Question

Expected Return and Standard Deviation / This problem will give you some practice calculating measures of prospective portfolio performance. There are two assets and three states of the economy

State of Economy	Probability of State of Economy	Rate of Return If State Occurs
		Stock A	Stock B
Recession	.20	-.15	.20
Normal	.50	.20	.30
Boom	.30	.60	.40

Expected Returns :

Stock A = (.20 * -.15) + (0.50 * .20) + (.30 * .60) = .25

Stock B = (.20 * .20) + (.50 * .30) + (.30 * .40) = .31

Standard Deviation :

Stock A = .20 * (-.15 - .25)^2 + .50 * (.20 - .25)^2 + .30 * (.60 - .25)^2 = 0.07

√0.07 = .2646, 26.46%

Stock B = .20 * (.20 - .31)^2 + .50 * (.30 - .31)^2 + .30 * (.40 - .31)^2 = 0.0049

√0.0049 = .07, 7%

Portfolio Risk and Return / Using the information in the precious problem, suppose you have $20,000 total. If you put $15,000 in Stock A and the remainder in Stock B. what will be the expected return and standard deviation of your portfolio?

Answer 1

Given:

	Expected Return (R)	Standard Deviation
Stock A	25%	26%
Stock B	31%	7%

Total Investments = $20,000
Investment in Stock A = $15,000
Investment in Stock B = $5,000

Step 1 : Calculation of Weights of Portfolio

Weight of Stock A in portfolio = $15,000 /  $20,000 = 0.75
Weight of Stock B in portfolio = $5,000 /  $20,000 = 0.25

Step 2 : Calculation of Covariance of Stock A & Stock B

Where, RA & RB = Return of Stock A & Stock B respectively in different economic sceario
ER(A) & ER(B) = Expected Return of Stock A & Stock B respectively

COV(A,B) = 0.20 * (-0.15 - 0.25)(0.20 - 0.31) + 0.50 * (0.20 - 0.25)(0.30 - 0.31) + 0.30 * (0.60 - 0.25)(0.40 - 0.31)
COV(A,B) = 0.0088 + 0.00025 + 0.00945
COV(A,B) = 0.0185

a) Calculation of Expected Return of portfolio

where, ER(A) & ER(B) = Expected Return of Stock A & Stock B respectively
WA & WB = Weight of Stock A & Stock B respectively

ERp = 0.25*0.75 +0.31*0.25
ERp = 0.265 or 26.5%

b) Calculation of Standard Deviation of portfolio

where, = Standard Deviation of Stock A & Stock B respectively
WA & WB = Weight of Stock A & Stock B respectively
COV(A,B) = Covariance of Stock A & Stock B

0.2159138 or 21.59%