Consider two stocks with returns RA and RB with the followingproperties. RA takes values -10 and +20 with probabilities 1/2. RBtakes value -20 with probability 1/3 and +50 with probability 2/3.Corr(RA,RB) = r (some number between -1 and 1). Answer thefollowing questions
(a) Express Cov(RA,RB) as a function of r
(b) Calculate the expected return of a portfolio that containsshare ? of stock A and share 1?? of stock B. Your answer should bea function of ? (c) Calculate the variance of the portfolio frompart B (Hint: returns are now potentially dependent)
(d) What value of ?* minimizes the variance of the portfolio?Your answer should be a function of r, denoted by ?*(r).
(e) For what range of values for r is your ?*(r) 6 1? What isthe solution to the above problem if r is outside of that range?(Hint: draw a graph and find ?* ? [0,1] that minimizes variance)(f) Is ?*(r) increasing or decreading? (Hint: take the derivativewith respect to r)
(g) Which r wouldtheinvestorprefertohave, positiveornegative?Whatistheintuition for that result? 3
