Question

Bonus (4 Marks) S Assume the following statistics for Stocks A, B, and C: SE Stock A Expected return NNNNNNNN 20.0% Standard deviation 23.2% Stock B 14.0% 13.6% Stock C 10.0% 19.5% Stock B Stock C The correlation coefficients between the three stocks are: Stock A Stock A TT Stock B 0.286 Stock C 0.132 -0.605 1. An investor seeks a portfolio return of 12 percent. Which combinations of the three stocks accomplish this objective? Which of those combinations achieves the least amount of risk? 2. An investor seeks a maximum variance of the portfolio of 1 percent. Which combinations of the three stocks accomplish this objective? Which of those combinations achieves the highest expected return? Equation Needed EUR) = É[xEUR)] σ' ΣΣ » », P,σσ where x = proportion of portfolio where x = proportion of total investment in Security i invested in security i and P. - correlation coefficient between

Answer 1

Solution:

Here equal weights are assumed for both securities in a combination.

1)

Retwen of Portfolid) = RAWA & ROWB A 209 TRA= Rp = R = Return Retwer Return on on on security A stock B stock c (stock - 14% = 10% WA weight WB - weight We a weight of of of security A security B. security c. cousination Here a) stock b) Stock c) stock are 3 A and A and B and B a C (2013) portfolio Here the 0.5 for metiens weight store A for are and combination (a) assumed 0.5 for stau B. - 120 x0.5) + ( 14 *0.) - 17% b) WA door i was w =0.5 -=[ 20x0.5) + C70 x0.5) = 15%. c) Wo=0.5 Wc=0.5 TUX015) + ( 10X0. 5 1 2% & combination objective B of and 12 c %. achieve Return the

Date Pace Rish i s denoted by a T= A + ow? + 2XLOVARTWAX WB 5 = retot = 2 risk of Poutfolio AB variance of stoull (here i stock can be A,B,or i Co-variance d ni stock. (2 stout can be AB, BC, AC). con 2 Stou - Rish of different to combinations TARJ (23.2²(0.5+ (13.67 (0.5² + 12x 0.286 x0=5X0.5 = 13.4527. N a - 2x 0.132x0.5 x 0.5 b) Ac = |(23.270:s)} + ( 195*co-sy' + 2 x 0-132 xo»5 x 0.5 = -15.1554,1 02 Joe (13.660.5² + (1905) (0.5)² + 2x(-0.605) x0.5x0.5 = 11.874 %. Contbination the least Band cx achieves Risu (ie 11-874%)
2)

Date Page deviation) Variance for combinations variance - T2 a2= (5) 2 (square of standard for AB = (13.452)² = 181 LAC = (15.155)² = 230 BC (11.874) ² = 141 None of the the combination objective . expected return combinations are for different a) AB 5) AC C B C = : = 17%. 15% 120. combination achieves lee 17% of the stom A and B highest Return expected-