Economics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=166
en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 21 Feb 2017 02:49:12 GMTTue, 21 Feb 2017 02:49:12 GMTNew applications in the Economics categoryhttp://www.mapleprimes.com/images/mapleapps.gifEconomics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=166
Classroom Tips and Techniques: Norm of a Matrix
http://www.maplesoft.com/applications/view.aspx?SID=1430&ref=Feed
The greatest benefits from bringing Maple into the classroom are realized when the static pedagogy of a printed textbook is enlivened by the interplay of symbolic, graphic, and numeric calculations made possible by technology. Getting Maple to compute the correct answer is just the first step. Using Maple to bring insights not easily realized with by-hand calculations should be the goal of everyone who sets a hand to improving the learning experiences of students. In this article we will show how Maple can be used to gain insight on what the norm of a matrix means.<img src="/view.aspx?si=1430/thumb.jpg" alt="Classroom Tips and Techniques: Norm of a Matrix" align="left"/>The greatest benefits from bringing Maple into the classroom are realized when the static pedagogy of a printed textbook is enlivened by the interplay of symbolic, graphic, and numeric calculations made possible by technology. Getting Maple to compute the correct answer is just the first step. Using Maple to bring insights not easily realized with by-hand calculations should be the goal of everyone who sets a hand to improving the learning experiences of students. In this article we will show how Maple can be used to gain insight on what the norm of a matrix means.1430Mon, 13 Feb 2017 05:00:00 ZDr. Robert LopezDr. Robert LopezLocal Volatility and Implied Volatility
http://www.maplesoft.com/applications/view.aspx?SID=4878&ref=Feed
This application explores two different methods of exploring financial data. The first example examines fitting an implied volatility surface based on data from S&P 500 call options. The second computes option prices and models the local volatility for simulated market data.<img src="/view.aspx?si=4878/volatility.png" alt="Local Volatility and Implied Volatility" align="left"/>This application explores two different methods of exploring financial data. The first example examines fitting an implied volatility surface based on data from S&P 500 call options. The second computes option prices and models the local volatility for simulated market data.4878Wed, 11 May 2016 04:00:00 ZMaplesoftMaplesoftIs a Stock Overvalued or Undervalued?
http://www.maplesoft.com/applications/view.aspx?SID=153740&ref=Feed
<p>This application calculates the fair value of a stock, given the current market prices and several growth assumptions. Simply pick an industry, stock exchange, and then a company.</p>
<p>Maple then downloads the current market share price, EPS (for the trailing 12 months) and dividends (for the trailing 12 months) from Yahoo Finance (hence a connection to the web is needed). Given a series of growth assumptions, a fair value is then calculated. The valuation process is described at the bottom of this application, and is most appropriate for stable companies with a history of dividend payments.</p>
<p>The stock is undervalued If the fair value is greater than the current market price, and vice-versa.</p>
<p>This application comes with an Excel spreadsheet with a list of over 25000 companies across multiple industries and international exchanges, and their corresponding ticker symbols. This spreadsheet is used to populate the interface with industries, exchanges and companies, and must be saved in the same location as the Maple worksheet.</p><img src="/view.aspx?si=153740/stockovervalued.png" alt="Is a Stock Overvalued or Undervalued?" align="left"/><p>This application calculates the fair value of a stock, given the current market prices and several growth assumptions. Simply pick an industry, stock exchange, and then a company.</p>
<p>Maple then downloads the current market share price, EPS (for the trailing 12 months) and dividends (for the trailing 12 months) from Yahoo Finance (hence a connection to the web is needed). Given a series of growth assumptions, a fair value is then calculated. The valuation process is described at the bottom of this application, and is most appropriate for stable companies with a history of dividend payments.</p>
<p>The stock is undervalued If the fair value is greater than the current market price, and vice-versa.</p>
<p>This application comes with an Excel spreadsheet with a list of over 25000 companies across multiple industries and international exchanges, and their corresponding ticker symbols. This spreadsheet is used to populate the interface with industries, exchanges and companies, and must be saved in the same location as the Maple worksheet.</p>153740Tue, 20 Jan 2015 05:00:00 ZSamir KhanSamir KhanDrawdown of Historical Stock Prices
http://www.maplesoft.com/applications/view.aspx?SID=153624&ref=Feed
<p>The drawdown of a stock indicates how much time it's spent "underwater" - it's essentially the percentage drop of its price from a peak to a trough, with the drawdown resetting to zero if a previous high is reached. The drawdown of a stock is a valuable risk measure and is employed by traders to gauge volatility.</p>
<p>This application:</p>
<ul>
<li>downloads historical stock prices from Yahoo Finance for a chosen ticker symbol (this requires a connection to the Internet),</li>
<li>defines a procedure that calculates the drawdown of the historical stock price</li>
<li>and plots the drawdown against the adjusted close price of the asset</li>
</ul>
<p>By changing the ticker symbol and the two dates, you can examine drawdown of any stock between any period.</p>
<p>The application uses Maple 18's improved Internet connectivity; you can now download data from a URL into a matrix using <span><a href="/support/help/Maple/view.aspx?path=ImportMatrix">ImportMatrix()</a></span>.</p><img src="/view.aspx?si=153624/2def9a8f2111f9b47d0bee568aed6035.gif" alt="Drawdown of Historical Stock Prices" align="left"/><p>The drawdown of a stock indicates how much time it's spent "underwater" - it's essentially the percentage drop of its price from a peak to a trough, with the drawdown resetting to zero if a previous high is reached. The drawdown of a stock is a valuable risk measure and is employed by traders to gauge volatility.</p>
<p>This application:</p>
<ul>
<li>downloads historical stock prices from Yahoo Finance for a chosen ticker symbol (this requires a connection to the Internet),</li>
<li>defines a procedure that calculates the drawdown of the historical stock price</li>
<li>and plots the drawdown against the adjusted close price of the asset</li>
</ul>
<p>By changing the ticker symbol and the two dates, you can examine drawdown of any stock between any period.</p>
<p>The application uses Maple 18's improved Internet connectivity; you can now download data from a URL into a matrix using <span><a href="/support/help/Maple/view.aspx?path=ImportMatrix">ImportMatrix()</a></span>.</p>153624Mon, 07 Jul 2014 04:00:00 ZSamir KhanSamir KhanDownloading Stock Prices and Plotting Returns Distributions
http://www.maplesoft.com/applications/view.aspx?SID=153539&ref=Feed
<p>This application:</p>
<ul>
<li>downloads historical stock prices from Yahoo Finance,</li>
<li>calculates the returns,</li>
<li>plots the distribution of the returns in a histogram,</li>
<li>and overlays a normal distribution with the same mean and standard deviation as the historical data.</li>
<li>The application uses Maple 18's improved Internet connectivity; you can now download data from a URL straight into a matrix using <span ><a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=ImportMatrix">ImportMatrix()</a></span>.</li>
</ul><img src="/view.aspx?si=153539/stockreturns.png" alt="Downloading Stock Prices and Plotting Returns Distributions" align="left"/><p>This application:</p>
<ul>
<li>downloads historical stock prices from Yahoo Finance,</li>
<li>calculates the returns,</li>
<li>plots the distribution of the returns in a histogram,</li>
<li>and overlays a normal distribution with the same mean and standard deviation as the historical data.</li>
<li>The application uses Maple 18's improved Internet connectivity; you can now download data from a URL straight into a matrix using <span ><a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=ImportMatrix">ImportMatrix()</a></span>.</li>
</ul>153539Thu, 03 Apr 2014 04:00:00 ZSamir KhanSamir KhanPoker Calculator
http://www.maplesoft.com/applications/view.aspx?SID=147711&ref=Feed
<p>We will in this worksheet calculate the pr-flop probability of <br />wining for player-1 given a random par of cards for a two <br />person poker game. <br /><br />Any combination of aces are superior if you want to win the game :-)<br /><br /></p><img src="/applications/images/app_image_blank_lg.jpg" alt="Poker Calculator" align="left"/><p>We will in this worksheet calculate the pr-flop probability of <br />wining for player-1 given a random par of cards for a two <br />person poker game. <br /><br />Any combination of aces are superior if you want to win the game :-)<br /><br /></p>147711Sun, 26 May 2013 04:00:00 ZMarcus DavidssonMarcus DavidssonLoan Amortization Table
http://www.maplesoft.com/applications/view.aspx?SID=145819&ref=Feed
<p>By entering the <strong>loan amount</strong>, the <strong>number of years to repay the loan</strong>, the <strong>payment frequency</strong>, the <strong>annual nominal interest rate</strong>, the number of <strong>compound periods</strong> per year, and hit the "<strong>Generate Amortization Table</strong>" button. The worksheet will calculate automatically the <strong>total payments</strong>, the <strong>total interest paid</strong>, and the <strong>payment per period</strong> as well as the <strong>amortization table</strong>. To open the amortization table, just click on the triangle beside the amortization table.<br /><br /></p><img src="/view.aspx?si=145819/loanamortization_thumb.png" alt="Loan Amortization Table" align="left"/><p>By entering the <strong>loan amount</strong>, the <strong>number of years to repay the loan</strong>, the <strong>payment frequency</strong>, the <strong>annual nominal interest rate</strong>, the number of <strong>compound periods</strong> per year, and hit the "<strong>Generate Amortization Table</strong>" button. The worksheet will calculate automatically the <strong>total payments</strong>, the <strong>total interest paid</strong>, and the <strong>payment per period</strong> as well as the <strong>amortization table</strong>. To open the amortization table, just click on the triangle beside the amortization table.<br /><br /></p>145819Fri, 12 Apr 2013 04:00:00 ZZinan WangZinan WangCar Loan Calculator
http://www.maplesoft.com/applications/view.aspx?SID=145174&ref=Feed
<p>This loan calculator facilitates the life of a borrower. By entering the <strong>purchase price</strong>, the <strong>down payment</strong>, the <strong>number of years</strong> it takes to repay the loan, the <strong>payment frequency</strong>, the <strong>annual interest rate</strong>, and clicking on the "<strong>calculate</strong>" buttom, the calculator will give you the <strong>amount of payment</strong> for each payment period.</p>
<p> </p>
<p>Want to make a loan? Try it out and see how things change with respect to each element.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Car Loan Calculator" align="left"/><p>This loan calculator facilitates the life of a borrower. By entering the <strong>purchase price</strong>, the <strong>down payment</strong>, the <strong>number of years</strong> it takes to repay the loan, the <strong>payment frequency</strong>, the <strong>annual interest rate</strong>, and clicking on the "<strong>calculate</strong>" buttom, the calculator will give you the <strong>amount of payment</strong> for each payment period.</p>
<p> </p>
<p>Want to make a loan? Try it out and see how things change with respect to each element.</p>145174Wed, 27 Mar 2013 04:00:00 ZZinan WangZinan WangMortgages
http://www.maplesoft.com/applications/view.aspx?SID=142213&ref=Feed
<p>Consider the problem of borrowing $250,000 to buy a house. You borrow the money at a fixed interest rate of 4.8% compounded monthly. The term of the mortgage is for 20 years. However, you decide against making minimum payments. Instead you decide to pay an additional $200 every month. How long will it take you to pay off the loan and how much have you saved on interest by paying off the loan early?</p><img src="/view.aspx?si=142213/b8fc2d4d03908eeda63c803f8bbd81c1.gif" alt="Mortgages" align="left"/><p>Consider the problem of borrowing $250,000 to buy a house. You borrow the money at a fixed interest rate of 4.8% compounded monthly. The term of the mortgage is for 20 years. However, you decide against making minimum payments. Instead you decide to pay an additional $200 every month. How long will it take you to pay off the loan and how much have you saved on interest by paying off the loan early?</p>142213Fri, 11 Jan 2013 05:00:00 ZDouglas LewitDouglas LewitGreat Expectations
http://www.maplesoft.com/applications/view.aspx?SID=127116&ref=Feed
<p>An investor is offered what appears to be a great investment opportunity. Unfortunately it doesn't turn out to be so great in the long run. This interactive Maple document explores the situation using simulation and analysis, and suggests a new strategy that would produce better results.</p>
<p>This is an example suitable for presentation in an undergraduate course on probability. No knowledge of Maple is required.</p><img src="/view.aspx?si=127116/expectation_thum.png" alt="Great Expectations" align="left"/><p>An investor is offered what appears to be a great investment opportunity. Unfortunately it doesn't turn out to be so great in the long run. This interactive Maple document explores the situation using simulation and analysis, and suggests a new strategy that would produce better results.</p>
<p>This is an example suitable for presentation in an undergraduate course on probability. No knowledge of Maple is required.</p>127116Thu, 27 Oct 2011 04:00:00 ZFloating Exchange Rate and Internal Balance
http://www.maplesoft.com/applications/view.aspx?SID=121119&ref=Feed
<p>This application examines how floating exchange rates affect the macroeconomic performance of an economy. In particular, it shows how an economy can maintain its internal and external balances with a floating exchange rate regime. The macroeconomic performance under the floating exchange rates is analysed in the framework of internal shocks to it from govenment marcroeconomic policies, such as monetary policy (money supply changes) and fiscal policy (government spending changes). Namely, the developed application from a set of sample data shows that the overall effect of these two policies to the macroeconomic performance of the country is different. The monetary policy proved to be more effective under the floating exchange rate and it increased real domestic production when the money supply was increased. On the other hand, fiscal policy proved to be effective under the floating exchange rates only when capital mobility is low. With higher capital mobility, the fiscal policy tended to be less effective than the monetary policy. </p><img src="/view.aspx?si=121119/384814\f10ad4ab24fcc5bdb42df2c8d27b4676.gif" alt="Floating Exchange Rate and Internal Balance" align="left"/><p>This application examines how floating exchange rates affect the macroeconomic performance of an economy. In particular, it shows how an economy can maintain its internal and external balances with a floating exchange rate regime. The macroeconomic performance under the floating exchange rates is analysed in the framework of internal shocks to it from govenment marcroeconomic policies, such as monetary policy (money supply changes) and fiscal policy (government spending changes). Namely, the developed application from a set of sample data shows that the overall effect of these two policies to the macroeconomic performance of the country is different. The monetary policy proved to be more effective under the floating exchange rate and it increased real domestic production when the money supply was increased. On the other hand, fiscal policy proved to be effective under the floating exchange rates only when capital mobility is low. With higher capital mobility, the fiscal policy tended to be less effective than the monetary policy. </p>121119Sat, 04 Jun 2011 04:00:00 ZBekzod MakhmudovBekzod MakhmudovInternational Trade Model
http://www.maplesoft.com/applications/view.aspx?SID=120866&ref=Feed
<p>This application demonstrates how international trade occures in a simple case between two countries and in one product market. The application starts with given supply and demand functions in two separate countries, country A and country B. Then it proceeds to identify domestic equilibrium prices and quantities in these two countries for a given product market. The difference between the domestic prices plays a role in determining the direction of trade flows, i.e. exports and imports. In this given application, country A imports and country B exports products as the domestic price is lower in country B than in country A. Then the application shows how equilibrium international price and international quantity (exports and imports) can be identified given specific domestic supply and demand functions of the two countries. Moreover, this application also demonstrates interactively how setting import tariff and import quota in country A can restrict international trade and how this will affect import price, quantity, and welfare of economic agents in importing country. The application is created for study purposes of international trade model by using Maple program.</p><img src="/view.aspx?si=120866/384396\3d8359703bf9dcce1b49dfbc4fccfc5d.gif" alt="International Trade Model" align="left"/><p>This application demonstrates how international trade occures in a simple case between two countries and in one product market. The application starts with given supply and demand functions in two separate countries, country A and country B. Then it proceeds to identify domestic equilibrium prices and quantities in these two countries for a given product market. The difference between the domestic prices plays a role in determining the direction of trade flows, i.e. exports and imports. In this given application, country A imports and country B exports products as the domestic price is lower in country B than in country A. Then the application shows how equilibrium international price and international quantity (exports and imports) can be identified given specific domestic supply and demand functions of the two countries. Moreover, this application also demonstrates interactively how setting import tariff and import quota in country A can restrict international trade and how this will affect import price, quantity, and welfare of economic agents in importing country. The application is created for study purposes of international trade model by using Maple program.</p>120866Wed, 01 Jun 2011 04:00:00 ZSarvar RuzmatovSarvar RuzmatovAre you a Genius or not?
http://www.maplesoft.com/applications/view.aspx?SID=103260&ref=Feed
<p>I was watching "What Makes a Genius" on BBC Horizon.<br />There Marcus du Sautoy, professor of mathematics at the <br />University of Oxford, tries to answer the question whether <br />geniuses are born or made?!<br /><br />I one section of the program a coloured spots test, performed <br />at John Hopkins University, tries to show if people have a <br />natural talent for mathematics.<br /><br />Since I had not done any programming in Maple for a while<br />I decided it could be a fun challenge :-)</p><img src="/view.aspx?si=103260/322829\71168ae8d71a5a45203c9cc10ec3c228.gif" alt="Are you a Genius or not?" align="left"/><p>I was watching "What Makes a Genius" on BBC Horizon.<br />There Marcus du Sautoy, professor of mathematics at the <br />University of Oxford, tries to answer the question whether <br />geniuses are born or made?!<br /><br />I one section of the program a coloured spots test, performed <br />at John Hopkins University, tries to show if people have a <br />natural talent for mathematics.<br /><br />Since I had not done any programming in Maple for a while<br />I decided it could be a fun challenge :-)</p>103260Tue, 29 Mar 2011 04:00:00 ZMarcus DavidssonMarcus DavidssonPortfolio Simulation and Quadratic Programming
http://www.maplesoft.com/applications/view.aspx?SID=100604&ref=Feed
<p>We will in this maple worksheet explore portfolio theory and quadratic optimization.<br />We will start by simulating some data for 50 stocks and then optimize the portfolio.<br />We will also use empirical data to backtest our portfolio strategy.</p><img src="/view.aspx?si=100604/maple_icon.jpg" alt="Portfolio Simulation and Quadratic Programming" align="left"/><p>We will in this maple worksheet explore portfolio theory and quadratic optimization.<br />We will start by simulating some data for 50 stocks and then optimize the portfolio.<br />We will also use empirical data to backtest our portfolio strategy.</p>100604Mon, 03 Jan 2011 05:00:00 ZMarcus DavidssonMarcus DavidssonThe Knapsack Problem
http://www.maplesoft.com/applications/view.aspx?SID=100353&ref=Feed
<p>This maple worksheet will explore the 0/1 knapsack problem <br />which is a famous problem in combinatorial optimization. <br />We will solve the problem by using dynamic programming. <br />We will then confirm such a solution graphically by using <br />Maples combinat() package.</p><img src="/view.aspx?si=100353/maple_icon.jpg" alt="The Knapsack Problem" align="left"/><p>This maple worksheet will explore the 0/1 knapsack problem <br />which is a famous problem in combinatorial optimization. <br />We will solve the problem by using dynamic programming. <br />We will then confirm such a solution graphically by using <br />Maples combinat() package.</p>100353Mon, 20 Dec 2010 05:00:00 ZMarcus DavidssonMarcus DavidssonOptimal Stopping - Take Two
http://www.maplesoft.com/applications/view.aspx?SID=99621&ref=Feed
<p>This application will discuss optimal stopping both<br />when we maximize the expected value recursively <br />and when we maximize the probability of success <br />i.e. the secretary problem</p><img src="/view.aspx?si=99621/maple_icon.jpg" alt="Optimal Stopping - Take Two" align="left"/><p>This application will discuss optimal stopping both<br />when we maximize the expected value recursively <br />and when we maximize the probability of success <br />i.e. the secretary problem</p>99621Tue, 30 Nov 2010 05:00:00 ZMarcus DavidssonMarcus DavidssonUniversal Portfolio
http://www.maplesoft.com/applications/view.aspx?SID=97487&ref=Feed
<p>The reason why I started to get interested in this universal <br />portfolio stuff was because of Brian Chen's paper <em>Review </em><br /><em>of Universal Portfolios with Side Information</em> where he writes:<br /><br />"A key insight in the development of these universal <br />portfolios is that the average of a set of exponentials <br />grows exponentially as fast as the largest exponential"<br /><br />The purpose of this worksheet is to test if this is true.</p><img src="/view.aspx?si=97487/maple_icon.jpg" alt="Universal Portfolio" align="left"/><p>The reason why I started to get interested in this universal <br />portfolio stuff was because of Brian Chen's paper <em>Review </em><br /><em>of Universal Portfolios with Side Information</em> where he writes:<br /><br />"A key insight in the development of these universal <br />portfolios is that the average of a set of exponentials <br />grows exponentially as fast as the largest exponential"<br /><br />The purpose of this worksheet is to test if this is true.</p>97487Tue, 05 Oct 2010 04:00:00 ZMarcus DavidssonMarcus DavidssonOptimal Stopping Theorem
http://www.maplesoft.com/applications/view.aspx?SID=97244&ref=Feed
<p>I will in this Maple worksheet try to explore the <br />optimal stopping concepts introduced by: <br /><br />Bruss, T (2000) Sum the Odds to One and Stop, <br /><em>The Annals of Probability</em>, Vol 28, No 3, pp 1394 -1391 <br /><br />One important question that we will answer is : <br />How many times do we need to roll a dice if we want <br />to maximize the probability of finding one six?</p><img src="/view.aspx?si=97244/maple_icon.jpg" alt="Optimal Stopping Theorem" align="left"/><p>I will in this Maple worksheet try to explore the <br />optimal stopping concepts introduced by: <br /><br />Bruss, T (2000) Sum the Odds to One and Stop, <br /><em>The Annals of Probability</em>, Vol 28, No 3, pp 1394 -1391 <br /><br />One important question that we will answer is : <br />How many times do we need to roll a dice if we want <br />to maximize the probability of finding one six?</p>97244Tue, 28 Sep 2010 04:00:00 ZMarcus DavidssonMarcus DavidssonVaR and Portfolio Rebalancing
http://www.maplesoft.com/applications/view.aspx?SID=96564&ref=Feed
<p>I will in this worksheet first of all show that a <br />portfolio's VaR is a function of the portfolio <br />variance but also the portfolio expected return.<br /><br />I will then show that a simple diversified <br />50% bond and 50% momentum strategy can<br /> explains a lot of the portfolio returns. <br />The universe consists of 23 global stockmarket<br /> indicies.<br /><br />Such universe is very small but it still manage<br /> to produce attractive returns which is good <br />news for a disciplined small time investor.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="VaR and Portfolio Rebalancing" align="left"/><p>I will in this worksheet first of all show that a <br />portfolio's VaR is a function of the portfolio <br />variance but also the portfolio expected return.<br /><br />I will then show that a simple diversified <br />50% bond and 50% momentum strategy can<br /> explains a lot of the portfolio returns. <br />The universe consists of 23 global stockmarket<br /> indicies.<br /><br />Such universe is very small but it still manage<br /> to produce attractive returns which is good <br />news for a disciplined small time investor.</p>96564Wed, 01 Sep 2010 04:00:00 ZMarcus DavidssonMarcus DavidssonPicking the Largest Number
http://www.maplesoft.com/applications/view.aspx?SID=95033&ref=Feed
<p>In 1987 Thomas M. Cover introduced what is known as the z-strategy. <br />Such a strategy can be used to gain an advantage in a stochastic<br />game where the goal is to select the largest number. I will in this<br />Maple worksheet explore such a z-strategy in more detail. </p><img src="/view.aspx?si=95033/278030\e67a15175fbfa4b2034efdc8efeb3752.gif" alt="Picking the Largest Number" align="left"/><p>In 1987 Thomas M. Cover introduced what is known as the z-strategy. <br />Such a strategy can be used to gain an advantage in a stochastic<br />game where the goal is to select the largest number. I will in this<br />Maple worksheet explore such a z-strategy in more detail. </p>95033Tue, 13 Jul 2010 04:00:00 ZMarcus DavidssonMarcus Davidsson