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1.

A bond fund manager is considering an anomaly switch between two gilts. The data he has concerning current market values are: Redemption Date Clean price Yield % 4%% Treasury Stock 2020 7 March 2020 113.84 2.33 34% Treasury Gilt 2020 7 September 2020 107.88 2.46 (i) Demonstrate three methods to assess whether there is an opportunity here for an anomaly switch. [4] (ii) Outline additional factors that would need to be considered by an institutional investor considering a large anomaly switch. [5] (iii) Outline two methods by which an investor could take advantage of an anomaly whilst maintaining no overall market exposure (i.e. having a market neutral position) to the bond markets. [2]Consider an asset the annual return, X, on which has probability density function /(x). (i) Define the 5% Value at Risk for this asset. [1] (ii) Define the expected shortfall of the return on this asset below 2%. [2] Assume X has a Normal distribution with mean u = 5% and variance o' = 100%%. (iii) Calculate the 5% Value at Risk. [2] (iv) Discuss the limitations of using Value at Risk to measure the downside risk in an investment portfolio. [2]Let X" be a random variable with density f(x) = e " for x > 0. (i) Construct an algorithm for generating random samples from X. [2] A sequence of simulated observations is required from the density function h(x) = 2xe x>0. (ii) Construct a procedure using the Acceptance-Rejection method to obtain the required observations. [5] (iii) Calculate the expected number of pseudo-random numbers required to generate 10 observations from / using the algorithm in part (ii). [2](i) State the principle of correspondence as it applies to death rates. [1] A nightclub opens at 10.00 p.m. and closes at 2.00 a.m. It admits only people aged over 21 years on the production of an identity card giving date of birth. The table below shows the number of people entering in various intervals between 10.00 p.m. and 2.00 a.m. on 30 June 2013. No-one was admitted after 1.00 a.m., and you may assume that all those who enter the premises stay until 2.00 a.m. Year of 10.00-11.30 11.30-12.00 12.00 p.m.-1.00 a.m. birth P. m. P.m. 1989 100 300 200 1990 200 400 350 1991 150 400 300 1992 100 250 200 During the period of opening, 40 people aged 22 last birthday required medical attention for heat exhaustion. (ii) Calculate the rate per person-hour at which those attending the night club aged 22 last birthday required medical attention for heat exhaustion, stating any assumptions you make. [6] [Total 7]