To find the mean of the portfolio returns, we can calculate the weighted average of the returns of Stock X and Stock Y.

Given:

• Portfolio weight for Stock X: 20% (0.20)
• Portfolio weight for Stock Y: 80% (0.80)

Returns for each stock:

• Stock X: $3\%, -2\%, 9\%, 6\%, -1\%, -4\%, 11\%$
• Stock Y: $1\%, -4\%, 7\%, 12\%, 3\%, -2\%, -1\%$

Converting percentages to decimals:

• Stock X returns: $0.03, -0.02, 0.09, 0.06, -0.01, -0.04, 0.11$
• Stock Y returns: $0.01, -0.04, 0.07, 0.12, 0.03, -0.02, -0.01$

Step 1: Calculate the weighted return for each period.

For each period, the portfolio return $r_p$ is given by:

$r_p = (0.20 \times r_X) + (0.80 \times r_Y)$

Step 2: Calculate the portfolio returns for each period.

I'll now calculate these returns:

$\text{Portfolio Returns} = 0.20 \times (0.03, -0.02, 0.09, 0.06, -0.01, -0.04, 0.11) + 0.80 \times (0.01, -0.04, 0.07, 0.12, 0.03, -0.02, -0.01)$

Let's calculate these values:The mean of the portfolio returns is $\mathbf{0.025}$ in decimal terms, rounded to the nearest thousandth.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How is the standard deviation of the portfolio returns calculated?
2. What would the mean return be if the portfolio allocation was 50% Stock X and 50% Stock Y?
3. How does portfolio diversification affect the overall risk of the portfolio?
4. Can you calculate the covariance between Stock X and Stock Y returns?
5. How would you calculate the Sharpe ratio of this portfolio?

Tip: When constructing a portfolio, consider both the expected return and the risk (volatility) to ensure that it aligns with your investment goals and risk tolerance.