Resource Allocation Neural Network in Portfolio Selection

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Resource allocation neural network in portfolio selection

Po-Chang Ko

a

, Ping-Chen Lin

b,*

a_{Department of Information Management, National Kaohsiung University of Applied Sciences, Taiwan} b_{Institute of Finance and Information, National Kaohsiung University of Applied Sciences, Taiwan}

Abstract

Portfolio selection is a resource allocation problem in a finance market. The investor’s asset optimization requires the distribution of a set of capital (resources) among a set of entities (assets) with the trade-off between risk and return. The ANN with nonlinear capability is proven to solve a large-scale complex problem effectively. It is suitable to solve NP-hard resource allocation problem. However, the tra-ditional ANN model cannot guarantee the summation of produced investment weight always preserves 100% in output layer. This article introduces a resource allocation neural network model to optimize investment weight of portfolio. This model will dynamically adjust the investment weight as a basis of 100% of summing all of asset weights in the portfolio. The experimental results demonstrate the feasibility of optimal investment weights and superiority of ROI of buy-and-hold trading strategy compared with benchmark Taiwan Stock Exchange (TSE).

Keywords: Resource allocation; Neural network; Portfolio; Investment; Optimization

1. Introduction

The resource allocation problem is a process of allocat-ing a set of resources among a set of entities or activities. It is a complex problem encountered in a variety of areas in operations economics and operation researches, such as portfolio selection, production planning, and computer scheduling. In general, the resource allocation is NP-com-plete if considering a variety of constrains and limitations which are common trade-offs. The intelligent computa-tional techniques such as artificial neural networks (ANNs) would be more suitable to improve the resource allocation problem. ANNs had attracted much more efforts from both academic scholars and industrial practitioners since Rosenblatt first applied single-layer perceptron to pattern classification learning in the late 1950s. Recently, a growing interest researches had been focused on using ANNs in finances and economics because they are powerful to imi-tate flexible nonlinear modeling relationship capabilities.

ANNs require no assumption about the distribution of the underlying data and no restriction about the causal relationship between the dependent variable and indepen-dent variable.

The commonly used neural networks involve five mod-els: (1) The Back-propagation network (BPN) model was proposed byRumelhart, Hinton, and Williams (1986). This model is based on the error-correction learning rule. In the forward pass, an input vector is propagated through the hidden layer to the output layer. Then, the error signal pro-duced in the output layer would be propagated backward through the network layer and correct the synaptic weight for each neuron recursively. (2) Radial basis functions (RBFs) model was introduced by Broomhead and Lowe (1988)which is proven to be well suited for approximation and pattern classification problems. It is traditionally associated with radial functions in some statistical manner (e.g. Gaussian distribution) in a single-layer network to reveal how learning proceeds. (3) Support vector machine (SVMs) was pioneered by Vapnik in the early 1990s ( Vap-nik, 1992). SVM is based on the statistical learning theory to construct a hyperplane for classification and regression with maximum margin (Vapnik, 1995, 1998). (4) Recurrent

*

Corresponding author. Tel.: +886 7 3814526 7530. E-mail address:[email protected](Ping-Chen Lin).

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Expert Systems with Applications 35 (2008) 330–337

Expert Systems with Applications

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networks described byElman (1990)is suitable to identify temporal patterns. This model contains recurrent connec-tions from the hidden neurons to a layer of context units. The context units store the association memory of one feedback loop. (5) Self organization maps (SOM) is charac-terized by the formation of a topographic map of the input patterns in which the spatial coordinates of the neurons in the lattices are indicative of intrinsic statistical features (Kohonen, 1990).

Portfolio selection is a resource allocation problem in the economic and finance area. Most investment profes-sionals or investors consider asset allocation as the most important part of portfolio construction. Asset allocation of portfolio is concerned with the percentage of the overall portfolio value allocated to each portfolio individual. The originally proposed by Markowitz, the mean variance model for the portfolio asset allocation is one of the best known models in finance. This model requires satisfying two conflicting optimization criteria which minimize risk with predetermined the expected return of portfolio. Even though the mean variance method searches an efficient frontier via quadratic programming, the optimization of asset allocation in a portfolio is still a complex and NP-harder problem. Besides, the mean variance model may be desirable to restrict the number of assets in a portfolio and the percentage of the portfolio attends to any specific asset. The searching of efficient frontier became much dif-ficult, if considering much more restrictions.

There are many researches in last decade concerning the ability of ANNs to forecast financial performance. Kryza-nowski, Galler, and Wright (1993) applied Boltzmann machine for ANNs to discriminate stock return as posi-tive, neutral and negative. They found the correct classifi-cation rate from results is more than 70% of all unseen data.Dropsy (1996)uses ANNs as a nonlinear prediction tool to forecast international equity risk premia. Both lin-ear and nonlinlin-ear forecasts’ results outperform than ran-dom work. Lam (2004) applied the back-propagation algorithm to integrate fundamental and technical analysis for financial performance prediction. The experimental results show that the ANNs outperform the benchmark. The criteria factor selection is an issue in ANNs. Qi and Zhang (2001) investigate the model selection criteria for ANNs time series forecasting. They discover Akaike and Bayesion information criterion as well as several exten-sions have been examined through time serial of S&P500. The hybrid evolutionary approach with ANNs is popular issue in business failure prediction (Ahn, Cho, & Kim, 2000; Plikynas, Salalauskas, & Poliakova, 2005).

Ko and Lin (2006)proposed an evolutionary modularized evaluation functions with ANNs to forecast financial dis-tress, which allows using any evolutionary algorithm to extract the set of critical financial ratios and integrates more evaluation function modules to achieve a better fore-casting accuracy by assigning distinct weights. This approach effectively helps improving final forecasting accuracy.

In portfolio applications, using ANNs to portfolio man-agement has gained interest in recent years. Hung, Liang, and Liu (1996) integrate the arbitrage pricing theory (APT) and ANNs to extracting risk factors and generating individual in portfolio. The empirical results indicate the integrated method beats the benchmark and ARIMA model.Chapados and Bengio (2001)demonstrated the suc-cess of ANNs with asset allocation framework according to a value-at-risk adjusted profit criterion for making asset allocation decisions. Both the forecasting and deci-sion models are significantly outperforming the benchmark market performance. Eakins and Stansell (2003) examine whether superior investment returns can be earned by using ANNs to perform forecasts based on a set of financial ratio to determine the intrinsic value of assets to enter the prop-erty portfolio. They find that the value ratio provides useful information that permits the selection of portfolio with superior investment returns than DJIA and S&P500.

Hung, Cheung, and Xu (2003) present an extended adap-tive supervised learning decision EASLD trading system to enhance the portfolio management. Their researches take a balance between the expected returns and risks.

Plikynas et al. (2005) use ANNs to control nonlinear dynamics of heterogeneous foreign investment impact on national capitalization structure. Their research results are better than multidimensional linear regression forecast-ing performance.Ellis and Wilson (2005)applied ANNs to the Australian property sector stocks to construct a variety of value portfolios. Their risk-adjusted performances show the value portfolios outperform the benchmark by as much as 7.14%.

However, the traditional ANN model cannot produce reasonable allocation ratios generally, i.e. the summation of produced allocation ratios cannot retain 100% in the tar-get portfolio during the training period. Most of them use additional correction steps, such as, division the output vector by its sum to fit constrains of problems. This extra fixing step would possibly mislead the final trained neural network. Therefore, it is an important issue to propose a novel resource allocation neural network (RANN) model. The aim of this paper is to introduce an allocated learning based neural network model to optimize the assets alloca-tion in portfolio. This approach proposes a dynamic synap-tic weight modification as a basis of 100% of summing all of allocation ratios in the portfolio. Through the examina-tion of final experimental results, our model would outper-form the market peroutper-formance.

This paper is organized as follows. Section 2 presents our resource allocation ANNs model for asset allocation. Then, we will conduct some experiments to compare its performance with benchmark market in Section3. Finally, we draw some conclusions in Section4.

2. Multi-layer resource allocation neural network (RANN) In this section, an allocated learning algorithm applied to multi-layer resource allocation neural network (RANN)

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are negative, they are also higher than the corresponding ROITSE (10.19%) and (8.97%). These results are also

shown inFig. 5. It demonstrates that RANN obtain better asset allocations eﬀectively.

Table 3is the summary of various asset allocation ratios in each sliding window. Let RAV,xdenote the average

allo-cation ratio for asset code x. It is reasonable that RAV,2002= 0.24 (Catcher Technology, the automobile

industry) and RAV,2201= 0.22 (China Steel, Iron & Steel

Industry) posses higher allocating ratio because of their higher ROIYM,2002= 15.5% and ROIYM,2201= 33.3%,

where ROIYM,xrefers to the annual ROI for asset code x.

Even though ROIYM,1326= 15.6% and ROIYM,2002=

15.5% have similar values, RAV,1326(0.16) is smaller because

of its higher risk r2 (0.12). It means that the MLRANN model suggests increasing investing ratio with high return and low risk; otherwise, it will decrease its allocation ratio. 4. Conclusions

The best asset allocation of portfolio is concerned with good performance of investment. The well-known mean variance method requires predetermined expected return to calculate the investing ratios of portfolio that becomes much more difficult and unrealistic forecasting securities investment strategies in the future. This approach uses spe-cific linear relationship and limitation to calculate the risk factor such as covariance metric. The neural network with nonlinear characteristics may be more suitable to improve the asset allocation of portfolio. However, the traditional ANN model could not produce fitness investment weight based on summation of these weight retain one.

This paper introduces a novel allocated learning based resource allocation neural network model to optimize

investment weight of portfolio that will outperform the market. This model proposes a dynamic weight modifica-tion as a basis of 100% of summing all of asset weights in the portfolio. Results on 21 companies selected to be our testing targets from Taiwan 50 Index Constituents demonstrate the feasibility of optimal investment weights and superiority of ROI based on buy-and-hold trading strategy. Through the experimental results, the complex portfolio asset allocation management would be solved effectively by our model. From our experiments, it appears that using allocated learning based neural network model will converge to two dimensions (the highest expected return and the lower RMSE), simultaneously. Using resource allocation neural network model produces better return of investment than TSE in each sliding window. Our resource allocation neural network model recom-mends increasing/decreasing investment weight of optimis-tic/pessimistic prospects of assets effectively.

Acknowledgement

This study is partially supported by the project Granted by National and Science Council in Taiwan, ROC under Contract NSC 96-2416-H-005.

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Table 3

Asset allocations and ROIMLRANNin each sliding window

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1302 0.07 0.05 0.07 0.05 0.06 0.05 0.04 0.09 0.03 0.05 5.1 0.06 1303 0.01 0.00 0.03 0.04 0.02 0.01 0.04 0.06 0.06 0.03 3.0 0.15 1326 0.14 0.15 0.15 0.17 0.17 0.18 0.20 0.24 0.21 0.16 15.6 0.12 1402 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 12.0 0.15 2002 0.23 0.28 0.29 0.29 0.28 0.27 0.29 0.24 0.21 0.24 15.5 0.07 2201 0.23 0.28 0.29 0.29 0.28 0.27 0.18 0.20 0.20 0.22 33.3 0.40 2301 0.12 0.06 0.02 0.01 0.01 0.02 0.04 0.00 0.05 0.03 12.5 0.02 2303 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 19.9 0.17 2308 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 16.8 0.02 2311 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 11.8 0.30 2317 0.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 13.7 0.03 2324 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 14.5 0.10 2325 0.02 0.02 0.02 0.00 0.00 0.00 0.00 0.00 0.02 0.01 4.3 0.45 2330 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 13.9 0.18 2352 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 22.2 0.11 2353 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 13.1 0.25 2354 0.10 0.09 0.08 0.07 0.08 0.09 0.08 0.06 0.14 0.08 0.2 0.35 2357 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 23.5 0.19 2382 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 14.7 0.21 2474 0.04 0.05 0.04 0.07 0.08 0.10 0.12 0.08 0.07 0.06 14.1 0.82 9904 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.00 12.6 0.11

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