Stock X

3%

-2%

9%

6%

-1%

-4%

11%

Stock Y

1%

-4%

7%

12%

3%

-2%

-1%

Consider a portfolio of 20% stock X and 80% stock Y.

**What is the mean of portfolio returns?**

Please specify your answer in decimal terms and round your answer to the nearest thousandth

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.

Consider a portfolio of 20% stock X and 80% stock Y. What is the mean of portfolio returns? Please specify your answer in decimal terms and round your answer to the nearest thousandth.

Discover how to calculate the mean of portfolio returns using a weighted average for a portfolio consisting of 20% Stock X and 80% Stock Y. Learn the key statistical concepts and formulas involved in this finance problem, suitable for undergraduate students.

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