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  1. 1. CRACKING THE CODE: A Mathematical Solution to the Stock Market Team 109
  2. 2. THE PROBLEM <ul><li>Unpredictable fluctuations in stock prices may cause investments to be weighted with large risks; however, through comprehensive research, savvy stockholders can get rich quick and follow the American dream. </li></ul><ul><li>An increase in the Free Cash Flow and Return on Invested Capital (ROIC), paired with a decrease P/E </li></ul><ul><li>ratio and P/S ratio, and a beta value near one would be indications of a sound one-year investment. </li></ul>
  3. 3. PROBLEM (cont.) <ul><li>Scandal and poor management decisions can increase the risk involved with educated decisions. </li></ul><ul><li>All stock options in this project are situated in the information and software technology fields. </li></ul><ul><ul><ul><li>As a result, many of the options are in direct competition. </li></ul></ul></ul><ul><ul><ul><li>As such, it is imperative to follow trends in greater detail and choose companies that show prospect to rise above the competition. </li></ul></ul></ul>
  4. 4. LIST OF ASSUMPTIONS AND JUSTIFICATIONS <ul><li>The market and market sector will be generally rising. </li></ul><ul><li>Constant Rate of Inflation. </li></ul><ul><li>Economic Fluctuation will not be accounted for. </li></ul><ul><li>Options other than buying and selling are not available. </li></ul><ul><li>Assumption of sound business practices. </li></ul>
  5. 5. IDENTIFICATION OF THE VARIABLES <ul><li>Free Cash Flow is calculated by either subtracting capital expenditures from cash flow or by dividing cash flow by the number of shares of stocks. </li></ul><ul><li>Return on Invested Capital (ROIC) is the total net income for the fiscal year divided by the invested capital over that period. </li></ul><ul><li>The Price to Earnings (P/E) ratio is a measure of how expensive a stock is relative to its profits. </li></ul>
  6. 6. IDENTIFICATION OF VARIABLES (cont.) <ul><li>The Price to Sales (P/S) ratio relates price per share of stock to the revenue per share of stock </li></ul><ul><li>Asset Turnover is the amount each dollar of assets has generated in dollars of revenue. </li></ul><ul><li>Beta, β , measures the volatility of a stock. </li></ul>
  7. 7. “ INDEX VALUES” <ul><li>An index value is a value given to a number that qualifies its total displacement in comparison with similar values. </li></ul><ul><li>Using an index value can only qualify a value in terms of other known and used values. It is only to be used as a means of comparison . </li></ul>
  8. 8. FINDING “INDEX VALUES” <ul><li>Find the percentage difference a sample is above or below the mean value of a given factor with all outlying values removed. </li></ul><ul><li>This value can now be used to compare to other similar index values, without skewing the data presented. </li></ul>
  9. 9. THE BASIC RELATIONSHIP <ul><li>A+B-C-D=Q </li></ul><ul><li>Q is a value that represents the quality of an investment in a given stock </li></ul><ul><li>A – index value for free cash flow </li></ul><ul><li>B - index value for ROIC </li></ul><ul><li>C - index value for P/E </li></ul><ul><li>D – index value for P/S </li></ul>
  10. 10. THE ADJUSTED RELATIONSHIP <ul><li>Q= (k 1 *A) + (k 2 *B) – (k 3 *C) – (k 4 *D) </li></ul><ul><li>Q, A, B, C, and D remain the same in this relationship </li></ul><ul><li>k 1 , k 2 , k 3 , and k 4 are constants that can be used to change the importance of each factor in the final value of Q. </li></ul>
  11. 11. ADJUSTING FOR VOLATILITY <ul><li>Q*V=P </li></ul><ul><li>Q is the same as in past equations </li></ul><ul><li>V is the value of β or volatility of the stock </li></ul><ul><li>P is a value for the profitability of a stock by combining the stocks volatility with its soundness of an investment to postulate the level of gains expected. </li></ul>
  12. 12. PICKING INVESTMENTS <ul><li>P 1 +P 2 +P 3 +P 4 =PT </li></ul><ul><li>P 1-4 are the four highest P values of all the stocks tested </li></ul><ul><li>PT stands for the total index of investment </li></ul>
  13. 13. PICKING INVESTMENTS <ul><li>(P x /PT)*T= F x </li></ul><ul><li>Investment is made based on the proportionality of the P values </li></ul><ul><li>P x is a P value from P 1 to P 4 </li></ul><ul><li>T is the total money to be invested </li></ul><ul><li>F 1-4 is the total capital that should be invested in a given stock </li></ul>
  14. 14. JUSTIFICATION OF PORTFOLIO ONE <ul><li>For Q= (k1*A) + (k2*B) – (k3*C) – (k4*D), k 1 =k 2 =k 3 =k 4 =1. </li></ul><ul><li>It was considered that for this portfolio, all four indicators hold equal weight in the strength of a company and the value of its stocks to an investor. </li></ul><ul><li>Based on these calculations, a total of $29,959.15 was invested by purchasing 309 shares of BMC , 247 shares of CAI , 285 shares of MSFT , and 56 shares of SRX . </li></ul>
  18. 18. JUSTIFICATION OF PORTFOLIO TWO <ul><ul><ul><li>For Q= (k 1 *A) + (k 2 *B) – (k 3 *C) – (k 4 *D) </li></ul></ul></ul><ul><ul><ul><li>k 1 =k 4 =3 and k 2 =k 3 =5 </li></ul></ul></ul><ul><ul><ul><li>Creating the equation, Q = 3A + 5B - 5C – 3D. </li></ul></ul></ul><ul><ul><ul><li>Coefficients were chosen to give more weight to high ROIC and low P/E values, which are strong indicators of the value of a stock. </li></ul></ul></ul>
  19. 19. JUSTIFICATION OF PORTFOLIO TWO (cont.) <ul><ul><ul><li>This new formula will give a more accurate rating of how much value a given stock would prove to have as a year long investment in comparison to portfolio one. </li></ul></ul></ul><ul><ul><ul><li>Based on these calculations, a total of $29,920.45 was invested in the following corporations by purchasing 278 shares of BMC , 163 shares of CAI , 168 shares of COGN , and 910 shares of QADI . </li></ul></ul></ul>
  23. 23. JUSTIFICATION OF PORTFOLIO THREE <ul><li>For Q = (k 1 *A) + (k 2 *B) + (k 3 *E) – (k 4 *D), </li></ul><ul><li>k 1 =k 3 =3 and k 2 =k 4 =5 </li></ul><ul><li>Creating the equation Q = 3A + 5B + 3E - 5D, where E is the index value for Asset Turnover </li></ul><ul><li>Asset Turnover rate is substituted for P/E because it could be a better indicator of a favorable stock. </li></ul>
  24. 24. JUSTIFICATION OF PORTFOLIO THREE (cont.) <ul><li>P/S is derived from sales, as compared to earnings for P/E, which is considered to be a more reliable indicator of business health . </li></ul><ul><li>Based on these calculations, a total of $29,894.29 was invested in the following corporations by purchasing 198 shares of CAI , 128 shares of INFY , 1,471 shares of QADI , and 86 shares of SRX . </li></ul>
  28. 28. HOW TO VALIDATE THE MATHEMATICAL MODEL <ul><li>The most accurate method to validate a forecasted model would obviously be to allow time to elapse . </li></ul><ul><li>It is possible to test the mathematical model at this current date and time using past information. </li></ul><ul><li>The model presented is not considered to be a way to give a stock a number that will quantify how much money it will make, it is simply a method of creating a sound investment strategy. </li></ul>
  29. 29. CONCLUSION <ul><li>Portfolio one is not a sound investment because it esteems the different indicators unilaterally , and some indicators are better than others in determining profitability </li></ul><ul><li>Portfolio three is flawed, mainly due to the inclusion of the asset turnover rate . </li></ul><ul><ul><ul><li>Using the asset turnover rate of a company is not as well proven as the P/E value, and therefore makes for a slightly more risky investment. </li></ul></ul></ul>
  30. 30. CONCLUSION (cont.) <ul><li>The decision was made to invest using the strategy of portfolio two , which calls for investment in: </li></ul><ul><ul><ul><li>278 shares of BMC Software Inc. (BMC) </li></ul></ul></ul><ul><ul><ul><li>163 shares of Caci International Inc. (CAI) </li></ul></ul></ul><ul><ul><ul><li>168 shares of COGNOS Inc. (COGN) </li></ul></ul></ul><ul><ul><ul><li>910 shares of QAD Inc (QADI) </li></ul></ul></ul><ul><li>This profile was chosen because it takes into account the different values that the indicators most likely hold, and it uses relevant and proven indicators to boot. </li></ul>
  31. 31. A Solution By Jessica Bloom Matt Giambrone Julia Haigney John LaCara Peter Werner Walt Whitman High School Team 109