Cutting the Cake: Allocation of Clients to Participants Item General introduc tion / Role in Simfi

Where?

Calculations

Description When the total number of clients NC ( p ) has been calculated, it can be determined how the loan products and deposit products are divided among the clients in the market. In the calculation, 1 client equals 1 contract. The loan products and deposit products are “Short term loans maturity 3 months”, “Short term loans maturity 6 months”, “Short term loans maturity 9 months”, “Short term loans maturity 12 months”, “Long term loans maturity 2 years”, “Long term housing loans maturity 5 years”, “Short term time deposits maturity 3 months”, “Short term time deposits maturity 6 months”, “Short term time deposits maturity 9 months”, “Short term time deposits maturity 12 months”, “Long term time deposits maturity 2 years” and “Demand deposits”. For each of these 12 products the number of available contracts is the same, and equal to the total number of clients NC ( p ) . Each client takes one contract for each product in each period p . The client can choose at which institution he will ask for a contract. Each participant in the simulation represents an institution. For any product, some institutions will have more clients than other institutions. The parameters to manipulate the Cutting the Cake formula can be adjusted by the trainer in: Institution>Exponential factor on … Institution>Weighting factor on … Setup>Other parameters>Exponential factor on … Setup>Other parameters>Weighting factor on … The number of allocated clients depends on the interest rate and average loan or deposit amount. If, for a certain loan product, a participant chooses a lower interest rate than other participants, then his loan products are more attractive, resulting in a higher number of clients for this product. More clients are also attracted when the average loan amount is greater. The percentage of allocated clients Ploan ( p, i ) of participant i depends on the interest and average loan amount, calculated by the following formula:

Ploan ( p, i ) = Wint ×

Cint (i ) N

∑C j =1

int

( j)

+ Wamount ×

C amount (i ) N

∑C j =1

amount

,

( j)

where:

Cint (i ) = competitive advantage of interest for participant i Wint = weight factor competitive advantage of interest C amount (i ) = competitive advantage of average loan amount for participant i Wamount = weight factor competitive advantage of average loan amount N = total number of participants. The background teams are included in N .

In the instructor site the weighting factors Wint and Wamount can be filled out in the setup of the menu item “Other parameters” or the menu item “Institution”. The competitive advantage C int (i ) is calculated by the following formula,

Cint (i ) = (2 × Max( Int ( j , p )) − Int (i, p )) Eint j

Where:

Int ( j , p ) = interest filled out by participant j , in period p , in the decision screen. In the formula, the maximum interest of all participants j is chosen and multiplied by 2. E int = Exponential factor, which can be filled out in the setup of the menu item “Other parameters” or the menu item “Institution”. Both Wint and E int determine the influence of interest on the allocation of clients. The competitive advantage Camount (i ) is calculated by:

C amount (i ) = Am(i, p ) Eamount ,

Where:

Am(i, p ) = average loan amount chosen by participant i in period p in the decision screen. E amount = Exponential factor, filled out in the setup menu item “Other parameters” or menu item “Institution”. Both Wamount and E amount determine the influence of average loan amount on the allocation of clients.

The formula to calculate the percentage of allocated clients Ploan ( p, i ) for a certain loan product can also be applied to deposit products. The competitive advantage, Camount (i ) , is calculated in the same way, but C int (i ) is different:

C int (i ) =

1 (2 × Max( Int ( j , p )) − Int (i, p )) Eint j

In this way a higher interest will attract more clients and a lower interest results in less clients. In the formula of the percentage of allocated clients Ploan ( p, i ) , it is seen that it only depends on interest and the average amount. In the decision screen, the participant can choose the amount of staff expenses and IT investments for each period. The staff expenses and IT investments have an

impact on performance. This is modelled by increasing the number of allocated clients if staff expenses or IT investments are increased, with respect to other participants. So in Ploan ( p, i ) additional terms must be added:

Ploan ( p, i ) = Wint ×

C int (i ) N

∑C j =1

int

∑C j =1

+ Wamount ×

j =1

amount

C netwIT (i ) N

∑C

( j)

N

∑C

( j)

+ WnetwIT ×

C amount (i )

j =1

netwIT

C staff (i )

+ Wstaff ×

∑C

( j)

+ WmangIT ×

( j)

+

N j =1

staff

( j)

C mangIT (i ) N

∑C j =1

mangIT

+ WtelcIT ×

( j)

where:

The competitive advantage of staff expenses C staff (i ) is calculated by:

C staff (i ) = Exp (i, p )

E stafft

, where:

Exp (i, p ) = Total staff expenses chosen by participant i in period p E staff = Exponential factor

C telcIT (i ) N

∑C j =1

telcIT

( j)

The competitive advantage of the IT expenses is calculated in the same way. The IT expenses are added to “Net property and equipment” in the balance sheet. These are depreciated on a five year basis. The total IT expenses from the balance sheet are used to calculate the competitive advantage. In this way the IT expenses in the current and previous periods contribute to the competitive advantage. For staff expenses, only the current period contributes. The weighting factors Wstaff , WheadqIT , WnetwIT , WmangIT and WtelcIT and exponential factors E staff ,

Ptot = ∑ Ploan ( p, i ) = 100% j =1

In some cases, the weights Wamount , Wint , etc can be chosen such that Ptot differs from 100%. To avoid this problem, a correction is carried out, where each percentage of allocated clients Ploan ( p, i ) is divided by Ptot :

Pcorrection ( p, i ) =

Pcorrection ( p, i ) Ptot

In that case the sum of corrected percentages is always 100%: N

∑P j =1

correction

( p, i ) = 100%

In the simulation, we always use the corrected percentages.

02 Cutting the Cake
02 Cutting the Cake

This document explains the 'Cutting the Cake' formula in SimFi