Question

Stock A has an expected return of 12%, a standard deviation of 24% on its returns, and a beta of 1.2. Stock B has an expected return of 15%, a standard deviation of 30% on its returns, and a beta of 1.5. The correlation between the two stocks is 0.8. If we invested $30,000 in Stock A and $20,000 in Stock B, what is the beta of our portfolio?

Select one:

a. 1.03

b. 1.25

c. 1.32

d. 1.40

e. 1.56

Answer 1

Using the given information we can calculate the beta of the portfolio as follows

Stock	Expected Return	Standard Deviation	Beta
Stock A	15%	30%	1.2
Stock B	12%	24%	1.5

As the Portfolio has Stock A and B both, we can prepare the Portfolio Table as below

Stock	Invested Amount	Weighted Average of Total Investment (Invested Amount / Total Investment)	Beta of Stocks	Weighted Beta (Weighted Average * Beta)
Stock A	$ 30,000	(30,000 / 50,000) = 60%	1.2	(60% * 1.2) = 0.72
Stock B	$ 20,000	(20,000 / 50,000) = 40%	1.5	(40% * 1.5) = 0.60
Total	$ 50,000	100%

Beta of the Portfolio = Weighted Beta of Stock A + Weighted Beta of Atock B

= 0.72 + 0.60

= 1.32

So, the beta of Portfolio if $ 30,000 is invested in Stock A and $ 20,000 is invested in Stock B comes out to be 1.32. Therefore the correct answer is option (c)

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