This document discusses regulatory liquidity measures and stochastic liquidity risk measures. It begins with an outline and background on the Basel Committee's work on liquidity risk. It then describes the regulatory liquidity measures of the Liquidity Coverage Ratio and Net Stable Funding Ratio, including details on their calculation methodology. The document also presents approaches to model total cash inflows and outflows stochastically and defines measures of liquidity risk using Monte Carlo simulation. It concludes by discussing potential extensions of the modeling framework.

1. Regulatory Liquidity Measures and
Stochastic Liquidity Risk Measures
1
By Fai Y. LAM
E-mail: faiylam@gmail.com
11 am to 12 noon, Tuesday 13 April 2010
Room R503, Hong Kong Polytechnic University
2
Outline
Background
Regulatory liquidity measures
Liquidity risk measures
3
Part I
Regulatory Liquidity
Measures
4
Basel committee on liquidity risk

2. 5
What happened during the period?
Basel new capital accord (Basel II)
Kicked off in January 2001
Finalized in May 2006
Glass–Steagall Act repealed on November 12, 1999
Commercial banks in US participated in investment banking activities
Paper On Default Correlation: A Copula Function Approach” by Dr. David X. LI’s, RiskMetrics
Group published in 2000
Acceleration of the CDO market
CDS market grew to US$ 45 tn notional in 2007
Subprime mortgage market grew to US$ 1.3 tn in 2007
Financial tsunami emerged in 2007
Basel Committee issued guideline “Principles for Sound Liquidity Risk Management and
Supervision” in Sep 2008
Basel Committee issued consultative paper “International framework for liquidity risk
measurement, standards and monitoring “ in Dec 2009
6
Regulatory liquidity
Standards
Liquidity coverage ratio
Net stable funding ratio
Monitoring tools
Contractual maturity mismatch
Concentration of funding
Available unencumbered assets
Market-related monitoring tools
Stock of high quality liquid assets
≥
≥ −
Stock of high quality liquid assets Cash outflows over a day time period
7
Liquidity coverage ratio
To ensure existing liquidity can support the cash
flows over a 30-day period under an acute liquidity
stress scenario
30
Cash lows over a day time period
Net cash outflows over a day time period
inf 30
100%
30
− −
−
8
High quality liquid assets
Fundamental characteristics
Low credit and market risks
Ease and certainty of valuation
Low correlation with risky assets
Listed on a developed and recognised exchange market
Market-related characteristics
Active and sizable market
Presence of committed market makers
Low market concentration
Flight to quality

3. 9
High quality liquid assets
Cash (100%)
Qualifying central bank receivables (100%)
Domestic sovereign or central bank debt in domestic currency (100%)
Qualifying marketable securities from sovereigns, central banks, public
sector entities, and multi-lateral development banks (100%)
Qualifying corporate bonds and covered bonds rated AA to AAA (80%)
Qualifying corporate bonds and covered bonds rated A- to AA- (60%)
10
Cash inflows
Amounts receivable from retail counterparties (100% of
planned inflows from performing assets)
Amounts receivable from wholesale counterparties (100% of
planned inflows from performing wholesale customers)
Receivables in respect of repo and reverse repo transactions
backed by illiquid assets and securities lending/borrowing
transactions where illiquid assets are borrowed (100%)
Other cash inflows, including planned contractual receivables
from derivatives
11
Cash outflows (1)
Retail deposits
Stable deposits (minimum 7.5%)
Less stable retail deposits (minimum 15%)
Unsecured wholesale funding
Stable, small business customers (minimum 7.5%)
Less stable, small business customers (minimum 15%)
Non-financial corporates, sovereigns, central banks and public sector entities with
operational relationships (25% of deposits needed for operational purposes)
Non-financial corporates, no operational relationship (75%)
Other legal entity customers and sovereigns, central banks, and PSEs without
operational relationships (100%)
Secured funding
Funding from repo of illiquid assets and securities lending/borrowing transactions
illiquid assets are lent out (100%)
12
Cash outflows (2)
Additional requirements
Liabilities related to derivative collateral calls related to a downgrade of up to
3-notches (100% of collateral that would be required to cover the contracts in
case of up to a 3-notch downgrade)
Market valuation changes on derivatives transactions (amount to be
nationally determined)
Valuation changes on posted noncash or non-high quality sovereign debt
collateral securing derivative transactions (20%)
ABCP, SIVs, Conduits, etc:
Liabilities from maturing ABCP, SIVs, SPVs, etc (100% of maturing amounts
and 100% of returnable assets)
Term Asset Backed Securities (including covered bonds) (100% of maturing
amounts)

4. 13
Cash outflows (3)
Currently undrawn portion of committed credit and liquidity facilities to:
Retail clients (10% of outstanding lines)
Non-financial corporates, credit facilities (10% of outstanding lines)
Non-financial corporates, liquidity facilities (100% of outstanding lines)
Other legal entity customers (100% of outstanding lines)
Other contingent funding liabilities (such as guarantees, letters of credit, revocable
credit and liquidity facilities, etc.) (to be determined by supervisors, specific to
needs at certain banks)
Planned outflows related to renewal or extension of new loans (retail or
wholesale) (100%)
Any other cash outflows (including planned derivative payables)
14
Net stable funding ratio
A minimum acceptable amount of stable funding
based on the liquidity characteristics of an
institution’s assets and activities over a one year
horizon
Availableamount of stable funding
quired amount of stable funding
100%
≥
Availableamount of stable funding Re
quired amount of stable funding
Re
≥
15
Available amount of stable funding
Capital
Preferred stock with maturity of equal to or greater than one
year
Liabilities with effective maturities of one year or greater
The portion of “stable” non-maturity deposits and/or term
deposits with maturities of less than one year that would be
expected to stay with the institution for an extended period
in an idiosyncratic stress event
16
Required amount of stable funding
The value of assets held and funded by the
institution, multiplied by a specific required stable
funding factor assigned to each particular asset type
The amount of off-balance sheet activity (or
potential liquidity exposure) multiplied by its
associated required stable funding factor

5. 17
Required stable funding (RSF) factor
The RSF factors assigned to various types of assets are parameters
intended to approximate the amount of a particular asset that could not
be monetised through sale or use as collateral in a secured borrowing on
an extended basis during a liquidity event lasting one year
The RSF factor applied to the reported values of each asset or off-balance
sheet exposure is the amount of that item that supervisors believe should
be supported with stable funding
Assets that are more liquid and more readily available to act as a source of
extended liquidity in the stressed environment identified above receive
lower RSF factors (and require less stable funding) than assets considered
less liquid in such circumstances and, therefore, require more stable
funding
18
Regulatory effort (1)
A big step from the Basel Committee guideline
“Principles for Sound Liquidity Risk Management and
Supervision” (Sep 2008)
Formally define regulatory liquidity in a consistent
and a measurable framework
Relatively easy to calculate
Deterministic, snapshot, rating factor approach
19
Regulatory effort (2)
Recognition of government related entities as the
top funding sources
Appreciation of high quality covered bonds
Regulatory liquidity economic liquidity
Limited details on derivatives
20
Regulatory effort (3)
HKMA Viewpoint article 11 June 2009
http://www.info.gov.hk/hkma/eng/viewpt/
20090611e.htm
*Source : Reorganisation of Banking
Departments in April 2010, HKMA

6. 21
Potential impacts to banking industry
Competition on high quality assets
= high cost of liquidity
Downward pressure on BBB rated corporate bonds and
covered bonds
Merge and acquisition of financial institutions
Political bias on funding to “too large to fail”
Acceleration of coverage to life insurance businesses
Stable and diversified funding from insurance premium
Mortality risk uncorrelated with credit market
More supervisory reporting, reviews and examinations
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A simple question
What is my bank’s funding liquidity risk?
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Outstanding questions
1. How to set funding liquidity risk limits?
2. Is the funding liquidity risk increasing or decreasing during
the last 12 months?
3. Which branch contributes the most funding liquidity risk?
4. How to diversify the funding sources?
5. How to perform funding liquidity stress testing?
6. What will be the potential loss in the next funding liquidity
crisis?
7. How to plan for contingency funding?
8. How to incorporate funding liquidity risk into cost?
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Part II
Liquidity Risk
Measures

7. 25
Modelling total cash inflow
Probability
Amount
Expected total
cash inflow
Total cash inflow
Calculated according to regulatory liquidity requirements
Greater than or equal to 0
Asymmetric
Long right tail
26
Modelling total cash inflow
Lognormal total cash inflow model
= +
μ σ
dI Idt IdW
= − + ⋅
I I T T Normal


= × − + ⋅
0 : Total contractual cash inflow
I


T : Total cash inflow with cash management incorporated
I
μI
: Drift of total cash inflow
σI
: Volatility of total cash inflow
( )
[ ] (0,1)
2
exp
) 0,1
2
exp (
2
2
0




I I I
I
T
I I I
I
T I
I
T Normal
T
E I
σ
σ
σ
σ
μ
27
Modelling total cash outflow
Probability
Amount
Expected total
cash outflow
Total cash outflow
Calculated according to regulatory liquidity requirements
Greater than or equal to 0
Asymmetric
Long right tail
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Modelling total cash outflow
Lognormal total cash inflow model
2
= +
μ σ
dO Odt OdW
= − + ⋅
O O T T Normal


= × − + ⋅
0 : Total contractual cash outflow
O


T : Total cash outflow with cash management incorporated
O
μO : Drift of total cash outflow
σO : Volatility of total cash outflow
( )
[ ] (0,1)
2
exp
) 0,1
2
exp (
2
0




O O
O
T
O O
O
T O
O
T Normal
T
E O
σ
σ
σ
σ
μ

8. 29
Regulatory liquidity surplus
gulatory liquidity surplus
Stock of high quality liquid assets
Total cash low next
inf month
Re
Total cash outflow next
=
+
−
A random variable subject to
month
Expected total cash inflow and expected total cash outflow
Volatilities of total cash inflow and total cash outflow
Correlation between total cash inflow and total cash outflow
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Regulatory liquidity surplus
A random variable following a multi-lognormal
distribution
No closed form solutions
To be realized easily with Monte Carlo simulation
gulatory liquidity surplus
Stock of high quality liquid assets



[ ] ( ) [ ] ( )
+ × − + ⋅
Correlation[ (0,1), (0,1)]
0,1
× − + ⋅ 
2
0,1 - exp
2
exp
Re
2 2
I O
O O
O
I I T
I
T
Normal Normal
T Normal
T
T Normal E O
T
E I
=




=
ρ
σ
σ
σ
σ
31
Liquidity risk measures
Probability of regulatory liquidity shortage
What is the chance of having net cash outflow not covered
by current stock of high quality liquidity assets?
obability of regulatory liquidity shortage
[ ] Re 0 1
Pr
= gulatory liquidity surplus E
Regulatory liquidity surplus at 99.9% of confidence
level (once every 1,000 months)
Will there be any regulatory liquidity
shortage under extreme conditions?
32
Monte Carlo simulation in Excel

9. 33
Regulatory liquidity shortage
34
Findings of common sense
Regulatory liquidity 0
== probability of regulatory liquidity shortage = 0
$1 mn high quality liquid assets $1 mn planned
cash inflow
$1 mn planned cash inflow $1 mn planned cash
outflow
Two small funding sources are better than one large
funding source
Two small lending customers are better than one
large lending customer
35
Applications of liquidity risk measures
Trend analysis
What is the change of liquidity risk during last year?
Peer analysis
Which branch is the outlier?
Which branch contributes the most liquidity risk?
Liquidity risk limit
Positive regulatory liquidity surplus at 99.9% confidence level
Diversification analysis
What is the benefit of adding more funding sources?
Scenario analysis
How much more regulatory liquidity is required if a new branch is opened in
Shanghai?
Stress testing
Manipulation of expected cash inflow level, cash outflow level, volatilities and
correlation
36
Further extensions
Internal definition of liquidity and cash flows
Total cash inflow and total cash outflow broken
down by business line, funding source and customer
base
gulatory liquidity surplus
Stock of high quality liquid assets
M
Σ
=
k
Σ
=
=
+
−
N
k
Total cash low next
inf month
Total cash outflow next
1
k
1
k
month
Re

10. 
37
Variance-covariance method
Approximate the multi-lognormal distribution with
multi-normal distribution
Closed form solutions available
A huge saving on computing power


gulatory liquidity surplus
Stock of high quality liquid assets

[ ] ( ) [ ] ( )
Σ Σ
⋅ + − × − 
+ × − + ⋅
= =

Stock of high quality liquid assets

Σ [ ] ( ) Σ [ ] ( )
⋅ + − × − 
+ × − + ⋅
= =




≈




=
N
k
O k O k
O k
T k
M
k
I k I k
I k
T k
N
k
O k O k
O k
T k
M
k
I k I k
I k
T k
T Normal
T
T Normal E O
T
E I
T Normal
T
T Normal E O
T
E I
1
, ,
2
,
,
1
, ,
2
,
,
1
, ,
2
,
,
1
, ,
2
,
,
0,1
2
0,1 1
2
1
0,1
2
0,1 exp
2
exp
Re
σ
σ
σ
σ
σ
σ
σ
σ
38
Your opinions
To download paper and simulation model
http://sites.google.com/site/quanrisk