DolaDola Investment specializes in creating new investment instruments from existing funds in the market. They create new instruments primarily based on the following two funds. The table below shows the average return and potential loss for each fund in terms of the percentage of the amount invested in the fund. For example, every dollar invested in Fund A will generate a 30% average return and a 45% potential loss. Investing in these funds would incur trading costs. For Fund A, the trading cost is approximately 1.5% of the amount invested, whereas for Fund B, the trading cost is 1.2% of the amount invested.
(a) The firm aims to create two new investment instruments, a High-Yield Investment and a Low-Risk Investment both composed of differing proportions of Fund A and B. The High-Yield Investment must have at least a 25% average return, whereas the Low-Risk Investment cannot have more than a 30% potential loss. The firm has in total 1 million dollars of capital to invest in Fund A and B to create the new investment instruments. Formulate an algebraic model that enables the firm to minimize the total trading costs while creating the new investments. Do not solve the model.
(b) Suppose that the DolaDola Investment decides to create only one new investment (i.e. if the High-Yield investment is created than the Low-Risk investment cannot be created). Formulate this requirement as constraints to be added to the original formulation in (a).
Average return Potential loss
Fund A 30% 45%
Fund B 20% 25%