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An insurance company has three types of policyholders: Standard, Premium and Elite. If a Standard policyholder does not make a claim in a given year, they move to being a Premium policyholder the following year. If a Standard policyholder makes a claim in a given year they stay as a Standard policyholder for the following year. If a Premium policyholder makes a claim in a given year, they move to being a Standard policyholder for the following year. If a Premium policyholder does not make a claim in a given year, they move to being an Elite policyholder the following year. Similarly if an Elite policyholder makes a claim in a given year, they move to being a Premium policyholder for the following year. If an Elite policyholder does not make a claim in a given year, they stay as an Elite policyholder for the following year. You may assume the probability of more than one claim in a given year is negligible. The transition probability matrix for the change in the policyholder type for each year is: Type next year Standard Premium Elite Current type Standard 80% 20% 0% Premium 50% 0% 50% Elite 0% 90% 10% (i) Set out three algorithms (one for each possible initial policyholder type) which simulate the policyholder type for each of the next three years, using the inverse transform method. [5] Assume the starting policyholder type is Standard and that the random numbers drawn from a Uniform [0,1] distribution for the first simulation are 0.89, 0.64 and 0.12. (ii) Determine how the policyholder type evolves over a three year period in this simulation, including statement of how many claims are simulated to have occurred. [4] [Total 9]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 75.6 Stock C 50 15 60 15 72 Fixed Income Bond D 120 5 126 15 129.78 Bond E 100 8 103 108.15 Bond F 90 12 99 10 101.97 Commodities Gold 1110 11 1110 1443 Dil 150 6 165 214.5 Cocoa 50 11 $1 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]A company's ordinary shares have a nominal value of 25p. The current market price of a share is 90p. The directors are planning to issue new shares. Which of the following statements best describes the restrictions on the issue price for the new shares? A The directors are not permitted to issue the shares for less than 25p or for more than 90p. B The directors are not permitted to issue the shares for less than 25p and are unlikely to be able to sell them for more than 90p. C The directors are not permitted to issue the shares for more than 90p, but can sell them for any amount below that. D The directors are not permitted to sell the shares for less than 90p. [2]