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A large Pension Fund has made a $50m investment in a small boutique hedge fund which runs a long-only multi-asset class fund. The Trustees of the Pension Fund wish to assess performance attribution in respect of the investment and have obtained the following information from the hedge fund: 2012 2013 2014 Start Holding Start Holding Start Price Price % Price Global Equities Stock A 60 25 66 15 72.6 Stock B 70 0 63 5 75.6 Stock C 50 15 60 15 72 Fixed Income Bond D 120 5 126 15 129.78 Bond E 100 103 5 108.15 Bond F 90 12 99 10 101.97 Commodities Gold 1110 11 1110 S 1443 150 6 165 5 214.5 Cocoa 50 11 51 20 56.1 Cash Money market fund 99 7 99 5 99 The assets listed represent the entire investment universe available. Assumptions: The benchmark assumes equal weighting on all assets in the investment universe. Allocation decisions are taken at the start of each year. . For the purpose of this investigation, all cash flows can be ignored. (i) Calculate the performance of the portfolio manager relative to the benchmark for each year. [10] (ii) Calculate the performance generated by stock selection for each year. [4] (iii) Calculate the performance generated by sector selection for each year. [4] [Total 18]The table below shows cumulative claim amounts incurred on a portfolio of insurance policies. Accident Year Development Year 0 2 2011 1.509 1,969 2,106 2,207 2012 1.542 2,186 2.985 2013 1,734 1,924 2014 1,773 Annual premiums written in 2014 were 4,013 and the ultimate loss ratio has been estimated as 93.5%. Claims can be assumed to be fully run off by the end of development year 3. Estimate the total claims arising from policies written in 2014 only, using the Bornhuetter-Ferguson method. [7]Suppose that X is an AR(1) process given by the equation: X,41 = 0.75X, + 0.25e,I where the e,, are independent, identically distributed /(0,1) random variables independent of Xo- (i) (a) State the distribution of X,+ | conditional on the value of X, . (b) Show that the distribution of X,+, conditional on the distribution of X is N(0.75'X,, 0.252 + 0.254+...+ 0.252). [3] (ii) (a) Show that the distribution of X, converges to a stationary distribution. (b) State this distribution. [2] The process In(Y,), with Y, the multiplicative increase in a retail price index in year (, is believed to be an AR(1) process with the same parameters as X above. (iii) Determine E[Y,|Yo = 1.21]. [3] (iv) Determine the long-run mean annual increase in the retail price index. [3] [Total 11](i) Explain what is meant by a proportional hazards model. [3] (ii) Outline three reasons why the Cox proportional hazards model is widely used in empirical work. [3] [Total 6]