6. Risk Management

Portfolio Theory — Quiz

Test your understanding of portfolio theory with 5 practice questions.

Practice Questions

Question 1

In the context of mean-variance optimization, if an investor's utility function is given by $U(E[R_p], \sigma_p) = E[R_p] - \frac{1}{2}A\sigma_p^2$, where $A$ is the risk aversion coefficient, what does a higher value of $A$ imply about the investor's preference for portfolios on the efficient frontier?

Question 2

Consider a portfolio of $n$ assets. The portfolio variance is given by $\sigma_p^2 = \sum_{i=1}^{n}\sum_{j=1}^{n}w_i w_j \text{Cov}(R_i, R_j)$. If all assets have the same variance $\sigma^2$ and the same covariance $\rho\sigma^2$ with each other, and equal weights $w_i = 1/n$, what happens to the portfolio variance as $n \to \infty$?

Question 3

According to the Capital Asset Pricing Model (CAPM), if a security's expected return plots below the Security Market Line (SML), what does this imply about the security?

Question 4

In mean-variance optimization, the introduction of a risk-free asset allows for the creation of the Capital Market Line (CML). Which of the following statements about the CML is true?

Question 5

An investor has a portfolio with an expected return of 15% and a standard deviation of 20%. The risk-free rate is 5%, and the market portfolio has an expected return of 10% and a standard deviation of 12%. Calculate the Sharpe Ratio of the investor's portfolio.