(a) Consider a market where there are only three assets available to invest in, and where short selling is allowed: Asset Expected return Standard deviation of return A 1% 3% B 5% 15% 4% 10% The correlation of returns between assets A and C is 0.6. The returns on asset B are uncorrelated with the returns of the other assets. Using a Lagrangian approach, find the minimum variance portfolio with an expected return of 5% (assuming it will be fully invested in this market). (b) In a market where the assumptions of the CAPM hold, there is one risk-free asset (Asset 1) with an annual rate of return of 2% and two risky assets with the following properties: Rate of return (p.a.) State Probability | Asset 2 Asset 3 1 0.2 10% 14% 2 0.4 20% 10% 3 0.3 16% 21% 4 0.1 25% 9% The market capitalisation of Asset 2 is 20,000 and the market capitalisation of Asset 3 is 80,000. The market portfolio is defined by the market capitalisations. i. Determine the market price of risk. ii. Calculate the beta of each risky asset.