Question

o achieve a zero standard deviation for a portfolio, calculate the weights of stock A and stock B, assuming the correlation coefficient is −1. Use the following information. (Round intermediate calculations to 4 decimal places, e.g. 31.2125 and the final answers to 2 decimal places, e.g. 31.21%.)

State of the economy		Probability of occurrence		Expected return on stock A in this state		Expected return on stock B in this state
High growth		30%		42.5%		57.5%
Moderate		25%		22.5%		27.5%
Recession		45%		-12.5%		-22.5%

Answer 1

solution: The values e provided in the questions are as follows (WA) Weight of stock A =? (WB) Weight of stock B = ? (RAB) Correlation of stock A and Stock B = -1 (op) Standard deviation for a portfolio=0 first of all, we will calculate of expected Retum of Stock A and stock B, Expected Relaim of stock A = 0.3 x42.5+0.25x22.5+0.45%-12.5 Expected Return of Stock A = 19.75+ 5.625-5.625 → Expecteel Relum of Stou A = 12.75 Expected Relaim of stock B = 0.30% 57.5 +0.25x27.5+0.45X-22.5 Expected Relum of stock 8 = 17.25+6.875+(-10.125) → Expected Relaim of stock B = 14 | Variance 4 Stock A = 0. 30x(425-12.756.25%(23.5-12.7470.4521-12.5-12.75)? Variance of STOCKA = 0.30/29.15)+0.25x(4.75)+0.45*(-85.25) Vanance of StoUKA = 0.308885.0625 +0.25x95.0625 +0.45*637.5625 vanance y Stock A = 265.51875+23.765625+286.903125 Variance of stockA = 576.1875 Standard deviation of stockA (TA) = Jvariance = 1576-1875 standard deviation of stockA (TA)= 24.00% | 13.

Variance of stock 8 = 0.306(57-5-14)*+ 01254(275-14) * 0.45X(-22.5 -14) Variance of stock B = 0.30x(43.5)2+0.25% (13.5) 70.45X(-36.5)2 Variance of stock B 2 0.30x1892.25+ 0.25* 182.25 +0.45X1332.25. vanance of stock 8 = 567.675 +45.5625 +599.5125 Vanance of stock B = 1212.75 Standaod levialtos of stock B (CB) = { variance - 1212.75 Standard deviation of stock B (CB) = 34.82 The formula to calculate weight of stockA (WA) is as follows: 2 : h, os – се бе 1-де TA²+83² - STAFORAB . Using the values providing in the question, WA = (34.02 ) ?- 24x3482x- :: (24.00) +(34-02)2- 2 x 24x 3482 x-1 WAS 1912.4324 +835.68 576 +1213.4324 +1671.36 3459.7924 | (WA) weight of stock A = 0.59 : 2040.1124 813

We know that, weight of stock A (WA) + Weigestof stolec 8 (WB) = 1 WAT WB=1 Now putting the value of weight of stock A(WA) in the above mentioned formula, 0.59 +WBC 1 : WBS 1-0.59 Ch 8) Weight of stock B = 0.41 So, Weight + Stock A (WA) = 0.59 Weight of stock B (WB) = 0.41 313