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< Back Sustainability Dimensions of Stocks on the SIX:Render 1 Quantitatively assessing Brundtland's Dimensions (1987). The case of the SIX Previous Next

< Back ESG Strategies: Passive and Active Management Do the laws of passive and active strategies also affect sustainability investing? I recently concluded a sustainability data visualization project. The draft of the visualization is below Viewing the plot, I sought to understand the sustainability of stocks on the SIX. Parameters were used to identify sustainability in terms of ESG scores (70 and above) and Economic score (having an expected return above the market return). I developed four sustainable funds based on the ESG findings and market returns. Additionally I used ETHOS fund data found on Swiss Fund Data to develop the sustainable funds. The funds developed were: Negative Screening Best in Class Approach Thematic Approach ESG integration Against the staus quo, ESG integration was the only fund that was not "sustainable." Typcially ESG itegration is hailed as one of the most effective and practical strategies for promoting sustainability. Why is this the case? Unlike the first three strategies which are very basic to implement, when it came to the ESG integration fund, I randomly picked the ETHOS fund and duplicated the stock selectio - an in this case per the basic quantitaive metric developed, said fund was not . However, when I picked another ESG integrated fund its performace was sustainable. It appears that ESG integration has greater levels of subjectivity and the funds constructed across traders are likely to differ much greately than the previous 3 strategies. Thus, one can argue the element of the manager's skill in the active management of an ESG integrated fund plays a greater role in the fund's performance as compared to the other 3 strategies. Could this be the case of "passive" and active management of portfolios? Future works: Compare performace of ESG integrated funds Calculate the average return of ESG integrated funds vs "passive" strategies (Negative screening, Best In Class Approach ~ basic strategies) Do the variations of ESG integration strategies and basic sustainability stratigies vary across market types (Geographic and effeciency wise)? Previous Next

< Back Hedonic Valuation Model: Real Estate in Zurich With significant portions of banks portfolios consisting of mortgage loans, it is paramount to develop a strong model for valuating real estate. https://akweix.shinyapps.io/HedonicValuationModel/ Previous Next

Directory All Alternatives Data Tools Sustainability Emerging Markets EU & North America Project Name Short Project Description URL Photography Tool: Black & White Conversion A basic photo editor to convert PNG pictures from color to Black and White /projects-1/photography-tool%3A-black-%26-white-conversion How much time do I have left? - Version 2 Visualizing and Quantifying our most valuable asset: "Time"; Version 2 http://how-much-time-do-i-have-left?---version-2 Prisoner's Dilemma: Player 2 Allowing users to participate in Robert Axelrod's 1980 Computer Tournament. /projects-1/prisoner's-dilemma%3A-player-2 Initial margin requirement for Derivative Trading A simplified VaR-based approach to calculate the initial margin requirement for Derivative Trading /projects-1/initial-margin-requirement-for-derivative-trading Expected Loss Calculator A simple tool to calculate the Expected Loss for a credit portfolio. /projects-1/expected-loss-calculator Value at Risk (VaR) for a portfolio Simple Tool using a historical simulation to find VaR http://value-at-risk-(var)-for-a-portfolio Game Theory: Prisoner's Dilemma Strategies Tools Recreating and Simulating Robert Axelrod's 1980 Computer Tournament. /projects-1/game-theory%3A-prisoner's-dilemma-strategies-tools How Much Time Do I have left? Visualizing and Quantifying our most valuable asset: "Time" /projects-1/how-much-time-do-i-have-left%3F Hollywood Boulevard to Wall Street: Futurism in Movies and Tech-Stock Prices This study investigates the relationship between the box office sales of futurism-themed movies and the performance of the tech stock index. /projects-1/hollywood-boulevard-to-wall-street%3A-futurism-in-movies-and-tech-stock-prices frankenstein.io - Draft 1 Restructuring & Simplifying "Frankenstein codes" /projects-1/frankenstein.io---draft-1 Data Visualization of the Dynamic Efficiency of Oil and Gas Production in Ghana A comprehensive tool for understanding the Real-time Efficiency of Oil and Gas production in Ghana /projects-1/data-visualization-of-the-dynamic-efficiency-of-oil-and-gas-production-in-ghana Hedonic Valuation Model: Real Estate in Zurich With significant portions of banks portfolios consisting of mortgage loans, it is paramount to develop a strong model for valuating real estate. /projects-1/hedonic-valuation-model%3A-real-estate-in-zurich Manipulating File Paths: Backward to Foward Slashes A program made to convert backward slashes in file path names to foward slashes. Targeted for Windows users when copying paths to R or Pthon. /projects-1/manipulating-file-paths%3A-backward-to-foward-slashes Beta of Fan Milk Ltd (FML): Ghana Stock Exchange (GSE) Finding the Beta of FML on the GSE using Python (Jupyter Notebook) /projects-1/beta-of-fan-milk-ltd-(fml)%3A-ghana-stock-exchange-(gse) Fixed Deposits Offers in Ghana A simple directory that shows Fixed Deposit offers in Ghana /projects-1/fixed-deposits-offers-in-ghana Plain Vanilla Bond Price Calculator A web application that takes the arguments of FV, Coupon Rate, YTM and Periods to price a Plain Vanilla Bond /projects-1/plain-vanilla-bond-price-calculator Convering Excel to CSV: Web Application A basic Web application written in HTML and Javascript to convert excel files to CSV. /projects-1/convering-excel-to-csv%3A-web-application Electricity Consumption as a proxy of production: Draft 1 Using publicly available data on Swiss Power Consumption, this exploration seeks to identify an association with power consumption and select firms output /projects-1/electricity-consumption-as-a-proxy-of-production%3A-draft-1 Ghana Stock Exchange: Real-Time Prices Web App V1 A basic web-application to find real time summaries of stocks on Ghana's Stock Exchange (GSE) /projects-1/ghana-stock-exchange%3A-real-time-prices-web-app-v1 Do Sustainable Funds in Switzerland outperform the Market? What is the performance of "sustainable" funds in relation to the market? Let's explore the case of the SIX Swiss Exchange /projects-1/do-sustainable-funds-in-switzerland-outperform-the-market%3F Dynamic View of Trading Hours: SIX Swiss Exchange V1 Dynamic View of the opening and closing hours of the SIX Swiss Stock exchange for 2024. Additionally, current summary of the market's activity is stated. /projects-1/dynamic-view-of-trading-hours%3A-six-swiss-exchange-v1 Sustainability Dimensions of Stocks on the SIX:Render 3 Quantitatively assessing Brundtland's Dimensions (1987). The case of the SIX https://www.akweidata.com/sixsustainabilitydimensions Web-Scrapper V1: Web Application Web Application for web-scrapping news articles /projects-1/web-scrapper-v1%3A-web-application Is ignorance truly bliss? Investigating the link between the lack of general information and the conception of the economy in Ghana. Project from 2018 /projects-1/is-ignorance-truly-bliss%3F- Alternative Data Regressor: V1 A Python Program to attain a linear regression of some alternative data against financial asset prices . A CSV file is the input. The output is the regression results. /projects-1/alternative-data-regressor%3A-v1 Alternative Data Regressor Framework: Flow Chart A framework for linear regression of alternative data against financial asset prices - the flow chart /projects-1/alternative-data-regressor-framework%3A-flow-chart Paradox of Choice and Utility Maximization: Music Traditional Asset Pricing models are conceptually based on utility maximization. However, what about the role of the quantity of choices in utility maximization? /projects-1/paradox-of-choice-and-utility-maximization%3A-music ESG Strategies: Passive and Active Management Do the laws of passive and active strategies also affect sustainability investing? /projects-1/esg-strategies%3A-passive-and-active-management Web scrapping Box Office Sales A python code used to web scrape data from Box Office Mojo's Website. /projects-1/web-scrapping-box-office-sales Alternative Data Regressor Framework: Draft 1 A framework for linear regression of alternative data against financial asset prices /projects-1/alternative-data-regressor-framework%3A-draft-1 Scrapping Oil related articles Run on python via GoogleCollab /projects-1/scrapping-oil-related-articles Sustainability Dimensions of Stocks on the SIX:Render 2 Quantitatively assessing Brundtland's Dimensions (1987). The case of the SIX /projects-1/sustainability-dimensions-of-stocks-on-the-six%3Arender-2 Smartphone App for University Students An all-purpose app for Ashesi students. Project from 2017 /projects-1/smartphone-app-for-university-students Proving the Butterfly Effect Within the context of metreology and physics, we can explore the butterfly effect /projects-1/proving-the-butterfly-effect Cocoa Production: Ghana and Ivory Coast - Historic Trend Work in progress /projects-1/cocoa-production%3A-ghana-and-ivory-coast---historic-trend Cocoa Production: West Africa - 2022 Work in progress /projects-1/cocoa-production%3A-west-africa---2022 Cocoa Production: Ghana and Ivory Coast - 2022 Summary of Cocoa Production in Ghana and Ivory Coast in 2022. /projects-1/cocoa-production%3A-ghana-and-ivory-coast---2022 Commentary: Washington’s Decision to “Normalize” Relations with Cuba..." An economic commentary on the article "Washington’s Decision to “Normalize” Relations with Cuba: Impede China’s Growing Influence in Latin America" /projects-1/commentary%3A-washington%E2%80%99s-decision-to-%E2%80%9Cnormalize%E2%80%9D-relations-with-cuba...%22 Commentary: Brexit could lead to recession, says Bank of England An economic commentary on the article "Brexit could lead to recession, says Bank of England" /projects-1/commentary%3A-brexit-could-lead-to-recession%2C-says-bank-of-england Commentary: Ghana fixes new cocoa price to control smuggling An economic commentary on the Article, "Ghana fixes new cocoa price to control smuggling" /projects-1/commentary%3A-ghana-fixes-new-cocoa-price-to-control-smuggling Sustainability Dimensions of Stocks on the SIX:Render 1 Quantitatively assessing Brundtland's Dimensions (1987). The case of the SIX http://sustainability-dimensions-of-stocks-on-the-six%3Arender-1 The Solow Model and Human Capital in Developing Economies How can human capital enrichment lead to long-run economic growth? /projects-1/the-solow-model-and-human-capital-in-developing-economies Scrapping Data using Python A Python application designed to generate a histogram depicting the frequency of articles published on Google News in 2022 concerning '@celebjets'. /projects-1/scrapping-data-using-python Dynamic View of Ghana's Unemployment Investigating the trend and segmentation of employment in Ghana /projects-1/dynamic-view-of-ghana's-unemployment Google News Scrapper Scrape Google News articles for a particulair keyword and date range /projects-1/google-news-scrapper Dynamic view of Ghana's Insurance Industry Work in progress /projects-1/dynamic-view-of-ghana's-insurance-industry Snapshot Macroeconomic Summary of ECOWAS States: 2022 As at the end of 2022, this is was the macroeconomic status of each ECOWAS state http://snapshot-macroeconomic-summary-of-ecowas Dynamic Forestry and Agricultural Summary of ECOWAS states Work in progress /projects-1/dynamic-forestry-and-agricultural-summary-of-ecowas-states Financial Performance of Ghana's political regimes from 1960 - 2000 Analysis of Economic Growth in Ghana, 1960 – 2000 – ARYEETEY & FOSU /projects-1/financial-performance-of-ghana's-political-regimes-from-1960---2000 Dynamic view of Ghana's Forestry Work in progress /projects-1/dynamic-view-of-ghana's-forestry Project Name Short Project Description URL Photography Tool: Black & White Conversion A basic photo editor to convert PNG pictures from color to Black and White /projects-1/photography-tool%3A-black-%26-white-conversion How much time do I have left? - Version 2 Visualizing and Quantifying our most valuable asset: "Time"; Version 2 http://how-much-time-do-i-have-left?---version-2 Prisoner's Dilemma: Player 2 Allowing users to participate in Robert Axelrod's 1980 Computer Tournament. /projects-1/prisoner's-dilemma%3A-player-2 Initial margin requirement for Derivative Trading A simplified VaR-based approach to calculate the initial margin requirement for Derivative Trading /projects-1/initial-margin-requirement-for-derivative-trading Expected Loss Calculator A simple tool to calculate the Expected Loss for a credit portfolio. /projects-1/expected-loss-calculator Value at Risk (VaR) for a portfolio Simple Tool using a historical simulation to find VaR http://value-at-risk-(var)-for-a-portfolio Game Theory: Prisoner's Dilemma Strategies Tools Recreating and Simulating Robert Axelrod's 1980 Computer Tournament. /projects-1/game-theory%3A-prisoner's-dilemma-strategies-tools How Much Time Do I have left? Visualizing and Quantifying our most valuable asset: "Time" /projects-1/how-much-time-do-i-have-left%3F frankenstein.io - Draft 1 Restructuring & Simplifying "Frankenstein codes" /projects-1/frankenstein.io---draft-1 Data Visualization of the Dynamic Efficiency of Oil and Gas Production in Ghana A comprehensive tool for understanding the Real-time Efficiency of Oil and Gas production in Ghana /projects-1/data-visualization-of-the-dynamic-efficiency-of-oil-and-gas-production-in-ghana Hedonic Valuation Model: Real Estate in Zurich With significant portions of banks portfolios consisting of mortgage loans, it is paramount to develop a strong model for valuating real estate. /projects-1/hedonic-valuation-model%3A-real-estate-in-zurich Manipulating File Paths: Backward to Foward Slashes A program made to convert backward slashes in file path names to foward slashes. Targeted for Windows users when copying paths to R or Pthon. /projects-1/manipulating-file-paths%3A-backward-to-foward-slashes Beta of Fan Milk Ltd (FML): Ghana Stock Exchange (GSE) Finding the Beta of FML on the GSE using Python (Jupyter Notebook) /projects-1/beta-of-fan-milk-ltd-(fml)%3A-ghana-stock-exchange-(gse) Fixed Deposits Offers in Ghana A simple directory that shows Fixed Deposit offers in Ghana /projects-1/fixed-deposits-offers-in-ghana Plain Vanilla Bond Price Calculator A web application that takes the arguments of FV, Coupon Rate, YTM and Periods to price a Plain Vanilla Bond /projects-1/plain-vanilla-bond-price-calculator Convering Excel to CSV: Web Application A basic Web application written in HTML and Javascript to convert excel files to CSV. /projects-1/convering-excel-to-csv%3A-web-application Ghana Stock Exchange: Real-Time Prices Web App V1 A basic web-application to find real time summaries of stocks on Ghana's Stock Exchange (GSE) /projects-1/ghana-stock-exchange%3A-real-time-prices-web-app-v1 Sustainability Dimensions of Stocks on the SIX:Render 3 Quantitatively assessing Brundtland's Dimensions (1987). The case of the SIX https://www.akweidata.com/sixsustainabilitydimensions Web-Scrapper V1: Web Application Web Application for web-scrapping news articles /projects-1/web-scrapper-v1%3A-web-application Alternative Data Regressor: V1 A Python Program to attain a linear regression of some alternative data against financial asset prices . A CSV file is the input. The output is the regression results. /projects-1/alternative-data-regressor%3A-v1 Alternative Data Regressor Framework: Flow Chart A framework for linear regression of alternative data against financial asset prices - the flow chart /projects-1/alternative-data-regressor-framework%3A-flow-chart Web scrapping Box Office Sales A python code used to web scrape data from Box Office Mojo's Website. /projects-1/web-scrapping-box-office-sales Scrapping Oil related articles Run on python via GoogleCollab /projects-1/scrapping-oil-related-articles Sustainability Dimensions of Stocks on the SIX:Render 2 Quantitatively assessing Brundtland's Dimensions (1987). The case of the SIX /projects-1/sustainability-dimensions-of-stocks-on-the-six%3Arender-2 Proving the Butterfly Effect Within the context of metreology and physics, we can explore the butterfly effect /projects-1/proving-the-butterfly-effect Google News Scrapper Scrape Google News articles for a particulair keyword and date range /projects-1/google-news-scrapper Project Name Short Project Description URL Data Visualization of the Dynamic Efficiency of Oil and Gas Production in Ghana A comprehensive tool for understanding the Real-time Efficiency of Oil and Gas production in Ghana /projects-1/data-visualization-of-the-dynamic-efficiency-of-oil-and-gas-production-in-ghana Beta of Fan Milk Ltd (FML): Ghana Stock Exchange (GSE) Finding the Beta of FML on the GSE using Python (Jupyter Notebook) /projects-1/beta-of-fan-milk-ltd-(fml)%3A-ghana-stock-exchange-(gse) Fixed Deposits Offers in Ghana A simple directory that shows Fixed Deposit offers in Ghana /projects-1/fixed-deposits-offers-in-ghana Ghana Stock Exchange: Real-Time Prices Web App V1 A basic web-application to find real time summaries of stocks on Ghana's Stock Exchange (GSE) /projects-1/ghana-stock-exchange%3A-real-time-prices-web-app-v1 Is ignorance truly bliss? Investigating the link between the lack of general information and the conception of the economy in Ghana. Project from 2018 /projects-1/is-ignorance-truly-bliss%3F- Scrapping Oil related articles Run on python via GoogleCollab /projects-1/scrapping-oil-related-articles Smartphone App for University Students An all-purpose app for Ashesi students. Project from 2017 /projects-1/smartphone-app-for-university-students Cocoa Production: Ghana and Ivory Coast - Historic Trend Work in progress /projects-1/cocoa-production%3A-ghana-and-ivory-coast---historic-trend Cocoa Production: West Africa - 2022 Work in progress /projects-1/cocoa-production%3A-west-africa---2022 Cocoa Production: Ghana and Ivory Coast - 2022 Summary of Cocoa Production in Ghana and Ivory Coast in 2022. /projects-1/cocoa-production%3A-ghana-and-ivory-coast---2022 Commentary: Ghana fixes new cocoa price to control smuggling An economic commentary on the Article, "Ghana fixes new cocoa price to control smuggling" /projects-1/commentary%3A-ghana-fixes-new-cocoa-price-to-control-smuggling The Solow Model and Human Capital in Developing Economies How can human capital enrichment lead to long-run economic growth? /projects-1/the-solow-model-and-human-capital-in-developing-economies Dynamic View of Ghana's Unemployment Investigating the trend and segmentation of employment in Ghana /projects-1/dynamic-view-of-ghana's-unemployment Dynamic view of Ghana's Insurance Industry Work in progress /projects-1/dynamic-view-of-ghana's-insurance-industry Snapshot Macroeconomic Summary of ECOWAS States: 2022 As at the end of 2022, this is was the macroeconomic status of each ECOWAS state http://snapshot-macroeconomic-summary-of-ecowas Dynamic Forestry and Agricultural Summary of ECOWAS states Work in progress /projects-1/dynamic-forestry-and-agricultural-summary-of-ecowas-states Financial Performance of Ghana's political regimes from 1960 - 2000 Analysis of Economic Growth in Ghana, 1960 – 2000 – ARYEETEY & FOSU /projects-1/financial-performance-of-ghana's-political-regimes-from-1960---2000 Dynamic view of Ghana's Forestry Work in progress /projects-1/dynamic-view-of-ghana's-forestry Project Name Short Project Description URL Initial margin requirement for Derivative Trading A simplified VaR-based approach to calculate the initial margin requirement for Derivative Trading /projects-1/initial-margin-requirement-for-derivative-trading Expected Loss Calculator A simple tool to calculate the Expected Loss for a credit portfolio. /projects-1/expected-loss-calculator Value at Risk (VaR) for a portfolio Simple Tool using a historical simulation to find VaR http://value-at-risk-(var)-for-a-portfolio Data Visualization of the Dynamic Efficiency of Oil and Gas Production in Ghana A comprehensive tool for understanding the Real-time Efficiency of Oil and Gas production in Ghana /projects-1/data-visualization-of-the-dynamic-efficiency-of-oil-and-gas-production-in-ghana Fixed Deposits Offers in Ghana A simple directory that shows Fixed Deposit offers in Ghana /projects-1/fixed-deposits-offers-in-ghana Do Sustainable Funds in Switzerland outperform the Market? What is the performance of "sustainable" funds in relation to the market? Let's explore the case of the SIX Swiss Exchange /projects-1/do-sustainable-funds-in-switzerland-outperform-the-market%3F Sustainability Dimensions of Stocks on the SIX:Render 3 Quantitatively assessing Brundtland's Dimensions (1987). The case of the SIX https://www.akweidata.com/sixsustainabilitydimensions ESG Strategies: Passive and Active Management Do the laws of passive and active strategies also affect sustainability investing? /projects-1/esg-strategies%3A-passive-and-active-management Scrapping Oil related articles Run on python via GoogleCollab /projects-1/scrapping-oil-related-articles Sustainability Dimensions of Stocks on the SIX:Render 2 Quantitatively assessing Brundtland's Dimensions (1987). The case of the SIX /projects-1/sustainability-dimensions-of-stocks-on-the-six%3Arender-2 Smartphone App for University Students An all-purpose app for Ashesi students. Project from 2017 /projects-1/smartphone-app-for-university-students Cocoa Production: Ghana and Ivory Coast - Historic Trend Work in progress /projects-1/cocoa-production%3A-ghana-and-ivory-coast---historic-trend Cocoa Production: West Africa - 2022 Work in progress /projects-1/cocoa-production%3A-west-africa---2022 Cocoa Production: Ghana and Ivory Coast - 2022 Summary of Cocoa Production in Ghana and Ivory Coast in 2022. /projects-1/cocoa-production%3A-ghana-and-ivory-coast---2022 Commentary: Ghana fixes new cocoa price to control smuggling An economic commentary on the Article, "Ghana fixes new cocoa price to control smuggling" /projects-1/commentary%3A-ghana-fixes-new-cocoa-price-to-control-smuggling Sustainability Dimensions of Stocks on the SIX:Render 1 Quantitatively assessing Brundtland's Dimensions (1987). The case of the SIX http://sustainability-dimensions-of-stocks-on-the-six%3Arender-1 Dynamic Forestry and Agricultural Summary of ECOWAS states Work in progress /projects-1/dynamic-forestry-and-agricultural-summary-of-ecowas-states Dynamic view of Ghana's Forestry Work in progress /projects-1/dynamic-view-of-ghana's-forestry Project Name Short Project Description URL Hedonic Valuation Model: Real Estate in Zurich With significant portions of banks portfolios consisting of mortgage loans, it is paramount to develop a strong model for valuating real estate. /projects-1/hedonic-valuation-model%3A-real-estate-in-zurich Electricity Consumption as a proxy of production: Draft 1 Using publicly available data on Swiss Power Consumption, this exploration seeks to identify an association with power consumption and select firms output /projects-1/electricity-consumption-as-a-proxy-of-production%3A-draft-1 Do Sustainable Funds in Switzerland outperform the Market? What is the performance of "sustainable" funds in relation to the market? Let's explore the case of the SIX Swiss Exchange /projects-1/do-sustainable-funds-in-switzerland-outperform-the-market%3F Dynamic View of Trading Hours: SIX Swiss Exchange V1 Dynamic View of the opening and closing hours of the SIX Swiss Stock exchange for 2024. Additionally, current summary of the market's activity is stated. /projects-1/dynamic-view-of-trading-hours%3A-six-swiss-exchange-v1 Sustainability Dimensions of Stocks on the SIX:Render 3 Quantitatively assessing Brundtland's Dimensions (1987). The case of the SIX https://www.akweidata.com/sixsustainabilitydimensions Web scrapping Box Office Sales A python code used to web scrape data from Box Office Mojo's Website. /projects-1/web-scrapping-box-office-sales Sustainability Dimensions of Stocks on the SIX:Render 2 Quantitatively assessing Brundtland's Dimensions (1987). The case of the SIX /projects-1/sustainability-dimensions-of-stocks-on-the-six%3Arender-2 Commentary: Washington’s Decision to “Normalize” Relations with Cuba..." An economic commentary on the article "Washington’s Decision to “Normalize” Relations with Cuba: Impede China’s Growing Influence in Latin America" /projects-1/commentary%3A-washington%E2%80%99s-decision-to-%E2%80%9Cnormalize%E2%80%9D-relations-with-cuba...%22 Commentary: Brexit could lead to recession, says Bank of England An economic commentary on the article "Brexit could lead to recession, says Bank of England" /projects-1/commentary%3A-brexit-could-lead-to-recession%2C-says-bank-of-england Sustainability Dimensions of Stocks on the SIX:Render 1 Quantitatively assessing Brundtland's Dimensions (1987). The case of the SIX http://sustainability-dimensions-of-stocks-on-the-six%3Arender-1 Project Name Short Project Description URL How much time do I have left? - Version 2 Visualizing and Quantifying our most valuable asset: "Time"; Version 2 http://how-much-time-do-i-have-left?---version-2 Prisoner's Dilemma: Player 2 Allowing users to participate in Robert Axelrod's 1980 Computer Tournament. /projects-1/prisoner's-dilemma%3A-player-2 Game Theory: Prisoner's Dilemma Strategies Tools Recreating and Simulating Robert Axelrod's 1980 Computer Tournament. /projects-1/game-theory%3A-prisoner's-dilemma-strategies-tools How Much Time Do I have left? Visualizing and Quantifying our most valuable asset: "Time" /projects-1/how-much-time-do-i-have-left%3F Hollywood Boulevard to Wall Street: Futurism in Movies and Tech-Stock Prices This study investigates the relationship between the box office sales of futurism-themed movies and the performance of the tech stock index. /projects-1/hollywood-boulevard-to-wall-street%3A-futurism-in-movies-and-tech-stock-prices Electricity Consumption as a proxy of production: Draft 1 Using publicly available data on Swiss Power Consumption, this exploration seeks to identify an association with power consumption and select firms output /projects-1/electricity-consumption-as-a-proxy-of-production%3A-draft-1 Dynamic View of Trading Hours: SIX Swiss Exchange V1 Dynamic View of the opening and closing hours of the SIX Swiss Stock exchange for 2024. Additionally, current summary of the market's activity is stated. /projects-1/dynamic-view-of-trading-hours%3A-six-swiss-exchange-v1 Web-Scrapper V1: Web Application Web Application for web-scrapping news articles /projects-1/web-scrapper-v1%3A-web-application Is ignorance truly bliss? Investigating the link between the lack of general information and the conception of the economy in Ghana. Project from 2018 /projects-1/is-ignorance-truly-bliss%3F- Alternative Data Regressor: V1 A Python Program to attain a linear regression of some alternative data against financial asset prices . A CSV file is the input. The output is the regression results. /projects-1/alternative-data-regressor%3A-v1 Alternative Data Regressor Framework: Flow Chart A framework for linear regression of alternative data against financial asset prices - the flow chart /projects-1/alternative-data-regressor-framework%3A-flow-chart Paradox of Choice and Utility Maximization: Music Traditional Asset Pricing models are conceptually based on utility maximization. However, what about the role of the quantity of choices in utility maximization? /projects-1/paradox-of-choice-and-utility-maximization%3A-music Web scrapping Box Office Sales A python code used to web scrape data from Box Office Mojo's Website. /projects-1/web-scrapping-box-office-sales Alternative Data Regressor Framework: Draft 1 A framework for linear regression of alternative data against financial asset prices /projects-1/alternative-data-regressor-framework%3A-draft-1 Scrapping Oil related articles Run on python via GoogleCollab /projects-1/scrapping-oil-related-articles Proving the Butterfly Effect Within the context of metreology and physics, we can explore the butterfly effect /projects-1/proving-the-butterfly-effect Scrapping Data using Python A Python application designed to generate a histogram depicting the frequency of articles published on Google News in 2022 concerning '@celebjets'. /projects-1/scrapping-data-using-python Google News Scrapper Scrape Google News articles for a particulair keyword and date range /projects-1/google-news-scrapper

Quant Projects View Directory Notable Projects Data Visualization of the Dynamic Efficiency of Oil and Gas Production in Ghana Zurich Real Estate Hedonic Valuation Model Real-time: Ghana Stock Exchange Data Viewer The Solow Model and Human Capital in Developing Economies Sustainability Dimensions of Stocks on the SIX:Render 4 Google News Scrapper Proving the Butterfly Effect Alternative Data Regressor: V1

< Back Prisoner's Dilemma: Player 2 Allowing users to participate in Robert Axelrod's 1980 Computer Tournament. Previous Next

< Back Snapshot Macroeconomic Summary of ECOWAS States: 2022 As at the end of 2022, this is was the macroeconomic status of each ECOWAS state *All data is in current US dollars. Sources: World Bank IMF Trading Economics Previous Next

< Back Financial Performance of Ghana's political regimes from 1960 - 2000 Analysis of Economic Growth in Ghana, 1960 – 2000 – ARYEETEY & FOSU "Economic Growth in Ghana, 1960 - 2000" by Ernest Aryeetey and Augustin Kwasi Fosu examines the fluctuating economic growth in Ghana over four decades, marked by frequent policy changes and military coups. The study highlights the transition of Ghana's economy and its impact on the livelihoods of its citizens. Period Key Factors Impact on Growth Post-Independence (1960-1965) Kwame Nkrumah implemented his 7-year Plan, emphasizing high investments into public infrastructure and industry creation. The economy grew rapidly due to the investments, but the high government spending led to inflation and a decline in living standards. Busia and the Military (1966-1971) Busia and the military regime ushered pro-private capital policies, devaluing the Ghanaian Cedi and liberalizing the external sector. The economy initially grew due to the pro-business policies, but the devaluation of the cedi caused inflation and public anger, leading to another coup d'état. The Era of Five Regimes (1972-1983) This period was marked by economic decline due to high government intervention policies, low productivity, and external shocks such as drought and food shortages. The economy contracted significantly during this period, with GDP growth averaging only 2.2% per year. Inflation soared to 112% in 1983, and the government deficit reached 17% of GDP. After the Economic Reforms (1984-2000) The government launched the Economy Recovery Program (ERP) under the World Bank and the IMF, which liberalized the economy and led to increased growth. The ERP helped to stabilize the economy and promote growth, with GDP growth averaging 5.3% per year during this period. Inflation fell from 112% in 1983 to 10% in 1992, and the government deficit was reduced to 4% of GDP. Previous Next

< Back Hollywood Boulevard to Wall Street: Futurism in Movies and Tech-Stock Prices This study investigates the relationship between the box office sales of futurism-themed movies and the performance of the tech stock index. This study investigates the relationship between the box office sales of futurism-themed movies and the performance of the tech stock index. Utilizing regression analysis across three models, the research reveals significant insights: Tech Movies and Tech Stock Index: A strong positive correlation was found between the box office sales of tech movies and the tech stock index, with an Adjusted R-squared value of 0.8263, indicating a substantial predictive power of tech movie sales on tech stock prices. Top 10 Box Office and Tech Stock Index: A broader analysis including the top 10 box office sales showed a positive but less pronounced impact on the tech stock index, suggesting that the influence of tech movies is more specific and potent. Tech Movies and General Market Index: Tech movie sales also positively correlate with the general market index, though the relationship is weaker compared to the tech-specific index. In essence, the findings suggest that futurism movies, particularly those in the tech genre, have a noticeable impact on tech stock prices, offering valuable insights into the interplay between behavioral bias, entertainment and financial markets econometrics_project .pdf Download PDF • 542KB Previous Next

< Back Is ignorance truly bliss? Investigating the link between the lack of general information and the conception of the economy in Ghana. Project from 2018 I am an avid lover of George Orwell’s book 1984. Within the book, a major concept that plays on is that ignorance is bliss. Hence, people living in poverty (the proles) with limited availability to information on the economy somehow live happily. So, I started to ponder upon how such a concept plays within my continent. Is ignorance truly bliss? With poverty in Africa being so high, is the absence of information about the economy to the general members of the society the cause of social stability in spite of economic turmoil (Asogwa, Eze, & Ezema, 2017)? When the economy is in shambles and the political sphere is in disarray are we still under the misconception that all is well? Does happiness exist in poverty?(Graham, 2011) Research Topic: Is ignorance truly bliss? Investigating the link between the lack of general information and the conception of the economy in Ghana. Is the conception of the present economic condition in a country by members of the public associated with how often they use the internet as a source of news? Data & methods This sample is taking from the Afro – barometer. It depicts 2400 respondents from Ghana answering questions pertaining to their perception of the economy and their use of the internet as a source of news. In relation to the research topic, investigating the use of the internet as a source of news is what is being presented as “general information.” Other sources such as the radio (Fombad, Madeleine, & Jiyane, 2016) or newspapers (Omolewa, 2008) are not suitable sources of information for this project. However, the nature of the internet makes it the best source of estimating ones general knowledge (Stilwell, 2018) The observations from this sample were achieved via surveys. Thus, using the two categorical variables of “Conception of the economy” and “frequency of the use of the internet as a source of news.” According to the Chi – squared test, there is an association between these two variables Results: Univariate Analysis From the graph above, we come to find that 85% of Ghanaians have a negative conception of the economy whereas for positive conception it is only 15%. As depicted above, we come to find that within the rural setting there is a greater positive conception of the economy as compared to the urban setting. Results: Bivariate Analysis Key Findings From the univariate analysis key proportions are brought to light. From the sample, most Ghanaians have a negative conception of the economy. The Urban rural relationship simply sheds light to the relative differences –this graph is a bonus feature. However, we come to find that per or Bivariate Analysis there is an association between “Perception of the economy” and “Use of the internet as a source of Information” It must be said, the association is not extremely strong – although there is still an association Moreover, as the use of the internet increases, the more likely one perceives the Ghanaian economy in a positive manner As the use of the internet decreases, the more likely one perceives the Ghanaian economy in a negative manner Conclusion The overarching question from my research question being Is ignorance bliss appears to be less likely the case in Ghana –using the internet as a source of awareness. I have come to find out that from my sample, the lower one’s usage of the internet as a source of news, the more likely they are to rate the economy negatively. Thus, ignorance is not bliss, but awareness is rather. Why is this the case, contrary to other research works and the 1984 book? Two huge lurking variables are the availability of information and technology in low income households as well as and ones competency with the internet due to their education level (Ajakaiye, Olu, & Kimenyi, 2011). Hence, with a low income and inability to use the internet most likely due to a low education level, such a person is more likely to be living in undesirable conditions, thus, they have a negative conception of the economy. However, this claim arising from the lurking variables can be refuted with the simple logic that this paradox of “Poverty and happiness/bliss” has been proven (Graham, 2011) So why are the findings as such? Why is it so that the higher one’s usage of the internet as a source of news, the more likely they are to have a positive conception of the Ghanaian economy? This is so because the Ghanaian economy is relatively perfoming well. Though there is much poverty and low infrastructure capacity, there is still a significant amount of development. With a strong economic growth and increasing standards of living, the state o the Ghanaian economy is not as bad as many would claim – especially in relation to other low income countries. Hence, the higher one’s use of the internet, the more likely they are to know about the economy, especially in relation to other low income countries. They come to understand that all is not as bad as it seems, hence, tend to have a higher perception of the Ghanaian economy. Thus, the answer to the overarching question Is ignorance bliss? Yes – but only if things are going bad. In the case of Ghana’s economy, things are actually going well, hence, ignorance is not bliss in this case. So, fellow Ghanaians, put the pitchforks down, for no revolts are required here. The Ghanaian economy is doing well and those with access to the best source of information – the internet –are most likely to know this, hence are more likely to have a more positive conception of the economy. This research has introduced another aspect to the age old question of, Is ignorance bliss? By depicting that such is most likely to be the case if and only if the surroundings are in a tumultuous state. References Ajakaiye, Olu, and Mwangi S. Kimenyi. “Higher Education and Economic Development in Africa: Introduction and Overview.” Journal of African Economies 20, no. suppl_3 (August 1, 2011): iii3–13. https://doi.org/10.1093/jae/ejr027 . Asogwa, Brendan Eze, and Ifeanyi Jonas Ezema. “Freedom of Access to Government Information in Africa: Trends, Status and Challenges.” Records Management Journal 27, no. 3 (August 18, 2017): 318–38. https://doi.org/10.1108/RMJ-08-2015-0029 . Fombad, Madeleine C., and Glenrose Veli Jiyane. “The Role of Community Radios in Information Dissemination to Rural Women in South Africa.” Journal of Librarianship and Information Science, September 22, 2016, 0961000616668960. https://doi.org/10.1177/0961000616668960 . Graham, Carol. “Adaptation amidst Prosperity and Adversity: Insights from Happiness Studies from around the World.” The World Bank Research Observer 26, no. 1 (February 1, 2011): 105–37. https://doi.org/10.1093/wbro/lkq004 . OMOLEWA, MICHAEL. “ADULT LITERACY IN AFRICA: THE PUSH AND PULL FACTORS.” International Review of Education / Internationale Zeitschrift Für Erziehungswissenschaft / Revue Internationale de l’Education 54, no. 5/6 (2008): 697–711. Stilwell, Christine. “Information as Currency, Democracy, and Public Libraries.” Library Management 39, no. 5 (April 18, 2018): 295–306. https://doi.org/10.1108/LM-08-2017-0078 . Previous Next

< Back Commentary: Ghana fixes new cocoa price to control smuggling An economic commentary on the Article, "Ghana fixes new cocoa price to control smuggling" Date the commentary was written: 0 6/ 12 /2015 Read the original article on Theafricareport.com : Ghana fixes new cocoa price to control smuggling | West Africa by Dasmani Laary - 05.10.2015 The article under consideration is about an increase in the fixed price of cocoa in Ghana in order to curb the smuggling of cocoa into Ivory Coast. Ivory Coast and Ghana share a boarder cutting through their respective cocoa plantations hence, smuggling easily occurs. The article is also about a subsidy granted to the cocoa farmers to raise their output. The Ghanaian government imposed a higher fixed price of cocoa, this can viewed as the government imposing a higher minimum price on cocoa as the fixed price is above the equilibrium price. A fixed price is a market price imposed by the government and producers are only allowed to sell at exactly that price. Cocoa Board is a government-controlled institution, fixes the buying price for cocoa in Ghana. Thus the cocoa market in Ghana is planned. The price-fixing is to protect cocoa farmers from volatile prices on the world market as the article says. From the article under consideration, the new fixed price of cocoa per ton is $1759 is an increase from the former $1444. This increase would prevent cocoa farmers from smuggling their cocoa to Ivory Coast to sell it at the once better price of $1718 per ton. Price elasticity of demand or supply refers to the responsiveness of quantity demanded or quantity supplied due to a change in price. The price elasticity of demand for cocoa is relatively elastic as Ivorian (and South American cocoa) are perfect substitutes. The supply of Ghanaian cocoa is also elastic because of the smuggling of cocoa between Ghana and Ivory Coast which depends on price hence in effect affects the supply of Ghanaian cocoa positively or negatively. So if the price is high in Ghana (higher than Ivory Coast Cocoa) smuggling from Ghana to Ivory Coast would be curbed and rather cocoa grown in Ivory Coast would be smuggled into Ghana hence increasing the supplied quantity of Ghanaian Cocoa. The effect of increasing the fixed price is shown on this diagram: Figure 1: Increasing the fixed price As a result of this increase in quantity supplied there would be an excess supply (QS1 to QS2) of Ghanaian cocoa. However cocoa can be stored for a long time without losing its quality, but the government would then need to spend more on storage facilities (as the article makes reference to warehouses being built). An increase in the fixed price would also make Ghanaian cocoa less competitive globally, as Ivorian cocoa (and South American cocoa) would be winning the price war. This may be prove costly and highly inefficient for the Ghanaian government as 15% of their GDP alone is from cocoa. However the aim of increasing the fixed price was to curb the smuggling of cocoa to Ivory Coast from Ghana and this action would achieve this aim. But not only would the policy do so, but it would also stimulate the smuggling of cocoa from Ivory Coast to Ghana, reversing the tables. Although I have discussed the decrease in international competitiveness of Ghanaian cocoa (as PED is relatively elastic) that does not necessarily mean there shall be a decrease in revenue. Firstly at the old and new fixed price are relatively higher than the equilibrium price, hence PED may be inelastic at those high prices. Also, due to multiple contracts and deals in place with cocoa processing firms, Ghanaian farmers would still be able to sell to their previous customers for example Nestle. Not only that, but as there would be a higher supply of cocoa from Ghana, Ghanaian farmers would be able to meet their contract obligations with those cocoa processing firms whereas due to the reduction in cocoa in Ivory Coast, Ivorian farmers may not meet their obligations hence their deals and contracts would be passed on to Ghanaian firms In a bid to further increase the supply of cocoa in Ghana (as the article refers to the targeted 900,000 tones output for the 2015/2016 which is an increase from the actual 700,000 output of the previous year) the government is giving cocoa farmers a subsidy. The bonus of 5 cedi per bag of 64 kilogrammes, is a subsidy per unit. A subsidy is financial aid given to producers by the government in order to decrease their cost of production and in effect increase their total output. The effect of a subsidy is shown in Figure 2; F igure 2: Effect of subsidy in the Ghanaian Cocoa Market As illustrated in Figure 2 producers (Ghanaian farmers) would have a higher revenue due the subsidy, however the Ghanaian government would have to pay a lot for this subsidy. Either way, this decreases the cost of production for farmers and in effect are able to produce more cocoa. The combination of the two policies discussed in this paper is simply going to lead to a very large increase in supply of cocoa in Ghana. However this may not be so beneficial for all stakeholders. Initially farmers may enjoy larger incomes, but may have to eventually sell off the cocoa in excess supply at a lower price due to expensive storage. Government expenditure would increase due to the subsidy and the stabilization fund discussed in the article. However if the demand for cocoa continues to increase in the global market, Ghanaian government and farmers would benefit greatly. Previous Next

< Back Proving the Butterfly Effect Within the context of metreology and physics, we can explore the butterfly effect Exploration took place between Feburary 2016 and March 2017. Report was finalized on the 23 March 2017. Introduction Football is an exciting game. However, being an Arsenal fan, football turns out to be an extremely unpredictable and painful affair at times. Arsenal FC is a North London team which plays in the English Premier League. On the 2nd of March 2016, Arsenal played a game against a relatively weaker side, Swansea. Most predictions favored Arsenal, but as usual, Arsenal are just full of surprises. They lost pathetically. Appalled by the results and Arsenal’s inconsistency, I started to abstractly wonder what I could have done to change the score. Is it possible that if I had simply worn a different shirt at home whilst watching the game (although I live in Berlin and the game was in the UK), the results could have been different? I brought up this topic with a friend of mine. He simply rendered such a claim to be absurd. Even I believed it was absurd. But what if? We argued “hypothetically” around the topic for a while, up until he started to support my argument as he remembered the title of Edward Lorenz’s paper about chaos theory; “Does the flap of a butterfly’s wings in Brazil set of a Tornado in Texas?” Edward Lorenz was a mathematician, meteorologist and Math professor at MIT. He is generally accredited with establishing Chaos Theory, specifically the Butterfly Effect. The Butterfly effect is a “branch” of Chaos theory which observes extreme sensitivity dependent upon initial conditions. So, with the introduction of Chaos Theory to aid my argument, it can be mathematically “proven” that Arsenal could have won if I had simply worn a different shirt! Certainly an absurd proposition. Nonetheless, the concept of the butterfly effect does have significant applications accross multiple fields, namely meteorology, economics , physics, biology and psychology. What is the Butterfly Effect? I have earlier been interchangeably using the terms Chaos Theory and the Butterfly Effect. However, in this exploration specifically viewing the Butterfly effect. The Butterfly effect is a branch of Chaos Theory in which sensitivity of a dynamic system is observed by changing initial conditions in a small amount. Like the flap of a butterfly’s wings in the atmosphere causing a tornado. In truth, and as Edward Lorenz said, such a statement is quite absurd. However, that does not make it impossible. Edward Lorenz discovered the Butterfly Effect by accident. He was observing convection currents and other atmospheric conditions. Consequently, he devised 3 differential equations and made his famous Strange Attractor (Figure 1) also known as Lorenz Attractor (this shall be discussed later on) which described his observations. He then decided to print out the solution of his differential equations (the numerical iterations of his Strange Attractor) that he made on his computer. During the printing time, Edward decided to get a cup of coffee. When he came back to collect his printed solutions he was shocked to find an entire set of different numerical solutions and thus a different Strange Attractor printed out from what he had on his computer screen. He quickly came to learn that his set of initial values were rounded up when he excuted the print. Typically, rounding up the values should not be an issue because such small changes are generally considered as insignificant. However he found out that an extremely small change in the initial values for the specific atmospheric conditions model being observed actually led to a completely different weather forecast. Figure 1 *Figure 1 from https://math.dartmouth.edu/archive/m53f07/public_html/ An attractor is simply a set of numerical values towards which a system tends to evolve for a wide variety of starting conditions of a dynamic system. In mathematics, a dynamic system is a system in which a function describes the time dependence of a point in a geometrical space. Thus the input of the function is time. Examples of a dynamic system include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, etc. Abstractly, an attractor can be viewed as the trajectory of a moving marble in a bowl, where the center of the bowl is the point at which the system evolves about. But what exactly is the Strange Attractor? Well it is the solution to Lorenz’s three differential equations. This is later explained in my exploration. Due to the aesthetic shape of the attractor, the name Butterfly Effect was assigned to his discovery of extreme sensitivity in chaotic systems. But one attractor proves nothing about the butterfly effect. The butterfly effect is only proven when another attractor is made, but using slightly different initial values. Then the difference in distance between the two separate attractors are calculated with respect to time. By observing the graph of their distance differences, only then is the beauty of chaos and the butterfly effect proven. Lorenz equations were used to generate plots for the y variable. The initial conditions for x and z are kept the same but those for y are slightly changed. Such slight differences in the initial values gave rise to completely different solutions. Chaos must not be associated with disorder or randomness. What one must understand about chaos is that there is order in chaos. With respect to Edward Lorenz’s work on the Butterfly Effect and that of my research, the systems are deterministic, meaning that their future is fully determined by their initial conditions with no random elements involved. Furthermore, as defined by Edward Lorenz, Chaos: When the present determines the future, but the approximate present does not approximately determine the future . Chaos theory is a new field in abstract mathematics, hence many mathematicians and physicist have different views on the topic. However, in this investigation, I shall not be diving into the great abstract depths of Chaos Theory, hence my applications and explanations of Chaos Theory is supported by definitions and concepts which are generally agreed on by most respected academic institutions. Aim of Exploration The aim of this exploration is to prove the Butterfly Effect. I shall do this by mathematically observing chaotic systems. As earlier mentioned, the butterfly effect can be applied to meteorology, economics, physics, but also; biology, psychology and many more. In this exploration I shall be observing the fields of meteorology and physics. . In the field of meteorology, I shall vividly explain and prove the Butterfly effect just as Edward Lorenz did. In the field of physics, I have used an online simulator, to simulate a double pendulum experiment. I shall then explore its sensitive and chaotic nature. The other fields may be occasionally referred to, but I shall not be mathematically observing them. For example, the application of the Butterfly effect in psychology is more abstract than mathematical. Furthermore, more abstract and creative claims of the Butterfly effect, such as time travel (like the movie “Back to the Future”... or better yet, my experience with Arsenal), were extremely small changes in the past can completely alter the once known future are very interesting, but personally claims of mathematical applications in the chaos found in those fields appear as pseudoscience instead of genuine mathematical evidence. Application in Meteorology “Does the flap of a butterfly’s wings in Brazil set of a Tornado in Texas?” I shall now vividly go through the steps and procedures Edward Lorenz used to create his strange attractor. Whilst studying thermal variations in an air cell underneath a thunderhead, he came up with these three ordinary differential equations. An ordinary differential equation is a differential equation containing one or more functions of one independent variable and its derivatives Lorenz’s system of ODEs were; σ,ρ and β are positive parameters which represent physical characteristics of air flow. x corresponds to the amplitude of convective currents, y to the temperature change between rising and falling currents and z to the deviation of the temperature from the normal temperature in the cell. With these atmospheric variables (and more), a weather forecast can be made. For his attractor, the parameters of σ,ρ and β were 10, 28 and 8/3 respectively. Solving Differential equations In this research I shall be working with Ordinary Differential Equations (ODEs). In layman terms, an ODE refers to an equation in which one is not solving for a value or values for x and y but rather for the function f(x) itself by working with its derivatives and there is only one independent variable. If there is more than one independent variable, the differential equation is called a Partial Differential Equation (PDE), but such are not being discussed here. An example of an ODE is; In this example the solution is not unique as, intuitively one can solve for f(x) and find out that the equation satisfies e^(-3x) or e^x and an infinitely amount of other functions. As seen below f(x)= e^x is indeed a solution. Considering f^'' (x)= e^x and f^' (x)= e^x The solution exists as a set of functions. More information, is needed to find out the specific function being viewed. But most differential equations cannot be solved intuitively. Hence there are many other ways of finding the solution(s) of an ODE. Mainly by a system of integration, Euler’s Method, calculated guesses, vector fields or numerical integration . I shall be using Numerical Integration. This method approximates the values for solutions of differential equations, hence, recovers the original function. Numerical Integration is done by using numerical programs. I am using an ODE solver from the program Octave. Numerical integration is the method Octave uses to solve ODEs. I shall now explain how numerical integration solves Lorenz’s differential equations Above is the general rule of integration. However, this rule is ironically not used in numerical integration. Below is c(t) the solution that I shall be trying to find. I am working in 3D plane hence points have the coordinates x,y,z. Furthermore, with Lorenz’s system of ODEs (equations (1), (2) and (3)), we know what c'(t) is Furthermore, Now using the first ODE, I shall reveal how the approximations are done Now, the vital assumption or better said approximation taken during numerical integration is that t_i+h=t_(i+1). Furthermore, as I am solving for x(t_(i+1) ), I shall multiply both sides by h, And eventually by rearranging the equation I get: As you can see from the expression above, in order to find an x component (also for y and z components) one must know what the previous value was. We cannot find t_(i+1) if we do not know t_i. Thus, this series of approximations relies heavily on what the initial values are. So, from Lorenz’s work, I know that the initial values for x,y,z are respectively are 0, 0.0001 and 0 (he arbitrarily used these). As every other value technically relies on the initial value, I would numerically (instead of algebraically as above) show how is found by using Using the expression above, Just as a reminder the parameters are 10, 28 and respectively. And is simply the initial value of the given component. h is simply an extremely small value (0.000001) Just as I have solved for x(t_1) and I can also find the y and z components of c(t_1) and all other successive solutions. From c(t_1), I can find c(t_2), then c(t_3)…and so on. This is what is done by Octave. These numerical solutions are eventually graphed and the Strange Attractor is made. (Figure 2) Figure 2 But creating one attractor does not prove anything. Another attractor must be created, with the same parameters, except; the initial value must have an extremely slight change from the other attractor. Using Octave, (a graphing software) I found the solution to Lorenz differential equations shown in Figure 2. However I need to explain some of these computations I made. I created a trajectory that runs from 0 to 100 seconds and between these times I specified for 1000 points. The initial values I used for x,y,z are respectively are 0, 0.0001 and 0 respectively. Just as Lorenz did I would create another attractor using a slightly different y initial value. Only the initial y value is being changed. One should be expecting a very little change or at most a slight shift in every point in the y direction by just that amount. But that is not the case whatsoever. In figure 2 I used a y value of 0.0001, but for the second attractor (figure 3) I have changed it to 0.001. Due to the quality of my screenshots and the nature of strange attractors one may not see any difference between figure 2 and figure 3. But there is a big difference. Figure 3 Now I shall graph the difference between the two attractors. As both attractors are sets of numerical values with respect to time, I can find the distance between the points on the two different attractors at the same time. Hence I shall be graphing time against change in distance. Every iteration can be seen as a point x,y,z and furthermore a vector all with respect to time. I shall once again use Octave to find the differences between the two attractors. Nonetheless, I shall explain how it is done my Octave. One must visualize both attractors existing on the same graph. Every point is defined as a vector with respect to time. Thus, I am simply using the same input value t on both attractors and finding their resultant vector. Now, I shall find the magnitude of that resultant vector, which would be the distance between the two points. So arbitrarily I shall refer to the first attractor as A and the second as B. So for every iteration, this is done to find the change in distance. Below is the graph of time against change in distance for my 10000 iterations. Figure 4 This unorthodox and unforeseen differences in distance is what proves that a system is sensitive as a small change in the initial values leads to a very different solution or in Lorenz’s case, an entirely different weather forecast. This proves the butterfly effect. Application in Physics “Can the drilling of oil in Ghana cause an earthquake in Italy?” As you can see I have also decided to propose my own absurd question to open up the Butterfly Effect’s application to the field of physics. Using an online simulator, I have decided to mathematically observe the chaotic nature of a double pendulum set up, with regard to small changes in the initial conditions. This online simulator is from the website, http://www.tapdancinggoats.com . Although the name of the website is quite…interesting, the double pendulum simulator on the site is actually sublime. This simulator was implemented in HTML5. A double pendulum setup is simply two pendulums attached end to end. As this system is chaotic, a set of ODE’s can be used to determine its motion. That’s what I will be attempting to do. A screenshot of the simulator can be seen below: Figure 5 As seen in figure 5, the conditions mass, initial angles, initial angular velocities (ω) and length of strings can all be controlled. The motion of this simulation is restricted to 2 dimensions only. Before formulating the differential equations, I would illustrate the sensitivity of a double pendulum experiment by viewing its trajectories. I shall keep all variables constant except the initial angle 〖 θ〗_2 which is visually illustrated in Figure 6. Figure 6 Below are two trajectories I produced with two different θ2 values. The initial values for θ2 are 90 and 91 degrees respectively. With 1 degree being their difference. I allowed both simulations to run for 15 seconds and then I took a screenshot of their trajectories. Below are my observations: The orange circles represent angular velocities (ω). Both initial velocities were set at 1 degree per second. Both point masses m_(1 ) and m_2 in both simulations are 1kg each. l_1 and l_2 are 20 cm each, in the two simulations. A small change of 1 degree has caused a huge difference in the trajectories and angular velocities. This system is sensitive, which is a characteristic of a chaotic system. I am quite shocked (considering I also made the angular velocity just 1 degree per second) with the large difference created by literally one small change in the initial conditions. Now I shall start formulating the differential equations which describe the double pendulum system. So as illustrated in Figure 6, I was working with the two point masses m_(1 ) and m_2. These are attached to l_1 and l_2 respectively. These strings/wires are assumed to be massless for experimentation sake. Furthermore, the angles made with the vertical are denoted by 〖 θ〗_1 and 〖 θ〗_2 .The force of gravity is denoted with g. With respect to a Cartesian plane, the x position of the bobs (the masses on the pendulum) reveals where it is horizontally. And that of the y position reveals where the bobs are vertically. As I already mentioned, the motion of the pendulum was restricted to 2 dimensions only. The subscripts 1 and 2 represents the first and second bobs respectively. Positions of the bobs are given by These formulas come about from visualizing the position of the bobs as points on a Cartesian plane, which change depending on the angles θ_1 and〖 θ〗_2. Now to work out the potential energy (PE) in the system: Note: Formulas for PE and KE are general formulas from Physics. Hence I shall simply substitute equations (4) and (6). However, I shall start to denote PE, with the letter V. I am doing this in order to easily express the function as a Lagrangian. A Lagrangian is a function of the generalized coordinates containing information about the dynamics of the system. A Lagrangian function summarizes the dynamics of an entire system. Instead of using forces, a Lagrangian uses the energies in the system , in this case PE and KE. Technically, Newtonian mechanics can be used, but as I am working closely with trajectories with generalized coordinates (Cartesian coordinate system), Lagrangian mechanics would be more suitable. Hence, Now to work out kinetic energy (KE) in the system: Once again, I would refer to KE differently for the sake of a Lagrangian expression. KE = T. However before moving on, I must acknowledge the new variable in the formula. Velocity v . Velocity is simply the derivative of displacement. Thus v= ds/dt with s being the function of position. Therefore, I need to find the derivatives for all the position functions listed above. After finding the derivatives, I am now a step closer to finding the functions for velocity. I need to use the derivatives for the horizontal and vertical position functions because v=x^'+y' (where v is velocity.) Hence (x_1' + y_1') and (x_2' + y_2') represent v_1 and v_2 respectively. Hence I shall substitute equations (7), (8), (9) and (10) to find KE (T) of the system; Note: The T represents KE and NOT total energy. The Lagrangian of a system is defined to be the difference between the kinetic energy and potential energy : L=T-V For L to be true, the Euler-Lagrange differential equation (a fundamental equation of calculus variations) must meet this condition: The Euler-Lagrange differential equation is a second-order partial differential equation. Unlike the ODEs examined earlier, partial differential equations (PDEs) contain multivariable functions and their partial derivatives. A partial derivative is a derivative of a function of two or more variables with respect to one variable as the other is treated as a constant. For instance The symbol ∂ “del” is used to distinguish partial derivatives from ordinary derivatives. In my Lagrangian θ_1 and θ_2 are my variables. Thus partials for the Lagrangian θ_1 Now I shall substitute these into the Euler-Lagrangian Equation Now I would make (θ_1 )^'' the subject because this would eventually enable me to create two dependent differential equations. (12) Similarly I shall solve for the partials of θ_2 Thus partials for the Lagrangian θ_2 Now I shall substitute these into the Euler-Lagrangian Equation Now after simplifying I would make (θ_2 )^'' the subject. (13) These second-order PDEs (12) and (13) can be solved numerically using Octave. This is illustrated below in Figure 9 for only〖 θ〗_2 (I only need one angle to prove my point). It shows the changes in the angle with respect to time in the system for particular initial values. Due to its complicated motion (illustrated below) a different set of initial values even with a highly small difference would alter the course of the systems dynamics because it is chaotic, hence sensitive to initial values. And Figure 10 below shows the two angles with respect to time. Interestingly an attractor is formed. Figure 9 One can observe the chaotic, yet sublime “order” of a double pendulum experiment. The butterfly effect has been proven in the field of physics. With this knowledge in mind, I have started to wonder how precise and accurate one must be when working with machines that apply the motion of a double pendulum. Figure 10 Conclusion It has been fascinating to learn about the “small” things in life. By proving the existence of the Butterfly Effect in multiple fields, I can now clearly understand the old phrase “It’s the little things in life that matter.” It is quite interesting to know that one air molecule can make the difference between a sunny, azure sky day and a rainy lightning storm! The Butterfly Effect has to be one of the most advanced and most extraordinary theory discovered in the mathematical world. The sublime order in chaos has to be the greatest irony I have come across. From this exploration I have learned a lot about graphing software and the large role programs play in approximations and models. This theory however has got me thinking. How could other fields apply this theory? Then one area came across my mind: Finance . What if they are just mistaking chaotic for randomness? Previous Next