1. (a) Suppose that there are 2 possible states of nature and 2 assets with the following prices in each state: State Asset A Asset B 1 2 3 2 4 1 Asset A currently sells for 3 and B for 1.75. i. What are the prices of pure state 1 and 2 securities? ii. Derive the risk neutralised probabilities for the two states. What do these mean? iii. Derive the risk-free interest rate. iv. Suppose that a riskfree bond that will pay 1 in both states is now selling for 0.80. Does there exist an arbitrage opportunity? If so, describe how to profit from it. (b) Suppose that there are two stocks with mean, standard deviation and correlation as follows A B mean return 4% 8% standard deviation 2% 12% correlation 25% i. You make up a portfolio with 0.25 of your wealth in A, 0.5 in B and the remainder in the riskfree asset which has return of 1%. What is the mean return of this portfolio? ii. Derive the standard deviation of the portfolio return. iii. Suppose that you make up a portfolio of assets A and B only, without the riskfree asset. What combination will minimize portfolio variance?