"How does the relationship between the average return and the historical volatility of individual stocks differ from the relationship between the average return and the historical volatility of large, well-diversified portfolios?"

Relationship between Individual Stock average return and historical volatility is insignificant but is strong for Portfolios

Explanation:

The relationship between the average return and the historical volatility of individual stocks has been found to consistently be POSITIVE BUT INSIGNIFICANT for the majority of markets that were sampled.

The relationship between the average return and the historical volatility of large, well-diversified portfolios on the other hand have been shown to have a STRONG POSITIVE RELATIONSHIP. That means that Portfolios with higher returns usually have higher volatilities as well.

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