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.

rational decision making is a multi-step process for making choices between alternatives. the process of rational decision making favors logic, objectivity, and analysis over subjectivity and insight. the word “rational” in this context does not mean sane or clear-headed as it does in the colloquial sense.

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