The Benefits of Adding the Risk-Free Asset to Your Portfolio

A

Adding the risk-free asset to a portfolio of risky assets will have an impact on the portfolio's standard deviation. To understand the effect, let's examine each answer choice:

A. Decrease portfolio standard deviation because it is uncorrelated with risky assets: This answer choice suggests that the risk-free asset, being uncorrelated with the risky assets in the portfolio, would decrease the portfolio's standard deviation. However, this statement is incorrect. Adding an uncorrelated asset to a portfolio of risky assets does not necessarily reduce the portfolio's standard deviation. The reduction in standard deviation depends on the expected returns and the weight of the risk-free asset in the portfolio.

B. Not affect portfolio standard deviation because it is uncorrelated with risky assets: This answer choice states that the risk-free asset, being uncorrelated with the risky assets, would have no effect on the portfolio's standard deviation. This statement is also incorrect. Although the risk-free asset's correlation with risky assets does not directly impact the standard deviation, the weight of the risk-free asset in the portfolio does influence the portfolio's overall risk.

C. Decrease portfolio standard deviation due to its negative correlation with risky assets: This answer choice suggests that the risk-free asset has a negative correlation with the risky assets, resulting in a decrease in the portfolio's standard deviation. However, this statement is also incorrect. The risk-free asset, by definition, has a correlation of zero with risky assets since its returns are certain and do not fluctuate with market conditions.

To understand the impact of adding the risk-free asset to a portfolio, we need to consider the concept of diversification. The risk-free asset, such as Treasury bills or cash, has a stable and certain return and is considered to have no risk. When combined with a portfolio of risky assets, the risk-free asset allows an investor to adjust the risk-return trade-off.

Adding the risk-free asset to a portfolio will affect the overall risk and return characteristics of the portfolio. The key factor that determines the impact is the weight of the risk-free asset in the portfolio. As the weight of the risk-free asset increases, the portfolio's risk decreases.

Specifically, the addition of the risk-free asset allows an investor to construct a portfolio along the Capital Allocation Line (CAL). The CAL represents a combination of the risk-free asset and the efficient frontier of risky assets. The efficient frontier represents portfolios with the highest expected return for a given level of risk.

By adjusting the weight of the risk-free asset in the portfolio, an investor can move along the CAL and choose a portfolio that best suits their risk tolerance. A higher weight of the risk-free asset will result in a lower portfolio standard deviation. However, it's important to note that the expected return of the portfolio will also decrease as the risk-free asset's weight increases.

In summary, adding the risk-free asset to a portfolio of risky assets allows an investor to adjust the risk-return trade-off. The weight of the risk-free asset in the portfolio determines the overall risk and return characteristics. While the risk-free asset has a correlation of zero with risky assets, its inclusion in the portfolio influences the portfolio's risk through diversification. Therefore, none of the answer choices provided accurately describe the impact of adding the risk-free asset on the portfolio's standard deviation.