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 below.

a. If the returns of assets Alpha and Beta are perfectly positively correlated (correlation coefficient = +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 of Alpha and Beta could achieve?

b. If the returns of assets Alpha and Beta are uncorrelated (correlation coefficient = 0), over what range would the average return on portfolios of these stocks vary? Using Equation 5.2, 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 = -1), over what range would the average return on portfolios of these stocks vary? Over what range would the portfolio standard deviation vary? Use Equation 5.2 to calculate the standard deviation of a portfolio that invests 62.5% in Alpha and 37.5% in Beta.

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Asset Alpha Beta Average Return, T 6% 11% Risk (Standard Asset Deviation), s 30% 50%