Question

You plan to invest your money in a portfolio consisting of 2 shares, A and B , table 3.1 below contains information on the expected returns, standard deviation and weighting in the portfolios of the 2 shares. It also includes information on the correlation coefficients in the 2 shares.

		share a	share b
expected return		12%	24%
standard dev		5%	15%
weighting in portfolio		30%	70%
correlation coefficient between 2 shares ®		0,8

3.1 use data contains in the table 3.1 and answer the following questions:

3.1.a calculate the expected return of the portfolio

3.1.b using the formula for portfolio variance calculate the expected standard deviation of the portfolio

3.2. how would you answer in q3b have differ if the correlation coefficient between the 2 shares have to be 0,2 instead of 0.8

3.2a calculate the new standard deviation of the portfolio

3.2.b explain the difference between your answer in 3.1.b and 3.2.a

Answer 1

Portfolio Expected return is calculated by solving the following equation:

If the correlation is 0.2, the standard deviation will be as follows:

Standard deviation of the portfolio

reduces when the correlation reduces because the portfolio is better diversified when lower correlated assets are added which react differently under the same economic conditions and therefore it is less risky to invest in such a portfolio.