Final answer:
When Marleen adds a security to her portfolio that is not perfectly positively correlated, the overall risk, as measured by the standard deviation, is expected to decrease due to diversification benefits.
Step-by-step explanation:
The correct answer is option decrease. When Marleen adds security Y to her portfolio that is less than perfectly positively correlated with the portfolio, diversification benefits come into play.
Since security Y has the same standard deviation as the portfolio, one might initially assume that risk, as measured by standard deviation, would remain unchanged.
However, the key lies in the correlation between security Y and the rest of the portfolio. Because they are not perfectly positively correlated, adding security Y will provide diversification, which is expected to reduce the overall portfolio risk.
The new combined standard deviation will be lower than that of the individual security or the original portfolio due to the mitigating effect of diversification on total risk.
This reduced volatility is a fundamental concept in portfolio theory and is a primary reason why investors seek to diversify their holdings.
The correct answer is option c. The standard deviation of the sampling distribution of the means will decrease, making it approximately the same as the standard deviation of X as the sample size increases.
When Marleen adds a security to her portfolio that is less than perfectly positively correlated with the portfolio, it introduces diversification. Diversification reduces the overall risk of the portfolio. As a result, the standard deviation of Marleen's portfolio is most likely to decrease after adding the security.
This is because the correlation between the security and the portfolio will result in a reduction in the volatility and standard deviation of the portfolio. The more negatively correlated the security is to the portfolio, the greater the decrease in standard deviation will be.