According to Carlo's stock broker, Investment A has relatively high historical rates of return, and so he is recommending the purchase of Investment A. Carlo's insurance advisor, on the other hand, is recommending the purchase of Investment B based on its historical rates of return. And still another advisor is recommending the purchase of a third investment (Investment C) based on its historical returns. Carlo is trying to determine which of the three investments is best, and he is focusing his decision making process on the concepts of risk and return.

Investment A is an equity (stock) investment in an American company. Returns on this Investment for the past 6 years are detailed in the table below, and Carlo expects the returns of the next 6 years to be the same as the last 6 years.

(Table) year return

1 +80%

2 -50%

3 +70%

4 -50%

5 +40%

6 -5%

1.With respect to Investment A, if the annual returns are each considered to be equally likely to occur, calculate the standard deviation of the returns.____________

2.What is the expected average annual rate of return on Investment A? __________

3.An investor who invested $10,000 in Investment A at the beginning of year 1 would have how much in the investment at the end of year 6?_____________

4.Taking only the beginning and ending balances of the investment into account in order to smooth the returns and to avoid the problem of multiple rates of return that can occur when returns are both positive and negative, what is the compound annual growth rate of Investment A over the 6-year period?____________

5.What is the relevant annual rate of return per unit of risk (expressed as one number) for Investment A over the 6-year period?_____________

Investment B is represented by the cash value of a whole life insurance policy. Returns on this Investment for the past 6 years are detailed in the table below, and Carlo expects the returns of the next 6 years to be the same as the last 6 years.

(Table) year return

1 +4.9%

2 +5.0%

3 +4.6%

4 +5.1%

5 +4.9%

6 +4.8%

1.With respect to Investment B, if the annual returns are each considered to be equally likely to occur, calculate the standard deviation of the returns.____________

2.What is the expected average annual rate of return on Investment B?___________

3.An investor who invested $10,000 in Investment B at the beginning of year 1 would have how much in the investment at the end of year 6?______________

4.Taking only the beginning and ending balances of the investment into account in order to smooth the returns and to avoid the problem of multiple rates of return that can occur when returns are both positive and negative, what is the compound annual growth rate of Investment B over the 6-year period?___________

5.What is the relevant annual rate of return per unit of risk (expressed as one number) for Investment B over the 6-year period?____________

Investment C is an equity (stock) investment in a British company. Returns on this Investment for the past 6 years are detailed in the table below, and Carlo expects the returns of the next 6 years to be the same as the last 6 years.

(Table) year return

1 +4.9%

2 +5.0%

3 +4.6%

4 +5.1%

5 +4.9%

6 +4.8%

1.With respect to Investment C, if the annual returns are each considered to be equally likely to occur, calculate the standard deviation of the returns.____________

2.What is the expected average annual rate of return on Investment C?___________

3.An investor who invested $10,000 in Investment C at the beginning of year 1 would have how much in the investment at the end of year 6?_____________

4.Taking only the beginning and ending balances of the investment into account in order to smooth the returns and to avoid the problem of multiple rates of return that can occur when returns are both positive and negative, what is the compound annual growth rate of Investment C over the 6-year period?_____________

5.What is the relevant annual rate of return per unit of risk (expressed as one number) for Investment C over the 6-year period?____________

6. Summarize your results from above in a table that shows the relevant details.

TITLE A B C

(Table) Standard Deviation

Average Annual rate of return

End of year 6 value

Compound Annual growth rate (CAGR)

Relevant annual return per unit of risk

1.Thus far we have calculated two different types of annual returns for the three investments. Which of the two types of returns is the most relevant in terms of guiding Carlo in his selection process relative to choosing the best alternative among the three investments? _______________________________________

2.If the rate of return per unit of risk is considered to be the appropriate measurement of the goodness of an investment, then which of the three investments is the best choice for a rational investor? _________________