Suppose you hold a large, well-diversified portfolio and are considering adding to that portfolio either Stock X or another stock, Stock Y, which has the same beta as Stock X but a higher standard deviation of returns. Stocks X and Y have the same expected returns: = = 10.6% . Which stock should you choose?

I would choose Stock X.

Since Stock X has the same beta as Stock Y and same expected returns being equal to 10.6%, the difference in value between the two stocks lies in their standard deviations.  Stock Y that has a higher standard deviation is riskier than Stock X.  The standard deviation defines the variability of the returns.  Stock Y's returns varies more than Stock X's returns.  Therefore, Stock X is preferable to Stock Y.

Explanation:

Standard Deviation is a statistical measure of the amount of variation or dispersion of a set of values.  A lower standard deviation means that the values do not differ much from each other.  A higher standard deviation implies that the values differ much from each other.

Beta is a measure of the market risk.

Standard Deviation of Returns measures returns' volatility or risk. A larger return standard deviation means larger variations to the returns.

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