Question

4. Consider two stocks with returns ?_A and ?_B with the following properties. ?_A takes values -10 and +20 with probabilities 1/2. ?_B takes value -20 with probability 1/3 and +50 with probability 2/3. ????(?_A,?_B) = ? (some number between -1 and 1). Answer the following questions

   1. (a) Express C??(?_A,?_B) as a function of ?

   2. (b) Calculate the expected return of a portfolio that contains share ? of stock ? and

      share 1 − ? of stock ?. Your answer should be a function of ?

   3. (c) Calculate the variance of the portfolio from part ? (Hint: returns are now potentially dependent)

   4. (d) What value of ?* minimizes the variance of the portfolio? Your answer should be a function of ?, denoted by ?*(?).

5. (e) For what range of values for ? is your ?*(?) ≤ 1? What is the solution to the above problem if ? is outside of that range? (Hint: draw a graph and nd ?* ∈ [0, 1] that minimizes variance)

6. (f) Is ?*(?) increasing or decreading? (Hint: take the derivative with respect to ?)

7. (g) Which ? would the investor prefer to have, positive or negative? What is the intuition for that result?

Answer 1