Question

The weighted average of the standard deviations of the assets in Portfolio C is 12.9%. Which of the following are possible values for the standard deviation of the portfolio?

Multiple select question.

10.9%


14.9%


12.9%

Answer 1

To determine which of the presented options could be possible values for the standard deviation of Portfolio C, we must consider the concept of weighted averages and how standard deviations work in the context of a portfolio.

The weighted average standard deviation of the assets in Portfolio C is 12.9%. This means that the contributions of individual assets’ standard deviations to the portfolio's overall standard deviation will result in an aggregate value of 12.9%. However, it does not restrict the portfolio standard deviation to be exactly 12.9%; instead, the standard deviation of an entire portfolio can vary based on the correlation between different assets and their weights in the portfolio.

### Given Options:

1. **10.9%**: This value is below the weighted average of 12.9%. It is possible for the overall portfolio standard deviation to be lower than the weighted average if the assets are negatively correlated, which can lead to diversification benefits.

2. **14.9%**: This value is above the weighted average of 12.9%. This can occur if the assets are positively correlated and move in tandem, which can increase the overall portfolio risk.

3. **12.9%**: This value matches the weighted average, indicating that it is a potential outcome for the portfolio’s standard deviation.

### Conclusion:
Based on the reasoning that the portfolio standard deviation can be lower than, equal to, or greater than the weighted average of the individual asset standard deviations:

- **Possible values for the standard deviation of the portfolio include:**
- **10.9%**
- **14.9%**
- **12.9%**

Thus, **all three options (10.9%, 14.9%, 12.9%) are possible values for the standard deviation of the portfolio.**