ACADEMY OF ECONOMIC STUDIES
BUCHAREST
DOCTORAL SCHOOL OF FINANCE AND BANKING
Cash management service
– Cash Pooling –
Supervisor
PhD. Professor Moisă ALTĂR
Student
Teodor DINU
Bucharest, 2007
The scope and aims of the paper
1.
2.
Introduction
Create a short description of the cash management service –
Cash Pooling
2.1. Definition
2.2. Notional Cash Pooling
2.3. Real Cash Pooling
3.
Present the theoretical approaches regarding Cash Pooling
service
3.1. The cash flow attributes (mean and variance)
3.1.1. Pooling for random cash flows
3.1.2. Pooling with internal physical cash movement
3.1.3. Pooling with booking internal transaction
3.2. The influence of the cash flow on the result of cash pooling
4.
Present the econometric estimations and results
4.1. Time series and stationary analysis
4.2. Identification of ARMA(p,q) processes and forecast functions
4.3. Models estimation results
Introduction
The business environment development, the increasing competition on
the banking market, as new international players enters the domestic financialbaking market, in the same time with the dynamic increase of the corporate
clients’ needs and requests (especially the multinational companies) offered to
the cash management concept a greater importance, pushing it closer to the
features specific to the international markets.
Thus, the cash management concept requested a rapid
accommodation of the banks according the quick evolution of the corporate
clients’ requests and also leaded to the identification of some new methods
of satisfying these requests, through the implementation of banking products
and services, simultaneously with the development of the partnership bank –
client.
In the last period of time, from the category of cash management
banking products and services, the cash pooling service is one of the most
important, as it is one of the most complex banking service, special structured
according to the needs of each corporate client (tailor made service).
Cash Pooling Definition
The Cash Pooling service is a cash management service based on
which the corporate clients can offset the debit balances afferent to some
current accounts with the credit balances afferent to other current accounts
and maximize the financial activity results by eliminating bid/ask spread of
the interest rates quotations.
The main goals of the cash pooling service can be achieved through:
– notional techniques (notional cash pooling)
– real techniques (real cash pooling)
The eligible corporate clients for cash pooling service are:
– corporate clients that are members of a group of companies
– corporate clients with a significant number of production units and/or outlets
Some of the main Cash Pooling service benefits:
– maximizing the financial results by minimizing the cash deficits, by minimizing
the usage of the short term banking loans and by an efficient investment of the
temporary excess of liquidities;
– reducing the banking costs (interest and fees) etc.
Notional Cash Pooling (1/2)
The financial result without notional cash pooling
Shadow account N
0 lei
Current account A
+ 200 lei
Current account B
+ 300 lei
Interest for current account A = + 2 lei
Interest for current account B = + 3 lei
Interest for current account C = - 4,5 lei
Consolidated interest = 2 lei + 3 lei - 4,5 lei = 0,5 lei
Hypotheses:
Interest rate for loans = 3%
Interest rates for deposits = 1%
Current Account C
- 150 lei
Notional Cash Pooling (2/2)
The financial result with notional cash pooling
Shadow account N
350 lei
Current account A
+ 200 lei
Current account B
+ 300 lei
Consolidated position of the shadow account = + 350 lei
Interest for shadow account = + 3,5 lei
Consolidated interest = 2 lei + 3 lei - 4,5 lei = 0,5 lei
Notional Cash Pooling benefit = 3 lei
Hypotheses:
Interest rate for loans = 3%
Interest rates for deposits = 1%
Current Account C
- 150 lei
Real Cash Pooling (1/2)
The financial result without real cash pooling
Master account N
0 lei
Current account A
+ 200 lei
Current account B
+ 300 lei
Interest for current account A = + 2 lei
Interest for current account B = + 3 lei
Interest for current account C = - 4,5 lei
Consolidated interest = 2 lei + 3 lei - 4,5 lei = 0,5 lei
Hypotheses:
Interest rate for loans = 3%
Interest rates for deposits = 1%
Current Account C
- 150 lei
Real Cash Pooling (2/2)
The financial result with real cash pooling
Master account N
350 lei
Current account A
0 lei
Current account B
0 lei
Consolidated position for the master account = + 350 lei
Interest for master account = + 3,5 lei
Consolidated interest = 2 lei + 3 lei - 4,5 lei = 0,5 lei
Real Cash Pooling benefit = 3 lei
Hypotheses:
Interest rate for loans = 3%
Interest rates for deposits = 1%
Current Account C
0 lei
The cash flow attributes
The mean and the variance are the main analysis criteria for the cash
flow attributes.
There will be analyzed the mean and the variance at two levels: at the
group level and at each participant level.
The daily cash flow represents the net cash flow on a particular day
and the total cash flow represents the sum of net cash flows on a certain
period.
The positive values represent cash inflows, while the negative values
represent cash outflows.
Pooling for random cash flows (1/7)
The expected value for the cash flow of each participant is the cash
flow of the last day and the net cash flow is a stochastic process:
CFti  CFt 1i   ti
(1)
In the situation when there is no cash pooling then
– the actual total cash flow of the group of companies is:
M
N
 CF
(2)
ij
i 1 j 1
– the expected daily cash flow is:
M
E CFgrup  
N
 CF
i 1 j 1
ij
(3)
N
– the variance of cash flow of the participant i is:
VarCFi    CFij   N E CFi 
N
j 1
2
2
(4)
Pooling for random cash flows (2/7)
In the situation when there is cash pooling then
– the cash flow of the pool is:
 CF
i 1
i1
M
M
M
,
 CF
i 1
i2
 CF
…
i 1
in
(5)
– the total cash flow of the pool is again:
M
N
 CF
i 1 j 1
ij
(6)
– the expected value daily cash flow of the pool is:
M N

  CFij 


i 1 j 1


E CFcashpooling  
N
(7)
The conclusion is that using the cash pooling service will not influence the
expected value of either daily cash flow or total cash flow.
Pooling for random cash flows (3/7)
However, the variance in the situation when there is cash pooling can
be written as follows:
M
M
Var CashPooling    Wi  VarCFi   
2
i 1
W W CovCF , CF 
M
i 1 j 1, j i
i
j
i
j
(8)
– if it is assumed that the participants have the same size, then the variance in
the situation when there is cash pooling can be written as follows:
 1 M
 1 M M
Var CashPooling    2 VarCFi    2   CovCFi , CF j 
 M  i 1
 M  i 1 j 1, j i
(9)
and further on:
 M

M2
Var CashPoolin g   Lim 2 Var CFi   2 CovCFi , CF j   CovCFi , CF j 
M  M
M



where Var CFi  and Cov CFi , CF j
the average covariance

(10)
are the average variance, respectively
Pooling for random cash flows (4/7)
The conclusion is that the cash pooling service converts the risk from
a group of participants’ variance into the average covariance between two
participants, similar to the diversification of an investment portfolio.
An approach for the risk of a single participant is that of evaluating its
own contribution in the pool. If there is calculated a partial derivative for the
Equation (8) in respect with Wi results:
M
Var (CashPoolin g )
(11)
 2WiVar CFi   2W j CovCFi , CF j 
Wi
j 1
It is known that when the number of the participants increases, then the
weight of any participant decreases and the marginal rate of decrease of
volatility decreases as well. Thus, when the corporate client ads new
participants to the cash pool, the total variance of the pool decreases at a
faster rate than that of increase in participants. As the number of
participants increases, the variance of the pool decreases more and more
slowly as the marginal rate is decreasing.
Pooling for random cash flows (5/7)
The simulation of the cash pooling for 15 random cash flows
15
30
20
10
10
0
-10
5
-20
-30
0
-40
1
13
25
37
49
61
73
85
97
109
121
133
145
157
169
181
193
205
217
229
241
253
265
277
289
-50
-5
-60
-70
-10
-80
CF of a Participant
Daily CF of Pool
Total CF of a Participant
Total CF of Pool
Pooling for random cash flows (6/7)
As it is known, the daily cash flow cash flow of a participant is
CFt = CFt-1 + εt so that the total cash flow is TotalCFt = (t-1)CF1 + [(t-1)ε2 + (t-2)
ε3 + … εt] where represents the cash flow on Day 1. Taking into consideration
the fact that the daily cash flow starting with the one on Day 1 is a stochastic
process, the total cash flow on Day i-1 is uncertain. The total cash flow of the
last period is always the starting point of the total cash flow in the next period, so
that the starting point of the total cash flow on Day i is uncertain. As it can be
seen in the next slide, the starting point of total cash flow on Day i could be
above (point 1), or equaling (point 2) or below (point 3) the expected value.
More than that, the changes of the cash flow on Day 1 are also uncertain. The
net cash flow can be either positive or negative, so that the total cash flow can
move close to or parallel to or away from the expected value (three arrows in the
next slide).
Pooling for random cash flows (7/7)
The increasing volatility of total cash flow
Cash
Flow
The expected value of
the cash flow
1’
2’
3’
1
2
3
Time
Day i
Day i+1
Pooling with cash movement (1/3)
Here we will analyze the cash flows of two participants in the situation
when between two participants exists internal purchase and sale transactions.
It is assumed that the correlation between the expected values of the
cash flows of the two participants is not zero. Therefore, the cash flow of a
participant is a function of its historical cash flow and the cash flow of the other
participants:
CFti  1CFt 1i   2 CFtj   ti
(12)
It is considered the case that the internal purchase and sale transactions
determine daily physical movements of cash. Thus, the cash outflow of one
participant is exactly the cash inflow of the other participant. So lets assume that
from day i to day m the values of the daily cash flow of the participants have the
same absolute values, but inverse signs.
The cash pooling service doesn’t modify the expected value of the
cash flow, even in the situation of internal purchase and sale transactions
between the participants.
Pooling with cash movement (2/3)
The variance of the pool has changed and can be written as:
Var (CashPoolin g )  W1  Var CF1   W2  Var CF2   2W1W2 CovCF1 , CF2  (13)
2
2
From Day 1 to Day i-1, because the real cash flow follows a stochastic
process, the characteristics of the cash flow during this period are exactly the
same as those presented in the last section – cash pooling for random cash
flows – in the way that during this period the variance of the pool should
decrease.
For the period Day i – Day m, the expected value of the daily cash
flows of the two participants compensates each other and the change of the
cash flow of the pool is expected to be stable. Therefore, because there will be
either no variation at all or ignorable variation caused by shocks, the variance of
daily cash flow of the pool is expected to be zero. This situation is quite like
investing in two perfect inverse correlated assets.
Pooling with cash movement (3/3)
The simulation of cash pooling of two participants with internal netting
30
25
20
15
10
5
0
1
14
27
40
53
66
79
92
105
118
131
144
157
170
183
196
209
222
235
248
261
274
-5
-10
CF Participant A
Total CF Participant
CF Cash Pooling
Total CF Cash Pooling
287
300
Pooling with intern booking transaction
The simulation of the cash pooling with internal booking
10
65
8
6
45
4
25
2
5
0
1
13
25
37
49
61
73
85
97
109
121
133
145
157
169
181
193
205
217
229
241
253
265
-2
277
289
-15
-4
-35
-6
-55
-8
-10
-75
Daily CF of Pooling
CF Outlet Unit
CF Production Unit
Net CF of Pooling
Time series
Stationary analysis
The stationary analysis of the time series was done in Eviews using:
– the time series correlogram analysis
– the tests for finding the presence of the unit root: Augmented Dickey Fuller and
Phillips Peron tests.
The results of the stationary analysis are:
– time series for Company X is stationary, respectively integrated of order 0
– time series for Company Y is stationary in first difference, respectively
integrated of order 1
– time series for Company Z is stationary, respectively integrated of order 0
– time series for Result is stationary, respectively integrated of order 0
The identification ARMA(p,q) processes
It has been chosen the model 7 as being the best to describe the time
series for Company X:
xt  a1  xt 1   t   2   t 2
The identification ARMA(p,q) processes
It has been chosen the model 5 ca as being the best to describe the
time series in first difference for Company Y:
dy t  a1  dy t 1  a 2  dy t 2   t   8   t 8
The identification ARMA(p,q) processes
It has been chosen the model 8 as being the best to describe the time
series for Company Z:
zt  a0  a2  zt 2   t  1   t 1   2   t 2   3   t 3
The forecast functions
The expected values of
xt  j
– for j  1 : Et xt 1  xt  a11   2   t 1
– for j  2 : Et xt  j  xt  a1j   2  a1j 2 *  t   2  a1j 1   t 1
The expected values of dy t  j
– for j  1 : Et dyt 1  a1 * dyt  a2  dyt 1   8   t 7
– for j  2 : Et dyt  2  a1 * a1  dyt  a2  dyt 1   8   t 7   a2  dyt   8   t 6
– and so on
The expected values of z t  j
j
1
2
j
2
2
– for j  2  n : Et z t  j  a 0   a  a  z t  a
i 0
– for j  2  n  1 :
j 1
2
Et z t  j  a 0   a  a
i 0
i
2
j 1
2
2
i
2
 z t 1  a
j 1
2
2
j
1
2
2
 1   t  a
j 1
2
2
 2 t  a
j
1
2
2
  2   t 1  a
j 1
2
2
  3   t 1
  3   t 2  a
j 3
2
2
 3   t
Estimation of model 1
In order to establish the influence of each participant’s cash flow on
the negative result of the cash pooling service (Result negative) there
should be determined the coefficients of the following equation:
resultnegativei    CFi1    CFi 2    CFi 3
Testing the validity of the estimated model:
1. The significance of the model’s parameters:
– tested with: the value of t-statistic
– conclusion: all three estimated coefficients are significant different from zero
2. The autocorrelation of the residuals:
– tested with: Durbin Watson indicator, Correlogram of residuals (Ljung Box Qstatistic Test), Breusch-Godfrey Serial Correlation LM Test
– conclusion: the residuals are autocorrelated
Estimation of model 1
3. The homoskedasticity/heteroskedasticity of the residuals:
– tested with: White Heteroskedasticity Test (no cross terms) and White
Heteroskedasticity Test (cross terms)
– conclusion: the absence of the residuals heteroskedasticity
4. The normal distribution of the residuals:
– tested with: Residual histogram
– conclusion: the residuals are normally distributed
Estimation of model 2
In order to establish the influence of each participant’s cash flow on
the positive result of the cash pooling service (Result positive) there
should be determined the coefficients of the following equation:
resultposi tivei    CFi1    CFi 2    CFi 3
Testing the validity of the estimated model:
1. The significance of the model’s parameters:
– tested with: the value of t-statistic
– conclusion: all three estimated coefficients are significant different from zero
2. The autocorrelation of the residuals:
– tested with: Durbin Watson indicator, Correlogram of residuals (Ljung Box Qstatistic Test), Breusch-Godfrey Serial Correlation LM Test
– conclusion: the residuals are autocorrelated
Estimation of model 2
3. The homoskedasticity/heteroskedasticity of the residuals:
– tested with: White Heteroskedasticity Test (no cross terms) and White
Heteroskedasticity Test (cross terms)
– conclusion: the presence of the residuals heteroskedasticity
4. The normal distribution of the residuals:
– tested with: Residual histogram
– conclusion: the residuals are normally distributed
Conclusions for model 1 and model 2
As it was expected from the analysis of the time series representing the
balances of the current accounts of the three cash pooling participants
Company Z has a contribution in the way of diminishing the net negative
results and increasing the net positive results of the cash management service,
as all the time the account balances are always on credit.
As for Company X and Company Y it can be concluded that they have a
contribution in the way of increasing the net negative results and diminishing
the net positive results of the cash management service, as these participants
encounter very frequently debit balances in the current account.
Selected bibliography
Andersen, Arthur – „A Shared Service Centre for Treasury Operations”, Treasury
Management International, edition online, http://www.treasury-management.com, 1999;
Bas Rebel, Zanders – „Cash Pooling: Finding a Cost Efficient Equilibrium”, Global
Treasury News, online edition, http://www.gtnews.com/article/6118.cfm, Treasury &
Finance Solutions, 2005;
Bergen, Joost – „The Euro and Cash Pooling”, Global Treasury News, online
edition, http://www.gtnews.com, 1998;
Bergen, Joost – „Cash Pooling in euroland”, Global Treasury News, online edition,
http://www.gtnews.com, 1999;
Bergen, Joost – „Europooling”, Global Treasury News, online edition,
http://www.gtnews.com, 1999;
Bergen, Joost – „Organisation for Cash Management”, Global Treasury News,
editie online, http://www.gtnews.com, 1999;
Citibank – „Oportunities for Post-Euro Integration”, Treasury Management
International, online edition, http://www.treasury-management.com, 1999;
Citibank – „A Treasurer’s Guide to EMU Strategies”, Treasury Management
International, online edition, http://www.treasury-management.com, 1998;
Citibank – „A Treasurer’s EMU Survival Guide”, Treasury Management
International, online edition, http://www.treasury-management.com, 1998;
Selected bibliography
Danila, Nicolae; Anghel, Lucian Claudiu; Danila, Marius Ioan – „Banking
Liquidity Management”, Economica, 2002;
Davidsson, P. – „Euro Cash Poling”, Global Treasury News, online edition,
http://www.gtnews.com, 1999;
Generale Bank Group – „Cross Border Notional Pooling in Euroland”, Treasury
Management International, online edition, http://www.treasury-management.com, 1998;
Hong, Liang; Wannfors, Mats – „Euro cash pooling and shared financial
services”, Masters Thesis, 2000;
IBOS Association – „Impact of Basel II on Notional Pooling”, Global Treasury
News, online edition, http://www.gtnews.com/article/5602.cfm, 2004;
Treasury Alliance Group – „Cash Pooling – Improving the balance sheet” online
edition, http://www.phoenixhecht.com/TreasuryResources/PDF/pooling.pdf, 2005;
Tudorel, Andrei – „Statistics and econometrics”, Economica, 2005;
Ulsenheimer, Stefan – „Thin Capitalization Rules and Impact on Cash Pooling”,
Global Treasury News, online edition, http://www.gtnews.com/article/6208.cfm, 2005;
Wolfgang, Messner – „Creating value for Multinational Customers through Cash
Management”, Special Report, Corporate Treasury in Germany 2003;
Walter, Enders – „Applied Econometric Time Series” John Wiley and Sons, INC.