In a year's time a stock will be valued either at $15 or $30. A certain derivative will give a payoff of $5 or $20 in each case, respectively. Assume that the risk-free interest rate is 5%. In both questions that follow, do not simply use ready formulae from the course material. Instead, you are expected to briefly present the steps involved in identifying the components of the portfolios. (a) Find a replicating portfolio for this derivative today, stating clearly whether each portfolio component is a long or a short position. [8] (b) Find a riskless portfolio for this derivative today, stating clearly whether each portfolio component is a long or a short position. [8]