Question

Stock A is expected to produce the following returns given various states of the economy:
Table 1 - Stock A

State of Economy	Probability of state of Economy	Possible Return
Good	70%	20%
Bad	30%	12%

Table 2 - Stock B and Stock C

Stock	Expected Return	Standard Deviation	Correlation Coefficient with A
B	25%	15%	0.8
C	18%	12%	-0.2

1) What is the expected return of stock A?
2) What is the standard deviation of the expected return of stock A?
3) If an investor is considering combine stock A with another stock to build a two-stock portfolio, which one of the two (Stock B or Stock C) is a better choice with the given information in Table 2 and why?

Please show all the work.

Answer 1

(1) Expected return of stock A:

Given, Possibility of Stock A in Good state of economy = 70% and

Possible return at that state = 20%

Possibility of stock A in Bad state of economy = 30% and Possible return at that state = 12%

Expected return of stock A

= 20%×0.7+12%×0.3 = 17.6%

(2) Standard Deviation of expected return of stock A:

State of economy	Probability	Possible return	Deviation from Expected return	Square of Deviation
Good	0.70	20%	2.4	5.76
Bad	0.30	12%	-5.6	31.36
		Expected return = 17.6%

Standard Deviation

= √probability of good state of economy×square of Deviation+ probability of bad state of economy×square of Deviation

= √0.70×5.76+0.30×31.36

= √13.44

= 3.67%

(3) whether stock B or stock C is better in combination with stock A:

Given, Expected return of stock B = 25%

Expected return of stock C = 18%

Standard deviation of stock B = 15%

Standard deviation of stock C = 12%

Correlation coefficient of stock A and B = 0.8

Correlation coefficient of stock A and C = -0.2

Analysis: stock B is better because stock B gives higher expected return compared to stock C and in respect of standard deviation, stock B is riskier at negligible percentage and has positive Correlation between stock B with stock A and hence it is better to select stock B