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(Diversifying Portfolios MC)

\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{1}{|c|}{ Investment } & Portfolio 1 & Portfolio 2 & Portfolio 3 \\
\hline
Stock in Large, Old Corporation & \[tex]$500 & \$[/tex]2,000 & \[tex]$2,000 \\
\hline
Stock in Emerging Company & \$[/tex]5,000 & \[tex]$500 & \$[/tex]1,000 \\
\hline
U.S. Treasury Bond & \[tex]$3,000 & \$[/tex]500 & \[tex]$1,000 \\
\hline
Certificate of Deposit & \$[/tex]500 & \[tex]$6,000 & \$[/tex]3,000 \\
\hline
\end{tabular}

Which of the following shows the portfolios' levels of risk from highest to lowest?

A. Portfolio 2, Portfolio 3, Portfolio 1
B. Portfolio 1, Portfolio 3, Portfolio 2
C. Portfolio 2, Portfolio 1, Portfolio 3
D. Portfolio 3, Portfolio 2, Portfolio 1



Answer :

GinnyAnswer
To determine the risk levels of the portfolios from highest to lowest, we consider the portion of the investments in the more volatile assets, specifically the "Stock in Emerging Company." Here is the step-by-step process:

1. Calculate the total investment for each portfolio:
- Portfolio 1:
[tex]\[ 500 + 5000 + 3000 + 500 = 9000 \][/tex]
- Portfolio 2:
[tex]\[ 2000 + 500 + 500 + 6000 = 9000 \][/tex]
- Portfolio 3:
[tex]\[ 2000 + 1000 + 1000 + 3000 = 7000 \][/tex]

2. Calculate the risk score for each portfolio:
- The risk score is determined by the proportion of the "Stock in Emerging Company" to the total investment for each portfolio.
- Portfolio 1:
[tex]\[ \text{Risk Score} = \frac{5000}{9000} \approx 0.5556 \][/tex]
- Portfolio 2:
[tex]\[ \text{Risk Score} = \frac{500}{9000} \approx 0.0556 \][/tex]
- Portfolio 3:
[tex]\[ \text{Risk Score} = \frac{1000}{7000} \approx 0.1429 \][/tex]

3. Compare the risk scores:
The calculated risk scores for the portfolios are:
- Portfolio 1: [tex]\(0.5556\)[/tex]
- Portfolio 2: [tex]\(0.0556\)[/tex]
- Portfolio 3: [tex]\(0.1429\)[/tex]

4. Order the portfolios based on their risk scores from highest to lowest:
- Portfolio 1 has the highest risk score of [tex]\(0.5556\)[/tex].
- Portfolio 3 has the second highest risk score of [tex]\(0.1429\)[/tex].
- Portfolio 2 has the lowest risk score of [tex]\(0.0556\)[/tex].

Thus, the portfolios' levels of risk from highest to lowest are:
- Portfolio 1, Portfolio 3, Portfolio 2

Therefore, the correct answer is:
- Portfolio 1, Portfolio 3, Portfolio 2.

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