problem1) An investor seeks to make a portfolio from three types of securities: Treasury Bills (T), Corporate Paper (C), and Junk Bonds (J). Table lists the expected rates of return for the asset types and their average risk (on a 1–5 scale, where ‘5’ denotes maximum risk). Investor look for portfolio allocations (T + C + J = 1) which will maximize the expected return on her portfolio, while maintaining an overall risk of no more than ‘3’.

Security           Return (%)            Risk
Treasury Bills         2.5                  2.0
Corporate Papers     5.0                  2.5
Junk Bonds          8.0                  5.0

(a) Formulate the investor’s linear programming problem.

(b) Find out the investor’s optimal portfolio allocation and the maximum expected return on her portfolio. (To find out the optimal portfolio allocation, you would require to use your constraints from part (a). To find maximum expected return on her portfolio, use the objective function equation from part (a) and the optimal asset allocation.) (Hint: the two assets in the optimal portfolio are corporate papers and junk bonds)