For an equally weighted portfolio with a large number of assets, the portfolio's variance can be expressed as:

$\sigma_p^2 = \frac{\sigma^2}{N} + \left(1 - \frac{1}{N}\right) \cdot \text{Cov}$

As N (the number of assets) becomes large, the first term ($\frac{\sigma^2}{N}$) diminishes, making the contribution of individual asset variances negligible. The second term approaches the average covariance between the assets, indicating that the portfolio's risk is primarily driven by the covariance among the assets. Therefore, the correct answer is C, as the portfolio's variance approaches the average covariance between the individual assets' returns.