subject ca2-model documentation, analysis and reporting

TheActuarialEducationCompanyonbehalfoftheInstituteandFacultyof

Actuaries

Modeldocumentation,analysisandreporting

SubjectCA2

COURSENOTESFOREXAMSIN2015

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IFE: 2015 Examinations The Actuarial Education Company

The Actuarial Education Company IFE: 2015 Examinations

Subject CA2 Introduction

Section 1 Objectives and overview Page 7 Principles

Section 2 Analysing data Page 19 Section 3 Developing a model Page 25 Section 4 Creating an audit trail Page 29 Section 5 Creating a project summary Page 37 Section 6 Presenting results Page 45 Software

Section 7 Using Excel Page 55 Section 8 Using Word Page 83 Exam technique, Worked example and FAQs

Section 9 Exam technique Page 91 Section 10 Worked example Page 93 Part 1 instructions Page 95 Project plan Page 100 Spreadsheet Page 102 Audit trail Page 111 Part 2 instructions Page 114 Summary report Page 123 Marking criteria Page 129 Section 11 FAQs (Frequently asked questions) Page 131 Background Reading

Section 12 Syllabus and background reading Page 139 Reference

Section 13 Further reading Page 153 Section 14 Solutions to self-assessment questions Page 155 Section 15 Checklists Page 167 Section 16 Notes Page 169


Introduction


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CA2: Section 1 Objectives and overview Page 7


1 Objectives and overview

1.1 The Subject CA2 Exam Parts 1 and 2

The CA2 exam consists of two computer-based assessments, taken on different days, each consisting of a 3-hour paper plus 15 minutes reading time at the start. To pass the exam, you must pass both parts in the same sitting. The two papers will relate to different projects. For Part 1 you will be required to construct a spreadsheet model for a project and to write an audit trail documenting your model. For Part 2 you will be given a spreadsheet and audit trail prepared by another student, and you will be required to write a summary report for the project. The exam can be taken at an exam centre or online. The exam centres are normally university computer labs or conference centres equipped with laptop computers. In the exam, you will be given a printed set of instructions for the assessment project and usually a data set to work with (which will be preloaded onto your computer). Once you have completed your assessment, the invigilator will collect your files for marking. For the online exam, the materials for the exam and your completed work are sent by email. More detailed information relating to the CA2 exam, including the objectives and format of the exam and links to the sample projects, can be found in the Guide to CA2 on the IFoA website at www.actuaries.org.uk/students/pages/practical-exams.

CA2: Section 1 Objectives and overview


1.2 Objectives of the exam

The CA2 syllabus and background reading produced by the IFoA are set out in Section 12. The syllabus objectives are as follows:

Objectives of the exam The successful candidate will be able to demonstrate:

analysis of data development of a model with clear documentation (including an audit trail for a

fellow student and senior actuary)

ability to analyse the methods used and the models outputs ability to apply and interpret the results communication of the approach, results and conclusions to a senior actuary. The principles underlying these objectives are covered in Sections 2 to 6 of these notes under the headings:

analysing data (Section 2) developing a model (Section 3) creating an audit trail (Section 4) creating a project summary (Section 5) presenting results (Section 6). The relevant syllabus objectives and the corresponding sections of the background reading are shown in the Topics covered box at the start of the each chapter.

1.3 What the exam is about

Looking at the objectives, you can see that the exam is basically testing whether you can carry out a systematic investigation based on a set of data, documenting your model and presenting your results and conclusions in a clear way. It complements CA3, which tests whether you can communicate effectively to a non-technical audience. Perhaps at some point while you were doing the exams in the early subjects you thought: If only I had a spreadsheet to do these calculations, it would be so much easier. Well, nows your chance!



1.4 What the exam is not about

Although your CA2 assignment project may be based on an actuarial topic from one of the CT subjects, the exam is not testing your detailed knowledge of these subjects. So theres no need to dig out the chapter summaries from your old courses and start memorising all the equations. In the exam youll be provided with a PDF version of all the Core Reading from the CT subjects and CA1, and a PDF version of the orange Tables in case you want to refer to these. The assessment project itself will be computer-based and carried out using an Excel spreadsheet. However, the exam is not testing whether you can produce a flashy spreadsheet using advanced features of the software. In fact, we strongly recommend that you stick to the simpler features. Also, most employers have in-house best practice guidelines designed to make things run smoothly in the office and to avoid mistakes. These typically include:

conventions for naming files, worksheets and variables conventions for entering data and formulae conventions for fonts, colours and shading a list of banned functions that have been found to cause problems. You can continue to use a house style if you wish, but make sure you explain in your audit trail any features that might not be familiar to the examiner marking your work.

Exam tip We will see later that most of the marks are for the audit trail and summary report, not for the modelling techniques. So it is best to keep your model quite simple.



1.5 What the projects might be about

To give you an idea of the types of projects that could come up, here is a list of some example projects with actuarial themes: Subject Model Project

CT1 Loan schedule Calculating repayments on a mortgage Cashflow projection Replacement ratios for a personal pension

CT2 Accounting analysis Comparing different tax rules

CT3 Regression model Modelling personal income and expenditure Sampling theory Determining an appropriate sample size

CT4

Markov chain Comparing No Claims Discount systems Jump process Pricing disability insurance Cox model Investigating the effect of smoking Parametric graduation Graduating lapse rates

CT5 Life tables Projecting population numbers Discounted cashflow model Calculating transfer values Profit test model Setting premium rates

CT6 Loss distributions Reviewing reinsurance arrangements Time series model Modelling a financial index Generalised linear model Modelling claim numbers

CT7 Production function Maximising a companys profits

CT8

Utility theory Predicting sales of lottery tickets Portfolio theory model Calculating risk levels of managed funds Binomial tree Pricing options Black-Scholes model Hedging a portfolio of shares

These are just examples and this list is by no means exhaustive. In fact the examiners have said that the actual exam projects may not have an overtly actuarial theme at all they could involve models from any field. For example, some of the past exam projects have related to sporting events, animals and product sales. You probably do very similar things at work to some of the projects listed here. In fact, it is likely that you have chosen an actuarial career precisely because you are good at this type of work. So it should all be familiar stuff.

At this point you can have a look at the project instructions for the Worked Example (see Section 10.1) to give you an idea of what a CA2 project might look like.



1.6 Sample projects

There are a number of sample projects you can use to help in your preparation for the CA2 exams. Sample projects on the IFoAs website At the time of writing, the following sample projects are available on the IFoA website: Pre-March 2015 Post-March 2015

Auctioneers Rabbit populations Banana distribution A cats lives Mobile phone contracts Greyhound racing Assurance premiums

Actuaria (Part 1) sample project Actuaria (Part 2) sample project

The pre-March 2015 projects are actual projects that were used in past assessments, but have now been retired. Although these are in the old CA2 exam format (when the CA2 was a single 7 hour exam), the specimen solutions still provide a good indication of what a CA2 spreadsheet, audit trail and summary should look like. You can download these by following the More information link in the CA2 section on the IFoA website at www.actuaries.org.uk/students/pages/practical-exams. The post-March 2015 project, which is in the new format, illustrates what the new-style exams might look like. Remember that, if you attempt these projects yourself, your work may appear slightly different, depending on the settings for your software, eg you may have different fonts or a different screen size setting. Remember also that there is no single right answer and different approaches are possible. In the real exam youll be provided with a PDF version of all the Core Reading from the CT subjects and CA1, and a PDF version of the orange Tables. (It is an open-book exam, so you can use your own Tables book if you prefer.) We recommend that you study the specimen projects and attempt the sample project as a practice exam. You should also read the Guide to CA2 on the IFoA website, which includes some other useful information and guidance.



Worked Example project Section 10 of these Course Notes contains a worked example. This section includes the instructions for an example project and a full analysis of a solution produced by a student attempting it under exam conditions. ActEd Marked Assignment Projects and Preparation Days There are two additional projects available from ActEd:

Marked Assignment Project #1 (MAP1) for CA2 Part 1 Marked Assignment Project #2 (MAP2) for CA2 Part 2. ActEds Marked Assignment Projects are intended to be attempted under exam conditions and then sent to ActEd for marking. You can use these in the same way as a mock exam, to help you identify any areas you need to focus on in your preparation for the exam itself. These must be purchased together (product code CA2-PM-15), but you do not need to submit both at the same time. To get the maximum benefit, we recommend that you submit the Marked Assignment Projects to ActEd at least 4 weeks before your exam. (Note that if you submit your work for marking very close to your exam date, we may not be able to mark it and return it to you before your exam.) We also offer a CA2 Preparation Day, which can be taken either as a face-to-face tutorial or as a live webinar. See also Section 1.10.

1.7 How to use these notes

To get the most out of these notes, we suggest you follow the flow chart shown on the next page. We estimate that it will typically take around 50 hours to work through the ActEd Notes and study a selection of the specimen projects on the IFoA website. If you are also doing the ActEd Marked Assignment Projects, these will take at least 3 hours each to complete. You can send any queries about the ActEd Course Notes to [email protected].



After reading Section 1 (Objectives and Overview), have a look at the instructions for the Example project (see Section 10.1) to get a

feel for what a CA2 project might be like.

Read through Sections 2 to 6 (Principles) and Sections 7 and 8

(Software), and have a go at the self-assessment questions. (The solutions are in Section 14.)

Read the Syllabus and background reading in Section 12.

Read the advice in Section 9 (Exam Technique) and then read

carefully through the worked example in Section 10.

Read Section 11 (Frequently Asked Questions).

Study the spreadsheets and specimen solutions for the specimen

projects on the IFoA website, using one of them as a practice project to try yourself on a computer before looking at the specimen solutions

and marking schedule.

Attempt the ActEd Marked Assignment Projects under exam conditions and submit your work for marking and/or attend a

Preparation Day. Study the feedback carefully when you get it back.

You should then be ready to do the actual exam.



1.9 Recap

Plan to spend around 50 hours working through the ActEd Notes and studying the specimen projects on the IFoA website. Allow for another 3 hours plus follow-up time per assignment if you are also doing the ActEd Marked Assignment Projects.

Be prepared for any type of project to come up. Try to get into the particular way of thinking required for this exam, where the

emphasis is on effective communication (via the audit trail and summary), rather than testing your technical knowledge and spreadsheet expertise.



1.10 ActEd Marked Assignment Projects and Preparation Days

ActEd offer two marked assignment projects to help students prepare for the exam. We also offer a CA2 Preparation Day tutorial, which includes another practice project. For further details, see our study brochure or visit our website at www.acted.co.uk.

I think Ive got my timing rightnow. Im feeling a lot moreconfidentabouttherealexam.

IrealisedwhenIstarteddoingthe first Marked AssignmentProject that CA2 projects areharderthanIinitiallythought!

The Marked AssignmentProjects helped me identifythethingsIwasdoingwrong.

I liked the detailed comments you get in thefeedback, especially the marking schedule, whichshowsyouexactlywhereyougainedandlostmarks.

IthinkalotofpeopledontknowabouttheCA2 Preparation Days. A friend at workrecommendedmetogotoone.

The feedback from the markerwasveryuseful.InowknowwhatIneedtofocusonintherunuptotheexam.

Andtheymarkedmyassignmentveryquickly.


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CA2: Section 2 Analysing data Page 19


2 Analysing data

Topics covered In this chapter we will cover the following topics:

validating (cleaning) a data set summarising a data set extracting the relevant information from a data set Background reading: UNIT 3, TAS(D) Syllabus objective: I

2.1 Introduction

Data sets A typical assessment project will present you with a data set to work with. In most cases, however, the data set you are given will not be in the precise form you require. For example, you might be provided with a set of values of the FTSE 100 index, which you must first convert into rates of return. As a result, some pre-processing of the data will usually be required. Also, the data you are given might contain errors. If these are not dealt with, the results of the analysis will be meaningless. So it is important to validate or clean the data, ie identify and deal with any errors. You may also be asked to summarise the data set, ie calculate some key statistics that describe the shape of the data. Note that you may be asked to create your own data! This is not as silly as it might sound you may be asked to use a particular model to simulate a set of results, which will then form your data set. We will look at how to do this in Section 7 (Using Excel).

Exam tip Make sure you understand the data youve been given. If you dont take the time to do this, there is a danger that you will set off on the wrong track.

CA2: Section 2 Analysing data


2.2 Cleaning the data

Types of data errors Errors in numerical data in computer files usually consist of:

wrong numbers outliers omissions or duplicates. Wrong numbers can occur because of incorrect inputting. Particularly common are:

omitted digits, eg 21553 instead of 215553 anagrams, eg 2456 instead of 2546 mistakes involving repeated digits, eg 1223 instead of 1233. Outliers are extreme data values that dont appear to be consistent with the model they dont fit the pattern. In real life, important data sets are sometimes input twice independently and then compared by computer. This will identify any inputting problems involving wrong numbers, omissions and duplicates, but will not pick up outliers.

Question 1

The data set provided for the worked example we will look at later consists of a list of the amounts of a portfolio of insurance claims. Suppose that, in subsequent discussions with the client, you discover that the original data consisted of a set of typed lists copied from international records, which were then input by hand onto a spreadsheet and cleaned. What types of types of data errors do you think might have been present in this data set before it was cleaned?

The solutions to the self-assessment questions can be found in Section 14 (starting on page 155).

Exam tip You should assume that the data set has not been cleaned and may contain errors. So you should check the data, and make corrections as necessary, then document the checks you have applied and any corrections you have made.



How can I identify data errors? In the exam, you will not be able to look for the more subtle types of data error or to go back to the original documents to check things out. Usually, it will be sufficient to:

scan through the data by eye to spot any obvious problems (eg missing entries) calculate a few summary statistics, such as the number of data values and the

maximum/minimum values

apply some reasonableness checks to the summary statistics reconcile the summary statistics with any additional information you have been

given in the project specification. Scanning through the data by eye will usually allow you to spot problems such as missing values or repeated values. However, depending on the size of the data set, this may not pick up all the errors. So, where possible, try to incorporate some Excel formulae that will provide an automated check of the data and will highlight any errors. The summary statistics should highlight any outliers, as these may fall outside the normal range of values. The summary calculations will also throw up an error if you have applied an Excel function to data that contains invalid characters for example, a letter O instead of a zero. It is good practice to keep the original data set intact and work from a copy within Excel. This means that if a different, or corrected, data set is used later, it will be possible to compare the two data sets. Ideally your spreadsheet should show separately the original raw data with any warning messages from the Excel checks that were applied and the modified clean data with the corresponding Excel checks now saying OK.

Exam tips Try to incorporate some automated checks on the data and include a description of this in the audit trail. For large data sets, automated checks are more reliable than reviewing by eye. Document all the data checks you apply and any remedial action you take (even if no remedial action is required) and give reasons for your approach. However, dont spend too long working on the data. It is important to move on to develop the rest of the model.

CA2: Section 2 Analysing data


How do I fix data errors? If you spot a data error that you think would significantly affect the results, you should modify the data as you think best, and document clearly in your audit trail what you have done and why. We will see an example of this in the Worked Example in Section 10, where we have to supply some missing data values that were not provided.

Exam tip Try to set up your spreadsheet so that any changes made to the data at a later stage (possibly by someone else) will automatically be reflected in the subsequent calculations. Where possible avoid copying and pasting values since this means that changes to the data will not be reflected later in the calculations. Use cell references instead. If, for some reason, you cannot avoid pasting values, document very clearly what you have done so that someone else would be able to replicate your work.

2.3 Summarising a data set

The purpose of summarising a data set is to get an idea of the distribution of the values the shape of the data. This normally involves finding:

the number of data values the highest and lowest values sample moments, such as the mean and standard deviation. We will look at the Excel functions that can be used for summarising data in Section 7.

2.4 Extracting the relevant information from a data set

In some cases you may need to convert the data from its original form. For example, you might need to convert a history of market values of an asset into rates of return or you might need to convert dates of birth into ages before proceeding. This conversion should be done after you have sorted out any problems with the original data.



2.5 Recap

Make sure you understand the data youve been given. Clean the data by identifying any obvious errors. Apply reasonableness checks to identify any outliers. Include some automated checks. Document all the data checks you apply, even if no remedial action is required. Calculate summary statistics, such as totals and averages. Reconcile the summary statistics with any additional information given. Prepare the data eg calculate any derived quantities and/or subdivide the data. Be prepared to create your own data set for a simulation. Dont spend too long working on the data, especially if there dont appear to be

any problems. Not all data sets will need all the steps outlined above. You will need to demonstrate that you can apply the appropriate steps. See also the TAS(D) section in Unit 3 of the background reading (page 147), which describes the data requirements of the Technical Actuarial Standards.

CA2: Section 3 Developing a model Page 25


3 Developing a model


what constitutes a model? setting up the model Background reading: UNITS 1, 2, 4, TAS(M) Syllabus objective: II

3.1 Introduction

Developing a model might sound rather grandiose, or like a nebulous business-speak expression. In fact, it just involves creating a mathematical specification of the situation, as illustrated in the diagram below, and then setting up a spreadsheet to carry out the required calculations.

PARAMETERS for the modelEQUATIONS defining the modelASSUMPTIONS underlying the model

INPUT (data) OUTPUT

MATHEMATICAL / STATISTICALMODEL

An example of a parameter might be the numerical value for the rate of inflation assumed in the calculations, eg 2%. An example of an assumption might be that this rate of inflation is assumed to remain constant in the future.

Exam tip Note how the word assumption is used in CA2. In the office you might hear someone say We need to repeat these calculations using a different assumption, perhaps referring to a change in the interest rate. In CA2 we would say We need to repeat the calculations using a different parameter value.

CA2: Section 3 Developing a model


3.2 What constitutes a model?

The mathematical specification of a model will usually consist of a set of definitions of the quantities involved and a procedure involving one or more equations for expressing the output values in terms of the input values and the parameters. In the case of a statistical model, the equations will involve statistical distributions. The model will usually require some assumptions. These need to be stated. In most cases in the CA2 exam, the project specification will tell you what type of model to use. So this stage of the process will have been done for you. What you will need to focus on is describing the model in the appropriate place in your project summary and setting up a spreadsheet to do the calculations.

3.3 Setting up the model

It is important at the outset to decide on a suitable approach to use for the calculations and how you are going to structure your spreadsheet. You will need to decide the best order in which to do the tasks, how you are going to break the calculations down into separate worksheets and how you are going to accommodate the flexible elements (the data set and the input parameters). It is also a good idea to think about ways that you can check your calculations to prevent errors creeping in. The aim is to produce a logically-structured flexible spreadsheet that can produce all the required results, but is simple and easy to use, and will give confidence to the user that the answers are correct. We will discuss in more detail the dos and donts of setting up your spreadsheet later on in Section 7 (Using Excel). A large part of the background reading relates to the development of the model. Although you will not be asked specific questions on the details of the Technical Actuarial Standards (TASs) in the CA2 exam, we recommend that you read the sections of background reading specified in the Topics covered box above at this point to acquaint yourself with the issues.

Exam tips Be clear what the purpose of the investigation is. Make sure you spend sufficient time thinking about the project and planning the model and outputs. The examiners have said that many candidates lose a lot of marks by

CA2: Section 3 Developing a model Page 27


diving straight into the project before they have given it enough thinking time. So, get into the habit of considering the whole project and planning your model accordingly, so that you dont fall into this trap. Use the reading time at the start of the exam to identify the key building blocks for the project and to decide on a logical sequence for linking these components together. Try also to make your model flexible, so that you can easily adapt it to allow for a different data set, different parameter inputs or to generate extra results. This habit will be useful in the office as well as in the CA2 exam.

Warning! Markers have told us that some candidates have tried to use templates from other projects when working through the assignments. You should avoid doing this, and start each project from scratch. However, its a good idea to settle on a preferred style you are comfortable with. For example, how will you set out your tables and what colour scheme will you use? You should be able to develop this as you work through the ActEd Notes and the practice projects. If you dont have to spend time deciding on presentational issues such as these in the exam, you will have more time to focus on the project itself.

3.4 Recap

Be clear what the purpose of the investigation is. Identify the input and output variables. Familiarise yourself with the data. Identify the parameters for the model. Specify the equation(s) or statistical distribution(s) involved. Remember to state any additional assumptions you make. Plan your spreadsheet before diving in. Practise creating new spreadsheets from scratch. See also the list of points in the Objectives of and requirements for building a model section in Unit 1 of the background reading (page 143) and the TAS(M) section in Unit 4 (page 148), which describes the modelling requirements of the Technical Actuarial Standards.

CA2: Section 4 Creating an audit trail Page 29


4 Creating an audit trail


what is an audit trail and why do we need one? what am I expected to do in the exam? content of the audit trail narrative versus descriptive styles guidelines for audit trails examples of good and bad audit trails Background reading: UNITS 1, 4, TAS(M) Syllabus objective: II

4.1 Introduction

The audit trail is one of the most important parts of the assessment.

Exam tip Remember that the audit trail accounts for around half of the available marks.

4.2 What is an audit trail and why do we need one?

Preparing an audit trail is often referred to as documenting your work. It involves outlining the steps involved in setting up the model, explaining any important decisions/assumptions you have made and describing how you handled any tricky issues.

Exam tip The examiners have said that a good audit trail is one that allows the model to be followed by a senior actuary and to be corrected and worked on by a fellow student.

CA2: Section 4 Creating an audit trail


The idea is that, if you have to come back to the project at a later date, or if you are ill and a colleague has to finish off what you started or use your spreadsheet for a similar project, you/they will be able to work out very easily what was done previously, and can amend it or continue it. The audit trail also needs to be suitable for a senior actuary to be able to sign off the project without having to take the trouble to look at each formula in the spreadsheet to check what has been done. This process is particularly important in computer-based projects or programming because it is very difficult to deconstruct a computer program placed in front of you if the program includes no explanation of what the various sections of the program actually do and what each variable represents.

Question 2

Give some other, very important, practical reasons for having an audit trail for a project.

In real life, audit trails are also used for purposes such as recording the precise locations of the computer files and which versions of the data and software were used. For the CA2 exam, you dont need to worry about these issues. In fact, you have used audit trails previously in other actuarial exam subjects. When you are asked to show your working or to define the notation you use or to state any assumptions you make, these provide an audit trail for your calculations. Usually, there are method marks available for these parts of your solutions, and you will get these even if you have made a mistake in your calculations. Similarly in CA2 there are marks for an audit trail that clearly explains what you have done and why, even if the modelling steps are not correct. In fact there are far more marks for the audit trail than for the modelling steps.

4.3 What am I expected to do in the exam?

We recommend that you prepare your audit trail for the CA2 exam as a self-contained Word document (as weve done here). It is also possible to present the audit trail as a column of cells on a separate worksheet in your Excel spreadsheet, but this can be quite restrictive if you want to include special formatting in your work. The exam rules allow you to use either approach. So use whichever method you feel most comfortable with. The audit trail will consist of a set of sentences, very short paragraphs or annotations. We strongly suggest that you write your audit trail as you go, rather than trying to remember what you did at the end. A great advantage in CA2 that you dont have in the other exams is that you can edit your work later and even spell-check it!



It is often helpful to supplement your main audit trail with a small number of annotations within your worksheets to explain the use of individual cells or formulae. This can be done using the Excel comment feature or by typing an annotation in a nearby cell. But these points should be explicitly mentioned in your audit trail as well.

4.4 Content of the audit trail

An approach that works well in the CA2 exam is to prepare your audit trail as a Word document with the following structure: start with a brief overview, stating what the spreadsheet does, and listing the

worksheets in your workbook and any special conventions you intend to use

follow this with a section describing the data and its source, and highlighting any issues relating to the data

follow this with a section giving the main assumptions you have made in preparing the model

follow this with a separate headed section for each calculation worksheet (tab) in your workbook, explaining what you did (including any checks you applied), and highlighting any aspects that might not be obvious to another user (including any additional assumptions you have made).

Another student will be using your audit trail in conjunction with your spreadsheet and a senior actuary will be using it to get an overview. So your audit trail doesnt need to describe every equation youve used, but it does need to explain how the calculations were done, so that the reader can be confident that it is technically correct. Observations and conclusions should be included in your summary report, rather than your audit trail. Dont include in the audit trail detailed items that are specific to this particular project, eg the particular numerical values used for the parameters or copies of summary statistics or actual results, as the model needs to be flexible for future use.

Exam tips The examiners recommend that you start your audit trail with an overview stating the purpose of the model. It is also useful to provide a contents for your workbook giving a summary description of each worksheet. You can do this either in the spreadsheet or in the audit trail, but you dont need to do it in both. A good way to describe in the audit trail what the model does is to write out and explain the key equations in words rather than in symbols.



4.5 Narrative versus descriptive styles

One style of audit trail is the traditional school science experiment approach, illustrated in the box below. This gives a chronological diary for the project and could be described as a narrative style.

Audit trail (narrative style)

Step 1: I checked the data for errors.

Step 2: I calculated some summary statistics and the annual returns.

Step 3: I fitted a normal distribution.

Step 4: I carried out a chi-square goodness-of-fit test.

Step 5: I produced a graph comparing the fitted distribution with the original data values.

An alternative approach that is often used nowadays is a descriptive style. Here the audit trail takes the form of a user guide containing explanatory notes on how the spreadsheet has been used to carry out the project. This may be supplemented by local comments within the spreadsheet that relate to specific cells, eg to explain the use of individual cells. Official documents, such as tax returns, passport application forms and insurance proposal forms, are often designed in this way. The descriptive version of the audit trail for this example might look like this:

Audit trail (descriptive style)

Sheet 1: The historical values of the FTSE 100 index are shown in column A.

These are used to calculate the annual returns in column B.

Sheet 2: The summary statistics shown on this worksheet have been calculated using standard Excel functions.

These can be used to check for any anomalies in the data.

Sheet 3: The sample mean and variance have been used to fit the normal distribution plotted in the graph.

Sheet 4: This worksheet shows a comparison of actual and expected returns (derived from the normal distribution), together with the results of a chi-square goodness-of-fit test.

These are just short examples for illustration. Neither would do well as a real CA2 audit trail, as they dont include enough detail and dont explain the methods used fully.



The examiners say that either the narrative or descriptive approach is acceptable in CA2. However, as you start to produce larger models in your daily work you will find the descriptive approach more suitable. The narrative style has the weakness that it can be difficult to allow for updates to the model without a significant amount of rewriting (even during the CA2 exam itself). The descriptive style makes it easier to allow for such changes and also facilitates the inclusion of instructions to other users.

Exam tip The narrative style tells you everything that was done to develop the model, whereas the descriptive style focuses on the final product and how to use it. We recommend that you use the descriptive approach for your CA2 audit trails (as we have in the worked example in Section 10). However, either style is acceptable.

The specimen solutions for the sample projects on the IFoA website illustrate different styles that would be acceptable in the exam.

4.6 Guidelines for audit trails

When writing your audit trail (whichever style you adopt), you should aim to:

start with an overview, stating the purpose and signposting the way through the project

state the assumptions you have made and, if appropriate, why explain all key steps and decisions write one sentence, short paragraph or annotation for each item (brevity is good,

but you should make certain that you get your message across)

give a sufficiently detailed description of your spreadsheet to prevent someone who is using your audit trail (eg the examiner!) from having to hunt around or reinvent the wheel.

You should avoid:

being too brief or being too detailed (eg quoting Excel formulae verbatim) simply repeating instructions from the question quoting hard-coded question-specific details, eg parameter values or results including irrelevant details or meta-comments (ie comments about your

thought processes or the assessment itself).



You need to judge carefully the level of detail to give. Remember that the audience of the audit trail is a fellow student (who may be checking/correcting/repeating your work) or a senior actuary (who may be reviewing your work). You should assume that a fellow student will have the same level of knowledge as yourself, and will be primarily interested in the formulae and the numbers. The senior actuary, on the other hand, will primarily be interested in the actuarial aspects, not the Excel details.

Exam tips Your audit trail should act as a bridge between the project specification, the user, your spreadsheet and your summary. You should include adequate signposting and labelling in your audit trail so that the work on each worksheet is clear and is clearly referenced. The audit trail should explain:

what you have done why you have done it where you have done it and how you have done it. Imagine that you will have to repeat the project next year using different data. Your audit trail should enable you to carry out the project efficiently next year, without having to work out what goes where, or struggling to remember how you did something, or having to look up the same formulae again. It should also allow you to check that all the decisions you made last year are still appropriate for the new data and to assess whether your conclusions have changed.

It is possible to document a spreadsheet by including comments and text boxes throughout the spreadsheet. However, this approach requires, in addition, a good clear guide (the audit trail) that will allow another user to navigate through the spreadsheet. A fellow student may need some help to find their way around and it can be dangerous to assume that they have a good understanding of the problem you are trying to solve. We recommend that you keep your audit trail all in one place if only because that gives the examiner a greater chance of finding all your work. Remember that an Excel spreadsheet is not like a traditional exam answer booklet where the examiner can just read all the way through it page by page. You should use comments and explanatory text in your spreadsheet to support your audit trail as appropriate. Larger projects at work may suffer from a lack of central documentation and it is considered good practice to have a single audit trail.



4.7 Examples of good/bad audit trails

Question 3

Criticise the audit trail below, which a student has submitted (in narrative style). How could it be improved? Note that, if an audit trail is good, you shouldnt need to refer to the original instructions for the project. The audit trail should be self-explanatory.

Audit trail 1. I checked the data. 2. Then I did the graphs. I didnt like the original colours on the graph, so I changed

them a few times. 3. My computer crashed while I was working out the geometric returns and I had to

reboot it twice. 4. I calculated the summary statistics using the Excel functions from the Notes. 5. The answer was 0.669. 6. I started writing a macro to count the claims, but couldnt get it to work. So I

decided to write the numbers down on paper instead. 7. I assumed that a histogram was the same as a bar chart. I couldnt work out

how to get the normal distribution on the same graph, so Ive done two seperate ones.

8. The assessor reminded me how to work out the simulated values. 9. I looked up the percentiles on page 162 of the actuarial tables. 10. I finished by doing the summary and writing my conclusions.

We will see an example of a good audit trail in the Worked Example in Section 10.4.

Exam tip After youve completed a project, read through your audit trail and ask yourself:

Suppose I had to repeat this project next year with different data. Based on what Ive written in my audit trail, would I be able to redo it efficiently, without struggling to remember what I did, and avoiding any pitfalls? And will my boss be able to understand what Ive done? You should also check for spelling mistakes and typos at the same time.



4.8 Recap

We recommend that you use a descriptive, rather than a narrative, style. A good audit trail should:

enable you or a colleague to work efficiently on the project again at a later time and enable your boss to have confidence that your model is correct

include one point for each key step be written clearly in good English describe how you dealt with any issues that required judgement or a decision to

be made

describe the reasonableness tests you applied and highlight any important issues that came to light

be easy to find and all in one place. It should not:

include irrelevant details or simply repeat instructions that were given to you include question-specific details, such as actual parameter values or results. Note, however, that it is acceptable to quote specific results within the audit trail as part of a reasonableness check. However, you should highlight that the figures are temporary and may change subsequently.

Question 4

A project involves calculating new term assurance premiums for a range of ages and terms for men and women. Suggest some reasonableness checks you could apply.

See also the TAS(M) section in Unit 4 (page 148), which describes the modelling requirements of the Technical Actuarial Standards.

Exam tip Remember: Focus on the audit trail and the summary!

CA2: Section 5 Creating a project summary Page 37


5 Creating a project summary


what should I include in the summary? guidelines for summaries style of English examples of good and bad summaries generating ideas for conclusions and next steps Background reading: UNIT 5, TAS(R) Syllabus objectives: III, IV, V

5.1 Introduction

As part of your assessment you will be required to produce a few pages in Word (typically 4 or 5 pages) summarising the project.

Exam tip Dont underestimate the importance of the summary section, which accounts for around half the marks of the assessment project, and should be given sufficient attention. The summary also provides an opportunity for you to add value by showing the examiner that you have understood what the project is about.

Exam tip The examiners have said that the project summary should give a reasonable overview of the model and the results. They have emphasised in particular the importance of giving a clear description of the model itself, ie the mathematical framework used for the calculations.

CA2: Section 5 Creating a project summary


5.2 What should I include in the summary?

The diagram below outlines the items you should include in your summary.

INTRODUCTION a statement of the purpose of the project

DATA

an outline of the data provided an outline of the data preparation process the checks / adjustments you applied to the data

APPROACH / ASSUMPTIONS

the approach you used a description of the model the steps you applied to derive the results the assumptions underlying your model

RESULTS / CONCLUSIONS

the graphs / tables / comparisons requested your observations and comments on your results the conclusions you have derived from your results

NEXT STEPS

any additional data / clarification you would like to obtain any assumptions you would like to investigate any alternative models you would like to consider any other investigations you would like to pursue

As this is an exam in communication, the summary should include meaningful conclusions drawn from the results presented, as well as suggested next steps.



5.3 Guidelines for summaries

A good project summary should:

provide a summary of the entire project start with a clear statement of the purpose of the project describe the data analysis, the model, the assumptions you made and the

analyses you carried out

state your observations, conclusions and recommended next steps include a clear visual presentation of your results present the relevant information in a clear and structured way include any extra items that were specifically asked for be kept as simple as possible and not include irrelevant details be written in good English, using appropriate language.

5.4 Style of English

To save time, you may be tempted to write your summary just using short bullet points. However, as CA2 is an exam in communication, we recommend that you write in clear, properly constructed sentences. The examiners are not looking for extensive essay-type answers, but there are marks available for using a suitable style of English. The audience is usually a senior actuary who will then present the results to a client. So the style should be fairly formal and professional, and the results and conclusions in particular should be tailored towards the ultimate clients needs.

5.5 Examples of good/bad summaries

The following exercises illustrate some of the pitfalls to avoid in your summary.

Question 5

Have a look at the page below, taken from a students summary for a project that involved comparing the past performance of an investment index with one of the component assets in the index. Identify at least 6 ways in which it could be improved.



Page 2 Index + Component Stats for the Geo. Returns Mean 0.0301 0.05 Standard deviation 1.14% 2.61% Variance 0.000130 0.000683 Skew. 0.24417926 0.26499358 Kurt. 4 4 Both means were close to zero since daily returns over a long period and both finish close to start point. Average return higher for component.

I found that the standard deviation or variance was much higher for component, as indicated on the graph below:

The skewness was negative for both.

Some sections of your summary will involve writing around a graph or a table of results, as in this example. In these cases you should make the graph or table the centrepiece, introducing it with a brief explanation (The following bar chart shows the number of ) and following it with your conclusions (The graph shows that the distribution is ). While a picture can paint a thousand words, you should not rely on your chart telling the examiner your thoughts on the results. When you include a chart in your summary you should comment on what it is showing and explain whether this is consistent with your other results and what you would have expected. In particular, if the chart shows a strange or unexpected result you should try to explain why this has happened. This will give the client confidence in your results and help the client to understand them.

Exam tip When you are preparing your summary, try to remember the purpose of the project. Dont allow yourself to become so engrossed in the calculations and other details that you miss the big picture of what its all about.

Index vs Component Dai ly Returns

-25 .0 0%-20 .0 0%-15 .0 0%-10 .0 0%-5 .0 0%0 .0 0%5 .0 0%

10 .0 0%15 .0 0%20 .0 0%

-10.00 % 0.0 0% 10.00 %

Component Da ily Return

Ind

ex D

aily

Ret

urn



5.6 Generating ideas for conclusions and next steps

As mentioned above, your summary should cover each of the following areas:

the data analysis you carried out a description of the model the analyses you carried out your results and conclusions recommended next steps. Students often find it difficult to interpret their results and come up with ideas to include in the conclusions and next steps sections (and lose a lot of marks as a result). The diagram below shows some questions you can ask yourself to help generate ideas. There is a more detailed list of questions relating to each aspect of the modelling process in the text below. When applying these, make sure you tailor your suggestions to the specific situation, rather than just making generic statements. Try also to come up with a range of different ideas.

DATA

MODEL ASSUMPTIONSPARAMETERS

OUTPUT

NEXT STEPS

Any anomalies or outliers?Any corrections?Is it reliable / believable / credible?Independent sources?Extra info?

Reliable / reasonable values?Method of estimation?Missing variables?Sensitivity / stress testing?Interactions?

Any refinements to the ... data / model / parameters / assumptions / output?What else would I try?

Conclusions? As expected?Original suspicions? Comparisons?Reasonableness checks?Independent verification?Explanations? Correctly calculated?Doubts?

Criticisms? Realistic?Verification? Oversimplified?Tacit assumptions?Caveats / disclaimers?

Would I have used this model?Does it capture the real-life situation?Does it respond appropriately?Will it solve the problem?What are its shortcomings?Can I think of a better model?Are any important aspects ignored?Could it go horribly wrong?How could I improve it?



Data Are there any anomalies in the data? Are there any outliers, ie values that appear to be inconsistent with the model? Did I have to make any corrections? Does the data appear reliable? Do I believe the information Ive been given? Have I got enough data for it to be credible, ie to form the basis for a model? Is there an independent data source I could use? Is there any additional information that might help me clarify things? Model Is this the model I would have used in this situation? Does the model capture the key features of the real-life situation? Does the model respond in the same way as the real-life situation? Has this model solved the problem/answered the original question? Does the model have any obvious shortcomings? Can I think of a better model? Does the model ignore any aspects that might be important? Are there any circumstances when the model would go horribly wrong? Could I make the model more accurate/more versatile/more informative? Parameters Are the parameter values I am using reliable? Do their values seem reasonable? Is there a better way of estimating the parameter values? Are there any missing variables that we have ignored? What would happen if I changed each of the parameter values a little (sensitivity

testing)?

What would happen if I changed each of the parameter values a lot (stress testing)?

How do the parameter values interact with each other?



Assumptions What criticisms would I make of the assumptions? Are the assumptions realistic? Can I test / verify any of the assumptions? In what ways have we oversimplified the real-life situation? Does the model make any tacit (unstated) assumptions? Are there any important caveats / disclaimers I should mention? Output What conclusions can I draw? Is that what I would have expected? Do the results support the original suspicion/observation? How do the different answers in the output compare? Are there any reasonableness checks I can apply and comment on? Can I verify the results independently? Can I explain all the results? Am I sure my calculations are correct? Do I have any doubts about the results? Next steps Most of the ideas for next steps can be deduced by considering the individual components. What refinements to the DATA might be worth investigating? What refinements to the MODEL might be worth investigating? What refinements to the PARAMETERS might be worth investigating? What refinements to the ASSUMPTIONS might be worth investigating? What refinements to the OUTPUT might be worth investigating? What else would I try if I was doing this in the office and I had more time? Some of the reasonableness checks you apply may also give you ideas for conclusions and next steps.



Exam tip To help come up with ideas for next steps that have the right focus, you can ask yourself Ive set up this spreadsheet, but what might my boss or the client ask me to do next on this project?

5.7 Recap

A good project summary should:

provide a summary of the entire project start with a clear statement of the purpose of the project describe the data analysis, the model, the assumptions you made and the

analyses you carried out

state your observations, conclusions and recommended next steps include a clear visual presentation of your results present the relevant information in a clear and structured way include any extra items that were specifically asked for be kept as simple as possible and not include irrelevant details be written in good English, using appropriate language be set out neatly. See also the TAS(R) section in Unit 5 (page 149), which describes the reporting requirements of the Technical Actuarial Standards.

Exam tip Remember: Focus on the audit trail and summary!

CA2: Section 6 Presenting results Page 45


6 Presenting results


guidelines for visual aids examples of good and bad graphs common methods of graphical presentation tables Background reading: UNIT 5 Syllabus objective: V

6.1 Introduction

In this section we will look at issues relating to designing effective graphs and other visual aids.

6.2 Guidelines for visual aids

A good visual aid should:

present the key information clearly use an appropriate presentational device emphasise the important features be clearly labelled show the units of measurement used use appropriate scales (not too spread out or too cramped) not contain irrelevant distractions.

CA2: Section 6 Presenting results


6.3 Examples of good/bad graphs

Question 6

Have a look at the graph below. Identify at least 6 ways in which it could be improved.

6.4 Common methods of graphical presentation

Graphs are called charts in Excel. If you are working in Excel and select the Insert menu tab in Excel, you will see most of the commonly used methods of graphical presentation. The ones that are likely to be the most useful in a Subject CA2 assessment are described below. For information on how to create charts in Excel, see Section 7.7. Pie charts Although pie charts are commonly used in newspaper articles, television reports and on the internet, they are only effective when used to present small amounts of very basic data. So these would not usually be the best chart type to use in a CA2 project.



Bar charts These are commonly used to show the statistical distribution of the values of a single variable. The height of each bar shows the count for each value.

To produce a bar chart for a discrete variable, you just need the observed frequency of each value. For a continuous distribution (as in the example shown here), you first need to choose a set of bands (eg between 0% and 1%, between 1% and 2% etc) and then count the number of values falling in each band. To set up a bar chart in Excel, you need to have:

one column containing the x-values (eg 0%) the Category (X) axis labels another column containing the y-values (eg 893) the Values. You then need to select the Column option for your chart type.

Technical point A histogram is a bar chart where the frequencies are represented by the areas of the bars.

Excel also offers more advanced forms of bar charts, such as clustered bar charts, which allow you to display two or more data sets together using bars arranged side-by-side with different colours for each data set. These can be useful for presenting new-versus-old results or for comparing different scenarios.



Line charts These are commonly used to show the relationship between the values of one or more variables whose values depend on a single independent variable. The independent variable is often time.

To set up a line chart in Excel, you need to have:

one column containing the x-values (eg 05-Sep-00) the X Values. You then need to set up each line as a separate Series. For each series you need to have:

a column containing the y-values (eg 2050.89) the Y Values. You then need to select the Line option for your chart type.



Scatter diagrams These are commonly used to show the relationship between the values of two variables. The points show the ( , )x y coordinates for each pair of values.

To set up a scatter diagram in Excel, you need to have:

one column containing the x-values (eg 6.99%) the X Values another column containing the y-values (eg 11.98%) the Y Values. You then need to select the Scatter option for your chart type. In fact, scatter diagrams are a very flexible type of chart. If you create a scatter diagram, then right-click on one of the points and select Format Data Series, then Automatic for the Line color option, Excel will join the points together, so that it looks like a line chart.



6.5 Tables

Often the most effective method of presenting results is to use a table, instead of a graph. These are particularly useful for:

comparing different scenarios (as an alternative to the clustered bar charts mentioned above)

presenting results involving non-numerical variables presenting the values of a third variable whose value depends on two (or more)

independent variables. In a table involving very large quantities (eg monetary amounts such as 5,000,000) or very small quantities (eg mortality rates such as 0.00035), you should present your values in terms of the most appropriate unit size (eg m or per 100,000).

Question 7

Which form of presentation would you use if you wanted to show: (a) the value of an investment portfolio that was valued at an irregular set of dates

over the last 10 years (b) mortgage payments for a repayment mortgage and an endowment mortgage

based on interest rates of 4%, 5%, 6%, 7% and 8% (c) the inflation rate in four different countries for each of the last 10 years?



6.6 Recap

For your summary report:

Present the relevant information in a clear and structured way. Dont include any irrelevant details. Make graphs / tables the centrepiece. Explain the features brought out by each graph or table. For graphs:

Choose the most appropriate presentational device. Emphasise the important features. Label your graph clearly (including the units of measurement used). Use appropriate scales in your graphs. For tables:

Label the rows and columns clearly. Use the most appropriate units (eg m).


Software

CA2: Section 7 Using Excel Page 55


7 Using Excel


the basics of Excel guidelines for spreadsheets examples of good and bad spreadsheets Excel functions other useful spreadsheet features simulations creating charts useful tricks dos and donts pitfalls to watch out for Background reading: EXCEL KNOWLEDGE Syllabus objectives: I, II

7.1 The basics of Excel

It is a prerequisite for attending the exam that you have a basic knowledge of computers and spreadsheets. In particular, you need to know how to:

create, open or close an Excel workbook save a workbook (under the same name or a new one) create, access, (re)name, move or copy an individual worksheet navigate within a worksheet select (highlight) a cell, an array of cells or a row or column edit the contents of a cell move, copy or delete a cell or an array of cells create a formula involving values from other cells use basic arithmetic operators (+, , *, /, ^) use standard mathematical functions such as SQRT, EXP, LN, SUM

CA2: Section 7 Using Excel


use special functions such as COUNTIF(S), VLOOKUP, LARGE use financial functions such as NPV, IRR, PMT use logical operators (IF, AND, OR, NOT) change the appearance or format of a cell create a chart (graph) select, edit (change features of) a graph export a graph to Word use the Help facility. The table on the next page (which is not intended to be comprehensive) gives a summary of these basic Excel features. In the table:

Menu1 > Menu2 > ... represents a sequence of Excel menu selections [Key] represents a keyboard selection Note that the Office button in Excel 2007 corresponds to the File menu in Excel 2010. If you arent confident with these operations, you can either explore the Help files in Excel itself or you can buy a book with a title such as Excel for Beginners or Excel for Dummies. See Section 13 for a list of recommended books. See also the Excel Knowledge section at the end of the background reading (page 150). In the rest of this section we will focus on the Excel features that are most likely to be required for Subject CA2. Even if you are an experienced and confident Excel user, we recommend you read though this material as it contains general guidance on good practice that you should aim to use in the CA2 exam and at work.

Note on software versions From May 2013 the CA2 exams have been using Excel 2007. All the examples shown in these Course Notes are based on the Excel 2007/2010 format (which use the .xlsx file extension). The interface for these versions (with the introduction of the ribbon) is significantly different from the earlier Excel 2003. It is important that you are familiar with one of these versions (which are essentially the same), so that you dont waste time in the exam working out how to use the software. This is particularly true when working with charts, which take a bit of getting used to.



TABLE summarising basic Excel features (Excel 2007) Task How to do it Open an existing workbook In Windows Explorer: double-click on the file name

In Excel: Office button > Open and double-click on the file name Create a new workbook In Excel: Office button > New or [Ctrl]-N Close a workbook Click on the close icon ()

(You will be prompted as to whether you wish to save it) Save (under the same name) Office button > Save or [Ctrl]-S Save (under a different name) Office button > Save as ... Create a new worksheet within a workbook

Click on the new worksheet icon (displayed after the last tab name at the bottom of the screen)

Access an individual worksheet within a workbook

Click on the worksheet tab or [Ctrl]-[Page Up] / [Ctrl]-[Page Down] to move to the next / previous worksheet

Rename a worksheet Double-click on the worksheet tab, type a new name and [Enter] Move or copy a worksheet Right-click on the tab name and select Move or copy sheet and click to

select the new position. (Tick the Create a copy box to copy it) Navigating within a worksheet

To go to the top left (cell A1): [Ctrl]-[Home] To move left or right: Use the arrow keys To move up or down: Use the arrow keys or [Page Up] / [Page Down]

Select a cell Click on the cell Select an array of cells Click on the first cell and hold down the mouse button while you drag

over the other cells (or hold down [Shift] and use the arrow keys) Select a row or column Click on the row number or the column letter (round the edges) Edit the contents of a cell Select the cell and then click in the = field Move a cell (or array of cells) Select the cell(s), [Ctrl]-X, click to the new position, [Ctrl]-V Copy a cell (or array of cells) Select the cell(s), [Ctrl]-C, click to the new position, [Ctrl]-V Delete a cell (or array of cells) Select the cell(s), [Delete] Delete a row or column Select the row or column, then press [Delete] to blank it out or right-

click and select Delete to remove it completely Insert a new row or column Select the number of the row below where you want the new row or the

letter of the following column, then right-click and select Insert Create a formula Select the cell and type the formula, starting with =

(You can select cells the formula refers to with the mouse, rather than typing their cell references)

Use basic arithmetic operators Type from the keyboard Use built-in functions Type from the keyboard or select using the fx icon on the toolbar Change the appearance of a cell

Select the cell(s), then select the required options (eg font colour or number of decimals) from the Font, Alignment or Number sections on the Home menu, or right-click the cell and select from the toolbar

Create a chart (graph) Insert, then click on the icon for the required chart type Select a graph Click anywhere on the graph Edit a graph Right-click on the graph and select the feature you want to change (You

will get different choices depending where you click) Export a graph to Word First select the graph in Excel, press [Ctrl]-C, then change to Word,

click at the correct position and press [Ctrl]-V Help Click on the ? icon (in the top-right corner) or press [F1]



7.2 Guidelines for spreadsheets

Before we look at some of the more detailed issues relating to spreadsheets, here are some general guidelines to observe:

Create each worksheet like a book to be read from left to right and top to bottom using each column/row for a single purpose.

Label your columns/rows clearly. Use blank columns to stop your spreadsheet looking cluttered. Choose appropriate numbers of decimal places. Use the simplest calculation method that is reasonable. Stick to simple functions. Avoid hard-coding pure numbers in your formulae. Use variables and

formulae instead, referring to parameters as appropriate.

Try to avoid features and functions that will require manual intervention to update the calculations if changes are made subsequently to the data values or parameters (although sometimes it might be difficult to avoid using a goal seek).

Use a different background colour to distinguish cells containing input parameters that can be varied by the user from those containing formulae. And keep the parameters together in the same part of the spreadsheet.

Highlight any dangerous cells, eg ones dependent on a goal seek result or that cant be copied down columns or across rows.

Try to set up your spreadsheet so that it is flexible (ie additional calculations can be incorporated easily) and scalable (ie additional data can be incorporated easily).

Break up complicated calculations to avoid mistakes and repetition. Incorporate checks in your calculations.

Exam tips Dont spend ages sexing up your spreadsheet. You need to make sure that your work is clearly labelled and easy to follow, but dont waste time in the exam creating elaborate colour schemes, differing font sizes etc. The examiners have said that poor modelling techniques such as hard-coding of parameters (eg interest rates or time periods) are penalised in the assessment.



Question 8

You are doing some calculations based on an interest rate of 5%.

Why is it not a good idea to hard-code the 5% in your spreadsheet formulae? What is the best way to incorporate the 5% in your calculations?

Question 9

State four methods you can use to check an answer calculated on your spreadsheet.

7.3 Examples of good/bad spreadsheets

Question 10

You are an assessor presented with the spreadsheet below, which was produced by a student. Criticise this students work.

Rows 8 to 3910 have been hidden here.



7.4 Excel functions

Functions for summarising data The following functions are particularly useful for summarising data. All are applied to ranges of cells. Ranges are specified using the notation First cell:Last cell. You can type the colon either as : or as .. (which will then be displayed as :). Function Description

COUNT Gives the number of entries (excluding blanks)

MIN Gives the minimum (the lowest value)

MAX Gives the maximum (the highest value)

SUM Calculates the total

AVERAGE Calculates the average (the arithmetic mean)

VAR, STDEV Calculates the variance / standard deviation Several of these functions were used in the worksheet we just looked at and are also used in the improved version shown opposite. For example, the formula in cell O4 has been used to count the number of entries in the block of cells from H4 to H3915. (We will explain the dollar signs ($) shortly if you havent seen these before.) To insert any of these functions in your spreadsheet, it is usually easiest just to type them directly. All formulae start with an equals sign (=).

Question 11

What formulae were used for calculating cells O9 and O10?

As a technical point, the function VAR gives the sample variance, ie it estimates the underlying variance using a denominator of 1n - . There is a corresponding function VARP (the P stands for population), which gives the actual variance of a population of equally likely values, ie it is calculated using a denominator of n . When working with large data sets, its not vital which one you use.

Statistical functions in Excel 2007 and 2010 A number of statistical functions have been given new names in Excel 2010 that contain a dot. For example, VARP is now officially called VAR.P. However, we recommend you use the Excel 2007 names, without the dots, as these can be used in both versions.



There are also functions such as SKEW and KURT for calculating higher sample moments for a data set. The function CORREL calculates the correlation between two sets of values. Other less commonly used functions you might like to investigate include the QUARTILE, MEDIAN and MODE functions.

Question 12

The worksheet above is part of an improved version of the one in Question 10. This part shows the daily returns on an investment index (I) and one component (C) of the index. Why do you think we have worked out the smallest and largest daily returns here?

The functions LARGE and SMALL calculate the k th largest and the k th smallest values in a range of cells.

Example If you wanted to calculate the 3rd largest daily return for the index in the worksheet above, you would use the following formula: =LARGE (H$4:H$3915, 3)



Question 13

What answer would this calculation give?

Special functions There are a number of special functions, which are used frequently in actuarial work and in CA2 projects. The functions COUNTIF and SUMIF work in the same way as COUNT and SUM, except that they only include cells whose values satisfy a specified condition. The condition can either be an exact value (such as 0.05) or an inequality (such as



Example The extract below shows the left-hand portion of the example worksheet. If we wanted to find the index value on 9 September 1999, for example, we could use the following formula: =VLOOKUP (DATE(1999,9,9), A$4:B$3916, 2, FALSE)

Question 14

(i) Explain the arguments 2 and FALSE used in the formula in this Example. If youre not familiar with this function, you can use the Help feature to find out

how it works. (Go to an empty cell, click on the xf icon in the formula bar, type the function name and ask for Help on this function.)

(ii) How would you modify this formula to find the value of the component on

9 September 1999?

The HLOOKUP function works in a similar way, but searches horizontally.



Logical functions and operators There are also some logical functions such as IF. This can be used where different formulae are required in different circumstances. The use of the IF function, the logical operators AND, OR and NOT, and the logical values TRUE and FALSE are best understood by looking at some examples.

Examples Suppose that cell D1 contains the formula MOD(TODAY( ),7), which gives the remainder when the serial number for todays date is divided by 7. (The Excel calendar starts with Sunday 1 January 1900 = Day 1.) Consider the following formulae: (a) =IF (D1 = 3, Its Tuesday, Its not Tuesday) This uses the fact that a remainder of 3 always corresponds to a Tuesday. (b) =IF (OR(D1 = 0, D1 = 1), Its the weekend, Its a weekday) This works because a remainder of 0 corresponds to Saturday and 1 to Sunday. (c) =AND(D1 = 0, D1 = 1) This will give the answer FALSE, since the conditions cannot both be true. (d) =OR(D1 = D1, D1 = D1) Since one or more of the statements is true, this will give the answer TRUE. (e) =NOT(D1 D1) The operator (greater than or smaller than) is equivalent to not equal to. So, taking into account the double negative, this will give the answer TRUE.

Another useful if function is IFERROR. This allows you to override the answer to a formula if it results in an error. For example =IFERROR((1(1+I1)^(N1)) / I1,N1) will return the value of an annuity certain (with the interest rate in cell I1 and the term in cell N1). If the interest rate is 0%, the first part of the calculation will give a #DIV/0! error, which will be replaced with the correct value (which is equal to the term).



Financial functions The following financial functions might prove useful. For further explanation of the arguments of the functions, see the Help pages in Excel. NPV(rate, values) gives the net present value of a series of cashflows, discounted at a specified interest rate. (The interest rate is an effective rate i .) IRR(values) gives the internal rate of return for a series of cashflows. If necessary, you can specify an initial guess to use (eg 5%) by including this value as a second argument. PMT(rate, nper, pv) calculates the repayments required to pay off a loan, where rate is the interest rate, nper is the number or repayments and pv is the initial loan amount. Other useful functions Excel has many other functions. For example, the function RAND (and also RANDBETWEEN) is useful for generating pseudo-random numbers for simulations (which we will discuss later) and the NORMSDIST function can be used to find probabilities based on the standard normal distribution. Other functions you might need to use are ABS (absolute value), INT (integer part) and ROUND / ROUNDDOWN / ROUNDUP, which can be used to round answers to a specified number of digits or to restrict the number of significant figures shown.

Question 15

What answers do you think ROUND(12345.6789, 2) and ROUND(12345.6789, 2) would give?

To insert one of the more advanced functions in your spreadsheet, it is usually best to use the function icon ( xf ) on the formula bar. This has the following advantages:

It presents you with a list of all the available functions (which is useful if you cant remember the exact name).

When you select a function, it describes the arguments of the functions and the order in which they appear.

It allows you to pick out the input values directly from your spreadsheet (click on the icon on the right and then select the cell(s) you want using the mouse).

It shows you the value based on the arguments you have select

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