To calculate the variance of a three-stock portfolio, we need to know not just the individual returns of the stocks but also their covariances (how the returns of the stocks move together). The formula for portfolio variance is:

$\text{Var}(R_p) = w_1^2 \cdot \text{Var}(R_1) + w_2^2 \cdot \text{Var}(R_2) + w_3^2 \cdot \text{Var}(R_3) + 2 \cdot w_1 \cdot w_2 \cdot \text{Cov}(R_1, R_2) + 2 \cdot w_1 \cdot w_3 \cdot \text{Cov}(R_1, R_3) + 2 \cdot w_2 \cdot w_3 \cdot \text{Cov}(R_2, R_3)$

Where:

• $w_1, w_2, w_3$ are the weights of the stocks in the portfolio.
• $\text{Var}(R_1), \text{Var}(R_2), \text{Var}(R_3)$ are the variances of the returns of the individual stocks.
• $\text{Cov}(R_1, R_2), \text{Cov}(R_1, R_3), \text{Cov}(R_2, R_3)$ are the covariances between the returns of the stocks.

However, with just the returns provided (22%, 27%, and 32%), I do not have enough information to calculate the variance because the individual variances and covariances are missing. Variance calculations also depend on the historical returns of each stock over a certain period.

If the returns are based on one period (e.g., a year) and you're asking for the variance of a simple equal-weighted portfolio (assuming no covariances), we can proceed with a simplified assumption.

Assumptions for Simplified Calculation:

1. Equal weights for each stock (i.e., $w_1 = w_2 = w_3 = \frac{1}{3}$).
2. No covariance data provided (this will simplify the calculation, but it won't account for the relationship between stocks).

Given that we have no variance or covariance information, we can approximate the variance using the standard deviation of the portfolio returns. First, we calculate the mean return ($\mu$):

$\mu = \frac{22\% + 27\% + 32\%}{3} = 27\%$

Next, calculate the squared differences from the mean:

$(22\% - 27\%)^2 = 25$ $(27\% - 27\%)^2 = 0$ $(32\% - 27\%)^2 = 25$

Then, the variance of the portfolio's returns (using these values) would be the average of the squared differences:

$\text{Variance} = \frac{25 + 0 + 25}{3} = \frac{50}{3} \approx 16.67$

Thus, the variance of this three-stock portfolio, under these assumptions, is approximately 16.67%.

Final Answer:

$\boxed{16.67\%}$

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Would you like further details on this calculation or the method for a more precise variance including covariance information?

Here are some related questions:

1. How do you calculate the variance of a portfolio with unequal stock weights?
2. What are the implications of covariance in portfolio risk management?
3. What is the difference between variance and standard deviation in finance?
4. How does portfolio diversification affect variance?
5. What tools can be used to calculate portfolio risk with multiple assets?

Tip: Always ensure that you have enough historical data for the returns of the individual stocks and the correlations between them when calculating portfolio variance for precise risk analysis.