Question 5. (18 marks] You have investments in two rival companies of a well-performing market. You know that one of the companies will gain a large contract, so you review your investment. You know that the company which wins the contract yields a return of 10%, while the other company yields a loss of 5% as expectations are not met. With your knowledge of the market, you believe that company A has a 40% chance to win the contract, in the other case (with the remaining probability of 60%), company B gets the contract. In the following, we assume that your estimated probabilities are correct. winner return company A return company B likelihood Company A +10% -5% 40% Company B -5% +10% 60% (a) State the distribution of the random variables for each company's return individually and the joint distribution. (b) Compute your portfolio's expected return if you have invested equally in both companies. (c) Construct a portfolio with minimal variance. (d) Without short selling, or the possibility to lend money, construct a portfolio which maximises the expected return