Question

Assume you wish to evaluate the risk and return behaviors associated with various combinations of two​ stocks, Alpha Software and Beta​ Electronics, under three possible degrees of​ correlation: perfect​ positive, uncorrelated, and perfect negative. The average return and standard deviation for each stock appears​ here:

Assets	Average Return	Risk (S.D),s
Alpha	6.9%	30.8%
Beta	11.7%	49.3%

a. If the returns of assets Alpha and Beta are perfectly positively correlated​ (correlation coefficient equals plus 1=+1​), over what range would the average return on portfolios of these stocks​ vary? In other​ words, what is the highest and lowest average return that different combinations of these stocks could​ achieve? What is the minimum and maximum standard deviation that portfolios Alpha and Beta could​ achieve?

b. If the returns of assets Alpha and Beta are uncorrelated​ (correlation coefficient equals 0=0​), over what range would the average return on portfolios of these stocks​ vary? What is the standard deviation of a portfolio that invests​ 75% in Alpha and​ 25% in​ Beta? How does this compare to the standard deviations of Alpha and Beta​ alone?

c. If the returns of assets Alpha and Beta are perfectly negatively correlated​ (correlation coefficient equals negative 1=−1​), over what range would the average return on portfolios of these stocks​ vary? Calculate the standard deviation of a portfolio that invests​ 62.5% in Alpha and​ 37.5% in Beta.

Answer 1

A. Perfect positive correlation means that both stocks behave same in return to the market responses. Perfectly, positive correlation means the portfolio risk could be maximum.

• The average return on portfolio of these stocks would range between 6.9% - 11.7%, depends on the weight of stocks in the portfolio.
• The minimum standard deviation of portfolio of these stocks could be 30.8% and the maximum could 49.3%

B. Uncorrelated stocks means there is no relation between the behavior of the stocks. They behave independent of each other in return to the market responses.

• The average return on portfolio of these stocks would range between 6.9%-11.7%.
• Standard deviaton of a portfolio that invests 75% in Alpha and 25% in Beta

=26.18

• The risk of portfolio is less than what individual risk of each portfolio that with an average return of 8.1% that is more than stock Alpha with less risk.

C. Negative correlation means there is an inverse relationship between the stock. Both of them of respond exactly opposite in return to the market response. Perfectly negative correlation means portfolio risk could be minimum.

• The average return on portfolio of these stocks would range between 6.9%-11.7%.
• Standard deviaton of a portfolio that invests 62.5% in Alpha and 37.5% in Beta in correlation is -1

= (0.625*30.8)-(0.375*49.3)

=0.76%