Question

1. A portfolio consists of three stocks, S1, S2, and S3. X1, X2, and X3 represent the amount of money invested in each of the three stocks.
   1. The amount invested in stock 1 must not exceed 110% of the amount invested in stock 2 and 3 combined. Which constraint expresses this requirement?
      1. X1 – (X2 +X3) <= 110
      2. 1.1*X1 <= X2 + X3
      3. X1 >= 1.1(X2 + X3)
      4. None of the above
   2. The annual rates of return of the three stocks for two possible scenarios are:
      (i) Best case scenario 5.5%, 6.5%, and 8%. (ii) Worst case scenario -1.5%, 0.5%, 4%. Management wants to make sure the overall annual return does not fall short of $10000. Which constraint meet this requirement?
      
      1. 5.5%X1+6.5%X2+8%X3 >= 10000
      2. – 0.015X1 + 0.005X2 + 0.04X3 >= 10000
      3. (0.055+(– 0.015)X1 + (0.065+0.005)X2 + (0.08+0.04)X3 >=10000

d. None of the above

Answer 1

Answer D None of the above

The condition is the amount in A should not exceed 110% of Amount invested in stock B & C. So it should be less than or equal to 110%. Thus the equation shall be X1 < = 1.1(X2+X3)

Answer B – 0.015X1 + 0.005X2 + 0.04X3 >= 10000

The requirement is to have minimum income more than $10000 and the worst return that can happen is -1.5%, 0.5%, and 4%. So the total return from all the stocks in the worst case shall be more than 10000, ie.

– 0.015X1 + 0.005X2 + 0.04X3 >= 10000