1. Given the following relationship between two stocks, Tx and ry: rx = 3-5ry (1) Find the minimum variance portfolio (MVP) by investing stocks x and y. (10%) (2) Calculate the expected return and standard deviation of the MVP. (10%)
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- A person is interested in constructing a portfolio. Two stocks are being considered. Letx = percent return for an investment in stock 1, and y = percent return for an investment instock 2. The expected return and variance for stock 1 are e(x) = 8.45% and Var(x) = 25.The expected return and variance for stock 2 are e(y) = 3.20% and Var(y) = 1. Thecovariance between the returns is sxy = −3.a. what is the standard deviation for an investment in stock 1 and for an investment instock 2? Using the standard deviation as a measure of risk, which of these stocks isthe riskier investment?2. Suppose that the market model for stocks A and B is estimated with the following results: RA = 1% +0.9*RM+EA RB = -2% + 1.1*RM+EB The standard deviation of the markets returns is 20% and firm specific risk (standard deviation) equals 30% for A and 10% for B. a. Compute the risk (standard deviation) of each stock and the covariance between them. Suppose we form an equally weighted portfolio of stocks A and B. What will be the nonsystematic standard deviation of that portfolio? b.Assume the risk-free rate is r = 3%. Consider the data below:Stock(stock 1, stock 2)Expected Return(15%,7%)Volatility(40%,30%)a) Find the What the minimum variance portfolio when ρ12 = 0? and then computeits expected return and volatility?b) Find the minimum variance portfolio when ρ12= =0.4? and then compute itsexpected return and volatility?c) Determine the tangent portfolios & their respective mean returns and volatilities.
- 5. Consider the portfolios constructed from the two risky securities with expected returns, standard deviations of returns, and correlation between returns given in the following table. |1=0.10 M2 = 0.15 01 = = 0.28 02 = 0.24 P12 = -0.10 Find the equation of the minimum variance line w = μa + b.3. Suppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively. Answer the following questions. (a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?Assume that using the Security Market Line(SML) the required rate of return(RA)on stock A is found to be halfof the required return (RB) on stock B. The risk-free rate (Rf) is one-fourthof the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A(βA) to beta of B(βB).
- Consider the expected return and standard deviation of the following two assets: Asset 1: E[r1]=0.1 and σ1=0.2 Asset 2: E[r2]=0.3 and σ2=0.4 (a) Draw (e.g. with Excel) the set of achievable portfolios in mean-standard deviation space for the cases: (i) ρ12= -1, (ii) ρ12=0. (b) Suppose ρ12=-1. Which portfolio has the minimal variance? What is the variance and expected return of that portfolio? (c) Derive the formula for the variance of a portfolio with four assets.Consider the following information for four portfolios, the market, and the risk-free rate (RFR): Portfolio Return Beta SD A1 0.15 1.25 0.182 A2 0.1 0.9 0.223 A3 0.12 1.1 0.138 A4 0.08 0.8 0.125 Market 0.11 1 0.2 RFR 0.03 0 0 Refer to Exhibit 18.6. Calculate the Jensen alpha Measure for each portfolio. a. A1 = 0.014, A2 = -0.002, A3 = 0.002, A4 = -0.02 b. A1 = 0.002, A2 = -0.02, A3 = 0.002, A4 = -0.014 c. A1 = 0.02, A2 = -0.002, A3 = 0.002, A4 = -0.014 d. A1 = 0.03, A2 = -0.002, A3 = 0.02, A4 = -0.14 e. A1 = 0.02, A2 = -0.002, A3 = 0.02, A4 = -0.14Given: Calculate the expected returns and expected standard deviations of a two-stock portfolio having a correlation coefficient of 0.70 under the following conditions a. w1 = 1.00 b. w1 = 0.75 c. w1 = 0.50 d. w1 = 0.25 e. w1 = 0.05 Plot the results on a return-risk graph. Without calculations, draw in what the curve would look like first if the correlation coefficient had been 0.00 and then if it had been −0.70.
- Assume that using the Security Market Line(SML) the required rate of return(RA)on stock A is found to be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourthof the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A(A) to beta of B(B).Suppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively.(a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?Assume that using the Security Market Line(SML) the required rate of return(RA)on stock A is found to be halfof the required return (RB) on stock B. The risk-free rate (Rf) is one-fourthof the required return on A. Return on market portfolio is denoted by RM. Find the ratioof betaof A(A) tobeta of B(B). Thank you for your help.