March & Sanchis Investments Ltd.¶
Problem Definition¶
Suppose you are a financial advisor at March & Sanchis Investments Ltd. and your client has €1,000,000 to invest in four different types of assets: stocks, bonds, real estate, and crypto assets, with the Expected Returns and risk (an estimation of the risk per euro invested) expressed in the table below:
Asset Type |
Expected Return (%) |
Risk (%) |
|---|---|---|
Stocks |
10 |
1.25 |
Bonds |
6 |
0.5 |
Real Estate |
8 |
0.7 |
Crypto Assets |
15 |
2.1 |
Your task is to help the client select the optimal portfolio of investments, maximizing the Expected Return. Assume that the investments are independent and take into account the following constraints:
Budget: The total investment cannot exceed the budget of the client (€1,000,000)
Personal Preferences: The client wants to invest at least €200,000 in real estate due to personal interests in owning property, and does not want to invest more than €400,000 in crypto assets as she would like to be cautious and limit exposure.
Risk: The overall risk estimation cannot exceed 12% of the expected return
Model this problem as a continuous linear programming problem. What are the decision variables? What is the objective function? What are the constraints?