Question 1. There are four assets in the market. The following chart shows their possible payoffs. There are only four states. States 1 and 4 have the same probabilities. State 2 and 3 have the same probabilities. State 2 is more likely to happen than State 1 by a probability of 0.2 . [Total: 20 marks] i. What are the expected return and standard deviation of each asset? [4 marks] ii. What are the covariances and correlations between the pairs of assets? [5 marks] iii. What are the expected returns and standard deviations of a portfolio with half of its funds invested in: a. Asset 1 and Asset 2? [1 mark] b. Asset 1 and Asset 3? [1 mark] c. Asset 2 and Asset 3? [1 mark] d. Asset 1 and Asset 4? [1 mark] iv. Using the information in (i) and (ii), compare the portfolio standard deviations in (iii) to the average of the standard deviations of the individual assets. Explain what diversification is, and how the correlation coefficient affects the expected return and total risk of a portfolio. [7 marks]