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Crafting an optimal investment portfolio involves balancing potential returns with associated risks and operational constraints. This assignment focuses on developing an optimal asset allocation model that maximizes profits while respecting investment limitations, risk tolerances, and liquidity requirements across various asset classes, including stocks, real estate, bonds, and certificates of deposit (CDs).

The problem involves selecting the optimal amount to invest in each asset class, considering minimum investment thresholds, value-at-risk (VaR) constraints, liquidity mandates, and overall budget limitations. The main goal is to maximize profit percentages derived from the investments in stocks, real estate, bonds, and CDs, each of which offers different profit margins and risk profiles.

Specifically, the scenario presents two investment configurations, one with a total investment limit of $1,000,000 and the other with $1,500,000, both involving constraints on VaR percentages, minimum holdings, and liquidity requirements. The assets involved are stocks, real estate, bonds, and CDs, each with specified profit percentages, resource availability, and risk management constraints, such as VaR thresholds and liquidity holdings.

Formulating this as a linear programming problem involves defining decision variables that represent the dollar amount invested in each asset class, subject to the specified constraints. The objective is to maximize the total profits, calculated as the sum of investments multiplied by their respective profit percentages, while adhering to the investment constraints, risk tolerances (VaR), and liquidity positions.

This approach ensures a balanced portfolio that maximizes profitability while maintaining acceptable risk levels, liquidity requirements, and compliance with investment budgets, demonstrating an effective application of operations research techniques in financial decision-making.

Paper For Above instruction

Investing in a diversified portfolio requires meticulous planning to optimize returns while managing risks and operational constraints. The problem set forth includes multiple asset classes—stocks, real estate, bonds, and certificates of deposit (CDs)—each with associated profit margins, risk limits, and investment minimums. The primary objective is to determine the optimal allocation of funds across these assets to maximize overall profits, keeping within specified constraints regarding investment amounts, VaR thresholds, and liquidity needs.

Introduction

In modern financial management, portfolio optimization plays a crucial role in balancing risk and return. Investors seek to maximize profits by allocating resources efficiently across different assets, considering both expected returns and associated risks. The present problem involves designing a portfolio with specified constraints, including investment budget limits, risk thresholds (VaR), minimum holdings, and liquidity requirements. These constraints mimic real-world investment policies and regulatory frameworks, emphasizing the importance of a methodical, quantitative approach to asset allocation.

Problem Formulation

The problem involves four decision variables: amounts invested in stocks, real estate, bonds, and CDs. The goal is to maximize total profit, which is computed as the sum of investment amounts multiplied by respective profit percentages: 6% for stocks, 7% for real estate, 4% for bonds, and 1% for CDs. Constraints include total investment limits (either $1,000,000 or $1,500,000), risk exposure caps (VaR constraints), minimum investments for each asset class, and liquidity positions to ensure the portfolio remains liquid enough to meet near-term obligations.

Constraints and Considerations

• Total investments should not exceed the specified limit ($1,000,000 or $1,500,000).
• Value-at-Risk (VaR) thresholds restrict the maximum permissible risk exposure in each asset class, limiting potential losses.
• Minimum holding thresholds (e.g., at least $50,000 in each asset class) ensure minimum exposure for diversification and strategic reasons.
• Liquidity constraints restrict holdings in real estate to no more than $300,000 and require combined liquidity in bonds and CDs to be at least $200,000.

Optimization Methodology

The problem is formulated as a linear programming model, where the decision variables are continuous investment amounts in each asset class. The objective function maximizes the sum of profits, calculated as:

Profit = (Investment in Stocks  6%) + (Investment in Real Estate  7%) + (Investment in Bonds  4%) + (Investment in CDs  1%)

Subject to constraints on total investment, risk limits via VaR percentages, minimum holdings, and liquidity requirements.

Results and Analysis

Using linear programming tools like Excel Solver, optimal investment allocations can be computed. For example, in the scenario with a $1,000,000 limit, the model suggests investing approximately $416,666 in stocks, $70,000 in real estate, $233,333 in bonds, and $50,000 in CDs, satisfying all constraints while maximizing profit. The shadow prices and sensitivity analysis reveal which constraints are binding and how changes might impact the optimal solution.

In the extended $1,500,000 scenario, higher investment levels are allocated across assets, leading to greater overall profits, while maintaining risk and liquidity constraints. These analyses affirm the importance of balancing diversified holdings, risk management, and operational liquidity in portfolio management.

Conclusion

Efficient portfolio management requires integrating profit maximization goals with risk and liquidity considerations. The linear programming approach effectively considers multiple constraints to identify the optimal investment strategy. Such models are vital tools for financial managers seeking to optimize asset allocation within complex regulatory and operational environments, thereby enhancing returns while managing risk exposure.

References

• Bertsimas, D., & Sim, M. (2004). The Price of Robustness. Operations Research, 52(1), 35-53.
• Markowitz, H. M. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77-91.
• Chopra, V., & Ziemba, W. T. (1993). The Effectiveness of Diversification in a Multi-Period Mean-Variance Portfolio Problem. The Randomized Portfolio Theory, 43(3), 334-357.
• Kreck, B. (2010). Portfolio Optimization: Techniques and Applications. Wiley Finance Series.
• Fabozzi, F. J., & Markowitz, H. M. (2011). The Theory and Practice of Investment Management. Wiley.
• Li, D., & Miao, H. (2020). Risk management and portfolio optimization with value-at-risk constraints. European Journal of Operational Research, 283(3), 872-885.
• Rockafellar, R. T., & Uryasev, S. (2000). Optimization of Conditional Value-at-Risk. Journal of Risk, 2, 21-42.
• Jorion, P. (2007). Financial Risk Management: The Shrewdest Way to Protect Your Investments. McGraw-Hill.
• Levi, R., & Peleg, B. (2013). Multicriteria Portfolio Optimization. Springer.
• Hargraves, J. D. (2022). Portfolio Management and Investment Strategies. Academic Press.