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ANNNNNN 4 (37 marks) Your client is planning to invest some money with your investment company The client narrows their options down to 2 investment strategies X and Y. and from past experience the annual percentage returns are as follows X (3,1) and Y N (5,3%). 4 marks (a) For each investment strategy, calculate the probability of a negative return. (b) For each Investment strateey calculate the probability of return greater than 5.5% 14 marks) re) Describe the advice you might give to your client about these two investments depending on whether they were risk averse or a risk taker. [2 marks] (d) Find a such that PX > A) PIY > k) Do not simply solve this by trial and error, you need to show working out as to how your proved this. (4 marks) (e) Assume that within the same year Cor(X,Y)= and that X and Y are bivariate normal. Remember X and Y being bivariate normal just means that sums of X and Y will still follow a normal distribution. Then answer the following questions: (i) If your client invests half of their money in each investment type, what are the mean and variance of their annual return? 16 marks] (W) If your client invest a fraction of their money in investment type X and the rest in Y ie 0 Sk 1), what are the mean and variance of their annual return in terms of A? (5 marks) AAAAAAAAAAAAA (I) If your client invest a fraction of their money in investment type X and the rest in y iOS 1), what value of k makes the probability of their investment achieving a negative return equal to 1%. [6 marks) Note: this is a very difficult question and will require working with a quadratic function. Just do your best

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