Question

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

(a) Express Cov(RA,RB) as a function of r

(b) Calculate the expected return of a portfolio that contains share α of stock A and share 1−α of stock B. Your answer should be a function of α (c) Calculate the variance of the portfolio from part B (Hint: returns are now potentially dependent)

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

(e) For what range of values for r is your α*(r) 6 1? What is the solution to the above problem if r is outside of that range? (Hint: draw a graph and find α* ∈ [0,1] that minimizes variance) (f) Is α*(r) increasing or decreading? (Hint: take the derivative with respect to r)

(g) Which r wouldtheinvestorprefertohave, positiveornegative? Whatistheintuition for that result? 3

Answer 1