Assume you wish to evaluate the risk and return behaviors associated with various combinations of two stocks, Alpha Software and Betac. 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? Calculate the standard deviation of a portfolio that invests $62\mathrm{.}5\%$ in Alpha and $37\mathrm{.}5\%$ in Beta.

Data table

$($Click on the icon here

a spreadsheet.$)$

Electronics, under three possible degrees of correlation: perfect positive, uncorrelated, and perfect negative. The average return and standard

deviation for each stock appears here: $.$

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 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? 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? Calculate the standard deviation of a portfolio that invests $62\mathrm{.}5\%$ in Alpha and $37\mathrm{.}5\%$ in Beta.

a$.$ If the returns of assets Alpha and Beta are perfectly positively correlated $($correlation coefficient $=+1),$ the range is

between $5\mathrm{.}5\%$ and $10\mathrm{.}7\%($Round to one decimal place.$)$

The range of the standard deviation is between $30\mathrm{.}5\%$ and $50\mathrm{.}7\%($Round to one decimal place.$)$

b$.$ If the returns of assets Alpha and Beta are uncorrelated $($correlation coefficient $=0),$ the range is between $5\mathrm{.}5\%$ and $10\mathrm{.}7\%($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.$)$Data table

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a spreadsheet.$)$