Question

1 Approved Answer

Posted on Sep 04, 2024

You are investing in stock A and stock B. Based on their historical prices, the mean and standard deviation of their returns (i.e. and )

You are investing in stock A and stock B. Based on their historical prices, the mean and standard deviation of their returns (i.e. and ) are estimated as (=0.08,=0.12) and (=0.14,=0.20). Let denote the rate of return random variable for the constructed portfolio with investing proportion (in percentage) of your investment in stock A and the remaining proportion in stock B (hence +=1). Assume all variables are defined over the same time period and the investment is held over the same period. a. Let 0 be the initial amount available for investment. Show that the portfolio rate of return random variable is given by = + image text in transcribed

(20 marks) You are investing in stock A and stock B. Based on their historical prices, the mean and standard deviation of their returns (i.e. RA and Rs) are estimated as (HA = 0.08.04 = 0.12) and (Ug = 0.14,0g = 0.20). Let Rp denote the rate of retum random variable for the constructed portfolio with investing xa proportion (in percentage) of your investment in stock A and the remaining X proportion in stock B (hence XA + X3 = 1). Assume all variables are defined over the same time period and the investment is held over the same period. a. Let wo be the initial amount available for investment. Show that the portfolio rate of retum random variable is given by Rp = XARA+XgRg which does not depend on wo. b. Suppose XA = 0.4, determine Hp = E(Rp) and op = /Var(Rp) for pe {-1,-0.3,0,0.3,1}, where p is the correlation between the returns of stock A and stock B. Comment the role of p on your investment by interpreting the riskiness of your portfolio is captured by its standard deviation. min c. Suppose your initial investment amount is wo = $10,000. Express your expected return and standard deviation in Part (b) in term of dollar units. d. Suppose you are a very conservative investor and you wish to invest in a portfolio that has the least exposure to risk. Show that the portfolio weights for A and B are Var(R3) - Cov(RAR) Var(RA) + Var(R3) - Cov(RA.R3) xmin = 1 - xmin The resulting portfolio is commonly known as the minimum risk or minimum variance portfolio e. Suppose pe{-1,-0.3,0,0.3,1}, compute the portfolio weights, expected retum, and standard deviation for the minimum risk portfolio in Part (s). Comment on your results. f. Plot (Op, Mp) (1.e. Op as x-axis and \p as y-axis) for pe{-1, -0.3.0.0.3,1}. Comment on your results. (You may use R or Excel to complete this part) (20 marks) You are investing in stock A and stock B. Based on their historical prices, the mean and standard deviation of their returns (i.e. RA and Rs) are estimated as (HA = 0.08.04 = 0.12) and (Ug = 0.14,0g = 0.20). Let Rp denote the rate of retum random variable for the constructed portfolio with investing xa proportion (in percentage) of your investment in stock A and the remaining X proportion in stock B (hence XA + X3 = 1). Assume all variables are defined over the same time period and the investment is held over the same period. a. Let wo be the initial amount available for investment. Show that the portfolio rate of retum random variable is given by Rp = XARA+XgRg which does not depend on wo. b. Suppose XA = 0.4, determine Hp = E(Rp) and op = /Var(Rp) for pe {-1,-0.3,0,0.3,1}, where p is the correlation between the returns of stock A and stock B. Comment the role of p on your investment by interpreting the riskiness of your portfolio is captured by its standard deviation. min c. Suppose your initial investment amount is wo = $10,000. Express your expected return and standard deviation in Part (b) in term of dollar units. d. Suppose you are a very conservative investor and you wish to invest in a portfolio that has the least exposure to risk. Show that the portfolio weights for A and B are Var(R3) - Cov(RAR) Var(RA) + Var(R3) - Cov(RA.R3) xmin = 1 - xmin The resulting portfolio is commonly known as the minimum risk or minimum variance portfolio e. Suppose pe{-1,-0.3,0,0.3,1}, compute the portfolio weights, expected retum, and standard deviation for the minimum risk portfolio in Part (s). Comment on your results. f. Plot (Op, Mp) (1.e. Op as x-axis and \p as y-axis) for pe{-1, -0.3.0.0.3,1}. Comment on your results. (You may use R or Excel to complete this part)