Maximizing Returns and Minimizing Risk in the Stock Market Using Mathematical Modeling

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

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

PART A Initial Stock Picks

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

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

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

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

PART B Using More Data

Part BUsing More Data

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

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

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

PART C The Perfect Portfolio

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

Part CThe Perfect Portfolio

Part CThe Perfect Portfolio Table of Sharpe Ratios

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

Part C – 1st Trial

Part C – 2nd Trial

Part C – 3rd Trial

Part C – 4th Trial

Part C – 5th Trial

Part C – FINAL

Part D Validation of Model

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

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

Part DValidation of Model BMC DJIA S&P 500

Part DValidation of Model CAI DJIA S&P 500

Part DValidation of Model COGN DJIA S&P 500

Part DValidation of Model MFE DJIA S&P 500

Part DValidation of Model ORCL DJIA S&P 500

Part DValidation of Model INFY DJIA S&P 500

Maximizing Returns and Minimizing Risk in the Stock Market Using Mathematical Modeling