Question 6 [Total: 22 marks] Political conflicts play a significant role in affecting the stock market performance. Let

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Question 6 Total 22 Marks Political Conflicts Play A Significant Role In Affecting The Stock Market Performance Let 1 (56.26 KiB) Viewed 37 times

Question 6 [Total: 22 marks] Political conflicts play a significant role in affecting the stock market performance. Let W be a dummy variable such that W = 1 if there is a war in the coming month and W = 0 if there is no war. Let X be the market return in the coming month. Carol assumes the following model. The probability of a war in the coming month is 0.3. If a war occurs, the market return follows a normal distribution with mean -0.2 and variance 0.04; if a war does not occur, the market return follows a normal distribution with mean 0.1 and variance 0.01. The assumptions are summarised in the table below. W = 1 W=0 Probability 0.3 0.7 Distribution of X W N(-0.2, 0.04) N(0.1,0.01) (a) [2 marks] Are W and X independent? Explain briefly. (b) [3 marks] Suppose a war occurs in the coming month. What is the probability that the stock market will suffer a negative return? (c) [4 marks] Suppose the stock market suffers a negative return. What is the probability that a war occurs? (d) [3 marks] Find E(X). (e) [4 marks] Compute E(X²|W= 1) and E(X²|W = 0). (f) [3 marks] Using parts (d) and (e), compute E(X²) and Var(X). (g) [3 marks] Let W, denote the war status in month t, and let X, denote the stock market return in month t. Suppose the joint distribution of W, and X, are independent and identically distributed according to the above table across all the 12 months of 2022. Is the time series {X} strictly stationary? Why or why not?