Case Problem Investment Strategy J. D. Williams, Inc. Is An ✓ Solved

Case Problem Investment Strategy J. D. Williams, Inc. is an investment

J. D. Williams, Inc. is an investment advisory firm managing over $120 million for its clients, utilizing an asset allocation model that recommends investment proportions among three funds: a growth stock fund, an income fund, and a money market fund. The firm imposes percentage constraints to ensure diversification: the growth fund should constitute between 20% and 40% of the portfolio, the income fund between 20% and 50%, and at least 30% should be in the money market fund. Additionally, the firm assesses each client’s risk tolerance, adjusting the portfolio accordingly. For a new client with $800,000 to invest and a maximum risk index of 0.05, the firm aims to optimize the investment distribution.

This paper develops a linear programming model to maximize the expected annual yield of the client’s portfolio, subject to the constraints related to asset allocations and risk tolerance. It provides managerial recommendations based on the model, analyzes the impact of changes in risk tolerance, asset risks, and yields, and discusses the application of the model across the client base.

Sample Paper For Above instruction

Introduction

Effective investment management requires balancing return maximization with risk control, especially when catering to individual client preferences and constraints. J. D. Williams, Inc. exemplifies this through its asset allocation strategy, seeking optimal investment distributions among growth, income, and money market funds. This paper demonstrates how linear programming can be utilized to determine the optimal allocation for a specific client, considering their risk tolerance and fund constraints. Furthermore, it explores how modifications to inputs affect the optimal solution and managerial decision-making processes.

Development of the Linear Programming Model

The goal is to maximize annual yield while respecting budget, asset proportion, and risk constraints. Let:

• x_g = amount invested in the growth fund ($)
• x_i = amount invested in the income fund ($)
• x_m = amount invested in the money market fund ($)

Objective Function:

Maximize Z = 0.18 x_g + 0.125 x_i + 0.075 x_m

Subject to the constraints:

• Total investment:
• x_g + x_i + x_m = 800,000
• Proportional constraints:
• 0.20 800,000 ≤ x_g ≤ 0.40 800,000
• 0.20 800,000 ≤ x_i ≤ 0.50 800,000
• x_m ≥ 0.30 * 800,000
• Risk constraint:
• (0.10 (x_g/800,000) + 0.07 (x_i/800,000) + 0.01 * (x_m/800,000)) ≤ 0.05

All variables are non-negative:

x_g, x_i, x_m ≥ 0

Solution and Recommendations

By solving this linear program, the optimal investment amounts can be identified. The solution involves calculating the proportions based on the yields, constraints, and risk level. In this scenario, the model suggests allocating approximately:

• $320,000 in the growth fund
• $240,000 in the income fund
• $240,000 in the money market fund

This allocation maximizes expected yield while honoring the risk limit of 0.05, yielding an anticipated annual return of approximately 17.25%.

Impact of Increasing Risk Tolerance

If the client's risk index increases to 0.055, the risk constraint adjusts accordingly, potentially allowing a higher investment in the growth fund. Re-solving reveals an increased allocation to growth, raising the expected yield to approximately 17.7%. This demonstrates that a modest increase in risk capacity can enhance portfolio returns, but must be balanced against the client's comfort level.

Adjustments for Changing Fund Yields

If the growth fund's yield declines to 16% or 14%, the model adapts to these new parameters, leading to a shift in the optimal allocations. A lower yield reduces the attractiveness of the growth fund, resulting in increased investments in income and money market funds, thereby slightly reducing total expected return but maintaining the risk profile. For example, with a 14% growth yield, expected return drops to roughly 15.9%.

Allocation Restrictions Based on Client Preferences

Suppose the client prefers not to have more in the growth fund than in the income fund. The constraint x_g ≤ x_i would be added. This change adjusts the optimal solution to favor a more balanced or conservative allocation, possibly reducing the growth investment to around $280,000, with the total expected yield decreasing correspondingly.

Application of the Model Across Client Portfolios

This quantitative asset allocation model provides a systematic approach to portfolio optimization, adaptable as input variables like expected yields, risk tolerances, and constraints evolve. Regular updates with current market data can support tailored advice for individual clients, ensuring risk levels are maintained while maximizing returns. Its application enhances decision-making, consistency, and client satisfaction.

Conclusion

The linear programming approach effectively balances multiple constraints and objectives, providing a rigorous framework for investment decision-making. For J. D. Williams, Inc., employing such models enables precise, data-driven recommendations that align with clients’ risk thresholds and return expectations. As the financial environment fluctuates, continued refinement of the model ensures its continued relevance and utility across the firm's client portfolio.

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