As the CIO of this pension fund, you have a choices to invest in five portfolios
This quiz refers to the data presented in this Excel file:
A Pension Fund has $500,000,000 in assets. It has a 15 year liability shown below in “Cash required to pay liabilities”. As the CIO of this pension fund, you have a choices to invest in five portfolios:
- A high-yield Bond Portfolio 1, has a nominal price of $980/share, and pays $60 per year in coupon payments and matures after 5 years.
- A corporate bond Portfolio 2, has a nominal price of $970/share, and pays $30 per year in coupon payments and matures after 10 years.
- A long-term government Bond Portfolio 3, has a nominal price of $1,050/share, and pays $35 in coupon payments and matures after 15 years.
- A stock fund 1 at $1000/share nominal price, which is expected to pay a dividend of $24/year. For the next 15 years.
- A stock fund 2 at $1000/share nominal price, which is expected to pay a dividend of $30/year. For the next 15 years.
Note, the stock funds do not mature, and we assume they are expected to pay consistent dividends for 15 years. The terminal value of the stocks after 15 years are $2,500 and $2,000 respectively. Cash does not pay interest. Historical Returns of similar investments are listed in “Historical Return” Sheet.
Problem?
As the CIO of this pension fund, your job is
- allocating the initial $500MM to the 5 investment options such that you generate enough cash flow (coupone, principles and dividends) to cover cash liabilities.
- Make sure after 15 years, assets will grow to at least $600MM (that is $600,000,000).
- In addition you would like to keep the volatility of your portfolio in the first year as low as possible.
How would you allocate your capital?
Please note, you can own fractional shares. And your portfolio will be a buy-and-hold portfolio, i.e., no rebalancing.
Please complete the asset allocation/portfolio construction model using nonlinear constrained optimization. Clearly identify/label decision variables, objective function, and constraints. Please setup solver appropriately, and generate the optimal answer. Here is how the points will break down:
- Decision Variables: 2 points
- Objective Function: 1 point
- Constraints: 2 points
- Solver Setup: 2 points
- Correct Final Answer: 1 point.
- Model Setup Clarity: 2 points.