Moody’s Mega Math Challenge 2007

1. Moody’s Mega Math Challenge 2007 Risky Business: Using Mathematical Modeling to Maximize Returns and Minimize Risk in the Stock Market Team 104

2. Assumptions • The stock market will steadily increase: given in the problem • No more than $30,000 can be invested: given in the problem • Each portfolio created contains exactly six stocks: the problem sets the maximum at six, and it would be unwise to select less than six because portfolio diversification allows for both greater profitability and greater security • Any one stock’s value, and therefore the entire portfolio’s value, has an equal chance of increasing as decreasing: it would be unreasonable to expect complete security in the stock market. While the market as a whole will increase, individual securities fluctuate on a day-to-day and year-to-year basis • There will be no significant inflation over the next year: the inflationary increase that normally occurs over the course of one year would not affect the market in a large enough way so as to change the eventual outcome of this exercise

3. PART A Initial Stock Picks

4. Part AInitial Stock Picks Average P/S Ratio: 5.019 Average Cash Flow: 1.269

5. Part AInitial Stock Picks • One high risk • MFE • Four moderate risk – BMC, CAI, COGN, SPSS • One low risk – SRX

6. Part AInitial Stock Picks • $2,500 to invest in SRX  $27,500 left • Highest amount in MFE • Potential MFE losses offset by 2 moderate gains • $27,500 = 4x + y = 6x; y = 2x • x is amount for each moderate risk stock • y is amount for the high risk stock

7. Part AInitial Stock Picks The total value of the portfolio is $29,983.44, leaving a total of $16.56 that is not invested.

8. PART B Using More Data

9. Part BUsing More Data

10. Part BUsing More Data • Two high risk • CTXS, QADI • Four moderate risk • BMC, COGN, ORCL, MSFT

11. Part BUsing More Data • Potential high risk losses offset by 2 moderate gains • $30,000 = 4x + 2y = 8x • x is amount to invest in each “normal” stock • y is amount to invest in each “compensative” stock

12. Part BUsing More Data The total value of this portfolio is $29,992.99, leaving a total of $7.01 that is not invested.

13. PART C The Perfect Portfolio

14. Part CThe Perfect Portfolio • Sharpe Ratio – ratio between return and risk • R = return on the stock • Rf = risk-free rate of return • the 5.12% rate of return on a US Treasury bond •  = standard deviation of the stock over 5 years http://en.wikipedia.org/wiki/Sharpe_ratio

15. Part CThe Perfect Portfolio

16. Part CThe Perfect Portfolio

17. Part CThe Perfect Portfolio

18. Part CThe Perfect Portfolio

19. Part CThe Perfect Portfolio Table of Sharpe Ratios

20. Part CThe Perfect Portfolio • % of portfolio = Sharpe Ratio / Sum of Sharpe Ratios in the Portfolio • Portfolio Variance = Individual Variance x % of portfolio • Standard Deviation = square root of Portfolio Variance • Individual Stock Return in Portfolio = Average of returns over 5 years x % of portfolio • Expected Return of Portfolio = sum of all Individual Stock Returns in Portfolio

21. Part C – 1st Trial

22. Part C – 2nd Trial

23. Part C – 3rd Trial

24. Part C – 4th Trial

25. Part C – 5th Trial

26. Part C – FINAL

27. Part D Validation of Model

28. Part DValidation of Model • Professional Analysts’ Opinions • Comparisons to Indices • S&P 500 and Dow Jones Industrial Average

29. Part DValidation of Model Scale of 1 (strongly buy) to 5 (strongly sell)

30. Part DValidation of Model BMC DJIA S&P 500

31. Part DValidation of Model CAI DJIA S&P 500

32. Part DValidation of Model COGN DJIA S&P 500

33. Part DValidation of Model MFE DJIA S&P 500

34. Part DValidation of Model ORCL DJIA S&P 500

35. Part DValidation of Model INFY DJIA S&P 500