**Assignment Task**

**Task **

**Introduction to Actuarial Studies**

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Get Help Now!**The objectives of the assignment are to allow you to**

- Comprehend how the actuarial control cycle is used to identify and manage financial risks.
- Construct simple cash flow models which can be used for decision making and implement these in Excel or other software.
- Apply demographic data and statistical models to price policies, determine ruin probabilities and implement simulation models in Excel or other software.
- Explain why legislation, accounting standards, codes of conduct, and professional requirements are necessary and how the business environment affects the management of the financial services business.
- Identify and discuss the tools which can be used to manage risk, including the impact of diversification and leverage, capital, risk pooling and risk transfer.

**Context**

In the course so far, we have worked extensively on modelling retirement savings, which is a problem relevant to almost everyone. This is a natural point for some introspection – lets apply some of the learnings to the case of our own retirement savings. In the following assignment, we will look at your potential future earnings as an actuary, how much that translates to in terms of retirement savings and whether that will be enough to sustain your chosen standard of living in retirement. Additionally, we will examine the various risks that may affect our modelling, as we have already discussed in the course.

**The tasks**

In this assignment, you will be modelling the superannuation accumulation phase for an actuarial career. We will take a more modern approach, along for stochastic variation. We will then examine the retirement decumulation phase, assessing various risks and coming up with some retirement scenarios. Finally, you will be asked to write a concise report describing your results.

**Task 1: Accumulation phase modelling ****You are to build a spreadsheet in Excel that will model the accumulation phase of your superannuation account. You can assume that following:**

- Assume that you will start your actuarial job at exactly age 22. Your birthday is at the beginning of the year.
- Superannuation contributions are made at the end of each year, at a rate of 10% of your yearly salary.
- Salary increases are made at the end of each year, right after superannuation contributions are made.
- The superannuation contribution tax rates are 15%.
- The investment income tax rates are 15%.
- Superannuation administrative fees of $200 per year currently paid at the end of the year. These fees increase at a rate of 3% per year.
- You cancel your life insurance from your superannuation fund as you decide to purchase individual life insurance directly rather than through your super.
- Your investment manager charges a 1% investment management fee of funds under management. This 1% should be deducted from the after-tax returns.

You may need to do some external research to fill in other assumptions for modelling. You should design your spreadsheet so that all assumptions (apart from the starting age) can be changed without manually adjusting each of the formulas (including any assumptions not listed above that you have researched).

**Task 1 Part A: Generate 10,000 random simulations of the state of the economy over time.**

I have provided a template for you to do complete this task in the Worksheet “Task 1 Part A”.

Hint: You may want to turn your formula calculations (found in the formula tab) to “Manual

Calculations”. This will prevent Excel from refreshing your spreadsheet’s random numbers every time you make a small change. To refresh your random numbers, press the “Calculate Now” button or press F9.

In each of the cells of the table, each row of the table represents one simulation path from ages 22 to 67. The table consists of 10,000 rows.

Once the economy tracker is complete, the next task is to track the accumulated value of the superannuation accounts over time.

**Task 1 Part B: Generate 10,000 random simulations of your superannuation account value over time.**

In the second tab labelled “Task 1 Part B”, you should link each simulation path of your superannuation account value with the corresponding path in the economy tracker simulation. A template of the required table has been provided.

Note that if you would like to split up the working into more manageable portions, you can do this on other worksheets and link the step-by-step results using formulas that reference these other sheets (e.g. for example, if you are having some issues combining everything to complete the task, try having a separate spreadsheet that just contains how much your salary is for each simulation path).

**Task 2: Decumulation phase modelling **

In this section, you will be performing some deterministic modelling (so no stochastic assumptions are required). However, you will need to perform your own research and appropriately reference your research. You can complete all of your modelling and referencing in the Excel Spreadsheet Tab labelled “Task 2”. Make sure to set out your working nicely.

**Task 2: Determine the amount needed at retirement to fund retirement spending under different scenarios.**

We will use the Association of Superannuation Funds of Australia (ASFA) Retirement Standards as a starting point for our modelling. Read through the Retirement Standard and the Detailed Budget Breakdown, which can be found on the website. Determine for yourself what a suitable amount of yearly spending would be for your own circumstances in the year of retirement. This amount will need to be indexed to price inflation in subsequent years.

**Make modelling assumptions based on your own research (make sure to reference your sources appropriately) for the following quantities, which are assumed to be constant from the time of your retirement to the time of your death:****• **The inflation rate.**• **The investment rate at which your retirement funds accumulate.

**Using this information, you can calculate the required amount of savings at retirement age in order to adequately fund your retirement spending. Determine this amount assuming that you die at the following ages:• **75

**•**85

**•**95

**•**105

**In addition, consider the following adverse scenarios for each age:**

- Adverse Scenario 1: The inflation rate is 1% higher (additively) In total, you should have 3 different amounts for each age, one for each scenario: Normal, Adverse Scenario 1 and Adverse Scenario 2.
- Adverse Scenario 2: The investment rate is 1% lower (additively) Finally, use the distribution of accumulated superannuation savings to determine the probability of sufficiency for each scenario. In your report, which is Task 3 below, you should discuss whether these probabilities of sufficiency are comfortable for you and if necessary, what additional measures can be taken to mitigate the risks in retirement decumulation.

**Task 3: Report ****Your final task is to write a concise report documenting the assumptions, methodology and results of the previous task. Your report should consist of the following sections, with strict page limits provided in parentheses:1**. Executive Summary

**2**. Modelling methodology for Task 1

**3**. Model results for Task 1

**4**. Modelling methodology and results for Task 2

**5**. Final results and further assessment of limitations and risks

You may change the headings of the sections to whatever you wish but it should be clear which section you are referring to. In the final section, you should provide a final summary of your overall results and identify any potential limitations of the modelling, including risks that were not accounted for/identified. If you wish, you may include external references to consolidate your points in this section. The report should be presented in a professional manner marks are allocated to the presentation of this report, as can be seen in the marking rubric on the last pages of this document.

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