Optimal Financial Planning Under Constraints

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Kibabii University College *

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1110

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Finance

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Nov 24, 2024

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1 Optimal Financial Planning Under Constraints By (Name) Affiliation Course Instructor Date

2 Part 1 - The Investment Portfolio Introduction This section will examine several investment possibilities and apply linear programming to ascertain the best way to divide the client's $150,000 into shares and a savings account. In order to choose the best bank account and share alternatives, preliminary research will be done, taking into account variables like interest rates, fees, and possible returns. These will influence the linear programming problem's objective function and constraints. To illustrate how the ideal investment combination is determined based on maximizing returns within the client's risk profile, comprehensive computations and graphs will be shown. Assumptions and limitations will also be covered. Client Information Based on discussions with the client, it has been determined that they have $150,000 available to invest for a 1 year timeframe. The client is relatively conservative and risk-averse in their investment approach. They expressed a strong preference to minimize their exposure to volatile assets like shares. Specifically, the client specified that the amount invested in shares should be less than or equal to half of the amount invested in lower-risk savings accounts. This constraint will inform the linear programming analysis to determine the optimal investment portfolio allocation. Other factors such as expected returns, interest rates, fees and the client's desire to maximize their profits within their risk tolerance will also inform the analysis. A tailored investment portfolio recommendation will be presented to align with the client’s conservative risk appetite and goal of maximizing returns on their $150,000 lump sum investment. Word count: 150 Banking Options

3 After researching savings account options from major Australian banks, I recommend investing the savings portion of the portfolio into the RAMS Saver Account offered by Westpac. This account offers a competitive ongoing variable interest rate of 3.00% p.a. with no ongoing fees (Westpac, 2023). The account requires a minimum deposit of $200 to open and $0 to maintain the minimum balance. Interest is calculated daily and paid monthly. One limitation is that the interest rate is variable and subject to change, however the rate has remained steady at 3.00% for the past year indicating stability. The RAMS Saver Account was selected for its high interest rate, no fees, and easy online accessibility for the client to deposit, track, and withdraw funds. Based on an initial investment of $100,000 into this savings account at the current published rate of 3.00% p.a., the expected return after 1 year is $103,000, calculated as follows: Original Deposit: $100,000 Interest Rate: 3.00% p.a Interest Earned in 1 Year: $100,000 x 0.03 = $3,000 Balance after 1 Year: $100,000 + $3,000 = $103,000 In summary, the RAMS Saver Account is recommended to optimize returns on the savings portion of the client’s portfolio based on its highly competitive interest rate and no fees structure. Investment in Shares Options After researching companies listed on the Australian Securities Exchange (ASX), I recommend investing the shares portion of the portfolio into HMC Capital Ltd (HMC). HMC is an investment management services company that offers stable returns. As of November 16th, 2023, HMC is trading at $9.60 per share, up 2.1% from $9.40 per share at the start of the year

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4 (ASX, 2023). This indicates a healthy upwards trajectory and potential for further capital appreciation. Dividends are paid biannually and the current dividend yield is 5% or $0.48 per share annually. There are no trading fees to buy or sell HMC shares through most standard online brokers. Based on the current share price of $9.60 and dividend yield of 5%, the expected total return in the first year from investing $50,000 into HMC shares is: - Capital appreciation of 2.1% of $50,000 = $1,050 - Dividend income of 5% of $50,000 = $2,500 - Total expected return = $1,050 + $2,500 = $3,550 This equates to an expected return of $3,550 on an initial $50,000 investment, or 5.8% total return over the 1 year time horizon. In summary, investing in HMC shares is expected to provide the highest returns on the shares portion of the portfolio based on strong historical performance and steady dividend payments. Analysis To determine the optimal investment allocation, a linear programming model was formulated with the objective of maximizing total returns within the client's conservative risk tolerance. The decision variables were: x = amount invested in the RAMS Saver Account y = amount invested in HMC shares The constraints were: 1) x + y = $150,000 (Total amount available to invest) 2) y ≤ 0.5x (Amount in shares ≤ 50% of amount in savings)

5 3) x ≥ 0 and y ≥ 0 (Non-negativity constraints) 4) x ≤ $150,000 (Maximum amount to invest in savings) 5) y ≤ $150,000 (Maximum amount to invest in shares) The objective function was: Maximize: R = 0.03x + 0.058y Where 0.03 is the expected 3% return from the savings account, and 0.058 is the expected 5.8% return from HMC shares based on current performance. Optimal solution was obtained: Constraint Equation Values (x, y) 1 x + y =150,000 (0, 150,000), (100,000, 50,000) 2 y ≤32 x (0, 0), (100,000, 66,667) 3 y ≥0.5 x (0, 0), (100,000, 50,000) 4 x ≤100,000 (0, 50,000), (100,000, 50,000) 5 y ≤50,000 (0, 0), (100,000, 50,000) Appendix A

6 0 20000 40000 60000 80000 100000 120000 140000 160000 0 20000 40000 60000 80000 100000 120000 140000 160000 (100,000, 50,000) --------------- \ \ (0, 150,000) ------------------------ (100,000, 50,000) / (0, 0) -----------------------------/ (0, 50,000) x = $100,000 y = $50,000 Therefore, the maximum returns within the client's risk tolerance is achieved by investing $100,000 in the RAMS Saver Account and $50,000 in HMC shares. The total expected return after 1 year is: Return on $100,000 in savings at 3% interest = $3,000

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7 Return on $50,000 in shares at 5.8% return = $2,900 Total Expected Return = $3,000 + $2,900 = $5,900 This demonstrates that by optimizing the investment portfolio allocation using linear programming, the maximum first year returns possible within the client’s risk profile is $5,900. Conclusion In conclusion, this analysis determined an optimal portfolio allocation of $100,000 in a RAMS Saver Account and $50,000 invested in HMC shares to maximize expected returns within the client’s conservative risk tolerance. Applying linear programming led to an expected total return of $5,900 in the first year. This demonstrates an optimized investment strategy tailored specifically to the client’s financial situation and goals. While assumptions were made about expected returns, this provides a basis for an investment plan that aligns with the client’s objectives. Overall, a balanced approach between savings and shares was recommended to generate optimal returns on the client’s $150,000 lump sum investment.

8 Reference ASX. (2023). HMC Historical Share Prices. Retrieved from https://www.asx.com.au/HMC Westpac. (2023). RAMS Saver Account. Retrieved from https://www.westpac.com.au/personal- banking/bank-accounts/savings-accounts/rams-saver-account/

9 Appendix A 0 20000 40000 60000 80000 100000 120000 140000 160000 0 20000 40000 60000 80000 100000 120000 140000 160000 Appendix B Constraint Equation Values (x, y) 1 x + y =150,000 (0, 150,000), (100,000, 50,000) 2 y ≤32 x (0, 0), (100,000, 66,667) 3 y ≥0.5 x (0, 0), (100,000, 50,000) 4 x ≤100,000 (0, 50,000), (100,000, 50,000) 5 y ≤50,000 (0, 0), (100,000, 50,000)

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