On your first day as an intern at Tri$-$Star Management Pty Ltd the CEO asks you to analyse the following information pertaining to two ordinary share investments, Tech.com and Sam$$s Grocery. You are told that a one$-$year Treasury note will have a rate of return of $5\%$ over the next year. Also, information from an investment advisory service lists the current beta for Tech.com as $1\mathrm{.}68$ and for Sam$$s Grocery as $0\mathrm{.}52.$ You are provided a series of questions to guide your analysis.

Estimated Rate of Return $.$

Economy Probability Tech.com Sam$$s Grocery ASX $200$

Recession $30\%20\%5\%4\%$

Average $20\%15\%6\%11\%$

Expansion $35\%30\%8\%17\%$

Boom $15\%50\%10\%27\%$

Assignment

$1.$ Using the probabilistic approach, calculate the expected rate of return for Tech.com, Sam$$s Grocery, and the ASX $200$ Index.

$2.$ Calculate the standard deviations of the estimated rates of return for Tech.com, Sam$$s Grocery, and the ASX $200$ Index.

$3.$ Which is a better measure of risk for the ordinary share of Tech.com and Sam$$s Grocery $$ the standard deviation you calculated in Question $2$ or the beta?

$4.$ Based on the beta provided, what is the expected rate of return for Tech.com and Sam$$s Grocery for the next year?

$5.$ If you form a two$-$share portfolio by investing $$30,000$ in Tech.com and $$70,000$ in Sam$$s Grocery, what is the portfolio beta and expected rate of return?

$6.$ If you form a two$-$share portfolio by investing $$70,000$ in Tech.com and $$30,000$ in Sam$$s Grocery, what is the portfolio beta and expected rate of return?

$7.$ Which of these two$-$share portfolios do you prefer? Why?