SEEM3580 Risk Analysis for Financial Engineering
Review of Topic 6
Definition of liquidity risk



Inability for the FI to meet the financial claims from
its liability holders (liability-side of the balance sheet)
or to honor the asset purchase agreement (asset-side
of the balance sheet)
out of cash
unable to raise additional funds.
Liquidity risk at depository institutions (DIs)
Liability-Side
 the net deposit drains over [t1, t2]
NDD(t1, t2) = DW(t1, t2) – DA(t1, t2)
where
DW(t1, t2) is the deposit withdrawals over [t1, t2];
DA(t1, t2) is the deposit additions over [t1, t2].
Liquidity risk at depository institutions (DIs)
Three ways to manage the positivety of the NDD:

–
–
–
Purchased liquidity management
Stored liquidity management
Combine purchased and stored liquidity
management.
Liquidity risk at depository institutions (DIs)

Purchased liquidity management
–
–
Adjustments on the liquidity side
Issuing certificates of deposits or bonds
$5M net deposit
drain.
Liquidity risk at depository institutions (DIs)
The size of asset side
is preserved.
Increase the borrowed
funds by $5M.
Liquidity risk at depository institutions (DIs)

Stored liquidity management
–
–
–
Adjustment on the asset side
Liquidating assets
Opportunity cost of excess cash reserve
Liquidity risk at depository institutions (DIs)
$5M net
deposit
drain
Size of balance sheet
decrease by $5M.
Use $5M cash to fund
$5M net deposit drain.
Liquidity risk at depository institutions (DIs)
Asset-Side
The liquidity risk arises from insufficient funds
to cover the exercise of the off-balance-sheet
loan commitment agreement by borrowers.
The loan commitment agreement is a
contractual commitment to make a loan up to
a stated amount at a given interest rate in the
future.
Measurement of liquidity risk
Peer group ratio comparisons

The common key ratios include:
i.
ii.
iii.

loan to deposits
borrowed funds to total assets
commitments to lend to assets
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.
Measurement of liquidity risk

Liquidity index
N
Pi
I   wi *
Pi
i 1
where
wi is the percent of asset i in the portfolio based on the
face value of the assets ;
Pi and Pi* are the fire-sale asset price and fair market
price of asset i respectively.
Measurement of liquidity risk


I 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
The closer of I to 0, the higher the liquidity risk of the
FI.
Measurement of liquidity risk
Financing gap
 Classification of Payments
–
Scheduled payments
Unscheduled payments
Semidiscretionary payments
–
Discretionary transactions (available for use as needed )
–
–
Measurement of liquidity risk

daily financing gap ID
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;
Measurement of liquidity risk



R = (OU + OSD) – (IU + ISD)
ID = OS – IS + R
Assume R ~ R ,  2, 
then

R
I D ~  OS  I S  R ,  R2


The larger the R, the higher the liquidity risk of the DI
Measurement of liquidity risk

Define I as the solution of the following equation

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.
PrI D  I    %
I % O S  I S  R  z %   R
where z % is defined as
PrZ  z %    %
where Z ~ 0,1.
Measurement of liquidity risk

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
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.