Question

The investment universe consists of: a risk-free T-bill with annual yield of r = 3%; shares of common stock of company 1, with expected return of 1 = 9% and volatility of 1 = 16% shares of common stock of company 2, with expected return of 2 = 14% and volatility of 2 = 23%.

Portfolio selection and CAPM The investment universe consists of: . a risk-free T-bill with annual yield of r = 3%; . shares of common stock of company 1, with expected return of 111 9% and volatility ofơ1-16% · shares of common stock of company 2, with expected return of ,12 = 14% and volatility of σ2-23%. Assume that stock returns are uncorrelated. IL. ρ12-0. Market capitalizations of companies 1 and 2 are $600 million and $400 million. (a) Calculate the weights of stocks in the market portfolio, w and w2 (b) Calculate expected return and volatility of the market portfolio. ,411 and σΜ (c) Is volatilty of the market portfolio larger, smaller or equal to the weighted sum of individual stock volatilities? Why? (d) Draw a graph where axes are expected return and volatility. Indicate the points corresponding to the T-bill and the two stocks. Now, sketch the efficient frontier of risky assets. Draw the tangency line and indicate the position of the market portfolio (e) Use your class notes to write down the equation of the Capital Market Line (CML) Calculate and interpret its intercept and slope (f) Suppose you want to invest in a portfolio on CML such that its expected return is 10%. How should you allocate your investment between the T-bill and the two stocks? (g) Suppose you want to invest in a portfolio on CML such that its volatility is 6.65%. How should you allocate your investment between the T-bill and the two stocks? (h) If CAPM holds, what should be the beta for each asset?

Answer 1

Given,

Risk free return (Rf) = 3%

Expected Return of Security 1 (ERx) = 9%

Standard Deviation of Security 1 (SDx) = 16%

Expected Return of Security 2 (ERy) = 11%

Standard Deviation of Security 2 (SDy) = 23%

Coefficient of correlation = 0 (Hence, Covariance = 0)

(1). Weights of the securities

Weight of Security 1 (Wx)   = [ (SDy)^2 - (Covariance)x,y ]/[ (SDx)^2 + (SDy)^2 – 2(Covariance x,y)]

                                                 =[ (0.23)^2 - 0 ]/[ (0.16)^2 + (0.23)^2 - 2(0)]

                                                = ( 0.0529 – 0) /( 0.0256 + 0.0529 – 0)

                                                = 0.0529/0.0785

                                                = 0.6739             

Weight of Security 2 (Wy) = 1 – 0.6739

                                                = 0.3261

(2). Expected Return of Market Portfolio

        (Rm)    = (ERx)(Wx) + (ERy)(Wy)

                     = 9%(0.6739) + 14%(0.3261)

                    = 6.0651% + 4.5654%

                    = 10.6305%

     Portfolio Risk = (Wx)^2*(SDx)^2 + (Wy)^2*(SDy)^2 + 2(Wx)(SDx)(Wy)(SDy)(Coefficient of correlation)

                               = (0.6739)^2*16^2 + (0.3261)^2*23^2 – 2*0.6739*16*0.3261*23*0

                              = 116.26 +56.25

= 172.51

Volatility of Market Portfolio = Square root of 172.51 = 13.1343%

(3). Weighted Average of individual stock volatilities = 16%(0.6739) + 23%(0.3261)

= 10.7824% + 7.5003%

= 18.2827%

Hence, Volatility of market portfolio (13.1343%) is smaller than weighted average of individual stock volaitilities.