amount of adequate equity to write off the bad assets. Crises, in the view of the credit risk model, are unpredictable rare events. This paper introduces a independent liquidity risk model to show that banks’ liquidity safety depends on their ability to protect illiquid assets from exogenous deposit shocks, and the liquidity risk could be absorbed by both banks’ internal funds and external resources from the shadow banking system. • First, liquidity risk is not caused by assets price fluctuation. On the contrary, it is the reason to irrational price. The banks with solid assets can not stay away from the crisis, because the disappear of the interbank market cuts back their external resources to absorb the deposit shocks. All banks have to increase their liquidity assets, and a massive fire-sale of illiquid assets amplifies the deposit shocks and leads to bank panic. • Second, MBS, ABCP and derivatives are practicable Arrow-Debreu securities for banks to share and eliminate the deposit shocks. Banks reduce their exposure to exogenous deposit shocks by buying/selling ABCP. MBS creates mortgages’ liquidity through interbank market. The transfer of MBS among banks has less impact on housing price than restricting refinancing
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and foreclosure. Derivatives help banks to gain more control of their capital flow, then banks issue more long term loans without compromising safety. • However, derivative market has its limits, which are determined by idiosyncratic deposit shocks. Banks lack the knowledge to distinguish between idiosyncratic shocks and systematic shocks, and mistakenly believe that the market has unlimited depth. When banks issue too much long term loan, the market is overloaded and the banking industry as whole does not have enough liquid assets to absorb systematic deposit shocks. A small negative shock in a weak economy can trigger bank runs and crash the industry. The key differences between independent liquidity risk model and credit risk model are listed in the following table.
Table 11. Credit Risk v.s. Liquidity Risk Credit Risk
Liquidities Risk
The Origination to Risk
random future returns
realized deposit shocks
Risk Measurement
Price Fluctuation
Deposit/Loan Volatility
Risk Management
Predict Rare Events
Share and reduce deposit
Appropriate Pricing Model
shocks through Arrow-Debreu
Raise Capital
Securities
Market Collapse
mis-pricing
overloaded market
Crisis Prediction
not-available
Loan volatility Converges to Deposit Volatility.
Under the liquidity risk model, the subprime crisis is divided into three phases according to banks’ liquidity preference and the market evolution.
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• Before the deregulation, banks were largely absorbing the deposit shocks through their internal funding. Banks had to hold enough liquid assets to prepare unexpected withdrawal. The banking industry as whole required less liquid assets to absorb the systematic deposit shocks. The industry was safe but less efficient. • After the deregulation, banks learned to absorb the deposit shocks through the interbank market. Banks gradually reduced their liquid assets and reallocated the resources on high yield long term investments. The banking industry held less liquid assets, but its liquid assets were still enough to absorb systematic shocks. • At 2007, mortgages alone accounted 65% of banks’ assets, almost doubled their weight before 1995. The interbank market was overloaded and the banking industry as whole held too little liquid assets to prepare the deposit shocks. $500B loss during the subprime mortgage created enough deposit shocks to crash the market. Without the interbank market, all banks suddenly realized that their liquid assets were not enough to buffer the exogenous shocks. The simultaneously selling of mortgages and MBS ends in bank panic.
This paper sets up a framework to analyse bank liquidity risk, and provides supporting evidence from recent date. The results are helpful to the debate among restrictive government regulation and free market. While Alan Greenspan (former Fed Chairmna) disagrees with the idea of rolling back commercial banks to GlassSteagall era, Volcker (former Fed Chairman) and Joseph. Stiglitz, standing with other economists, argue that risky securities ’brought us to where we are today’,
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and ’a cleaner and safer banking system’ requires ’splitting banks from investment banks’. The common knowledge of bank liquidity risk helps the government and the Wall Street to work together to monitor the risks and prevent future banking crisis.
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Jianbo Tian, 363 Manning Blvd, apt2, Albany, NY 12206, [email protected]
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