Forecasting risk using auto regressive integrated …...tive role in market efficiency for price adjustment (Brunnermeier, M., Pedersen, L., 2009, Moussa, A., 2011). Asset pricing
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RESEARCH Open Access
Forecasting risk using auto regressiveintegrated moving average approach: anevidence from S&P BSE SensexMadhavi Latha Challa1* , Venkataramanaiah Malepati2 and Siva Nageswara Rao Kolusu 1
* Correspondence: [email protected] of Management Studies,Vignan’s Foundation for Science,Technology & Research, Guntur,Andhra Pradesh, IndiaFull list of author information isavailable at the end of the article
Abstract
The primary objective of the paper is to forecast the beta values of companies listed onSensex, Bombay Stock Exchange (BSE). The BSE Sensex constitutes 30 top mostcompanies listed which are popularly known as blue-chip companies. To reach out thepredefined objectives of the research, Auto Regressive Integrated Moving Averagemethod is used to forecast the future risk and returns for 10 years of historical datafrom April 2007 to March 2017. Validation accomplished by comparison of forecastedand actual beta values for the hold back period of 2 years. Root-Mean-Square-Error andMean-Absolute-Error both are used for accuracy measurement. The results revealedthat out of 30 listed companies in the BSE Sensex, 10 companies’ exhibits high betavalues, 12 companies are with moderate and 8 companies are with low beta values.Further, it is to note that Housing Development Finance Corporation (HDFC) exhibitsmore inconsistency in terms of beta values though the average beta value is lowestamong the companies under the study. A mixed trend is found in forecasted betavalues of the BSE Sensex. In this analysis, all the p-values are less than the F-stat valuesexcept the case of Tata Steel and Wipro. Therefore, the null hypotheses were rejectedleaving Tata Steel and Wipro. The values of actual and forecasted values are showingthe almost same results with low error percentage. Therefore, it is concluded from thestudy that the estimation ARIMA could be acceptable, and forecasted beta values areaccurate. So far, there are many studies on ARIMA model to forecast the returns of thestocks based on their historical data. But, hardly there are very few studies whichattempt to forecast the returns on the basis of their beta values. Certainly, the attemptso made is a novel approach which has linked risk directly with return. On the basis ofthe present study, authors try to through light on investment decisions by linking itwith beta values of respective stocks. Further, the outcomes of the present studyundoubtedly useful to academicians, researchers, and policy makers in their respectivearea of studies.
Keywords: Akaike Information Criteria (AIC), Bombay Stock Exchange (BSE), AutoRegressive Integrated Moving Average (ARIMA), Beta, Time series
Hindustan Unilever 4 ICICI Bank 4 Reliance Industries 4
Wipro 5 Adani Ports & SEZ 5 Maruti Suzuki 5
Source: Compiled by authors
Challa et al. Financial Innovation (2018) 4:24 Page 15 of 17
of the forecasting could be found for the validation purpose. To confirm the qual-
ity of accuracy Root Mean Square Error (RMSE) and Mean Absolute Error (MAE)
were calculated based on errors between forecasted and actual data, which is pre-
sented in Table 7.
Table 7 shows the results of validation or test results between the forecasted and ac-
tual values. The MAE is always less than the RMSE values in all the cases of registered
companies in BSE Sensex, which indicates that the error percentage is very less and the
values of actual and forecast showing the almost same results. Therefore, the estima-
tion ARIMA could be acceptable, and forecasted beta values are accurate.
FindingsFrom the analysis, authors have found the future beta values for the period of April
2017 to March 2019. From the Fig. 4 three categories of betas has been found. First
one is moderate beta, which indicates the same instability as compared with Sensex
and it equals to one. Second category is aggressive beta, which shows more instability
when compared to Sensex and it express the beta greater than one.
Last one is defensive beta; it represents the less instability with Sensex comparison
and it is less than one. According to the category the companies also segregated for the
convenience of investors.
Lower rank represents the less risk and higher vice versa. Higher risk taking investors
might get good returns in the future. Table 8 shows the less risky companies under
three divisions (Moderate, Aggressive, Defensive) of companies. The investors can take
investment decisions according to their choice.
ConclusionForecasting with Auto ARIMA provides a prediction based on historical data, in which
data has been applied by first order difference to remove white noise problems. In this
analysis Auto ARIMA estimated AIC values, which yielded the more accurate forecast
over the ten years period. In validation, the forecasted values are compared with actual
values over the hold back period of two years. From this analysis the more uncertainty
has been found when the forecast period is long term period, less uncertainty exists in
the case of short term period. From the analysis the different investors can choose
companies according to their risk aversion.
AbbreviationsACF: Auto Correlation Function; ADF: Augmented Dickie Fuller; AIC: Akaike Information Criteria; AR: Auto Regressive;ARIMA: Auto Regressive Integrated Moving Average; ARMA: Auto Regressive Moving Average; BSE: Bombay StockExchange; DW: Durbin –Watson; MA: Moving Average; MAE: Mean Absolute Error; PACF: Partial Auto CorrelationFunction; RMSE: Root Mean Square Error; S.E of Reg: Standard Error Regression; SC: Schwarz Criterion; Tata MotorsDVR: Tata Motors Differential Voting Right Share
Availability of data and materialsSource of Data sets are available in http://www.bseindia.com and http://finance.yahoo.com. Analyzed data uploadedas supplementary material files.
Authors’ contributionsStudy of conception and design: MLC, VM, SNRK. Acquisition of data: MLC. Analysis and interpretation of data: MLC.Supervision: VM, SNRK. Drafting of manuscript: MLC. Critical revision: VM, SNRK. All authors read and approved the finalmanuscript.
Authors’ informationCH. Madhavi Latha received her MBA degree in Finance from Jesus PG College, affiliated by JNTUH, Hyderabad,Telangana, India. She is pursuing Ph.D at Vignan’s Foundation for Science, Technology & Research, Guntur, Andhra
Challa et al. Financial Innovation (2018) 4:24 Page 16 of 17
Pradesh, India. She is also working as Assistant Professor in University of Gondar, Gondar, Ethiopia. She has more than5 publications in various international Journals / Conferences. Her research areas include Capital Asset Pricing,Dynamic changes in Stock market and Stock holders Interest.Dr. Venkataramanaiah Malepati obtained his M.Com., M.Phil., and PhD from Sri Venkateswara University, Tirupati andMBA from Pondicherry University. At present, he is Professor of Management, Department of Management Studies atGolden Valley Instigated Campus, Madanapally. So far, he has published 34 research papers/articles in reputed/referrednational/ international journals. Almost, the same number of papers/research articles has been presented in differentnational and international conferences/seminars. At present five books on his credit.Dr. K. Siva Nageswara Rao is working as an Assistant Professor of School of Management Studies at Vignan Foundationfor Science, Technology & Research, Guntur, Andhra Pradesh, India. He received his MBA degree in Finance fromAcharya Nagarjuna University, Andhra Pradesh, India and M.Phil Degree in Finance from MS University, Tiruelveli,Tamilnadu. He received his Ph.D degree from Acharya Nagarjuna University Guntur, Andhra Pradesh, India. He has15 years of teaching experience. He has more than 20 publications in various National and International Journals/Conferences. His main research interest includes Finance and Entrepreneurship.
Competing interestsAuthors declare that they have no competing interests.
Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Author details1School of Management Studies, Vignan’s Foundation for Science, Technology & Research, Guntur, Andhra Pradesh,India. 2Institute of Management Studies, Golden Valley Integrated Campus (GVIC), Madanapalli, Chittoor 517 325, India.
Received: 1 February 2018 Accepted: 1 October 2018
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