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  • 1. CRACKING THE CODE: A Mathematical Solution to the Stock Market Team 109
  • 2. THE PROBLEM
    • 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.
    • An increase in the Free Cash Flow and Return on Invested Capital (ROIC), paired with a decrease P/E
    • ratio and P/S ratio, and a beta value near one would be indications of a sound one-year investment.
  • 3. PROBLEM (cont.)
    • Scandal and poor management decisions can increase the risk involved with educated decisions.
    • All stock options in this project are situated in the information and software technology fields.
        • As a result, many of the options are in direct competition.
        • As such, it is imperative to follow trends in greater detail and choose companies that show prospect to rise above the competition.
  • 4. LIST OF ASSUMPTIONS AND JUSTIFICATIONS
    • The market and market sector will be generally rising.
    • Constant Rate of Inflation.
    • Economic Fluctuation will not be accounted for.
    • Options other than buying and selling are not available.
    • Assumption of sound business practices.
  • 5. IDENTIFICATION OF THE VARIABLES
    • 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.
    • Return on Invested Capital (ROIC) is the total net income for the fiscal year divided by the invested capital over that period.
    • The Price to Earnings (P/E) ratio is a measure of how expensive a stock is relative to its profits.
  • 6. IDENTIFICATION OF VARIABLES (cont.)
    • The Price to Sales (P/S) ratio relates price per share of stock to the revenue per share of stock
    • Asset Turnover is the amount each dollar of assets has generated in dollars of revenue.
    • Beta, β , measures the volatility of a stock.
  • 7. “ INDEX VALUES”
    • An index value is a value given to a number that qualifies its total displacement in comparison with similar values.
    • 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 .
  • 8. FINDING “INDEX VALUES”
    • Find the percentage difference a sample is above or below the mean value of a given factor with all outlying values removed.
    • This value can now be used to compare to other similar index values, without skewing the data presented.
  • 9. THE BASIC RELATIONSHIP
    • A+B-C-D=Q
    • Q is a value that represents the quality of an investment in a given stock
    • A – index value for free cash flow
    • B - index value for ROIC
    • C - index value for P/E
    • D – index value for P/S
  • 10. THE ADJUSTED RELATIONSHIP
    • Q= (k 1 *A) + (k 2 *B) – (k 3 *C) – (k 4 *D)
    • Q, A, B, C, and D remain the same in this relationship
    • 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.
  • 11. ADJUSTING FOR VOLATILITY
    • Q*V=P
    • Q is the same as in past equations
    • V is the value of β or volatility of the stock
    • 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.
  • 12. PICKING INVESTMENTS
    • P 1 +P 2 +P 3 +P 4 =PT
    • P 1-4 are the four highest P values of all the stocks tested
    • PT stands for the total index of investment
  • 13. PICKING INVESTMENTS
    • (P x /PT)*T= F x
    • Investment is made based on the proportionality of the P values
    • P x is a P value from P 1 to P 4
    • T is the total money to be invested
    • F 1-4 is the total capital that should be invested in a given stock
  • 14. JUSTIFICATION OF PORTFOLIO ONE
    • For Q= (k1*A) + (k2*B) – (k3*C) – (k4*D), k 1 =k 2 =k 3 =k 4 =1.
    • 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.
    • 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 .
  • 15. PORTFOLIO ONE
  • 16. PORTFOLIO ONE
  • 17. PORTFOLIO ONE
  • 18. JUSTIFICATION OF PORTFOLIO TWO
        • For Q= (k 1 *A) + (k 2 *B) – (k 3 *C) – (k 4 *D)
        • k 1 =k 4 =3 and k 2 =k 3 =5
        • Creating the equation, Q = 3A + 5B - 5C – 3D.
        • 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.
  • 19. JUSTIFICATION OF PORTFOLIO TWO (cont.)
        • 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.
        • 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 .
  • 20. PORTFOLIO TWO
  • 21. PORTFOLIO TWO
  • 22. PORTFOLIO TWO
  • 23. JUSTIFICATION OF PORTFOLIO THREE
    • For Q = (k 1 *A) + (k 2 *B) + (k 3 *E) – (k 4 *D),
    • k 1 =k 3 =3 and k 2 =k 4 =5
    • Creating the equation Q = 3A + 5B + 3E - 5D, where E is the index value for Asset Turnover
    • Asset Turnover rate is substituted for P/E because it could be a better indicator of a favorable stock.
  • 24. JUSTIFICATION OF PORTFOLIO THREE (cont.)
    • 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 .
    • 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 .
  • 25. PORTFOLIO THREE
  • 26. PORTFOLIO THREE
  • 27. PORTFOLIO THREE
  • 28. HOW TO VALIDATE THE MATHEMATICAL MODEL
    • The most accurate method to validate a forecasted model would obviously be to allow time to elapse .
    • It is possible to test the mathematical model at this current date and time using past information.
    • 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.
  • 29. CONCLUSION
    • Portfolio one is not a sound investment because it esteems the different indicators unilaterally , and some indicators are better than others in determining profitability
    • Portfolio three is flawed, mainly due to the inclusion of the asset turnover rate .
        • 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.
  • 30. CONCLUSION (cont.)
    • The decision was made to invest using the strategy of portfolio two , which calls for investment in:
        • 278 shares of BMC Software Inc. (BMC)
        • 163 shares of Caci International Inc. (CAI)
        • 168 shares of COGNOS Inc. (COGN)
        • 910 shares of QAD Inc (QADI)
    • 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.
  • 31. A Solution By Jessica Bloom Matt Giambrone Julia Haigney John LaCara Peter Werner Walt Whitman High School Team 109