Question

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:

    Expected Return   Standard Deviation
Firm A's Common Stock   0.16   0.16
Firm B's Common Stock   0.18   0.24
Correlation Coefficient   0.40   

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.

Answer 1

Expected Return on a portfolio is weighted average return of the constiuents of portfolio. It is not impacted by the correlation between two stocks. And hence, this would remain same for all levels of correlation.

Mathematically,

Expected Standard deviation is impacted by correlation between two stocks for a portfolio is given by the mathematical relation:

a. Correlation coeffcient is 0.40 (as given in question)

Expected return = (50% * 16%) + (50% * 18%) = 8% + 9% = 17%

For standard deviation

Standard deviation, hence = 16.876%

b. Correlation coeffcient is 0 (as given in question)

Expected return = (50% * 16%) + (50% * 18%) = 8% + 9% = 17%

For standard deviation

Standard deviation, hence = 14.422%

c. Correlation coeffcient is +1 (as given in question)

Expected return = (50% * 16%) + (50% * 18%) = 8% + 9% = 17%

For standard deviation

Standard deviation, hence = 20.000%

d. Correlation coeffcient is -1 (as given in question)

Expected return = (50% * 16%) + (50% * 18%) = 8% + 9% = 17%

For standard deviation

Standard deviation, hence = 4.000%

e. Return of portfolio is not impacted by the correlation coefficient between the portfolio constituents, and hence that remains the same for all parts.

Correlation is basically a measure of the degree to which returns on two risky assets move in tandem. A positive correlation means that asset returns move together. A negative correlation means returns move inversely.

Correlation can be used to manage risk or standard deviation of portfolio. Volatility (or standard deviation) of a portfolio can be reduced by choosing asset classes with a low or negative correlation.