Question

Consider a client, Parker, who would like to purchase Portfolio X consisting of four shares of Holden Aeronautics, two shares of Hossain Botanicals, and three shares of Yusun Corporation. Model this problem as a linear system and show that it is possible for Parker to purchase Portfolio X by buying a number of your curated Portfolios A, B, and C.

Show that Parker could ask for any Portfolio Y, and there would be some linear combination of Portfolios A, B, and C which would add up to Portfolio Y.
What happens if Parker asks for a portfolio consisting of a single share of Holden Aeronautics? Discuss whether or not your answer is financially reasonable.

Answer 1

Parker's desire for Portfolio X can be modeled as a linear system to determine if it can be created from Portfolios A, B, and C. Financially, purchasing individual shares may not be reasonable due to extra costs. Stock purchases can be made through exchanges or online brokers, and portfolio diversification is key to risk mitigation.

Step-by-step explanation:

Modeling Parker's request for Portfolio X as a linear system involves determining if Portfolios A, B, and C can combine to form the desired portfolio. Assume that Portfolios A, B, and C contain different quantities of shares of Holden Aeronautics, Hossain Botanicals, and Yusun Corporation. We can represent these as vectors or matrices to find a linear combination of A, B, and C that equals Portfolio X.

Suppose Parker wants a portfolio with only one share of Holden Aeronautics. In a financial sense, this is possible as long as there's a portfolio that offers single shares or the minimum unit of shares is one. However, financially, buying shares individually from separate portfolios may not be reasonable due to transaction costs, minimum purchase requirements, or the structure of investment portfolios.

To purchase stocks, an individual can go to a stock exchange or use an online brokerage platform. It is important to diversify your portfolio to mitigate risk by spreading investments across different asset classes and markets. Alphonso's scenario with bus tickets and burgers demonstrates a budget constraint and the trade-offs consumers face, which is conceptually similar to managing a diversified portfolio.