Sonny owns $5,000 worth of High Risk Enterprises (HRE) stock. HRE has a standard deviation of 16 percent and a beta of 2.0. He wants to invest another $5,000 and create a $10,000 portfolio that is equally as risky as the overall market. Which one of the following will accomplish his goal?
A. invest the additional $5,000 in a security that is equally as risky as the market
B. sell HRE and invest the entire $10,000 in risk-free securities
C. sell HRE and invest $5,000 in risk-free securities and $5,000 in a stock that has a standard deviation of 4 percent
D. invest the additional $5,000 in a stock that has a standard deviation of 4 percent
E. invest the additional $5,000 in risk-free securities
To answer this question, we need to understand the concept of beta and how it relates to portfolio risk. Beta measures the sensitivity of a stock's returns to the overall market returns. A beta of 1 implies that the stock's returns move in line with the market, while a beta higher than 1 indicates higher sensitivity to market movements, and a beta lower than 1 indicates lower sensitivity.
In this case, Sonny wants to create a $10,000 portfolio that is equally as risky as the overall market. Since HRE has a beta of 2.0, we need to find a combination of investments that will result in a portfolio beta of 1.0.
Let's analyze each option:
A. Invest the additional $5,000 in a security that is equally as risky as the market.
By investing in a security with the same risk as the market, we can achieve the desired portfolio risk. This option could potentially work, but we don't have enough information to determine if there is a security available with the same risk as the market.
B. Sell HRE and invest the entire $10,000 in risk-free securities.
Investing in risk-free securities will not match the risk of the overall market, as risk-free securities are not subject to market fluctuations. This option does not achieve the goal.
C. Sell HRE and invest $5,000 in risk-free securities and $5,000 in a stock that has a standard deviation of 4 percent.
While investing $5,000 in a stock with a lower standard deviation will reduce the overall risk, it does not necessarily match the risk of the overall market. This option does not achieve the goal.
D. Invest the additional $5,000 in a stock that has a standard deviation of 4 percent.
Investing in a stock with a lower standard deviation than HRE will reduce the overall risk of the portfolio. However, we still need to consider the beta of this new stock. Without knowledge of the new stock's beta, we can't determine if this option will achieve the goal.
E. Invest the additional $5,000 in risk-free securities.
Similar to option B, investing in risk-free securities alone does not match the risk of the overall market. This option does not achieve the goal.
Based on the given information, none of the options can be definitively determined to accomplish Sonny's goal. We need additional information about a security's risk and beta to determine the correct answer.