Question

The following are estimates for two stocks. Firm-Specific Standard Deviation Stock A B Expected Return 108 17 Beta 0.80 1.30 298 40 The market index has a standard deviation of 19% and the risk-free rate is 6%. a. What are the standard deviations of stocks A and B? (Do not round Intermediate calculations. Round your answers to 2 decimal places.) Stock A Stock B b. Suppose that we were to construct a portfolio with proportions: Stock A Stock B T-bills 0.30 0.45 0.25 Compute the expected return, standard deviation, beta, and nonsystematic standard deviation of the portfolio. (Do not round intermediate calculations. Enter your answer for Beta as a number, not a percent. Round your answers to 2 decimal places.) Expected return Standard deviation Beta Nonsystematic standard deviation

Answer 1

c) Variance Of Por Variance of portfolioon op? = Bholomit o ce p Bp = Poot yolio B I ) om = Stah daed Deviation of market. where Bbc shoe is the systematic component. and 67 cenu is 200 systematic Su Since desidugi ei are un correlated, Non systematic variana is 6 Cep) = w/ AX6² LEAJ+w² B x 6 LCB) two gx sied) = (003²x299)+ (0:45 x 40%) + 10:25 x) - 399.69. where 6tea) and 6 (CB) are firm specific nonsystematic grariance Of Stock Al B, and olefis non systematic Variance of T-Bins Lef) is non is zero

(6) calculation of Expected Return ECBpJewex ECRA) + WBXECRB) + 6( 8f WA = weight of Stocka WC L in T. Bins. RA = Expected Return Of A RB = i " B 07 = Risk free Return le T. Bills SRP) = (0.3x10%)+ 10.45X170)) +10125x67.) = 1215). Expected Return of portfolio = 12:15 10 The beta of a portfolio is similar to de a wlighted average of the betas of the Individival security t Bps wax BotWB XBB+ W8Y RB =0.340.80) + (0.45X103)+10:25x0. = 0.825

ne residual Standard deviation of my Portfolio is oleps= (399693172 = 19.99 08 22 Total variance of poot folio 20.69 i opu Poex 0.825*1923 +399.69 = 697.515 Total Standard deviation = V 699.515

(a) Computle Standard deviation of n&B P OI Standard deviation of A Va = C B;' + 6 m2 + 6(ei)) where Bi = Beta of stock A cm= Standard devia aid deviation of marrice't. Gleis = firm specific Standard Deviation S.D of Stock A mogli ) quo 2,12 60 = (0.82*192 +292992 V = 32.7440 5.0 of stock. I wa s ! 0B = (103** 19+4023 12 = 47.01 0 Standard deviation of stock A = 32.74%. Standard deviation of Stocic B = 47001 to