Transcript 6.3 Measurement of liquidity risk

Topic 6. Measuring Liquidity Risk
6.1 Definition of liquidity risk
6.2 Liquidity risk at depository institutions (DIs)
6.3 Measurement of liquidity risk
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6.1 Definition of liquidity risk

Liquidity risk (more precisely, funding liquidity risk) of
a FI refers to risk of running out of cash and/or unable
to raise additional funds to meet the financial claims
from its liability holders (liability-side of the balance
sheet) or to honor the asset purchase agreement (assetside of the balance sheet).
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6.2 Liquidity risk at depository institutions
(DIs)
Liability-Side
 A DI usually funds its long-term assets such as
mortgage loans, with short-term liabilities such as time
deposit accounts.
 In general, the DI only keeps small proportion of these
short-term financial deposits in cash asset (cash
reserve). If the liabilities claims are unusual high, it
may cause the liquidity problem to the DI.
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6.2 Liquidity risk at depository institutions
(DIs)

For a given period of time [t1, t2], where
0 (now) < t1 < t2, the net deposit drains over [t1, t2],
NDD(t1, t2), is defined as
NDD(t1, t2) = DW(t1, t2) – DA(t1, t2)
(6.1)
where
DW(t1, t2) is the deposit withdrawals over [t1, t2];
DA(t1, t2) is the deposit additions over [t1, t2].
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6.2 Liquidity risk at depository institutions
(DIs)


If NDD is abnormally high, it will make the DI which
does not have sufficient cash to meet the withdrawal
needs. As a result, it needs to raise the fund from
liquidating the assets at fire-sale prices or borrowings
with high borrowing cost.
The quality of managing the liquidity risk on the
liability side is heavily depend on the how accurate to
predict the distribution of NDD(t1, t2) in order to have
a good planning to raise up the required funds.
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6.2 Liquidity risk at depository institutions
(DIs)

Three ways to manage the positively of the NDD:
• Purchased liquidity management:
 To fund the positive NDD through the adjustment on the
liability side of the balance sheet. This can be done by
borrowing funds through issuing additional fixedmaturity wholesale certificates of deposit or selling
notes and bonds.
 The higher the cost of funding, the less attractive of the
purchased liquidity management.
 Under purchased liquidity management, the DI can
preserves the asset side of its balance sheet.
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6.2 Liquidity risk at depository institutions
(DIs)

Example 6.1 (Purchased liquidity management)
All the values in the following table are measured in
million of dollars.
$5M net deposit drain.
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6.2 Liquidity risk at depository institutions
(DIs)
All the values in the following table are measured in million of
dollars.
The size of asset side
is preserved.
Increase the borrowed
funds by $5M.
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6.2 Liquidity risk at depository institutions
(DIs)
• Stored liquidity management:
 To fund the positive NDD through the adjustment on the
asset side of the balance sheet. This can be done by
liquidating some of its assets such as using the excess cash
reserves or selling its assets.
 Decrease the size of its balance sheet.
 The cost of using the excess cash reserves is the
opportunity cost. The corresponding cash can not be
invested in other high-income-earning assets.
• Combine purchased and stored liquidity management.
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6.2 Liquidity risk at depository institutions
(DIs)

Example 6.2 (Stored liquidity management)
All the values in the following table are measured in million of dollars.
$5M net
deposit
drain
Size of balance sheet
decrease by $5M.
Use $5M cash to fund
$5M net deposit drain.
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6.2 Liquidity risk at depository institutions
(DIs)
Asset-Side
 The liquidity risk on asset-side arises from insufficient
funds to cover the exercise of the off-balance-sheet loan
commitment by borrower.
 The loan commitment offers an option to the borrower
to take down any amount of the loan up to the
contractual amount at any time over the commitment
period.
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6.2 Liquidity risk at depository institutions
(DIs)



In a fixed-rate loan commitment, the interest rate to be
paid on any takedown is established when the loan
commitment contract originates.
In a floating-rate loan commitment, the borrower pays
the loan rate in force when the loan is actually taken
down.
The liquidity risk on the asset side can also be managed
by purchased and stored liquidity management.
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6.2 Liquidity risk at depository institutions
(DIs)

Example 6.3
All the values in the following table are measured in
million of dollars.
Exercise $5M loan
commitment.
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6.2 Liquidity risk at depository institutions
(DIs)
All the values in the following table are measured in million of
dollars.
Increase the borrowed
funds by $5M.
Decrease the cash by
$5M.
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6.3 Measurement of liquidity risk
Peer group ratio comparisons
 To compare certain key ratios and balance sheet
features of the DI with those of DIs of a similar size and
geographic location. The common key ratios include:
loan to deposits
ii. borrowed funds to total assets
iii. commitments to lend to assets
i.

A high ratio of (i) and (ii) means that the DI relies
heavily on the purchased funds market rather than on
core deposits to fund loans. This could mean future
liquidity problems if the DI is at or near its borrowing
limits in the purchased funds market.
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6.3 Measurement of liquidity risk


The high value of (iii) indicates the need of a high
degree of liquidity to fund any unexpected takedowns
of these loans – high-commitment DIs often face more
liquidity risk exposure than do low-commitment DIs.
The major weakness of the peer group ratio
comparisons is that it can only show the relative risk
but not the absolute risk of the DI.
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6.3 Measurement of liquidity risk
Example
6.4
From Table 17-7, we observe that the three ratios ((i), (ii) and
(iii)) of Bank of America (BOA) are higher than Northern
Trust Bank (NTB). So, BOA exposes higher liquidity risk than
NTB. Further, the ratio of core deposits to total assets of NTB
is higher than that of BOA shows that NTB relies more on the
stable core deposits to fund its asset than BOA.
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6.3 Measurement of liquidity risk
Liquidity index
 The liquidity index, I, is defined as
N
Pi
I   wi *
(6.2)
Pi
i 1
where
wi is the percent of asset i in the portfolio;
Pi and Pi* are the fire-sale asset price and fair
market price of asset i respectively.
 From Eq. (6.2), it is obvious that 0  I  1.
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6.3 Measurement of liquidity risk

The liquidity index measures the potential losses an FI
could suffer from a sudden or fire-sale disposal of
assets compared with the amount it would receive at a
fair market value established under normal market sale
conditions – which might take a lengthy period of time
as a result of a careful search and bidding process. The
closer of I to 0, the higher the liquidity risk of the FI.
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6.3 Measurement of liquidity risk

Example 6.5
Consider a portfolio which consists of:
•
•
$20 million in Treasury bills (T-bills).
$50 million in Mortgage loans.
If the assets in the portfolio need to be liquidated at
short notice, the DI will receive only 99% of the fair
market value of the T-bills and 90% of the fair market
value of the mortgage loans.
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6.3 Measurement of liquidity risk
Let w1 and w2 be the weight of T-bills and mortgage loans
respectively.
$20M
w1 
 0.2857; w2  0.7143
$20M  $50M
From Eq. (6.2), the liquidity index is given by
I  0.2857 0.99  0.7143 0.90
 0.9257
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6.3 Measurement of liquidity risk
Financing gap
 Classification of Payments:
•
•
Scheduled payments are those which have previously been
agreed on by the counterparties. For example, scheduled loan
disbursements to customers (cash outflow) and scheduled loan
repayment from the customers (cash inflow).
Unscheduled payments arise from customer behavior. For
example, unscheduled loan disbursements to customers through
credit cards (cash outflow) and unscheduled checking-account
deposits by customers (cash inflow).
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6.3 Measurement of liquidity risk

Classification of Payments (cont.):
•
•
Semidiscretionary payments occur as part of the bank’s normal
trading operations but can be quickly changed if necessary. For
example, semidiscretionary payments for the purchase of
securities by bank (cash outflow) and semidiscretionary
payments from the sale of normal trading securities (cash
inflow).
Discretionary transactions are those carried out by the bank’s
funding unit to balance the net cash flow each day. For
example, discretionary lending to other banks in the short-term
interbank market (cash outflow) and discretionary borrowing
from other banks in the interbank market (cash inflow).
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6.3 Measurement of liquidity risk

The daily financing gap ID is defined as
I D  OS  OU  OSD   I S  IU  I SD 
where
OS: daily scheduled cash outflow;
OU: daily unscheduled cash outflow;
OSD: daily semidiscretionary cash outflow;
IS: daily scheduled cash inflow;
IU: daily unscheduled cash inflow;
ISD: daily semidiscretionary cash inflow;
(6.3)
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6.3 Measurement of liquidity risk




In fact, ID is the daily amount of the discretionary fund
to be raised in order to balance the net daily cash
outflow. Further, ID is similar to NDD in Eq. (6.1).
Define
R = (OU + OSD) – (IU + ISD)
(6.4)
Since the unscheduled and semidiscretionary flows
evolve randomly according to the behavior of
customers and the bank’s normal operation, R is a
random variable.
From Eqs. (6.3) and (6.4), we have
ID = OS – IS + R
(6.5)
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6.3 Measurement of liquidity risk

Assume R ~ R , R2  , then

I D ~  OS  I S  R , R2



(6.6)
R and R can be estimated by collecting historical data
for OU, OSD, IU and ISD to calculate R for each past day.
The larger the R, the higher the liquidity risk of the DI.
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6.3 Measurement of liquidity risk

Define I as the solution of the following equation
PrI D  I    %


(6.7)
It is clear than I is the level of the discretionary fund to
be raised daily in order to make the DI has  %
(confidence level) chance to meet the daily net cash
outflow.
With the normality condition of ID in (6.6), we have
I % O S  I S  R  z %   R
(6.8)
where z % is defined as
PrZ  z %    %
whereZ ~ 0,1.
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6.3 Measurement of liquidity risk

Example 6.6
Suppose  = 95, OS = $2M, IS = $1.5M, R = $3M
and R = 20%.
From Eq. (6.8),
I 95%  $0.5M  $3M  1.65 0.2  $3.83M
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6.3 Measurement of liquidity risk

With (6.6) holds and R from one day to the next are
uncorrelated, the required level of discretionary fund
over a period of T days for the confidence level  % is
given by
I %,T O S ,T  I S ,T  R  T  z %  T   R
(6.9)
where OS,T and IS,T are the scheduled cash outflow and
inflow over a period of T days.
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6.3 Measurement of liquidity risk
BIS approach
 Maturity ladder
•
•
For each maturity, assess all cash inflows versus outflows.
Daily and cumulative net funding requirements can be
determined in this manner.
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6.3 Measurement of liquidity risk

Example 6.7
Net funding requirement Using BIS Maturity Laddering Model (in millions of dollars)
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6.3 Measurement of liquidity risk
One-day:
$4 million in excess.
One-month:
Cumulative net cash shortfall of $46 million.
Six-month:
Cumulative excess cash of $1,104 million.
Therefore, the corresponding DI will need to start
planning to obtain additional funding to fill this net
funding requirement in the one-month period.
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6.3 Measurement of liquidity risk

Scenario analysis
•
Under the BIS scenario analysis, a DI needs to assign timing
of cash flows for each type of asset and liability by assessing
the probability of the behavior of those cash flows under the
scenario being examined.
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6.3 Measurement of liquidity risk
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