Question

Consider the following information:

  

		Rate of Return if State Occurs
State of Economy	Probability of State of Economy	Stock A	Stock B	Stock C
Boom	0.74	0.23	0.25	0.17
Bust	0.26	0.11	0.15	0.11
Requirement 1: What is the expected return on an equally weighted portfolio of these three stocks? (Do not round your intermediate calculations.) (Click to select)19.24%21.74%31.27%34.04%13.51%    Requirement 2: What is the variance of a portfolio invested 10 percent each in A and B and 80 percent in C? (Do not round your intermediate calculations.) (Click to select)0.0089430.0009430.0086430.0044430.006443

Answer 1

Question 1

Step 1: Calculation of Expected Return on each stock

Expected Return on stock A = (23*.74) + (11*.26) = 19.88%

Expected Return on stock B = (25*.74) + (15*.26) = 22.40%

Expected Return on stock C = (17*.74) + (11*.26) = 15.44%

Step 2: Calculation of Expected Return on portfolio

The return of a portfolio is the weighted average return of the securities which constitute the porfolio.

Stock	Weight	Expected Return (%)	Weight*Expected Return
A	0.33	19.88	6.6267
B	0.33	22.40	7.4667
C	0.33	15.44	5.1467

Expected Return on portfolio = 19.24% (6.6267+7.4667+5.1467)

Question 2

Step 1: Calculation of standard deviation of each stock

stock A (SD_A) =[ .74*(23-19.88)² + .26*(11-19.88)² ] = 27.7056 = 5.26

stock B (SD_B) =[ .74*(25-22.40)² + .26*(15-22.40)² ] = 19.24 = 4.39

stock C (SD_C) =[ .74*(17-15.44)² + .26*(11-15.44)² ] = 6.9264 = 2.63

Step 2: Calculation of Correlation

-Between A and B

State of economy	Probability(P)	Deviation (DA)	Deviation (DB)	P*DA*DB
Boom	0.74	3.12	2.6	6.0029
Bust	0.26	-8.88	-7.4	17.0851

Covariance between A and B = 23.0880 (6.0029+17.0851)

Correlation between A and B = Covariance between A and B/ (SD_A*SDB)

= 23.0880 / (5.26*4.39)

= 0.9999 = 1 (approximately)

-Between A and C

State of economy	Probability(P)	Deviation (DA)	Deviation (DC)	P*DA*DC
Boom	0.74	3.12	1.56	3.6017
Bust	0.26	-8.88	-4.44	10.2511

Covariance between A and C = 13.8528 (3.6017+10.2511)

Correlation between A and C = Covariance between A and c/ (SD_A*SD_C)

= 13.8528 / (5.26*2.63)

= 1.0014 = 1 (approximately)

-Between B and C

State of economy	Probability(P)	Deviation (DB)	Deviation (DC)	P*DB*DC
Boom	0.74	2.6	1.56	3.0014
Bust	0.26	-7.4	-4.44	8.5426

Covariance between B and C = 11.5440 (3.0014+8.5426)

Correlation between B and C = Covariance between A and c/ (SDB*SD_C)

= 11.5440 / (4.39*2.63)

= .9999 = 1 (approximately)

Step 3: Calculation of Variance

(.1*5.26)2 + (.1*4.39)2 + (.8*2.63)2 + (2*.1*.1*5.26*4.39*1) + (2*.1*.8*5.26*2.63*1) + (2*.1*.8*4.39*2.63*1)

9.43%