To find the expected return rate for this portfolio, we calculate $\text{E}(R)$, or $\text{mean}(R)$, which is the expected value of the portfolio return rate $R = 0.6X + 0.4Y$.

Given:

• $\text{mean}(X) = 16.5$
• $\text{mean}(Y) = -1.8$

The expected return $\text{E}(R)$ for the portfolio can be calculated using the linearity of expectation:

$\text{E}(R) = 0.6 \cdot \text{E}(X) + 0.4 \cdot \text{E}(Y)$

Substituting the given values:

$\text{E}(R) = 0.6 \cdot 16.5 + 0.4 \cdot (-1.8)$

Calculating each part:

1. $0.6 \cdot 16.5 = 9.9$
2. $0.4 \cdot (-1.8) = -0.72$

Thus,

$\text{E}(R) = 9.9 - 0.72 = 9.18$

Answer:

The expected return rate for this portfolio, $\text{mean}(R)$, is $9.18$.

Would you like a further breakdown of these calculations?

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Here are 5 related questions:

1. How would the expected return change if the portfolio weights were 50% in each stock?
2. How does the portfolio’s expected return compare to investing solely in Stock A?
3. What would happen to the expected return if the mean return of Stock B changed to a positive value?
4. How would changes in the weights impact the risk (standard deviation) of the portfolio?
5. What is the interpretation of a negative mean for Stock B's returns in the context of this portfolio?

Tip: In portfolio theory, diversification helps in managing risk by combining assets with varying correlations and expected returns.