Stochastic Forecasting of Stock Prices in Nigeria: Application of Geometric Brownian Motion Model

2021 ◽  
Vol 6 (2) ◽  
pp. 1-35
Author(s):  
Adolphus Joseph Toby ◽  
Samuel Azubuike Agbam
Keyword(s):  
Brownian Motion ◽  
Stock Prices ◽  
Stock Exchange ◽  
Investment Strategy ◽  
Time Frame ◽  
Geometric Brownian Motion ◽  
Percentage Error ◽  
Unique Contribution ◽  
Holding Period ◽  
Stochastic Forecasting

Purpose:  The purpose of the study is to model and simulate the trends and behavioral patterns in The Nigerian Stock Market and hence predict the future stock prices within the Geometric Brownian Motion (GBM) framework. Methodology: The methodology involves a comparison of forecasted daily closing prices to actual prices in order to evaluate the accuracy of the prediction model. Based on the model assumptions of the GBM with drift: continuity, normality and Markov tendency, the study investigated four years (2015 - 2018) of historical closing prices of ten stocks listed on The Nigerian Stock Exchange. The sample for this study is based on the most continuously traded stocks. Findings: The results show that in the simulation there are some actual stock prices located outside trajectory realization that may be from GBM model. Thus, the model did not predict accurately the price behavior of some of the listed stocks.  The predictive power of the model is declining towards the longer the evaluated time frame proven by the higher value of the mean absolute percentage error. The value of the MAPE is 50% and below for the one- to two-year holding periods, and above 50% for the three-year holding period. Unique Contribution to theory, Practice and Policy:  The MAPE and directional prediction accuracy method provide support that over short periods the GBM model is accurate. Meaning that the GBM is a reasonable predictive model for one or two years, but for three years, therefore, it is an inaccurate predictor. It is recommended that the technical analyst whose primary motive is to make gain at the expense of other participants should identify high volatile portfolio in any holding period for effective prediction Investors with long-range holding position as investment strategy should concentrate more on low capitalized stocks rather than stocks with large market capitalization. This is a unique contribution to theory, practice and policy. 

scholarly journals Forecasting Cyclical and Non-cyclical Stock Prices on the Stock Exchange of Thailand

2021 ◽  
Vol 17 (5) ◽  
pp. 550-565
Author(s):  
Rapin Sunthornwat ◽  
Yupaporn Areepong
Keyword(s):  
Decision Making ◽  
Brownian Motion ◽  
Stock Prices ◽  
Stock Exchange ◽  
Geometric Brownian Motion ◽  
Percentage Error ◽  
Initial Value ◽  
Minimum Error ◽  
Stock Exchange Of Thailand ◽  
And Performance

Forecasting is an important role in organizations for decision making and planning. This research is to forecast the cyclical and non-cyclical weekly stock prices on the Stock Exchange of Thailand by using the models of Geometric Brownian motion, Fourier’s series, and Cauchy initial value problem. The accuracy and performance of the models are based on the minimum root mean squared percentage error which is the error between actual and forecasted stock prices. The results showed that Geometric Brownian motion is suitable for forecasting both cyclical and non-cyclical stock prices because of minimum error. Moreover, the confidence intervals of forecasted stock prices are demonstrated. Therefore, Geometric Brownian motion should be selected to describe the movement of stock prices in Thailand.

scholarly journals Comparison of Stochastic Forecasting Models

2021 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Brownian Motion ◽  
Stock Prices ◽  
Absolute Error ◽  
Geometric Brownian Motion ◽  
Time Dependent ◽  
Confidence Bounds ◽  
History Of ◽  
Brownian Motion Model ◽  
Stochastic Forecasting ◽  
Two Parameters

In this work, we compare several stochastic forecasting techniques like Stochastic Differential Equations (SDE), ARIMA, the Bayesian filter, Geometric Brownian motion (GBM), and the Kalman filter. We use historical daily stock prices of Microsoft (MSFT), Target (TGT) and Tesla (TSLA) and apply all algorithms to try to predict 54 days ahead. We find that there are instances in which all algorithms do well, or do poorly. We find that all three stocks have a strong auto-correlation and a high Hurst factor which shows that it is possible to predict future prices based on a short history of past prices. In our geometric Brownian motion model, we have two parameters for drift and diffusion which are not time dependent. In our more general SDE model (TDNGBM), we have time-dependent drift and time-dependent diffusion terms which makes it more effective than GBM. We measure all algorithms on the correlation between the predicted and actual values, the mean absolute error (MAE) and also the confidence bounds generated by the methods. Confidence intervals are more important than point forecasts, and we see that TDNGBM and ARIMA produce good bounds.

scholarly journals Fuzzy Time Series and Geometric Brownian Motion in Forecasting Stock Prices in Bursa Malaysia

2019 ◽  
Vol 14 (2) ◽  
pp. 240-250
Author(s):  
Nor Hayati Shafii ◽  
Nur Ezzati Dayana Mohd Ramli ◽  
Rohana Alias ◽  
Nur Fatihah Fauzi
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Stock Market ◽  
Stock Prices ◽  
Stock Exchange ◽  
Investment Decisions ◽  
Geometric Brownian Motion ◽  
Fuzzy Time Series ◽  
Good Information ◽  
The Mean

Every country has its own stock market exchange, which is a platform to raise capital and is a place where shares of listed company are traded. Bursa Malaysia is a stock exchange of Malaysia and it is previously known as Kuala Lumpur Stock Exchange. All over the world, including Malaysia, it is common for investors or traders to face some loss due to wrong investment decisions. According to the conventional financial theory, there are so many reasons that can lead to bad investment decisions. One of them is confirmation bias where an investor has a preconceived notion about an investment without a good information and knowledge. In this paper, we study the best way to provide good information for investors in helping them make the right decisions and not to fall prey to this behavioral miscue. Two models for forecasting stock prices data are employed, namely, Fuzzy Time Series (FTS) and Geometric Brownian Motion (GBM). This study used a secondary data consisting of AirAsia Berhad daily stock prices for a duration of 20 weeks from January 2015 to May 2015. The 16-weeks data from January to April 2015 was used to forecast the stock prices for the 4-weeks of May 2015. The results showed that FTS has the lowest values of the Mean Absolute Percentage Error (MAPE) and the Mean Square Error (MSE), which are 1.11% and MYR20.0011, respectively. For comparison, for GBM, the MAPE is 1.53% and the MSE is MYR2 0.0017. The findings imply that the FTS model provides a more accurate forecast of stock prices. Keywords: Forecasted values, stock market, Fuzzy Time Series, Geometric Brownian Motion

Research of Building Intelligent Investment Decision Mode for Investment Portfolio — Using Taiwan Electronic Stock as an Example

2010 ◽  
Vol 13 (04) ◽  
pp. 621-645 ◽  
Author(s):  
Wen-Rong Jerry Ho ◽  
C. H. Liu ◽  
H. W. Chen
Keyword(s):  
Stock Returns ◽  
Stock Prices ◽  
Stock Exchange ◽  
Investment Decision ◽  
Investment Strategy ◽  
Return Rate ◽  
Selection Strategy ◽  
Stock Selection ◽  
Taiwan Stock Exchange ◽  
Book To Market Ratio

This research uses all of the listed electronic stocks in the Taiwan Stock Exchange as a sample to test the performance of the return rate of stock prices. In addition, this research compares it with the electronic stock returns. The empirical result shows that no matter which kind of stock selection strategy we choose, a majority of the return rate is higher than that of the electronics index. Evident in the results, the predicted effect of BPNN is better than that of the general average decentralized investment strategy. Furthermore, the low price-to-earning ratio and the low book-to-market ratio have a significant long-term influence.

scholarly journals The Geometric Brownian Motion of Indosat Telecommunications Daily Stock Price During the Covid-19 Pandemic in Indonesia

2021 ◽  
Vol 2084 (1) ◽  
pp. 012012
Author(s):  
Tiara Shofi Edriani ◽  
Udjianna Sekteria Pasaribu ◽  
Yuli Sri Afrianti ◽  
Ni Nyoman Wahyu Astute
Keyword(s):  
Brownian Motion ◽  
Stock Price ◽  
Service Providers ◽  
Main Idea ◽  
Geometric Brownian Motion ◽  
Government Policies ◽  
Percentage Error ◽  
Price Movement ◽  
Data Movement ◽  
Total Data

Abstract One of the major telecommunication and network service providers in Indonesia is PT Indosat Tbk. During the coronavirus (COVID-19) pandemic, the daily stock price of that company was influenced by government policies. This study addresses stock data movement from February 5, 2020 to February 5, 2021, resulted in 243 data, using the Geometric Brownian motion (GBM). The stochastic process realization of this stock price fluctuates and increases exponentially, especially in the 40 latest data. Because of this situation, the realization is transformed into log 10 and calculated its return. As a result, weak stationary in variance is obtained. Furthermore, only data from December 7, 2020 to February 5, 2021 fulfill the GBM assumption of stock price return, as R t 1 * , t 1 * = 1 , 2 , 3 , … , 40 . The main idea of this study is adding datum one by one as much as 10% – 15% of the total data R t 1 * , starting from December 4, 2020 backwards. Following this procedure, and based on the 3% < p-value < 10%, the study shows that its datum can be included in R t 1 * , so t 1 * = − 4. − 3 , − 2 , … , 40 and form five other data groups, R t 2 * , … , R t 6 * . Considering Mean Absolute Percentage Error (MAPE) and amount of data from each group, R t 6 * is selected for modelling. Thus, GBM succeeded in representing the stock price movement of the second most popular Indonesian telecommunication company during COVID-19 pandemic.

Financial Factors Affecting Price-to-Earnings Ratios in Canada

2021 ◽  
Vol 6 (2) ◽  
pp. 43-61
Author(s):  
Natalia Popa Antalovschi ◽  
Raymond A. K. Cox
Keyword(s):  
Financial Reporting ◽  
Stock Prices ◽  
Stock Exchange ◽  
Fiscal Year ◽  
Unique Contribution ◽  
Policy And Practice ◽  
Factors Affecting ◽  
Financial Factors ◽  
Natural Logarithm ◽  
Forward Price

Purpose: The purpose of this study is to ascertain which financial factors affect the price-to-earnings ratios of Canadian firms. Methodology: A sample of 578 Canadian firms, across 11 industries, listed on the Toronto Stock Exchange during 2011 to 2018 is examined. Stock prices and financial statements accounts data is collected from S & P Capital IQ. We compute 27 financial factors to use as independent variables to regress on the price-to-earnings ratio dependent variables employing the Statistical Package for Social Sciences (SPSS) utilizing the software program’s forced, forward, and backward selection methods. Robustness tests are conducted using alternative dates (after the fiscal year end) to discover which model of financial factors best explains the forward price-to-earnings ratio as well as other statistical methods such as analysis of variance. Results: We find a unique model for each of the 3 models based on the forward price-to-earnings ratio date. The financial factors that explain each of the dates after the end of the fiscal year (1 month, 2 months, and 3 months) are the 4 variables: net profit margin, return on investment, total asset turnover, and the natural logarithm of the total assets. For model 3 (1 month after fiscal year end), in addition to the previous 4 factors, the dividends per share is part of the regression equation. All 3 models have strong statistically significant results at an alpha level of one percent. Further, industry effects are deduced and presented. Unique contribution to theory, policy, and practice: The results are unique to a Canadian sample of firms post- International Financial Reporting Standards (IFRS) adoption. Companies can utilize the empirical findings to manage their financial performance to maximize their price-to-earnings ratio. A product of a firm’s higher price-to-earnings ratio is a lower cost of capital which expands the corporation’s investment opportunities. Investors can apply this research to develop investment strategies hinged on price-to-earnings ratios to augment investment returns.

scholarly journals Impact of Accounting Information on Share Price: Empirical Evidence from Pakistan Stock Exchange

2016 ◽  
Vol 3 (1) ◽  
pp. 124
Author(s):  
Muhammad Asif ◽  
Kashif Arif ◽  
Waqar Akbar
Keyword(s):  
Capital Market ◽  
Stock Prices ◽  
Stock Exchange ◽  
Explanatory Power ◽  
Accounting Information ◽  
Time Frame ◽  
Share Price ◽  
Share Prices ◽  
The Impact ◽  
The Relationship

Purpose—The purpose of this paper is to examine the relationship between accounting information and share price. In order to achieve this, a model that includes specific accounting ratios (earning per share, book value per share, capital employed per share and operating cash flow per share) and shares a price is developed. Design/methodology/approach—The data were collected from the companies listed in KSE-30 index. The time frame spans from 2006 to 2013 and OLS regression models were used to examine the relationshipsFindings—The resulting evidence suggest that accounting information parameters have significant influence on share price and they have joint explanatory power in determining stock prices. This research finds the consistent results with pervious empirical researches.Originality/value—The present study adds to the existing literature by examining the impact of accounting information on share prices within the context of an emerging capital market such as Pakistan Stock Exchange using KSE-30 companies. This is believed to be the first study which considers the aforementioned issues in the Pakistan’s capital market environment.

scholarly journals The application of model predictive control on stock portfolio optimization with prediction based on Geometric Brownian Motion-Kalman Filter

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Wawan Hafid Syaifudin ◽  
Endah R. M. Putri
Keyword(s):  
Brownian Motion ◽  
Kalman Filter ◽  
Model Predictive Control ◽  
Portfolio Optimization ◽  
Stock Returns ◽  
Predictive Control ◽  
Stock Prices ◽  
Geometric Brownian Motion ◽  
The Future ◽  
Stock Portfolio

<p style='text-indent:20px;'>A stock portfolio is a collection of assets owned by investors, such as companies or individuals. The determination of the optimal stock portfolio is an important issue for the investors. Management of investors' capital in a portfolio can be regarded as a dynamic optimal control problem. At the same time, the investors should also consider about the prediction of stock prices in the future time. Therefore, in this research, we propose Geometric Brownian Motion-Kalman Filter (GBM-KF) method to predict the future stock prices. Subsequently, the stock returns will be calculated based on the forecasting results of stock prices. Furthermore, Model Predictive Control (MPC) will be used to solve the portfolio optimization problem. It is noticeable that the management strategy of stock portfolio in this research considers the constraints on assets in the portfolio and the cost of transactions. Finally, a practical application of the solution is implemented on 3 company's stocks. The simulation results show that the performance of the proposed controller satisfies the state's and the control's constraints. In addition, the amount of capital owned by the investor as the output of system shows a significant increase.</p>

scholarly journals Comparative Analysis of ARIMA and GARCH Methods to Predict Stock Prices

2020 ◽  
Vol 4 (3) ◽  
pp. 405-415
Author(s):  
Atin Nuryatin
Keyword(s):  
Stock Prices ◽  
Stock Price ◽  
Mean Absolute Error ◽  
Stock Exchange ◽  
Secondary Data ◽  
Absolute Error ◽  
Percentage Error ◽  
Verification Methods ◽  
Secondary Data Sources ◽  
Forecasting Errors

Investment has a very important role in economic growth, when investors invest, GDP tends to rise when investment falls, so GDP also tends to decline. Investors must be vigilant in investing in banking companies. One of the ways to predict stock prices with technical analysis is by using the ARIMA and GARCH methods. The purpose of this study is to determine whether the ARIMA and GARCH methods are accurate in predicting stock prices. The research method used in this research is descriptive and verification methods with a quantitative approach. Sources of data taken in this study are secondary data sources for the bank sub-sector found on the Indonesia Stock Exchange (IDX), namely the annual stock price reports for the years 2014, 2015, 2016, 2017, and 2018 as many as 39 companies. Processing data from this study using the ARIMA and GARCH methods with an evaluation of forecasting errors using the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), or Mean Absolute Percentage Error (MAPE) analysis results using the E-View 9 program. shows that the ARIMA Method is accurate in predicting stock prices in 2015, 2016, and 2018. Meanwhile, the GARCH Method is accurate in predicting stock prices in 2014 and 2017.

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