Question

Stocks A and B have the following​ returns:

	Stock A	Stock B
1	0.11	0.06
2	0.07	0.04
3	0.13	0.03
4	−0.01	0.02
5	0.08	−0.03

​(Round to three decimal​ places.)

a. What are the expected returns of the two​ stocks?

b. What are the standard deviations of the returns of the two​ stocks?

c. If their correlation is 0.45​, what is the expected return and standard deviation of a portfolio of 70​%

stock A and 30​% stock​ B?

​(Round to three decimal​ places.)

Answer 1

Answer;

part a)

Expected Return

Stock A = 7.60%

Stock B = 2.40%

Part b)

Standard Deviation

Stock A = 4.80%

Stock B = 3.01%

Part c)

Expected Return of Portfolio = 6.04%

Standard Deviation of portfolio = 3.85%

Explanation;

Part c)

Stock A Weight = 70%

Stock B Weight = 30%

Stock A Expected Return = 7.60%

Stock B Expected Return = 2.40%

Correlation = 0.45

Standard Deviation Stock A = 4.80%

Standard Deviation Stock B = 3.01%

Expected Return of Portfolio =( Stock A Weight x Stock A Expected Return ) + (Stock B Weight x Stock B Expected Return)

Expected Return of Portfolio =0.70 x 7.60 + 0.30 x 2.40

Expected Return of Portfolio = 5.32% + 0.72%

Expected Return of Portfolio = 6.04%

Standard Deviation of Portfolio = [ (W_{A x} SDA)^2 + (W_{B x} SD_B)^2 +  2 x WA x SD_A x WB x SDB x CorrelationA&B ]^-2

Standard Deviation of Portfolio = [ (0.70 x 4.80)^2 + (0.30 x 3.01)^2 + 2 x 0.70 x.030 x 4.80 x 3.01 x 0.45]

Standard Deviation of Portfolio=[11.2896 +0.815409 + 2.730672]^-2

Standard Deviation of Portfolio= [14.835681]^-2

Standard Deviation of Portfolio = 3.85%

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