Problem 2-39
Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs $100 and provides an annual rate of return of 4%.
The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $60,000. According to Innis’s risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3; the higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis’s client also specifies that at least $300,000 be invested in the money market fund.
| Let S | = | number of units purchased in the stock fund |
| M | = | number of units purchased in the money market fund |
Assume no. of units in stock market = 4,000 units and in money market = 10,000 units
Minimum annual income is $ 60,000
Taking a base as $ 100 for the price per unit of stock and money market fund.
Therefore, return in stock fund will be 5% and in money market fund will be 4%.
So, annual income will be ($ 4000*5) + ($ 10,000*4) = $ 60,000
Value of investment is 8* no. of shares in stock fund i.e. 4,000 + 3* no. of shares in the money market fund i.e. 10,000
Therefore, total Value = ($ 4,000*8) +($ 10,000*3) = $ 62,000
But,
If everything is invested in the stock fund the return on investment will be much higher even after considering the 8% risk.
i.e. Investment in stock fund = $ 1,200,000
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