Asset Pricing and Artificial Neural Networks: A Case of Pakistan’s Equity Market


The job of forecasting the stock market returns in the emerging markets is challenging due to some peculiar characteristics of these markets. For years, conventional forecasting methods have been developed, but they have succeeded partially or have failed entirely to deal with the nonlinear and complex nature of stock returns. Artificial Neural Networks approach is a relatively new and promising field of the prediction of stock returns.

Neural networks approach is a mathematical model, flexible enough to accommodate both linear and non-linear aspect of stock returns and act like human brains to simulate the behavior of the stock prices. The literature review reveals that there are a large number of studies trying to forecast the stock market returns using conventional statistical techniques. However, there is a dearth of literature on the use of machine learning techniques in the area of asset pricing. The study is an attempt to fill this gap by addressing the major issue of using the asset pricing models for prediction of portfolio returns in the presence of Artificial Neural Networks.

We investigate the forecasting ability of single factor CAPM, Fama and French three factor and five factor model by using Artificial Neural Networks. This study employs the monthly returns of all the companies listed on Pakistan Stock Exchange for the period 2000-2015. Data on market capitalization, book-to-market ratio, total assets and operating profit is used to construct factors used in multifactor models. The factors of Size, value, investment, and profitability are constructed by following the industry standards. Thirty Portfolios are constructed by beta; resulting into high, medium and low beta portfolios based on monthly returns. These factors are used as inputs and outputs in the neural network system. We construct an artificial neural networks system to predict portfolio returns in two stages; in stage one, the study identifies the best-fit combination of training, testing, and validation along with the number of neurons for the three asset pricing models for a full sample from 2000 to 2015. In stage two, the study uses this best combination to forecast the model under 48-month rolling window analysis and evaluate its ability to forecast the stock returns in an emerging market. In-sample and out-sample comparisons, regression and goodness of fit test and actual and predicted values of the stock returns of the ANN model are conducted.

A comprehensive methodology of the neural networks is applied to achieve the primary purpose of forecasting. The methodology includes the initial architecture consists of three layers, i.e., an input layer, hidden layer, and an output layer. The hidden layer utilizes 1-50 neurons for processing. The study uses varying parameters for an effective Artificial Neural Networks system. The study also employs rolling windows to calculate and compare forecasting error among competing asset pricing models by using 16 data combinations. The Artificial Neural Networks take the values of monthly returns of the first 48 months as a training set and predict the 49th value for the monthly returns. Mean Squared Error measures the performance of the Artificial Neural Networks.

The significant findings of the study are: firstly, CAPM-based networks models have predicted 48%, while the Fama and French three factors and five factors models based networks returned 94% and 98% respectively of the time periods accurately. Secondly, the number of the optimum number of neurons does not follow some mathematical rule instead it is based on the presentiment of the researcher to apply an exhaustive search for the number of optimum neurons. Thirdly the performance of the CAPM-based networks is the best at the 75-10-15 dataset and 16 neurons.

The Fama and French three factors model generate the best results at 60-20-20 dataset and 27 neurons and the Fama and French five factors model return the best results at 28 neurons and 75-20-05 dataset. The magnification of the performance with the increase in the number of neurons is a useful heuristic for the future researchers. The fourth significant finding is that the difference of errors between the testing and training data set is minimum and the networks are not suffering from the over-fitting phenomenon.

The fifth finding is that the predicted value of high beta portfolios is better than the low beta and mid beta portfolios. This finding reinforces the investment principle that the market compensates the high-risk portfolios more than other classes. The Fama and French five factors model show more promising results as compared to the other two models. The best results are converging at 75-20-05 Dataset at 28 neurons, and the success rate of accurate prediction is 98%. This implies that the addition of the investment and profitability factors demonstrate good predictive power in this market. Our findings reinforce the investment principle that the markets compensate the high-risk portfolios more than the other classes. The proposed prediction methodology will significantly improve the return on investment against the buy and holds strategy.The proposed model achieves a significant improvement in the return on investment, and the investors can magnify their profitability.

Our methodology using ANN models,although, have accurately predicted the returns, it remains open to more experimentation. At this point, given the ‘black box’ nature of the ANN, it is difficult to offer any explanation beyond the wellknown ability of the ANN to capture ‘hidden’ relationships between inputs and outputs. Future researchers should focus on clustering, classification, hybridization of other nonlinear techniques with a neural network system. The portfolio selection can also be optimized using particle swarm optimization and other artificial intelligence techniques. We hope that future research in the fields of both asset pricing and artificial intelligence would be able to offer an opportunity for interdisciplinary research and present more challenges to the established investment theories.

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