Question

Suppose that the index model for stocks A and B is returns with the following resi RA - 1.58% .SSR Re -1.403. B.GR O = 18; R-square -8.25 Assume you create portfolio Pwith Investment proportions of 0.60 in A and 0 40 in B a. What is the standard deviation of the portfolio? (Do not round your intermediate calculations Round your answer places.) Answer is complete and correct 17.58 b. What is the beta of your portfolio? (Do not round your intermediate Answer is complete ani c. What is the firm-specific variance of your portfollo? (Do not round yo places.) Answer is complete but not entirely correct 0.0006 your d. What is the covariance between the portfolio and the market Index? (Do not found your Interme answer to 3 decimal places.) Answer is complete but not entirely correct. Covariance 324.000
I need the Firm-specific and the Covariance please

Answer 1

Summary :- 1)The standard deviation of the portfolio is 17.58%. 2)beta of the portfolio is 0.57. 3)firm specific variance of your portfolio is 124. 41. 4)the covariance between portfolio and market index is 184.68.   
Given; RA = 1.50% +0.55Rm+ CA - RB = -1.40% +0.60 RM + CB TM = 18% RsqureA=0.25, Rsquare B = 0.1 assume with investment Proportions of 0.60 in A 40.40 in B. a) Calculation of Standard deviation of Portfolio el 1 determining the variance by using the co-efficient of determination for stock A B R? = Explained variation = 6202 Total variation 2 For Stock A For Stock B A2 = BÅom BBM RA = (0.55)2 x(18) - = (0.60)2X (18)2 0.25 = 0.3025 X 324 = 0.36 x 324 0-25 A 392.04 Porc = 729 Step 2 find covariance between ALB (assuming that the residuals to be uncorrelated) it is given by CON CSA VB) = BAX B B x 5 = 0.55 X 0.60 X (18)2 = 106.92 P.T.O

Step 3 standard deviation of the Portfolio op - w, 2 x 4) + (wg ² x 03²) + 2 x W x W2X COVAB 10-60x392-04)+(0-40 x 729) + (2X0-6X04X 106.92 = $141.13 + 116.64+ 51.32 = 309.09 op = 17.58% 6) Beta of your portfolio Bp = (Wi XBA) + (W2 X 8o) = (0.60 x 0.55) + (0.480.60 0.33+ 0.24 .. ßp = 0.57 c) Firm specific variance of your portfolio I - o - pp xo he - 309.09 -(0.57 x(18)2) => 309.09 - (184.68) = 124.4) i Firm specific variance = 124.41 d) covariance between the portfolio of market index → step determination of std deviation for A B As calculated to part a Step 1 above we have varione for Stock A for Stock B 52 = 392.04 02 = 729 = 392.04 To = 5729 A = 19,8 TB = 27

step2 covariance btw each stock of market looke StockA Stock B COV (Ra, Rm) Cou (RB Rm) = PAXTAXom = PB XURXOM = 0.50 x 19.8 x 18 = 0.40 x 27 X 18 = 178.2 = 194.4 (Here PA = √R2 = 50.25 +0.50; Po= VR2 - Von = 0.40) Step 3 covariance between Portfolio of market index is given by = w, x Cov(Ra Rm) + W2X CON(Rob Rm) (0.60* 178.2) + (0.48194,4) = 106.92 + 77.76 = 184.68 I CON (ypom) = 184.68 Alternatively con(rpom) - Boom = 0.57 x(18) = 0.57X324 = 184.68 Notes w, = 0.60 W2 = 0.4, B = 0.5S, BB=0.60 JA = 19,8 TB = 27,5 A = 392.04, 02 - 729, CON (VAI "B) = 106.92, o p = 17.58%, ßp=0.57, on = (18,2 = 324 52 = 124,414 Cov(op I'm) = 184.68