1. Study table below and solve the questions.

(i) Show that: (Inx-p) 202 dx = pu+1/' Inb-u-o- Ina-H-G- [4] a V2no- A general insurance company writes claims, whose amounts have a lognormal distribution, with mean 300 and standard deviation 400. The insurance company purchases excess of loss reinsurance with retention 500 per claim. (ii) Calculate the average expected claim size payable by the insurance company. [6] Next year, claim inflation is 10%, but the retention amount remains the same. (iii) Explain whether the average expected claim size payable by the insurance company next year would increase by 10%. [2]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 8 103 5 108.15 Bond F 90 12 99 10 101.97 Commodities Gold 1110 11 1110 1443 Oil 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]