Transcript Lezioni ppt 2

Edmund Cannon
Banking Crisis
University of Verona
Lecture 2
2
Plan for today
Brief review of yesterday
Opportunity for questions
Leverage in the banking system
Effect of limited liability
Systemic risk
3
Remember yesterday!
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
4
What else is important about banks?
Banks engage in maturity transformation.
Another important feature of banks:
Banks are leveraged.
Nb other institutions are leveraged too:
Leveraged
Not leveraged
General assurance (insurance)
company
Life assurance company
Hedge fund
Supermarket
Mutual fund
Ratings agency
Stock broker
Accountant
Actuary
5
A very simple model of a bank’s balance sheet
(Simple definition):
Assets
Leverage =
Equity
Assets
Liabilities
Loans
€90
Equity
€8
Cash
€10
Deposits
€92
Total
€100
Total
€100
6
A More Detailed Model of a Bank Balance Sheet
7
Difference between equity and
depositors/bondholders.
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).
8
Contrast this model with basic money supply model
of banking (implications for macroeconomic models
such as IS-LM)
Money supply constrained by
M
{
£
m ´ H
{
{
Total
Money Supply
Money
Multiplier
Outside
Money
Money supply and credit constrained by
M
{
£
Total
Money Supply
M* £
{
Supply
of Credit
m ´ H
{
{
Money
Multiplier
Outside
Money
l ´ E
{
{
Leverage
Ratio
Equity
9
A mutual fund (“unit trust” in the UK)
Assets
Leverage =
= 1, i.e. not levered.
Equity
10
Selling short on equity (eg hedge fund)
Equity - "risky assets"
Leverage =
Equity
nb "risky assets" < 0
11
Losses and leverage
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 25
Lehman Bros 29
Merrill Lynch 32
12
Trends in leverage in USA and UK
Source: Turner Report
13
Is Leverage a “Good” or “Bad” Thing?
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)
14
Risk aversion: concave preferences
U
0
C
 2U
0
2
C
15
Limited liability and risk aversion: U = ln(W)
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).
16
Risk aversion with limited liability
Limited liability and risk aversion: U = ln(W)
17
Expected utility
0.14
0.13
0.13
0.12
0.12
0.11
0.11
0.10
0.10
Value of e
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0.09
18
Limited liability and risk aversion
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 banks
19
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 1999
USA: Frank-Dodd Act (2010)
UK: Vickers Commission proposal (2010)
Capital requirements (Basel I, etc)
Supervision or Regulation
Modelling / measuring risk (Basel II, second tier)
Making information publicly available (Basel II, third tier)
20
Capital Requirements: Basel I, II, III
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 requirements
Risk-weighted Assets
Leverage =
< 12 21
Total Capital
Basel I
(8% capital)
Basel II
Weight
Capital
Weight
Capital
0%
none
0%
none
AAA/AA
0%
none
0%
none
A
0%
none
20%
1.6%
BBB
0%
none
50%
4.0%
BB/B
0%
none
100%
8.0%
20%
1.6%
20%
1.6%
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%
Gov’t Bonds
Cash
Agency bonds
Assetbacked
securities
21
varies
22
Three sorts of capital requirement
Basel II
Basel III
Basel III +
countercyclical
buffer
UK’s
Vickers
Commission
Tier 1 Equity /
Risk-Weighted
Assets
2%
3½ %
6%
7%
Total Capital /
Risk-Weighted
Assets
8%
Tier 1 Equity /
Total Assets
10%
8%
3%
10½ %
23
Credit Ratings
e.g. Moody’s
Grade
Expected 10-year loss
Comment
Aaa
0.01%
Highest grade
Aa
0.06% - 0.22%
Very low risk
A
0.39% - 0.99%
Low risk
Baa
1.43% - 3.36%
Moderate risk
Ba
5.17% - 9.71%
Questionable quality
B
12.21% - 19.12%
Poor quality
Caa
35.75%
Extremely poor
Ca, C
Possibly in default
Investment
Grade
Speculative
Grade
(Junk bonds)
24
Problems with the credit rating industry
Ratings agencies have quasi-official status
ie 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)
Reputation
Needs 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.
25
Reducing Leverage
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)
26
Securitisation: Mortgages
US market is very different to Europe (where little
securitisation)
Prime mortgages
Sold with strict underwiting standards;
Passed on to Fannie Mae / Freddie Mac (state sponsored);
Then sold as agency RMBSs.
Sub-prime mortgages
Sold with weaker underwriting;
Bundled together into securities by investment banks.
Sold on as RMBSs.
Difficult to work out quality of underlying mortgages.
27
Creating “safe” assets: Collateralised Debt
Obligations (CDOs)
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).
28
Reasons for creating Collateralised Debt
Obligations (CDOs)
(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)
29
Simple Model
In this model there are two borrowers, X and Y.
Each borrower will either
Repay 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)
No correlation
Borrower X
Borrower Y
30
Default prob = 0.1 Repay prob = 0.9
Default prob = 0.1
0.01
0.09
Repay prob = 0.9
0.09
0.81
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)
31
Saving and borrowing without risk pooling (no FI)
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
2
st.dev. Loan X to A   900  30
Loan Y has the same characteristics as Loan X.
2
32
Saving and borrowing with risk pooling (mutual fund)
Each saver gets half of the money paid into the mutual fund.
33
0.81 ´ 200 + 0.18 ´ 100 + 0.01 ´ 0
é
ù
E êëEither X or Y ú
= 90
û=
2
2
2
var éêëEither X or Y ù
ú
û= 0.81 ´ (100 - 90) + 0.18 ´ (50 - 0)
2
+ 0.01 ´ (0 - 90)
= 450
st.dev. éêëEither X or Y ù
ú
û=
450 » 21
34
Saving and borrowing with tranching (securitisation)
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
35
ïï
p = 0.81ü
ïý
only one repays: 100 repaid p = 0.18ïïï
þ
X and Y repay: 200 repaid
neither repays: 0 repaid
p = 0.01
Senior tranche receives 100
Senior tranche receives zero
E éêëSenior trancheù
ú
û= 0.99 ´ 100 + 0.01 ´ 0 = 99
2
2
var éêëSenior trancheù
ú
û= 0.99 ´ (100 - 99) + 0.01 ´ (99 - 0) = 99
st.dev. éêSenior trancheù
ú» 10
36
X and Y repay: 200 repaid
Junior tranche receives 100
p = 0.81
ïï
only one repays: 100 repaid p = 0.18ü
ïý Junior tranche receives zero
neither repays: 0 repaid
p = 0.01ïïï
þ
E éêëJunior trancheù
ú
û= 0.81 ´ 100 + 0.19 ´ 0 = 81
2
2
var éêëJunior trancheù
ú
û= 0.81 ´ (100 - 81) + 0.19 ´ (81 - 0) = 1539
st.dev. éJunior trancheù= 1539 » 39
37
Discussion of Model
By pooling risky assets it is possible to reduce overall risk.
The underlying mortgage had a st.dev. of 30
A mutual fund of two mortgages had a st.dev. of 21
The 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.
38
Risk pooling with differing degrees of correlation
No correlation
0.1
0.9
Variance
0.1
0.01
0.09
0.9
0.09
0.81
Partial correlation in payoff
0.1
0.9
0.1
0.05
0.05
0.9
0.05
0.85
450
Variance
650
Perfect correlation in payoff
0.1
0.9
0.1
0.1
0
0.9
0
0.9
Negative correlation in payoff
0.1
0.9
0.1
0
0.1
0.9
0.1
0.8
Variance
Variance
900
400
Securitisation
39
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 assets
Tranche 2 (Senior) goes next
Tranche 3 (Mezzanine) goes next
Tranche 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
40
Securitisation: Mortgages
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 mortgages
Sold 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.
41
Insurance
42
Credit Default Swaps: part (i)
43
Credit Default Swaps: part (ii)
44
Nationwide House Prices
Ratio of first-time buyer houses to earnings
Source: http://www.nationwide.co.uk/hpi/
6
5
4
3
2
1
0
1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
Q1
Q1
Q1
Q1
Q1
Q1
Q1
Q1
Q1
Q1
Q1
Q1
Q1
Q1
Ratio of house prices to average earnings
Source: Nationwide, National Statistics, author’s calculations
6
5
4
3
2
1
0
1963
1965
1967
1969
1971
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
2009
45
46
Measuring risk – Value at Risk (VaR)
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).
47
Difficulty of estimating VaR from data
35
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)
30
25
20
15
10
5
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
48
Leverage and endogenous risk (Shin)
49
Endogenous risk – the crash
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).