# Question: Return to the example presented in Problem 1 Chapter 4 A

Return to the example presented in Problem 1, Chapter 4.

A. Assuming short selling is not allowed:

(1) For securities 1 and 2, find the composition, standard deviation, and expected return of the portfolio that has minimum risk.

(2) On the same graph, plot the expected return and standard deviation for all possible combinations of securities 1 and 2.

(3) Assuming that investors prefer more to less and are risk avoiders, indicate in red those sections of the diagram in Part 2 that are efficient.

(4) Repeat steps 1, 2, and 3 for all other possible pair wise combinations of the securities shown in Problem 1 of Chapter 4.

B. Assuming short selling is allowed:

(1) For securities 1 and 2, find the composition, standard deviation, and expected return of the portfolio that has minimum risk.

(2) On the same graph, plot the expected return and standard deviation for all possible combinations of securities 1 and 2.

(3) Assuming that investors prefer more to less and are risk avoiders, indicate in red those sections of the diagram in Part 2 that are efficient.

(4) Repeat steps 1, 2, and 3 for all other possible pair wise combinations of the securities shown in Problem 1 of Chapter 4.

C. Assuming that the riskless lending and borrowing rate is 5%, and short sales are allowed, find the location of the optimal portfolio from among those considered.

Repeat for a rate of 8%.

A. Assuming short selling is not allowed:

(1) For securities 1 and 2, find the composition, standard deviation, and expected return of the portfolio that has minimum risk.

(2) On the same graph, plot the expected return and standard deviation for all possible combinations of securities 1 and 2.

(3) Assuming that investors prefer more to less and are risk avoiders, indicate in red those sections of the diagram in Part 2 that are efficient.

(4) Repeat steps 1, 2, and 3 for all other possible pair wise combinations of the securities shown in Problem 1 of Chapter 4.

B. Assuming short selling is allowed:

(1) For securities 1 and 2, find the composition, standard deviation, and expected return of the portfolio that has minimum risk.

(2) On the same graph, plot the expected return and standard deviation for all possible combinations of securities 1 and 2.

(3) Assuming that investors prefer more to less and are risk avoiders, indicate in red those sections of the diagram in Part 2 that are efficient.

(4) Repeat steps 1, 2, and 3 for all other possible pair wise combinations of the securities shown in Problem 1 of Chapter 4.

C. Assuming that the riskless lending and borrowing rate is 5%, and short sales are allowed, find the location of the optimal portfolio from among those considered.

Repeat for a rate of 8%.

## Answer to relevant Questions

Answer the questions to Problem 1 with data from Chapter 4, Problem 2. In Chapter 4, Problem 2 Assume analysts provide the following types of information. Assume (standard definition) short sales are allowed. What is the optimum portfolio if the lending and borrowing rate is 5%? Show that the Vasicek technique leads to a simple proportional weighting of the market beta and the stock’s beta if the standard error of all betas is the same. Assume that all assumptions of the single-index model hold, except that the covariance between residuals is a constant K instead of zero. Derive the covariance between the two securities and the variance on a portfolio. Given the following data What is the optimum portfolio assuming no short sales if RF = 5% and p = 0.5?Post your question