Question

For simplicity and convenience of calculation, suppose there are only one risk-free asset with a return of 5% and two risky assets, Stock A and Stock B. Stock A Expected return (%) is 10 whilst Stock B is 8 and Standard deviation for A is 20 and the standard deviation of B is 10 (%) whilst the Correlation Correlation coefficient = 0.04 (a) Explain the concept of the minimum-variance portfolio (without the risk-free asset). Use the above information to calculate the investment weightings, expected return, and risk of the minimum-variance portfolio of this 2-stock portfolio. Illustrate your answer in a diagram.

Answer 1

The minimum-variance portfolio is a portfolio that contains a combination of assets that minimizes the portfolio's overall risk. The weightings, expected return, and risk of the minimum-variance portfolio of this 2-stock portfolio can be calculated using the given information. The minimum-variance portfolio can be represented in a diagram on the efficient frontier curve.

Step-by-step explanation:

The minimum-variance portfolio is a portfolio that contains a combination of assets that minimizes the portfolio's overall risk. In this case, without the risk-free asset, the minimum-variance portfolio of the 2-stock portfolio can be calculated using the formula:

Weight of Stock A = (Standard Deviation of Stock B)^2 / ((Standard Deviation of Stock A)^2 + (Standard Deviation of Stock B)^2)

Weight of Stock B = 1 - Weight of Stock A

Expected return of the portfolio = Weight of Stock A * Expected return of Stock A + Weight of Stock B * Expected return of Stock B

Risk of the portfolio = sqrt((Weight of Stock A)^2 * (Standard Deviation of Stock A)^2 + (Weight of Stock B)^2 * (Standard Deviation of Stock B)^2 + 2 * Weight of Stock A * Weight of Stock B * Correlation Coefficient * Standard Deviation of Stock A * Standard Deviation of Stock B)

Using the given information:

Weight of Stock A = (10)^2 / ((20)^2 + (10)^2) = 0.25

Weight of Stock B = 1 - 0.25 = 0.75

Expected return of the portfolio = 0.25 * 10 + 0.75 * 8 = 8.5%

Risk of the portfolio = sqrt((0.25)^2 * (20)^2 + (0.75)^2 * (10)^2 + 2 * 0.25 * 0.75 * 0.04 * 20 * 10) = 10.17%

You can represent the minimum-variance portfolio of the 2-stock portfolio in a diagram by plotting the expected returns on the x-axis and the risks on the y-axis. The minimum-variance portfolio will be a point on the efficient frontier curve, which represents the set of portfolios that provide the highest expected return for a given level of risk.