An investment company can invest in three stocks. From past data, the means and standard deviations of annual returns have been estimated as shown in Table 3. The correlations between the annual returns on the stocks are listed in Table 4.

The company has $100,000 to invest with the following requirements:

(i) No more than 50% should be invested on any stock.

(ii) Invest all $100,000 among the three stocks.

(iii) Invest at least $10,000 each in stocks 1 and 3.

(iv) Achieve maximum portfolio return.

(v) Achieve minimum portfolio variance.

a)Formulate the above problem as a bicriteria problem.

b)Reformulate the problem if the objective were to find a minimum variance portfolio that yields an average portfolio return of at least 12%.

Table 3 - Means & Standard Deviations (STDEV) Stock 1 Stock 2 Stock 3 Means 0.14 0.11 0.10 STDEV 0.20 0.15 0.08 Table 4- Correlations Stocks 1 & 2 Stocks 1 & 3 Stocks 2 & 3 Correlation 0.6 0.4 0.7