Solution

A. Incorrect

• Both Asset 1 and Asset 2 have lower standard deviations than Asset 3.
• A candidate may choose this because Asset 3 has the highest correlation with the market.

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B. Incorrect

• Both Asset 1 and Asset 2 have lower standard deviations than Asset 3.
• A candidate may choose this because Asset 3 has the highest beta.

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C. Correct

• Definition of beta: $$\beta_i = \rho_{i,m} \frac{\sigma_i}{\sigma_m} \quad \Rightarrow \quad \sigma_i = \frac{\beta_i \cdot \sigma_m}{\rho_{i,m}}$$

Where:

• $\rho_{i,m}$ = correlation between Asset $i$ and the market portfolio
• $\sigma_i$ = standard deviation of Asset $i$
• $\sigma_m$ = standard deviation of the market portfolio

Calculations:

• Asset 1: $(1.000 \times 0.2) / 0.8 = 0.25$
• Asset 2: $(1.225 \times 0.2) / 0.7 = 0.35$
• Asset 3: $(1.125 \times 0.2) / 0.5 = 0.45$

Conclusion:
The asset with the highest standard deviation is Asset 3, with $\sigma = 0.45$.

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Portfolio Risk and Return: Part II

• Calculate and interpret beta