Question

Emmy is analyzing a two-stock portfolio that consists of a Utility stock and a Commodity stock. She knows that the return on the Utility stock has a standard deviation of 40 percent and the return on the Commodity stock has a standard deviation of 30 percent. However, she does not know the exact covariance in the returns of the two stocks. Emmy would like to plot the variance of the portfolio for each of three cases—covariance of 0.050, 0, and –0.050 — in order to understand how the variance of such a portfolio would react. Do the calculation for all three cases (0.050, 0, and -0.050), assuming an equal proportion of each stock in the portfolio.

Case 1, σ12 = 0.050: (Round answer to 4 decimal places, e.g. 0.0768.) Variance LINK TO TEXT

Case 2, ρ = 0.0: (Round answer to 4 decimal places, e.g. 0.0768.) Variance LINK TO TEXT

Case 3, σ12 = -0.050: (Round answer to 4 decimal places, e.g. 0.0768.) Variance

Answer 1

Step 1: Variance is the square of standard deviation.

STANDARD DEVIATION OF A PORTFOLIO (SD) =

VARIANCE OF PORTFOLIO = (STANDARD DEVIATION)^2

--------------------------------------------------------------------------------------------------------------------------------------------------------

Step 2:

Stock 1 = Utility Stock

Weight of Utility Stock =50% ; Standard Deviation of Utility stock = 40%

Stock 2: Commodity Stock

Weight of Commodity stock =50% ; Standard Deviation of Commodity Stock = 30%

----------------------------------------------------------------------------------------------------------------------------------------------

Step 3: CASE 1 When Covariance( Utility Stock, Commodity Stock) = 0.050

Standard Deviation of the Portfolio is - Using the equation given in step 1

SD(Utility Stock, Commodity Stock) = SQRT [ {(0.5)^2 * (0.4)^2} + {(0.5)^2 * (0.3)^2} + {2* 0.5*0.5*0.05)

SD(Utility Stock, Commodity Stock) = 29.58%

Variance(Utility Stock, Commodity Stock) = SD((Utility Stock, Commodity Stock)^2 = 0.0875

---------------------------------------------------------------------------------------------------------------------------

Step 4: CASE 2 When Covariance( Utility Stock, Commodity Stock) = 0.0

Standard Deviation of the Portfolio is - Using the equation given in step 1

SD(Utility Stock, Commodity Stock) = SQRT [ {(0.5)^2 * (0.4)^2} + {(0.5)^2 * (0.3)^2} + {2* 0.5*0.5*0.0)

SD(Utility Stock, Commodity Stock) = 25.00%

Variance(Utility Stock, Commodity Stock) = SD((Utility Stock, Commodity Stock)^2 = 0.0625

---------------------------------------------------------------------------------------------------------------------------------------------------------

Step 5: CASE 3 When Covariance( Utility Stock, Commodity Stock) = - 0.050

Standard Deviation of the Portfolio is - Using the equation given in step 1

SD(Utility Stock, Commodity Stock) = SQRT [ {(0.5)^2 * (0.4)^2} + {(0.5)^2 * (0.3)^2} + {2* 0.5*0.5*-0.05)

SD(Utility Stock, Commodity Stock) = 19.36%

Variance(Utility Stock, Commodity Stock) = SD((Utility Stock, Commodity Stock)^2 = 0.0375