Pleease, be correct.

1. The manager of a large equity fund is expecting a significant inflow of cash in the

near future.

(i) Describe how the manager would protect the fund against a rising market in

this situation. [3]

(ii) Describe the residual risks that remain with the strategy you have described in

part (i). [4]

(iii) Suggest alternative reasons why the manager might want to hedge the

portfolio. [2]

[Total 9]

2. A wealthy investor is considering an investment in one of two funds, Fund A which

follows an active approach to investment and Fund B which follows a passive

approach.

(i) Describe the advantages and disadvantages of these two types of investing. [5]

The following information has been provided:

Return in year 1 Return in year 2

Fund A 18% 8%

Fund B 14% 4%

Index 14% 2%

Returns quoted are gross of investment management fees, where fees are significantly

higher for Fund A than for Fund B.

(ii) Calculate the return on each fund relative to the index return. [3]

(iii) Comment on your results in part (ii). [3]

3.

A defined benefit pension scheme provides members with a single life pension at age 65, which increases each year in line with price inflation. At retirement, members can choose any of the following options: . Exchange up to 25% of the pension for an immediate lump sum, calculated as $15 for every fl per annum of the member's pension given up. . Swap the pension that increases with price inflation for a pension that increases at a fixed 3% per annum. . Reduce the member's pension by 10% in order to provide a spouse's pension on death of 50% of the member's pension at the time of death. (i) Discuss the issues that members should consider in deciding whether to exercise these options. [15] Current price inflation is 2% per annum and it is expected to remain around this level in the short term. (ii) Suggest why the scheme sponsor offers the option to choose fixed pension increases of 3% per annum rather than inflation linked increases. [3] (iii) List the other main retirement options that could be made available to the member at retirement. [2]lI'Llrange trees are susceptible to the disease Citrus Greening. There is no known cure for this disease and, although trees often sunrise for some time with the disease, it can ultimately he fatal. A researcher decides to model the progression of the disease using a time- homogeneous continuous-time Markov model with the following state space: {Healthy {i.e. not infected with Citrus Greening}; Infected with Citrus Greening; Dead [caused by Citrus Greening}; Dead [other causes}} . The researcher chooses to label the transition rate parameters as follows: a mortality rate om the Healthy state, it a rate of infection with Citrus Greening, c a total mortality rate from the Infected state, p a mortality rate caused by Citrus Greening, r {i} Draw a transition diagram for the chosen model1 including the transition rates. [1] [ii] Determine Kolmogoroy's forward equations goyeming the transitions. specitying the generator matrix. [3] Infected trees display clear symptoms of the disease. This has enabled the researcher to record the following data on trees in the area of his study: Tree-months in Healthy State 1,2 Tree-months in Infected State Total number of deaths of trees 40 Number of deaths of Healthy trees 10 Number ofdeaths from Citrus Greening 30 {iii} Give the likelihood of these data. [3] {it} Derive the masinnnn likelihood estimator of the mortality rate caused by Citrus Greening. 'r. [3] {it} Estimate 1. [ll