Question

An investment company, intends to invest a given amount of money in four stocks. From past data, the means and standard deviations of annual returns have been estimated as follows: Stock Mean Standard Deviation 1 0.14 0.20 2 0.11 0.15 3 0.10 0.08 4 0.125 0.175 The correlations among the annual returns on the stocks are as follows: Combination Correlation Stocks 1 and 2 0.6 Stocks 1 and 3 0.4 Stock 1 and 4 0.3 Stocks 2 and 3 0.7 Stock 2 and 4 0.5 Stock 3 and 4 0.8 [a] Find a minimum variance portfolio that yields a mean annual return of at least 0.12. [b] Is stock 4 in any of the optimal portfolios on the efficient frontier?

Answer 1

To find a minimum variance portfolio with a mean return of at least 0.12, use portfolio optimization. Stock 4 is not included in the optimal portfolios on the efficient frontier.

Step-by-step explanation:

To find a minimum variance portfolio that yields a mean annual return of at least 0.12, we can use the concept of portfolio optimization. This involves calculating the weights or proportions of the investment in each stock that will minimize the portfolio variance while achieving the desired mean return.

First, we need to calculate the covariance matrix of the four stocks using the given correlation values and standard deviations. Once we have the covariance matrix, we can use the mean returns and standard deviations to calculate the portfolio standard deviation and mean return for different weight combinations. We can then solve for the weights that minimize the portfolio variance with the constraint of a minimum mean return of 0.12.

Stock 4 is not included in the optimal portfolios on the efficient frontier. The efficient frontier represents the set of portfolios that offer the highest return for a given level of risk. Since Stock 4 has a lower mean return and higher standard deviation compared to the other stocks, it is not included in the efficient portfolios.