Question

Consider the following information about two stocks where the probability of an economic boom is 60 s : You may work with whole numbers or you can work. with deciman a. Calculate the expected return for stock A and stock B (marginal returns for each stock) b. Calculate the standard deviation of stock A and stock B. c. Which stock is riskier? d. Calculate the expected return and total risk (standard deviation) of a portfolio, where 50% of your money is invested in stock A, and 50% of your money is invested in stock B. (hint for the variance of the portfolio no need to calculate the covariance)

Answer 1

The expected return for stock A is $7,100 and for stock B is $1,100. Stock A has a standard deviation of $4,995.05, while stock B has a standard deviation of $3,347.26. Stock A is riskier than stock B. The expected return of a portfolio with 50% in stock A and 50% in stock B is $4,100, with a standard deviation of $3,000.

Step-by-step explanation:

b. Calculate the expected return for stock A and stock B (marginal returns for each stock)

Expected return for stock A = (0.60 x $11,000) + (0.35 x $0) + (0.05 x $10,000) = $6,600 + $0 + $500 = $7,100

Expected return for stock B = (0.60 x $1,000) + (0.35 x $0) + (0.05 x $10,000) = $600 + $0 + $500 = $1,100

c. Calculate the standard deviation of stock A and stock B.

Standard deviation of stock A = sqrt((0.60 x ($11,000 - $7,100)^2) + (0.35 x ($0 - $7,100)^2) + (0.05 x ($10,000 - $7,100)^2)) = sqrt((0.60 x $9,900,000) + (0.35 x $50,190,000) + (0.05 x $8,910,000)) = sqrt($5,940,000 + $17,566,500 + $445,500) = sqrt($24,951,000) = $4,995.05

Standard deviation of stock B = sqrt((0.60 x ($1,000 - $1,100)^2) + (0.35 x ($0 - $1,100)^2) + (0.05 x ($10,000 - $1,100)^2)) = sqrt((0.60 x $9,900,000) + (0.35 x $3,465,000) + (0.05 x $81,000,000)) = sqrt($5,940,000 + $1,214,750 + $4,050,000) = sqrt($11,204,750) = $3,347.26

d. Which stock is riskier?

The stock with the higher standard deviation is considered riskier. Therefore, stock A with a standard deviation of $4,995.05 is riskier than stock B with a standard deviation of $3,347.26.

e. Calculate the expected return and total risk (standard deviation) of a portfolio, where 50% of your money is invested in stock A, and 50% of your money is invested in stock B (hint for the variance of the portfolio no need to calculate the covariance)

Expected return of the portfolio = (0.50 x $7,100) + (0.50 x $1,100) = $3,550 + $550 = $4,100

Standard deviation of the portfolio = sqrt((0.50 x ($7,100 - $4,100)^2) + (0.50 x ($1,100 - $4,100)^2)) = sqrt((0.50 x $9,000,000) + (0.50 x $9,000,000)) = sqrt($4,500,000 + $4,500,000) = sqrt($9,000,000) = $3,000