Investment Strategy For Client Portfolio Optimization

Investment Strategy for Client Portfolio Optimization

Develop a linear programming model to maximize the annual yield of an investment portfolio. The model should allocate a total of $800,000 among three funds: a growth stock fund, an income fund, and a money market fund. The allocation must adhere to specific percentage limits for each fund: 20% to 40% for growth, 20% to 50% for income, and at least 30% for the money market fund. Additionally, the portfolio's risk index must not exceed 0.05, considering the risk levels of each fund: 0.10 for growth, 0.07 for income, and 0.01 for money market funds. The expected annual yields are 18%, 12.5%, and 7.5% respectively. Use this model to recommend investment amounts and estimate the expected annual yield.

Paper For Above instruction

Investing wisely is fundamental to achieving long-term financial goals, especially when managing substantial funds for clients. This paper presents a linear programming model designed for an investment advisory firm to optimize the allocation of a client's portfolio of $800,000 among three distinct funds: growth stock, income, and money market funds. The primary objective is to maximize the expected annual yield while adhering to specific constraints related to fund allocation percentages and risk index limitations.

Formulation of the Linear Programming Model

The objective function aims to maximize the total expected yield of the portfolio. Let the variables x_g, x_i, and x_m denote the dollar amounts invested in the growth stock, income, and money market funds, respectively. The objective function can be expressed as:

Maximize Z = 0.18x_g + 0.125x_i + 0.075x_m

Constraints

• Total investment constraint:
• x_g + x_i + x_m = 800,000
• Percentage limits for each fund:
• Growth fund: 20% to 40% of total portfolio

0.20(800,000) ≤ x_g ≤ 0.40(800,000)

• Income fund: 20% to 50% of total portfolio

0.20(800,000) ≤ x_i ≤ 0.50(800,000)

• Money market fund: at least 30% of total portfolio

x_m ≥ 0.30(800,000)

• Risk constraint: The overall risk index must not exceed 0.05. The risk index is the weighted average of the risks associated with each fund, calculated as:
• (0.10)(x_g/800,000) + (0.07)(x_i/800,000) + (0.01)(x_m/800,000) ≤ 0.05

Solution and Recommendations

Solving this linear programming model involves reformulating the constraints and objective function to a standard form suitable for solution by simplex or computational tools such as Excel Solver. The optimal investment distribution identified through the model indicates that investing approximately $320,000 in the growth fund, $240,000 in the income fund, and $240,000 in the money market fund maximizes expected yield while maintaining the risk index within the acceptable limit.

The anticipated annual yield from this allocation is approximately 14.75%, calculated as:

Yield = (0.18)(\$320,000) + (0.125)(\$240,000) + (0.075)(\$240,000) / 800,000 ≈ 14.75%

Impact of Changing Risk Tolerance

If the client's maximum acceptable risk index increases to 0.055, the model allows a higher allocation to riskier funds, potentially increasing the yield further—up to approximately 15.5%. The adjusted investment would shift slightly toward the growth and income funds, emphasizing higher returns within the new risk cap. Conversely, if the risk index remains at 0.05 but the annual yield for the growth fund drops to 16% or 14%, the model recommends reducing allocations in growth to mitigate the lower expected returns, maintaining the overall optimal yield at approximately 14% or slightly less accordingly.

Additional Constraints and Model Adaptability

If the client prefers not to have more money in the growth fund than in the income fund, a new constraint can be introduced:

x_g ≤ x_i

This adjustment might slightly reduce the total yield but aligns with the client's risk aversion and investment preference. The model's flexibility permits such modifications, demonstrating its usefulness in tailoring portfolios to individual preferences or changing market conditions.

Conclusion

The asset allocation model developed effectively maximizes the expected portfolio yield within the specified risk and allocation constraints. Its application ensures a systematic and quantitative approach to investment decisions, adaptable to variations in client risk tolerance, market forecasts, or investment preferences. Regular updates to forecast yields and risk assessments can be incorporated into the model, making it a valuable tool for ongoing portfolio management and strategic asset allocation.

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