It Is Due In 12 Hours From Now Blair And Rosen Inc Br

It Is Due In 12 Hours From Nowblair And Rosen Inc Br Is A Broker

It is due in 12 hours from now. Blair and Rosen, Inc. (B&R) is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client who contacted B&R this past week has a maximum of $50,000 to invest. B&R's investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of 12%, while the Blue Chip fund has a projected annual return of 9%.

The investment advisor requires that at most $35,000 of the client's funds should be invested in the Internet fund. B&R services include a risk rating for each investment alternative. The Internet fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per thousand dollars invested. The Blue Chip fund has a risk rating of 4 per thousand dollars invested. For example, if $10,000 is invested in each of the two investment funds, B&R's risk rating for the portfolio would be 6(10) + 4(10) = 100.

Finally, B&R developed a questionnaire to measure each client's risk tolerance. Based on the responses, each client is classified as a conservative, moderate, or aggressive investor. Suppose that the questionnaire results classified the current client as a moderate investor. B&R recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 240.

Paper For Above instruction

The problem presented by Blair and Rosen, Inc. involves optimizing an investment portfolio for a client based on multiple criteria, including return maximization and risk management constraints. This scenario exemplifies a linear programming (LP) problem, aiming to maximize the annual return on investments while respecting risk limits and investment caps. The decision variables are the amounts invested in each of the two funds: the Internet fund and the Blue Chip fund. The resources constraining the solution include the total investment limit, the allocation cap for the risky fund, and the maximum risk rating aligned with the client's risk tolerance. The model is designed to allocate funds between the funds to maximize returns without exceeding the specified risk threshold or the available capital, ensuring a feasible and optimized investment plan.

The model incorporates the following components:

  • Decision variables: x₁ (amount invested in the Internet fund), x₂ (amount invested in the Blue Chip fund)
  • Objective function: Maximize total annual return: 0.12x₁ + 0.09x₂
  • Constraints:
  • Total investment cannot exceed $50,000: x₁ + x₂ ≤ 50,000
  • Investment in Internet fund cannot exceed $35,000: x₁ ≤ 35,000
  • Risk rating constraint for a moderate investor (maximum risk rating of 240): 6/1000 x₁ + 4/1000 x₂ ≤ 240
  • Non-negativity constraints: x₁ ≥ 0, x₂ ≥ 0

Linear Programming Model

Maximize: Z = 0.12x₁ + 0.09x₂

Subject to:

  • x₁ + x₂ ≤ 50,000
  • x₁ ≤ 35,000
  • 0.006x₁ + 0.004x₂ ≤ 240
  • x₁ ≥ 0, x₂ ≥ 0

Using Excel's Solver, the optimal solution is determined by setting up the decision variables, objective function, and constraints accordingly. The optimal investment amounts for the moderate investor should allocate funds such that the total return is maximized, while the risk rating remains under the specified limit. This solution indicates the precise amounts to invest in each fund, providing an investment strategy aligned with the client's risk tolerance and investment cap.

For the aggressive investor, with a maximum risk rating of 320, the constraints are similar but with a higher risk tolerance, allowing for potentially higher investments in riskier assets. The recommended investment portfolio under this strategy would involve increasing allocations to the Internet fund within the allowed limit. This approach potentially yields higher returns but also exposes the client to more risk, as indicated by the increased risk rating. The optimal solution would reflect a higher investment in the Internet fund, balancing the higher risk capacity with the goal of maximizing returns.

For the conservative investor, with a maximum risk rating of 160, the portfolio should be oriented toward safer investments. The LP model should be solved with these constraints, resulting in a portfolio with minimal exposure to risk. The slack variable concerning the total investment constraint indicates the unused portion of available funds, which in this case, would be zero or a small margin if the maximum investment limits are fully utilized. This slack variable's interpretation highlights the difference between the total funds available and the actual invested amount, reflecting the conservative approach's cautious nature.

Conclusion

The linear programming model effectively guides investment decisions by balancing maximum return against risk constraints tailored to clients' profiles. Using tools like Excel Solver simplifies solving such LP problems, enabling financial advisors to recommend optimized, customized portfolios. Sensitivity analysis further informs the stability of the solution, indicating how changes in constraints or parameters influence the optimal investment distribution, thus enhancing strategic decision-making in portfolio management.

References

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  • Bertsimas, D., & Tsitsiklis, J. (1997). Introduction to Linear Optimization. Athena Scientific.
  • Hiller, J. M., & Lieberman, G. J. (2015). Introduction to Operations Research. McGraw-Hill Education.
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