we have two stocks Stock A and Stock B, Both stocks have the same expected rate of return 11%, but have different Standard Deviation 12%, and 20% respectively. based on the information above can we conclude that any rational risk-averse investor will add stock A to a well diversified portfolio over stock B? Why? or Why not?
To determine whether a rational risk-averse investor would prefer stock A over stock B for a diversified portfolio, we need to consider the concept of risk and how it is measured in investment analysis.
The standard deviation is a widely used measure of risk in finance. It quantifies the variability or dispersion of returns around the average return. The higher the standard deviation, the greater the potential for fluctuations in returns and thus a higher level of risk.
In this case, stock A has a standard deviation of 12%, while stock B has a higher standard deviation of 20%. This implies that stock B has higher variability in returns compared to stock A, making it riskier in terms of potential price fluctuations.
Given that both stocks have the same expected rate of return (11%), a rational risk-averse investor would prefer stock A over stock B for the following reasons:
1. Lower Risk: Stock A has a lower standard deviation, indicating lower variability in returns and, therefore, lower risk compared to stock B. A risk-averse investor would generally prefer a lower-risk investment.
2. Equal Expected Returns: As both stocks have the same expected rate of return, there is no additional compensation in terms of higher potential returns for selecting stock B over stock A. Therefore, the investor may prefer the lower-risk option, which is stock A.
3. Diversification Benefits: Adding stock A to a well-diversified portfolio may contribute to reducing the overall risk of the portfolio. By combining assets with different risk profiles, investors can achieve a more stable return over time. However, the decision to add stock A or stock B to a portfolio should also consider factors such as correlation with other assets and overall portfolio objectives.
It is important to note that individual investor preferences and risk tolerance may vary. Therefore, investors should consider their own risk profile and investment objectives before making any investment decisions.