Question

# Assume you wish to evaluate the risk and return behaviors associated with various combinations of two​ stocks, Alpha Sof...

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,overbar r                   Risk (Standard Deviation), s
Alpha   5.1%   30.3%
Beta                    11.2%      50.5%

a. If the returns of assets Alpha and Beta are perfectly positively correlated​ (correlation coefficient equals plus 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​), 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​), 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.

________________________________

a. If the returns of assets Alpha and Beta are perfectly positively correlated​ (correlation coefficient equals plus 1​), the range is between ______​% and ______​% ​(Round to one decimal​ place.)

The range of the standard deviation is between _____​% and _____​% ​(Round to one decimal​ place.)

b. If the returns of assets Alpha and Beta are uncorrelated​ (correlation coefficient equals 0​), the range is between _______​% and ______% ​(Round to one decimal​ place.)

The standard deviation of a portfolio that invests​ 75% in Alpha and​ 25% in Beta is _____​%.​(Round to two decimal​ places.)

c. If the returns of assets Alpha and Beta are perfectly negatively correlated​ (correlation coefficient equals negative 1​), the range is between ______​% and _____​%

​(Round to one decimal​ place.)

The standard deviation of a portfolio that invests​ 62.5% in Alpha and​ 37.5% in Beta is ____​%. ​(Round to two decimal​ places.)

If the returns of assets Alpha and Beta are perfectly positively correlated​ (correlation coefficient equals plus 1​), the range is between 5.1% and 11.2​% ​(Round to one decimal​ place.)

The range of the standard deviation is between 5.1​% and 50.5% ​(Round to one decimal​ place.)

b. If the returns of assets Alpha and Beta are uncorrelated​ (correlation coefficient equals 0​), the range is between 5.1% and 11.2% ​(Round to one decimal​ place.)

The standard deviation of a portfolio that invests​ 75% in Alpha and​ 25% in Beta is 25.9964​%.​(Round to two decimal​ places.)

c. If the returns of assets Alpha and Beta are perfectly negatively correlated​ (correlation coefficient equals negative 1​), the range is between 5.1% and 11.2​%

​(Round to one decimal​ place.)

The standard deviation of a portfolio that invests​ 62.5% in Alpha and​ 37.5% in Beta is 0.08​%. ​

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