CRACKING THE CODE:A Mathematical Solution to the Stock Market

Team 109

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.

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.

LIST OF ASSUMPTIONS AND JUSTIFICATIONS

1. The market and market sector will be generally rising.

2. Constant Rate of Inflation.3. Economic Fluctuation will not be accounted

for.4. Options other than buying and selling are not

available.5. Assumption of sound business practices.

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.

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.

“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.

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.

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

THE ADJUSTED RELATIONSHIP

Q= (k1*A) + (k2*B) – (k3*C) – (k4*D)

Q, A, B, C, and D remain the same in this relationship

k1, k2, k3, and k4 are constants that can be used to change the importance of each factor in the final value of Q.

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.

PICKING INVESTMENTS

P1+P2+P3+P4=PT P1-4 are the four highest P values of all the

stocks tested

PT stands for the total index of investment

PICKING INVESTMENTS

(Px/PT)*T= Fx

Investment is made based on the proportionality of the P values

Px is a P value from P1 to P4 T is the total money to be invested F1-4 is the total capital that should be invested in

a given stock

JUSTIFICATION OF PORTFOLIO ONE

For Q= (k1*A) + (k2*B) – (k3*C) – (k4*D), k1=k2=k3=k4=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.

PORTFOLIO ONE

PORTFOLIO ONE

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Q

ADBE ADVS BMC CAI CDNS CTXS COGN INFY MSCS MFE MSFT NUAN ORCL QADI RHT SPSS SRX SYMCStock

PORTFOLIO 1Stock v. Q Value

PORTFOLIO ONEPORTFOLIO 1

P Values for Selected Stocks

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BMC CAI MSFT SRX

Stock

P

JUSTIFICATION OF PORTFOLIO TWO

For Q= (k1*A) + (k2*B) – (k3*C) – (k4*D) k1=k4=3 and k2=k3=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.

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.

PORTFOLIO TWO

PORTFOLIO TWO

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0

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Q

ADBE ADVS BMC CAI CDNS CTXS COGN INFY MSCS MFE MSFT NUAN ORCL QADI RHT SPSS SRX SYMCStock

PORTFOLIO 2Stock v. Q Value

PORTFOLIO TWO

PORTFOLIO 2P Values for Selected Stocks

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BMC CAI COGN QADI

Stock

P

JUSTIFICATION OF PORTFOLIO THREE

For Q = (k1*A) + (k2*B) + (k3*E) – (k4*D), k1=k3=3 and k2=k4=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.

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.

PORTFOLIO THREE

PORTFOLIO THREE

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Q

ADBE ADVS BMC CAI CDNS CTXS COGN INFY MSCS MFE MSFT NUAN ORCL QADI RHT SPSS SRX SYMCStock

PORTFOLIO 3Stock v. Q Value

PORTFOLIO THREE

PORTFOLIO 3P Values for Selected Stocks

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CAI INFY QADI SRX

Stock

P

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.

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.

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.

A Solution ByJessica Bloom

Matt GiambroneJulia HaigneyJohn LaCaraPeter Werner

Walt Whitman High SchoolTeam 109