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Edmund Cannon. Banking Crisis University of Verona Lecture 2. Plan for today. Brief review of yesterday Opportunity for questions Leverage in the banking system Effect of limited liability Systemic risk. Remember yesterday!. - PowerPoint PPT PresentationTRANSCRIPT
Edmund Cannon
Banking CrisisUniversity of VeronaLecture 2
Plan for today2
Brief review of yesterdayOpportunity for questionsLeverage in the banking systemEffect of limited liabilitySystemic risk
Remember yesterday!3
Banks are financial institutions that engage in “maturity transformation”:
Banks borrow short-term (a breve termine)Banks lend long-term (a lungo termine)
Diamond-Dybvig model – banks are unstable (two Nash equilibria).
Potential solutions:Central bank intervention (Bagehot)Deposit insurance
What else is important about banks?4
Banks engage in maturity transformation.Another important feature of banks:
Banks are leveraged.
Nb other institutions are leveraged too:
Leveraged Not leveragedGeneral assurance (insurance) companyLife assurance companyHedge fundSupermarket
Mutual fundRatings agencyStock brokerAccountantActuary
A very simple model of a bank’s balance sheet5
Assets LiabilitiesLoans €90 Equity €8Cash €10 Deposit
s€92
Total €100
Total €100
(Simple definition):AssetsLeverage Equity=
A More Detailed Model of a Bank Balance Sheet
6
Difference between equity and depositors/bondholders.
7
Depositors and bond-holders (should) have no risk.
They should not get back less than they deposit plus interest (no downside risk);They will not get back more than they deposit plus interest (no upside risk).
Equity holders (sometimes referred to as capital):Should bear all of the risk (upside and downside risk);They get the residual (= profit).
Contrast this model with basic money supply model of banking (implications for macroeconomic models such as IS-LM)
8
{ { { Total Money OutsideMoney Supply Multiplier Money
Money supply constrained by
M m H£ ´
{ { {
{ { {
Total Money OutsideMoney Supply Multiplier Money
Equity Supply Leverageof Credit Ratio
Money supply and credit constrained by
M m H
M El*
£ ´
£ ´
A mutual fund (“unit trust” in the UK)9
AssetsLeverage i.e. not levered.Equity 1,= =
Selling short on equity (eg hedge fund)
10
Equity "risky assets"Leverage Equity
nb "risky assets"
-
0
=
<
Losses and leverage11
Suppose a firm is levered by a factor of ten.The firm can bear losses of up to 10% (=1/10) before equity is exhausted.If leverage is twenty then the firm can only bear losses of 5%.Leverage in 2007:
Goldman Sachs 25Lehman Bros 29Merrill Lynch 32
Trends in leverage in USA and UKSource: Turner Report12
Is Leverage a “Good” or “Bad” Thing?13
Greater leverage allows more investment.Leverage allows risk to be shared in a particular way (equity bears more risk, bonds bear less risk)If assets are over-priced then short-selling helps correct the price – but short selling typically involves leverage.Too much leverage means that bond-holders are exposed to risk (which they are trying to avoid).Leverage results in limited liability for the equity holders: downside risk is borne by bond holders (or government).Leverage endogenises risk (Shin, 2009)
Risk aversion: concave preferences14
2
20 0
U UC C
Limited liability and risk aversion: U = ln(W)15
In the bad state of the world the payoff to the risky investment is 1.1 – e.This might be less than one (negative return). But our utility function is not defined for negative utility (perhaps because consumption cannot be negative).
Risk aversion with limited liability16
Limited liability and risk aversion: U = ln(W)17
0.09
0.10
0.10
0.11
0.11
0.12
0.12
0.13
0.13
0.14
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Expected utility
Value of e
Limited liability and risk aversion18
Even risk-averse agents may like riskier investments if they have limited liability.Banking: excessive risk means bad outcomes fall on bondholders, depositors and the government (via insurance).Limited liability may be one of the causes of the financial crisis (faulty incentives or bankers).
BUT:Perhaps bankers are risk-neutral or risk-loving;Perhaps bankers are irrational.
Reducing risks in banks19
Banks might be required or choose to self-insure.Ownership structure (partnerships) and competition.Separate retail and investment banking:
USA: Glass-Steagall Act (1933), repealed 1999USA: Frank-Dodd Act (2010)UK: Vickers Commission proposal (2010)Capital requirements (Basel I, etc)Supervision or RegulationModelling / measuring risk (Basel II, second tier)Making information publicly available (Basel II, third tier)
Capital Requirements: Basel I, II, III20
Basel I: International agreement of 1988: implemented in 1990s.Capital requirement of 8% so leverage of 12½.
Leverage is defined as ratio of capital (equity) to risk-weighted assets.
The risk weights depend upon credit ratings, determined by credit rating agencies.
Basel II and III changed the weights and ratios. USA introduced the “recourse rule” rather than Basel II (very similar).
Basel I and Basel II capital requirements21 Risk-weighted AssetsLeverage ( capital)Total Capital
1212 8%= <
Basel I Basel IIWeight Capital Weight Capital
Cash 0% none 0% noneGov’t Bonds
AAA/AA 0% none 0% noneA 0% none 20% 1.6%BBB 0% none 50% 4.0%BB/B 0% none 100% 8.0%
Agency bonds 20% 1.6% 20% 1.6%Asset-backed securities
AAA/AA 100% 8.0% 20% 1.6%A 100% 8.0% 50% 4.0%BBB/BB 100% 8.0% 100% 8.0%
Mortgages 50% 4.0% 35% 2.4%Business loans 100% 8.0% varies
Three sorts of capital requirement22
Basel II Basel III Basel III +
counter-cyclical buffer
UK’sVickers
Commission
Tier 1 Equity / Risk-Weighted Assets
2% 3½ % 6% 7%10%
Total Capital / Risk-Weighted Assets
8% 8% 10½ %
Tier 1 Equity / Total Assets
3%
Credit Ratings23
e.g. Moody’sGrade
Expected 10-year loss
Comment
Aaa 0.01% Highest grade
Investment Grade
Aa 0.06% - 0.22% Very low riskA 0.39% - 0.99% Low riskBaa 1.43% - 3.36% Moderate riskBa 5.17% - 9.71% Questionable
qualitySpeculative Grade(Junk bonds)
B 12.21% - 19.12% Poor qualityCaa 35.75% Extremely poorCa, C Possibly in default
Problems with the credit rating industry24
Ratings agencies have quasi-official statusie when a bank justifies the risk on its balance sheet to a regulator it uses a recognised agency’s ratings.Very few firms (Moody’s, Fitch, Standard & Poors)ReputationNeeds to be officially recognised.Too much reliance on ratings agencies.Agencies are paid by the issuer of an asset (ie the borrower) not the purchaser of the asset (the lender). This creates an incentive problem.
Reducing Leverage25
Both the regulated and the shadow banking system were constrained by lack of equity.
Savings glut from China, etc: large amounts of funds to invest.
Solutions:
Create new safe assets to put on balance sheet (securitisation: buy CDOs)
Move assets off balance sheet (conduits, sell CDOs)
Move risk off balance sheet by buying insurance (Credit Default Swaps)
Securitisation: Mortgages26
US market is very different to Europe (where little securitisation)
Prime mortgagesSold with strict underwiting standards;Passed on to Fannie Mae / Freddie Mac (state sponsored);Then sold as agency RMBSs.
Sub-prime mortgagesSold with weaker underwriting;Bundled together into securities by investment banks.Sold on as RMBSs.Difficult to work out quality of underlying mortgages.
Creating “safe” assets: Collateralised Debt Obligations (CDOs)
27
Collateralised debt obligations are similar to SIVs
except
they lend long and borrow long (no maturity transformation);
they are not open ended.
Tett describes how these were pioneered by JPMorgan.
When based on mortgages referred to as Collateralised Mortgage Obligations (CMOs) or Residential Mortgage-Backed Securities (RMBSs).
Reasons for creating Collateralised Debt Obligations (CDOs)
28
(i) (Simple situation) The bank acts as an intermediary but neither the asset nor the liability appear on the balance sheet. Therefore, this avoids capital requirements.
(ii) The bank can create new financial assets with differing levels of risk (securitisation; tranching)
Simple Model29
In this model there are two borrowers, X and Y.
Each borrower will eitherRepay a loan of £100 (probability of 0.9)Default and repay nothing (probability of 0.1)
(This model is not very realistic, but the maths is simple.)
We start by assuming that whether or not X repays is independent of whether or not Y repays.
Simple Model (continued)30
So there are three possibilities:Both borrowers repay (probability 0.81)Just one borrower repays (probability 0.18 = 0.09 + 0.09)Both borrowers default (probability 0.01)
No correlationBorrower X
Borrower Y
Default prob = 0.1
Repay prob = 0.9
Default prob = 0.1 0.01 0.09
Repay prob = 0.9 0.09 0.81
31
2 2
E Loan X to A 0.9 100 0.1 0 90
var Loan X to A 0.9 100 90 0.1 0 90 900
st.dev. Loan X to A 900 30
Loan Y has the same characteristics as Loan X.
Saving and borrowing without risk pooling (no FI)
32
Each saver gets half of the money paid into the mutual fund.
Saving and borrowing with risk pooling (mutual fund)
33
( ) ( )( )
E Either X or Y
var Either X or Y
st.dev. Either X or Y
2 2
2
0.81 200 0.18 100 0.01 0 9020.81 100 90 0.18 50 0
0.01 0 90450
450 21
´ + ´ + ´é ù= =ê úë ûé ù= ´ - + ´ -ê úë û
+ ´ -=
é ù= »ê úë û
34
So long as there is money available, the senior tranche gets paid (i.e., senior tranche gets paid first).The junior tranche only gets paid after the senior tranche
Saving and borrowing with tranching (securitisation)
35
( ) ( )E Senior tranche
var Senior tranchest.dev. Senior tranche
2 2
0.99 100 0.01 0 99
0.99 100 99 0.01 99 0 9910
é ù= ´ + ´ =ê úë ûé ù= ´ - + ´ - =ê úë ûé ù»ê úë û
X and Y repay: repaidSenior tranche receives
only one repays: repaid
neither repays: repaid Senior tranche receives zero
200 0.81100
100 0.18
0 0.01
p
p
p
üï= ïïýï= ïïþ=
36
( ) ( )E Junior tranche
var Junior tranche
st.dev. Junior tranche
2 2
0.81 100 0.19 0 81
0.81 100 81 0.19 81 0 1539
1539 39
é ù= ´ + ´ =ê úë ûé ù= ´ - + ´ - =ê úë ûé ù= »ê úë û
X and Y repay: repaid Junior tranche receives
only one repays: repaidJunior tranche receives zero
neither repays: repaid
200 0.81 100
100 0.18
0 0.01
p
p
p
=üï= ïïýï= ïïþ
Discussion of Model37
By pooling risky assets it is possible to reduce overall risk.
The underlying mortgage had a st.dev. of 30A mutual fund of two mortgages had a st.dev. of 21The senior tranche of a securitised CMO had a st.dev. of 10.
In the example the risky assets were uncorrelated. It is still possible to reduce risk in a mutual fund (equal sharing of assets) even if assets are positively correlated (so long as they are not perfectly correlated). The effect of correlation on the value of tranches is more complicated.
Risk pooling with differing degrees of correlation38
No correlation0.1 0.9
0.1 0.01 0.090.9 0.09 0.81
Variance 450
Partial correlation in payoff
0.1 0.90.1 0.05 0.050.9 0.05 0.85
Variance 650
Perfect correlation in payoff
0.1 0.90.1 0.1 00.9 0 0.9
Variance 900
Negative correlation in payoff
0.1 0.90.1 0 0.10.9 0.1 0.8
Variance 400
Securitisation39
Pool a group of risky assets into a Special Purpose Vehicle.The payouts of the SPV are then tranched:
Tranche 1 (Super-senior) gets first call on assetsTranche 2 (Senior) goes nextTranche 3 (Mezzanine) goes nextTranche 4 (Junk) gets anything left.
Possible to create AAA-rated assets from underlying assets with a much lower credit rating.
US: Special Purpose Entity; Eire: Financial Vehicle Corporation
Securitisation: Mortgages40
US market is very different to UK (where little securitisation)Prime mortgages
Sold with strict underwiting standards;Passed on to Fannie Mae / Freddie Mac (state sponsored);Then sold as RMBSs.Sub-prime mortgagesSold with weaker underwriting;Bundled together into securities by investment banks.Sold on as RMBSs.Difficult to work out quality of underlying mortgages. Pricing of any RMBS depends upon the correlation.
Insurance41
Credit Default Swaps: part (i)42
Credit Default Swaps: part (ii)43
Nationwide House PricesRatio of first-time buyer houses to earningsSource: http://www.nationwide.co.uk/hpi/
44
0
1
2
3
4
5
6
1983 Q1
1985 Q1
1987 Q1
1989 Q1
1991 Q1
1993 Q1
1995 Q1
1997 Q1
1999 Q1
2001 Q1
2003 Q1
2005 Q1
2007 Q1
2009 Q1
Ratio of house prices to average earningsSource: Nationwide, National Statistics, author’s calculations
45
0
1
2
3
4
5
6
1963
1965
1967
1969 1971
1973
1975
1977
1979
1981
1983
1985
1987
1989 1991
1993
1995
1997
1999 2001
2003
2005
2007
2009
Measuring risk – Value at Risk (VaR)46
Obvious measure of risk is variance (or standard deviation). But that is a general measure – we want to deal with downside risk (when things go wrong).
Difficulty of estimating VaR from data47
Distribution of VaR Measure - quantile Distribution of VaR Measure - t(10) N(s=0.114)
Distribution of VaR Measure - Normal approx Distribution of Returns ~ t(10)
-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5
5
10
15
20
25
30
35Distribution of VaR Measure - quantile Distribution of VaR Measure - t(10) N(s=0.114)
Distribution of VaR Measure - Normal approx Distribution of Returns ~ t(10)
Leverage and endogenous risk (Shin)48
Endogenous risk – the crash49
As asset prices fall (losses mount) leverage rises.Firms sell assets to reduce leverage.Firesale prices are an externality to other banks’ balance sheets (especially with mark-to-market pricing).