Optimizing Cash Management Model Using Computational Intelligence

In today’s technical era, the financial organizations have great challenges to optimize the cash management process. Maintaining minimum cash leads to customer frustration. At the same time, upholding excess cash is a loss to the organization. Hence, soft computing based cash management solutions are required to maintain optimal cash balance. An Artificial Neural Network (ANN) is one such technique which plays a vital role in the fields of cognitive science and engineering. In this study, a novel ANN-based cash Forecasting Model (ANNCFM) has been proposed to identify the cash requirement on daily, weekly and monthly basis. The six cash requirement parameters: Reference Year (RY), Month of the Year (MOY), Working Day of the Month (WDOM), Working Day of the Week (WDOW), Salary Day Effect (SDE) and Holiday Effect (HDE) were fed as input to ANNCFM. Trials were carried out for the selection of ANNCFM network parameters. It was found that number of hidden neurons, learning rate and the momentum when set to 10, 0.3 and 0.95, respectively yielded better results. Mean Absolute Percentage Error (MAPE) and Mean Squared Error (MSE) were used to evaluate the performance of the proposed model. MSE that was less than 0.01 proves the capability of the proposed ANNCFM in estimating the cash requirement.


INTRODUCTION
Forecasting cash demand needs to be more accurate for any financial organization, including banks (Fraydoon et al., 2010;Kumar and Walia, 2006;Alli et al., 2013).If the forecast is flawed, in addition to making financial losses to the banks, it results in customer dissatisfaction.In the banking industry, an earlier cash requirement study was made using a feed forward neural network with back propagation for short term data of two months (Kumar and Walia, 2006).Subsequently, another comparative study was made in the cash anticipation using a classic time series model and artificial neural networks (Fraydoon et al., 2010).The daily cash requirement models for a bank were optimized with particle swarm and compared with the least square method for short term data (Alli et al., 2013).The main objective of the paper is to design, develop and test a unique supervised method to forecast the cash requirement for banks from their historical data.
ANN background: ANN is an efficient tool in understanding the complexities of real world problems in all fields of our daily life (Haykin, 1994).It is used as a function optimizer for linear as well as nonlinear problems in science, engineering, technology, management and finance (Nakamura, 2006;Refenes and White, 1998;Aminian et al., 2006;Hanna et al., 2007;Gorr et al., 1994).Artificial neural network learning methods provides the best approach for approximating discrete, real and vector valued target functions (Zhang et al., 1998;Geem and Roper, 2009;Yokoyama et al., 2009), for complex problems, which are not possible to solve by conventional mathematical methods like analytical and numerical technique.ANN are applied in the forex market prediction, portfolio optimization, decision making, meteorological parameters forecasting (Bishop, 1999;Taubenböck et al., 2010;Tenti, 1996;Leigh et al., 2005;Manfred and Hans-Georg, 1997;Mabel and Fernandez, 2008;Sharda and Delen, 2006) etc..
The various ANN based approaches applied by researchers in finance field as an alternative to the traditional time series model include Financial and economic forecasting, credit authorization screening, simulation of market behavior, mortgage risk assessment, risk rate of investments and detection of regularities in security price movements (Tenti, 1996;Leigh et al., 2005;Manfred and Hans-Georg, 1997;Mabel and Fernandez, 2008;Sharda and Delen, 2006).

Design of proposed ANNCFM architecture:
The process of designing a neural network in many fields resulted in a satisfactory performance, but building a neural network forecast for a particular problem is nontrivial task.The modeling issues that affect the performance of the neural network must be selected carefully.

Selection of ANN parameters:
In general, the design of multilayer ANN can have many layers where a layer represents a set of distributed parallel processing nodes.The three layered ANN network with one input, one output and one intermediate hidden layer is sufficient to approximate any complex non-linear function.In the case of forecasting studies, many experimental results also confirm ANN with one hidden layer is enough to predict the required data (Refenes and White, 1998;Aminian et al., 2006;Hanna et al., 2007).The model architecture of ANNCFM is shown in the Fig. 1.
The important critical decision is to determine the architecture is:

Design of proposed ANN models:
The proposed ANNCFM model consists of one input, one hidden and an output layer as discussed in above section.In this study the data were collected from a semi-urban area bank located in India.The typical daily cash requirement for the bank for one year is shown in Fig. 2.
The collected data was for a period of three years (2010 to 2012) and was used for training and testing with the following input parameters: • RY-Reference year: Ranges between 1 to 3 as three years • MOY-Month of the year: Ranges from 1to 12, • WDOM-Working day of the month: Ranging from 1 to 27 • WDOW-Working day of the week: Ranging from 1 to 6 • SDE-Salary day effect: Ranging from 1 to 3 • HDE-Holiday and the weekend effect: Either 0 or 1 The fore mentioned parameters were used as six input neurons.In the hidden layer, the number of neurons varied from 8 to 50.The output layer had one neuron that corresponds to the optimal cash requirement for a day.Pseudocode-ANNCFM: 1 + e 4?H < //Determine the output neuron between hidden layer and output layer: 1 + e 4?H < e E = t E − y E //Compute the error signal between the output and hidden layer: //Update the weights between the output (k) and Hidden (j) layer; 1 + e 4?H < //Determine the output neuron between hidden layer and output layer: 1 + e

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Evaluation metrics: In order to derive and evaluate the performance of the most appropriate model that fulfills our objective of optimizing the cash management, few metrics were used.The accuracy of the proposed ANNCFM is evaluated using MAPE and MSE which are defined as follows: (1) where, X t = The actual data at period t F t = The forecast at period, t e t = The forecast error at period t n = The number of observations

RESULTS AND DISCUSSION
The data for a period of three years (2010-2012) was collected from a particular branch of City Union Bank to simulate the network using MATLAB.For the proposed study the total number of data for the three years is 879, in which the first two and half years, 737 data were used for training (80%) and the remaining six months 142 data sets (20%) were used for testing.Studies found that input data normalization with certain criteria, prior to the training process, is crucial to obtain good results, as well as to fasten significantly the calculations (Sola and Sevilla, 1997).Hence the input data was normalized before training.
In ANNCFM, 15 runs were made by varying the number of hidden neurons from 10 to 50 using gradient descent with momentum back-propagation (traingdm) for the default training parameters learning rate = 0.01, momentum = 0.95, Goal = 0 and number of iterations as 6000, are illustrated in Table 1 The convergence of ANNCFM is influenced by number of hidden neurons in which by varying the number of hidden neurons between 10 through 50.The error was minimal when the number of hidden neurons was set to 10, 20, 40, 45 and 50, by achieving an MSE of 0.0079 as observed from column 3 of Table 1.As the number of hidden neurons increase, there is a significant increase in the computational time.Hence the number of hidden neurons in the proposed study was fixed at 10.The pictorial representation for the optimal hidden neuron against its MSE are shown in Fig. 3.
The learning rate 'lr' arrives at a local optimum for the higher learning rate and global optimum for slow learning process.Different trials were made to identify the optimal learning rate to avoid the unstable condition and fluctuations in the results.The learning rate varied between 0.1 through 0.5 in which 0.3 yielded an optimal learning rate for the given data set, as shown in Fig. 4.
The momentum plays a vital role in identifying the convergence point.Momentum, when set too low, it may get stuck in local minima and if it is too high, the network will become unstable.So there is a need to identify the optimal momentum for ANNCFM, various momentum values were tested between 0.8 and 1.0, the trained results shows that the optimal momentum value was 0.95 are shown in the Fig. 5.
In the ANNCFM model to train and test the cash requirement for a day, week, month the following parameter values are selected based on their performance from the different number of runs made above: • The optimal selection of the above parameters helped in improving the performance, by minimizing the error rate.This is evident from Table 1, that shows the MSE achieved before and after parameter selection.
The ANNCFM was used to estimate daily, weekly and monthly cash requirement.The estimated values were compared with the actual values for the testing period are shown in Fig. 6 to 8, for the daily, weekly and monthly prediction.The obtained results show the ANNCFM was found to perform reasonably well for all the three models.The weights calculated by our ANNCFM were found to be sufficient for cash prediction in which RY, MOY, WDOM, WDOW are essential parameters and SDE, HDE is additional parameters.The connection weight approach was used to quantify the importance of input variable (Julian et al., 2004).The preference of the input parameters  was founded based on the weights obtained was evident from Table 2, column-3.The input parameters SDE and HDE play a vital role in the daily and weekly model as it was observed from the above table it effectively takes care the need of peak cash requirement at the beginning of every month and during holiday periods.The role of SDE in the weekly cash prediction could be easily understood for the weeks like 1, 5, 14, where the cash requirement is maximum since the beginning of the month lies within the week.However, for the 9 th and 10 th as well as for the 18 th and 19 th week cash requirement shows the new month starts between the weeks.The monthly model was plotted for six months as shown in Fig. 8 in which the experimental results shows that the estimated values were most influenced by WDOM.The cash required and predicted to be minimized for the fourth month in which WDOM was minimum.The MAPE and MSE for ANNCFM are shown in Table 3 The comparison made between the actual and forecast data shown from the figures indicates that the six input variables selected in our model are sufficient to identify the cash need which is changing from time to time.

CONCLUSION
The observations of the experimental results of this study show that ANNCFM is a useful tool to predict the cash requirement in emerging banking sector.ANNCFM using feed forward neural network training with back-propagation algorithm optimize the needs of cash on a daily, weekly and monthly basis.During the implementation process the data set used for the years between 2010 and 2012 were trained and tested to measure the performance.The input parameters were initialized and different runs were made to the proposed model to find out the optimal number of hidden neurons as 10, momentum as 0.95 and learning rate as 0.3 to train and test the network using a sigmoid transfer function.The estimated results were with minimal error for better performance with an accuracy of 91.23%.

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Number of layers • Number of neurons in each layer • Number of arcs which interconnect with nodes • Activation function of hidden and output nodes • Training algorithm • Data transformation or normalization • Training and test sets • Performance measures Tw D,E = w D,E w D,E = w D,E + temp } //Update bias between the output and hidden If itr =1 then { temp =∝ δ E Else Cw = w E − Tw > temp =∝ δ E + µ Cw End if Tw > = w E w E = w E + temp } //Update the weights between the input (i) and Hidden (j) layer; If itr ts, W,V, V oj, W ok ,t) returns output (y) { For each testsample ts //Feed forward computation //Determine the output neuron between input layer and hidden layer Net D