The table below provides risk and return data for three shares, plus the correlation coefficients for the return on each pairing of shares.

The market portfolio return was 18.76% with a standard deviation of returns of 12.48%. The risk-free return was 0.5%.

Required

a) Calculate the minimum-risk portfolio weightings for each pairing of the three assets in the table.

b) Using the weightings from part a), provide a profile of the risk and return for each two-asset portfolio.

c) Analyse the degree to which the risk-return results for the three pairs of assets support the arguments of portfolio theory.

d) Choose any one of the asset pairings and minimise the risk based on a correlation coefficient of minus 1. Analyse the resulting risk-return relation.

e) Construct an investment in the market portfolio with a risk equal to that of the two-asset portfolio offering the greatest return per unit of risk. Assess the difference between the returns on the two-asset portfolio and the investment in the market portfolio. (Assume that capital can be borrowed or saved at the risk-free rate).
 

Share 1 Share 2 Share 3 Return 12.42% 17.89% 20.36% Standard Deviation 11.65% 16.80% 19.10% Correlation Coefficients Share 1 Share 2 Share 3 0.43 0.51 0.21