Model Developments for Stock Returns
Creators: name: Konarasinghe, W.G.S.
Publisher: name: Zenodo
Year: 2016
Subjects: Fourier Transformation, Uniform Circular Motion, Covariance

description: Statistical modeling is vital in planning, forecasting and management in the fields of; Agriculture, Medicine, Engineering, Economics, Finance and many more. Stock market is the secondary capital market which gives investment opportunities to investors and liquidity to firms. Share trading affects all the stake holders; customers of the firms, employees of the firms, the government and society. As such, share trading is an important part of the economy of a country. Share market investments are considered as high risk, high return investments, but the investors are concerned about high return at low risk. Hence forecasting of risk and return are essential for share markets. The Capital Asset Pricing Model (CAPM) is the most commonly used model for forecasting share returns. However, CAPM has been subjected to empirical arguments over the decades. Literature gives enough evidence for the inefficiency of CAPM in forecasting returns. Yet, the Sri Lankan stock market depends on CAPM for forecasting risk and returns of securities. The study was focused to; test existing statistical models for forecasting Sri Lankan stock returns and develop suitable techniques for forecasting risk and returns. Daily closing share price data, monthly sector indices and All Share Price Index data were obtained from Colombo Stock Exchange (CSE). Monthly share returns of a random sample of companies from CSE were used for data analysis. Pattern recognition of returns was the first step of the study. It was found that the Sri Lankan stock returns are stationary type, follow wave like patterns. Then the covariance structure of Sri Lankan stock returns was identified. The central assertion of CAPM; linear relationship between individual company returns and the total market returns were not supported by the analysis, but there was a significant linear relationship between individual company returns and corresponding sector returns. Therefore individual company returns were modeled on sector returns. Thereafter, Auto Regressive Integrated Moving Average (ARIMA) models were tested on individual company returns. Finally, a technique based on Fourier transformation was applied on returns. The suggested model was named as the “Circular Model (CM)”. Goodness of fit of the models was tested by residual plots, Auto Correlation Functions and Partial Autocorrelation Functions of residuals, Ljung-Box Q statistics, Durbin Watson test statistic and Anderson Darling test. Forecasting errors were measured by the Root Mean Square Error and the Mean Absolute Deviation. The ARIMA and CM were successful in forecasting returns. However, pattern of ARIMA forecasts was not close to the patterns of actual returns, while CM forecasts followed the actual returns. It was concluded that the CM is the best model in forecasting Sri Lankan stock returns. In general, the risk of returns is measured by standard deviation or β coefficient of CAPM, but both methods are erroneous. In recent past, ARCH/GARCH models also were used for the purpose. The Engle’s ARCH test confirmed the non existence of ARCH effect in Sri Lankan stock returns. The study suggested a new approach for measuring risk of returns. The theory of uniform circular motion (Newton’s law) was applied in measuring risk. The suggested risk measurement, named as “Circular Indicator” was successful in measuring risk of returns. Wave like patterns are common in the fields of Medicine, Agriculture, Meteorology and many others. It is recommended to test the CM on forecasting wave like patterns in these fields. Also it is worth testing the suitability of Circular Indicator, as a risk measurement in the above fields and many more.