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An investment manager wants to determine an optimal portfolio for a wealthy client. The fund has $2.5 million to invest, and its objective is to maximize total dollar return from both growth and dividiends over the course of the coming year. The client has researched eight high-tech companies and wants the portfolio to consist of shares in these firms only. Three of the firms (S1-S3) are primarily software companies, three (H1-H3) are primarily hardware companies, and two (C1-C2) are internet consulting companies. The client has stipulated that no more than 40% of the investment be allocated to any one of these tree sectors. To assure diversification, at least $100,000 must be invested in each of the eight stocks. The table below gives estimates from the investment company's database relating to these stocks. These es- timates include the price per share, the projected annual growth rate in the share price, and the anticipated annual dividend payment per share. Stock Price per share Growth rate Dividend SI H3 CI C2 $40 $25 $2 S3 H1 H2 $50 $80 $60 $45 $60 $30 0.10 0.03 0.04 0.07 0.15 0.22 0.25 $2.00 $1.50 $3.50 $3.00 $2.00 $1.00 $1.80 $0.00 0.05 1. Formulate an optimization model for this planning problem (i.e., fractional outcomes for the decisions are acceptable). 2. Write an AMPL code to solve this problem. Report the maximum return on the portfolio. What is the optimal number of shares to buy for each of the stocks? What is the corresponding dollar amount invested in each stock? 3. Construct a graph that shows how the optimal dollar return varies with the minimum investment floor for the stocks (currently $100,000; vary it up to $300,000, by step of $100,000).

An investment manager wants to determine an optimal portfolio for a wealthy client. The fund has $2.5 million to invest, and its objective is to maximize total dollar return from both growth and dividiends over the course of the coming year. The client has researched eight high-tech companies and wants the portfolio to consist of shares in these firms only. Three of the firms (S1-S3) are primarily software companies, three (H1-H3) are primarily hardware companies, and two (C1-C2) are internet consulting companies. The client has stipulated that no more than 40% of the investment be allocated to any one of these tree sectors. To assure diversification, at least $100,000 must be invested in each of the eight stocks. The table below gives estimates from the investment company's database relating to these stocks. These es- timates include the price per share, the projected annual growth rate in the share price, and the anticipated annual dividend payment per share. Stock Price per share Growth rate Dividend SI H3 CI C2 $40 $25 $2 S3 H1 H2 $50 $80 $60 $45 $60 $30 0.10 0.03 0.04 0.07 0.15 0.22 0.25 $2.00 $1.50 $3.50 $3.00 $2.00 $1.00 $1.80 $0.00 0.05 1. Formulate an optimization model for this planning problem (i.e., fractional outcomes for the decisions are acceptable). 2. Write an AMPL code to solve this problem. Report the maximum return on the portfolio. What is the optimal number of shares to buy for each of the stocks? What is the corresponding dollar amount invested in each stock? 3. Construct a graph that shows how the optimal dollar return varies with the minimum investment floor for the stocks (currently $100,000; vary it up to $300,000, by step of $100,000).

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An investment manager wants to determine an optimal portfolio for a wealthy client. The fund has $2.5 million to invest, and its objective is to maximize total dollar return from both growth and dividiends over the course of the coming year. The client has researched eight high-tech companies and wants the portfolio to consist of shares in these firms only. Three of the firms (S1-S3) are primarily software companies, three (H1-H3) are primarily hardware companies, and two (C1-C2) are internet consulting companies. The client has stipulated that no more than 40% of the investment be allocated to any one of these tree sectors. To assure diversification, at least $100,000 must be invested in each of the eight stocks. The table below gives estimates from the investment company's database relating to these stocks. These es- timates include the price per share, the projected annual growth rate in the share price, and the anticipated annual dividend payment per share. Stock Price per share Growth rate Dividend $1 S2 $40 S3 H1 H2 H3 C1 C2 $50 $80 $60 $45 $60 $30 $25 0.05 0.10 0.03 0.04 0.07 0.15 0.22 0.25 $2.00 $1.50 $3.50 $3.00 $2.00 $1.00 $1.80 $0.00 1. Formulate an optimization model for this planning problem (i.e., fractional outcomes for the decisions are acceptable). 2. Write an AMPL code to solve this problem. Report the maximum return on the portfolio. What is the optimal number of shares to buy for each of the stocks? What is the corresponding dollar amount invested in each stock? 3. Construct a graph that shows how the optimal dollar return varies with the minimum investment floor for the stocks (currently $100,000; vary it up to $300,000, by step of $100,000).
Transcribed Image Text:An investment manager wants to determine an optimal portfolio for a wealthy client. The fund has $2.5 million to invest, and its objective is to maximize total dollar return from both growth and dividiends over the course of the coming year. The client has researched eight high-tech companies and wants the portfolio to consist of shares in these firms only. Three of the firms (S1-S3) are primarily software companies, three (H1-H3) are primarily hardware companies, and two (C1-C2) are internet consulting companies. The client has stipulated that no more than 40% of the investment be allocated to any one of these tree sectors. To assure diversification, at least $100,000 must be invested in each of the eight stocks. The table below gives estimates from the investment company's database relating to these stocks. These es- timates include the price per share, the projected annual growth rate in the share price, and the anticipated annual dividend payment per share. Stock Price per share Growth rate Dividend $1 S2 $40 S3 H1 H2 H3 C1 C2 $50 $80 $60 $45 $60 $30 $25 0.05 0.10 0.03 0.04 0.07 0.15 0.22 0.25 $2.00 $1.50 $3.50 $3.00 $2.00 $1.00 $1.80 $0.00 1. Formulate an optimization model for this planning problem (i.e., fractional outcomes for the decisions are acceptable). 2. Write an AMPL code to solve this problem. Report the maximum return on the portfolio. What is the optimal number of shares to buy for each of the stocks? What is the corresponding dollar amount invested in each stock? 3. Construct a graph that shows how the optimal dollar return varies with the minimum investment floor for the stocks (currently $100,000; vary it up to $300,000, by step of $100,000).
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