Question

Mary Guilott recently graduated from college and is evaluating an investment in two? companies' common stock. She has collected the following information about the common stock of Firm A and Firm? B:

Expected?????????? Returns???????????		Standard Deviation
Firm? A's common stock	0.16	0.14
Firm? B's common stock	0.07	0.05
Correlation coefficient	0.20

a. If Mary decides to invest 10 percent of her money in Firm? A's common stock and 90 percent in Firm? B's common? stock, what is the expected rate of return and the standard deviation of the portfolio? return?
b. If Mary decides to invest 90 percent of her money in Firm? A's common stock and 10 percent in Firm? B's common? stock, what is the expected rate of return and the standard deviation of the portfolio? return?
c. Recompute your responses to both questions a and b?, where the correlation between the two? firms' stock returns is negative ?0.20.
d. Summarize what your analysis tells you about portfolio risk when combining risky assets in a portfolio.

Answer 1

Expected Return:

Standard Deviation:

a)

Expected Return: 0.1*0.16 + 0.9*0.07

: 0.079

Standard Deviation: Suare root of ((0.1*0.1*0.14*0.14)+(0.9*0.9*0.07*0.07)+(2*0.1*0.9*0.14*0.07*0.2))

: 0.067

b)

Expected Return: 0.9*0.16 + 0.1*0.07

: 0.151

Standard Deviation: Suare root of ((0.9*0.9*0.14*0.14)+(0.1*0.1*0.07*0.07)+(2*0.1*0.9*0.14*0.07*0.2))

: 0.128

c)

Expected Return would be same in both the cases.

(1) Standard Deviation: Suare root of ((0.1*0.1*0.14*0.14)+(0.9*0.9*0.07*0.07)+(2*0.1*0.9*0.14*0.07*(-0.2)))

: 0.062

(2) Standard Deviation: Suare root of ((0.9*0.9*0.14*0.14)+(0.1*0.1*0.07*0.07)+(2*0.1*0.9*0.14*0.07*(-0.2)))

: 0.125

d)

When the weight of investment is more in more-risky asset as compared to the less-risky one, the expected return of the overall portfolio would increase along with increase in the riskiness.

The situation becomes vice-versa otherwise.