Question

An investor obtains the following probability distributions for two stocks:

                State_i       P_i             R_X      R_Y
                ______      ____     _____    ____
                                    1          30%      -10%     40%
                                    2          40%       10%   -20%
                                    3          30%       30 %     30
a. What are the expected returns for the Security X  and for Security Y?
b. What are the standard deviations of these two stocks?
c. What are the CVs for these two securities?

Answer 1

3 Given, State i Pi Rx Ry I 30% – 101. 40% 2 40% 10% - 20% 3. 301. 301 30%. a) Expected Returns for security & Expected Returns - Summation of Rx and its by multiplying with probability & Rx & Pi = (0.30*(-10°]+[0.40* 10')) + [0.30 * 30/.] = (-37) + (4*)) +(9%). = 10% Expected Returns for security Y - (same as above formula). & Ry* Pi = [0.30 * 40%]+[0.40*(-20%)] +[0.30 * 36/.] - 12%. + (-81) + 9.4. - 137

Expected return for stock X = 10%

Expected return for stock Y = 13%

Pi indicates Probability index

b) Standard Deviation for two stocks: For stock X: Formula for Standard Deviation - Pi where, xo = Return of security . EPi = 0.30+ 0.40+0.30 = 1.00 Standard deviation for stock x. 10.301-10-107 + 0.40/10 - 10] +0.30 [30-10) -1° 3(-20) + 0.40 (032 +0.30(2011 10.3(400) + 0 +0.3(400) J120 +120 - $240 = 15.491 approximately. for stock y: Standard Deviation formula = Pi (4:-7) 2 4 - Return of security 7. Standard Deviation for stucky 70.30(40 -133 +0.40(-20-13)*+ 0.30 (30 - 1332 = $0.30 (27)² + (0.40) (-33)² + 0.30 (1752 = 10.30 (129) + 0.40 (1089) + 0.30 (289) = 1218.7 + 435.6 +86.7 = 5741 = 27.221 approximately,

Standard deduction for stock X = 15.492

Standard deduction for stock Y = 27.221

3. Covariance of Covariance stocks X and Y. P ( x - 2) Cy; -7) Cv = 0.30 (40-10) (40-13) +0.4(10-10) (-20-13) +0.3 (30-10) (30-13) 0.3 + 0.4+0.3 = 0.30-20) (27) +0.4 (0) (-33) + 0.3 (20) (17) = -162 + 0 +102 = - Go. Where I = Expected = Expected Return Return of of stock x. stock y.

Covariance of stock X and Stock Y = -60