Investor X is comfortable with a risk premium of
8% and a portfolio standard deviation of 18%. The
risk-free rate amounts to 6%. The risky portfolio
available to the investor has an expected rate of
return of 12% and standard deviation of 20%.
 Calculate the following:

10. The risk aversion (A) applicable to investor X.

To calculate the risk aversion (A) applicable to investor X, we can use the formula:

\[
A = \frac{E(R_p) - R_f}{\sigma_p^2}
\]

Where:
- \( E(R_p) \) is the expected rate of return on the portfolio (12% or 0.12).
- \( R_f \) is the risk-free rate (6% or 0.06).
- \( \sigma_p \) is the standard deviation of the portfolio (20% or 0.20).

However, we need to adjust the formula to account for the fact that Investor X has a different portfolio standard deviation (\( \sigma_X = 18\% \) or 0.18). The risk aversion \( A \) reflects the investor's preference for risk given their comfort with a certain level of risk (in this case, an 8% risk premium).

Given that \( \text{Risk Premium} = A \times \sigma_X^2 \):

\[
A = \frac{\text{Risk Premium}}{\sigma_X^2}
\]

Let's calculate it:

\[
A = \frac{0.08}{0.18^2}
\]The risk aversion coefficient \( A \) applicable to Investor X is approximately 2.47.

Would you like more details or have any questions? Here are some related questions to explore:

1. What is the meaning of the risk aversion coefficient in portfolio theory?
2. How does a higher risk aversion coefficient affect an investor's portfolio choices?
3. What would the risk aversion coefficient be if the risk premium were different?
4. How does the standard deviation of a portfolio impact the calculation of the risk aversion coefficient?
5. Can the risk aversion coefficient change over time for an investor?

**Tip:** Understanding your own risk aversion helps in constructing a portfolio that aligns with your financial goals and comfort level with risk.

Learn how to calculate the risk aversion coefficient for Investor X's portfolio based on their risk premium, risk-free rate, and the characteristics of the available risky portfolio. Understand the implications of risk aversion in investment decisions. Suitable for advanced finance professionals and students.

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