Question 4 The portfolio manager of OneCapital, Elle, is deciding about what to invest for the company's 5 million cash reserve in the forthcoming quarter. Elle has two options: growth stocks and value stocks. However, the return of these two options depends on the overall economic growth rate in the forthcoming quarter. According to Elle's estimation, the probabilities of economic growth being high, medium, and low in the forthcoming quarter are 0.2, 0.5, and 0.3, respectively. The payoff (in thousands) under each different combination of decisions and states of nature can be summarised in the following table. (i) (ii) High (S1) Medium (S2) Low (S3) Growth stocks (d1) 100 50 -50 Value stocks (d2) 70 20 -10 Apply the opportunity loss approach to recommend a decision strategy to Elle. You must show all the necessary workings. (2 marks) According to Elle's prior estimation of the probabilities, draw a decision tree and recommend a decision to Elle. Clearly show your calculations and justify your decision strategy. (4 marks) (iii) In this decision problem, what is the expected value of perfect information? (2 marks) Before deciding which stock to invest in, Elle hired an economic institute to evaluate the economic growth rate in the forthcoming quarter. The economic institute will provide either a favourable (F) or unfavourable (U) evaluation of the economic condition in the forthcoming quarter. Some of the relevant conditional probabilities are as follows: P(F|S1)=0.9, P(F | S2) = 0.55, P(F | S3) = 0.10 (iv) Apply Bayes' Theorem to compute the posterior probabilities for Elle, for both the Favourable and Unfavourable evaluation outcomes. (6 marks) (v) What is Elle's optimal decision strategy? Draw the decision tree with clear labels, show all the necessary calculations, and provide justifications for your recommended decision strategy to Elle. (vi) What is the expected value of the economic institute's information? (10 marks) (1 mark)