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:

Asset Average Return,r Risk (Standard Deviation), s

Alpha. 5.95.9% 30.3%

Beta 10.2% 50.5%

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.