Annabelle Invests in the Market

A Case Study Presented to the

Decision Sciences and Innovation Department

The Ramon V. Del Rosario – College of Business

De La Salle University

In partial fulfillment

Of the requirements of the course

MANSCIE Section K32

SUBMITTED TO:

Dr. Emilina R. Sarreal

SUBMITTED BY:

Chua, Hazel Ann Y. R.

Gonzales, Raeanne Therese Q.

Mendoza, Darwyn Albert T.

Phillipneris, Anna Marie S.

Ramirez, Diana Marie M.

February 27, 2014

I. Brief Background of the Case

Annabelle Sizemore has paid some treasury bonds and a life insurance

policy that her parents had accumulated over the years for her. At the same

time, Annabelle has saved some money in certificates of deposit and savings

bonds since she graduated from college 10 years ago. As a result, she can

invest $120,000. Then she felt that she should invest the entire amount there,

given the recent rise in the stock market. Annabelle then decides on which is the

best stock market that she should invest in. She then chose an index fund from

Shield Securities and an Internet stock fund from Madison Funds, Inc. She has

also decided that the proportion of the dollar amount that she invests in the index

fund relative to the Internet fund should be at least one-third but she should not

invest more than twice the amount in the Internet fund that she invests in the

index fund. In short, she wants to balance her risk (of losing money) to some

degree.

II. Define the Problem1. How much money should Annabelle invest in each fund?

2. What will be the effect in eliminating the ⅓ constraint?

3. What will be the effect in eliminating the 2:1 constraint?

4. What can be said about her ROI strategy given that she invests $1 more? $2

more? $3 more?

III. Acquire Input Data

X1 X2 Symbol Right Hand Side

175 208 = $120,000

> 0.33

< 2

Profit (Z) 29.75 58.24

IV. Develop the Model Objective FunctionMax Z (ROI) = (0.17)(175)x1 + (0.28)(208)x2

Max Z (ROI) = 29.75 x 1 + 58.24 x 2

where, x1 = no. off shares of index fund, x2 = no. of shares of internet stock fundsubject to:1) 175x1+ 208x2= $120,0002) x1/x2 > 0.333) x2/x1 < 2

x1,x2 > 0

V. Develop the SolutionV.1. Solve for the Constraints

5.2 Graph the Solution

5.3 Corner Point Solution

175x1 + 208(2x1) = 120,000x2/x1 < 2

x2 = 2x1

175x1 + 208(2x1) = 120,000591x1 = 120000x1 = 203.05

175x1 + 208x2 = 120,000175 (203.05) + 208x2 = 120,000208x2 = 84,466.25 x2 = 406.09 (x1, x2) (203, 406)Max Z = 29.75x1 + 58.24x2

29.75(203.05) + 58.24(406.09) =29,691.42

5.1Solve for the Constraints

5.2Graph the Solution

5.3 Corner Point Solution

175x1+ 208x2= $120,000x1/x2 > 0.33

x1 = 0.33175(0.33) + 208x2 = 120000265.75x2 = 120000x2 = 451.55

Max Z = 29.75x1 + 58.24x2

29.75(0.33) + 58.24(451.55) =26,308.09

VI. Analyze the ResultsAccording to the data,

VII. Recommended SolutionAnnabelle could add more dollars to her investments since the rate of

return is relatively stable. Her profit will get higher by $0.25 every time she adds $1 to her investment.

VIII. ConclusionThe increasing the amount available to invest (e.g. $120,000 to $120,001)

will increase the profit from Max Z = $29,691.37 to Max Z = $29,691.62 or approximately $0.25. Each $1 increase in investment is equivalent to a $0.25 expected return in overall profit. Also, the marginal value of an extra $1 that Annabelle will invest is $0.25.

We can also conclude that Annabelle’s ROI is fairly good, because if the markets are stable, every $1 will yield a $0.25 return in profit. This means that her rate of return will get higher every time she adds a dollar to her investment. This strategy is better compared to a profit deficit.