(Computing the standard deviation for a portfolio of two risky investments) Mary
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Question
(Computing the standard deviation for a portfolio of two risky investments) Mary Guilott recently graduated from Nichols State University and is anxious to begin investing her meager savings as a way of applying what she has learned in business school. Specifically, she is evaluating an investment in a portfolio comprised of two firms' common stock. She has collected the following information about the common stock of Firm A and Firm B:
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a. If Mary invests half her money in each of the two common stocks, what is the portfolio's expected rate of return and standard deviation in portfolio return?
b. Answer part a where the correlation between the two common stock investments is equal to zero.
c. Answer part a where the correlation between the two common stock investments is equal to +1.
d. Answer part a where the correlation between the two common stock investments is equal to 1.
e. Using your responses to questions a—d, describe the relationship between the correlation and the risk and return of the portfolio.
Firm A's common stock Firm B's common stock Correlation coefficient Expected Return 0.13 0.17 0.70 Standard Deviation 0.19 0.22Explanation / Answer
A) Expected Return of Mary's Portfolio will be 0.5X0.13+0.5X0.17 = 0.15 or 15%. And Standard Deviation of the portfolio will be 20.5
B) Correlation, is a statistic that measures the degree to which two securities move in relation to each other. while a zero correlation implies no relationship at all. Meaning, there is no relationship between stock A and B.
C) Correlation between the two common stock investments is equal to +1 mean that both variables move in the same direction. When correlation is +1, it signifies that the two variables being compared have a perfect positive relationship; when one variable moves higher or lower, the other variable moves in the same direction with the same magnitude. For Eg, if Stock A rises by 10% with same magnitude stock B will also rise.
D) Correlation between the two common stock investments is equal to 1 which means that there is an inverse relationship two variable such that they move in opposite directions. For eg, If stock A rises by 15%, Stock B will fall by 15%.
E) In the above portfolio, Firm A's stock is less risky and providing less return as compared to Firm B's stock. Which means that if Mary wants to expect a higher return on its portfolio she has to bear more risk also.
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