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CA1: CMP Upgrade 2013/14 Page 1

The Actuarial Education Company IFE: 2014 Examinations

Subject CA1

CMP Upgrade 2013/14

CMP Upgrade

This CMP Upgrade lists all significant changes to the Core Reading and the ActEdmaterial since last year so that you can manually amend your 2013 study material tomake it suitable for study for the 2014 exams. It includes replacement pages andadditional pages where appropriate. Alternatively, you can buy a full replacement set ofup-to-date Course Notes at a significantly reduced price if you have previously boughtthe full price Course Notes in this subject. Please see our 2014 Student Brochure formore details.

This CMP Upgrade contains:

All changes to the Syllabus objectives and Core Reading.

Changes to the ActEd Course Notes, Series X Assignments and Question andAnswer Bank that will make them suitable for study for the 2014 exams.

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Page 2 CA1: CMP Upgrade 2013/14

IFE: 2014 Examinations The Actuarial Education Company

1 Changes to the Syllabus objectives and Core Reading

1.1 Syllabus objectivesSyllabus objective 1.3 has been changed to:

1.3 Outline the professionalism framework of the Institute and Faculty of Actuariesand the Financial Reporting Council.

1.2 Core Reading

All references to the Board for Actuarial Standards (BAS) have been changed to the

Financial Reporting Council.

All references to the Actuarial Profession have been changed to the Institute andFaculty of Actuaries.

All references to open-ended investment companies (OEICs) have been removed (this ismost significant for Chapter 18, therefore we mention this again below).

Chapter 1

Page 3

The following sentence has been deleted:

The strapline of the UK actuarial profession making financial sense of thefuture indicates the areas where the actuarial techniques learnt in the CTsubjects, and the application skills in this course and elsewhere lead to aparticular role for actuaries.

Chapter 7

Page 9

The first sentence now reads:

A pure endowment provides a benefit on survival ...

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Chapter 16

Page 4

The first sentence of Core Reading now reads:

The running yield ( ie rental yield) on property varies with the type of building.

Chapter 18

Page 7

As stated above, all references to OEICs have been deleted. Therefore this page has

been deleted.

Chapter 24

Page 3 6

Core Reading and ActEd text have been added. We recommend that you remove pages3 6 from your Course Notes and use replacement pages 3 6c provided below.

Chapter 29

Page 14

The following bullet point has been deleted:

run the model using selected values of the variables

Chapter 32

Page 8

The Core Reading has been amended and further ActEd explanation has been added.We recommend that you remove pages 7 8 from your Course Notes and usereplacement pages 7 8c provided below.

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Page 11

The following sentence of Core Reading has been added to the section on just-in-timefunding:

If the anticipated risk event does not happen then terminal funding or apay-as-you-go approach could be used.

Chapter 39

Page 12

Some Core Reading has been deleted and the ActEd text has therefore been amended.We recommend that you remove pages 11 12 from your Course Notes and usereplacement pages 11 12 provided below.

Page 13

These examples have been deleted.

Page 20

The second sentence has been changed to:

In the UK this is the definition used by the regulators, the Financial PolicyCommittee and the Prudential Regulation A uthori ty.

Chapter 43

Page 5

The Core Reading and ActEd text on Tail VaR has been re-written. We recommendthat you remove pages 5 6 from your Course Notes and use replacement pages 5 6c

provided below.

Chapter 47

Page 8

A new section of Core Reading and ActEd text has been added, discussing Basel III.We recommend that you remove pages 7 8 from your Course Notes and usereplacement pages 7 8e provided below.

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Page 9

In the first sentence of Core Reading, 2013 has been changed to 2014.

Glossary

Page 20

As stated above, the definition of an open-ended investment company (OEIC) has beendeleted.

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2 Changes to the ActEd Course Notes

All references to the Board for Actuarial Standards (BAS) have been changed to theFinancial Reporting Council (FRC).

All references to the Actuarial Profession have been changed to the Institute andFaculty of Actuaries.

All references to open-ended investment companies (OEICs) have been removed (this ismost significant for Chapter 18, therefore we mention this again below).

Chapter 13

Page 12

The last sentence now reads:

The running yield on money market instruments is roughly equivalent to that ongovernment bonds.

Chapter 14

Page 21

The following point has been deleted:

typically higher running yield than equities

Page 23

The first paragraph now ends:

...and it ignores expenses, tax and default risk.

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Page 25

The section on running yields now reads:

Historically, running yields on conventional bonds have typically been higher thanrunning yields on equities and property. This is because income on equities and

property is expected to grow over time, creating capital gains. Conversely, since theincome stream on a conventional bond is flat and the scope for capital gains is limited(if the bond is held to maturity), income levels tend to be higher.

(It has been much harder to compare running yields in recent years however, due toincreased volatility in the financial markets.)

Chapter 15

Page 11

The following sentence has been deleted:

lower running yield than government bonds as much of the return is expected to be made from future dividend growth

Page 14

The first sentence now reads:

Historically, the running yield on equities has been lower than that on bonds as the potential for capital growth is greater than on bonds. (Since the economic uncertaintythat followed 2008 however, running yields have been more volatile, which makes acomparison of asset classes more difficult.)

Chapter 16

Page 4

The sentence before the first set of bullet points now starts:

Historically, the running yield has usually been higher ...

The sentence after the second set of bullet points now starts:

Conversely, property rental yields have often been lower than conventional bond

running yields...

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Page 15

The thirteenth bullet point now reads:

running yield varies with the type of property

Chapter 18

Page 7

As stated above, all references to OEICs have been deleted. Therefore this page has been deleted.

Chapter 21

Page 3

The last sentence under Regulatory changes now reads:

Such a change in regulatory regime would increase the relative appeal to the lifeinsurance company of investments, such as bonds, which have historically offered ahigher running yield.

Chapter 24

Page 3 6

As stated above, Core Reading and ActEd text have been added. We recommend thatyou remove pages 3 6 from your Course Notes and use replacement pages 3 6c

provided below.

Chapter 32Page 8

As stated above, the Core Reading has been amended and further ActEd explanation has been added. We recommend that you remove pages 7 8 from your Course Notes anduse replacement pages 7 8c provided below.

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Chapter 39

Page 12

As stated above, some Core Reading has been deleted and the ActEd text has therefore been amended. We recommend that you remove pages 11 12 from your Course Notesand use replacement pages 11 12 provided below.

Page 32

The second bullet point has been changed to:

Liquidity is a measure of how quickly the asset can be converted into cash at a

predictable price.

Chapter 43

Page 5

The Core Reading and ActEd text on Tail VaR has been re-written. We recommendthat you remove pages 5 6 from your Course Notes and use replacement pages 5 6c

provided below.

Page 15

A new sentence has been added to the bottom of the page. This reads:

The TailVaR could also be defined as the expected shortfall, conditional on there beinga shortfall.

Page 17

A new question and solution has been written on Tail VaR. The question is included inthe replacement pages detailed above. For the solution, we recommend that youremove pages 17 18 from your Course Notes and use replacement pages 17 18c

provided below.

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3 Changes to the Q&A Bank

Part 4 Solutions

Page 4

In the last set of bullet points, the second bullet point now reads:

income on government bond is fixed, should be rises in property income []

Page 16

In the section on Return , the last half mark now reads:

Running yields have been more volatile since the economic uncertainty that followed2008 however, which makes comparisons between the two asset classes more difficult.

[]

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4 Changes to the X Assignments

This section provides details of material changes that have been made to the2013 X Assignments, so that you can continue to use these for the 2014 exams.

However, if you are having your attempts marked by ActEd, you will need to use the2014 version of the assignments.

Assignment X3 Solut ions

Page 17

The section on reinvestment risk now reads:

Historically, conventional bonds have generally earned a higher running yield thanequities. Consequently, they involve a greater risk of reinvestment of income onuncertain terms. []

However, recent economic uncertainty has made it more difficult to compare runningyields for different asset classes. []


Page 1

The sixth bullet point under Differences now reads:

property has historically offered higher running yields []


Page 12

In Solution X5.8, another half mark has been added to the section on conventionalgovernment bonds. This reads:

This assumes no default risk on government bonds. []

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Assignment X6 Solu tions

Page 5

The second point now reads:

Ordinary shares (and most properties) have historically given a lower running yield thangovernment bonds. []

Assignment X7 Solu tions

Page 12

In Solution X7.5 part (ii), replace the second and third points with:

because this is mainly a unit linked product ... []

... and the investment risk will be mostly borne by the policyholders. []

Page 14

In Solution X7.6, the second and third points in this solution should read:

waiting periods this is the period after the sale of the policy, before coverstarts

[]

deferred periods this is the amount of time the policyholder must be ill for, before the benefit becomes payable []

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5 Other tuition services

In addition to this CMP Upgrade you might find the following services helpful with

your study.

5.1 Study material

We offer the following study material in Subject CA1:

ASET (ActEd Solutions with Exam Technique) and Mini-ASET

CA1 Bitesize

Flashcards

Mock Exam A and Additional Mock Pack (AMP) Revision Notes

MyTest

Sound Revision.

For further details on ActEds study materials, please refer to the 2014 Student Brochure , which is available from the ActEd website at www.ActEd.co.uk .

5.2 Tutorials

We offer the following tutorials in Subject CA1:

a set of Regular Tutorials (lasting three full days)

a Block Tutorial (lasting three full days)

a series of webinars (lasting approximately an hour and a half each)

the Online Classroom (a valuable add-on to a face-to-face tutorial or a greatalternative to a tutorial)

For further details on ActEds tutorials, please refer to our latest Tuition Bulletin , whichis available from the ActEd website at www.ActEd.co.uk .

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5.3 Marking

You can have your attempts at any of our assignments or mock exams marked byActEd. When marking your scripts, we aim to provide specific advice to improve yourchances of success in the exam and to return your scripts as quickly as possible.

For further details on ActEds marking services, please refer to the 2014 Student Brochure , which is available from the ActEd website at www.ActEd.co.uk .

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6 Feedback on the study material

ActEd is always pleased to get feedback from students about any aspect of our study programmes. Please let us know if you have any specific comments ( eg about certainsections of the notes or particular questions) or general suggestions about how we canimprove the study material. We will incorporate as many of your suggestions as we canwhen we update the course material each year.

If you have any comments on this course please send them by email to [email protected] or by fax to 01235 550085 .

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CA1-24: Valuation of asset classes and portfolios Page 3


1.3 The analysis

The relative value of different asset classes can be analysed by considering therelationship between the expected and required returns . The expected returnand the required return can each be broken into component parts:

1. The total return comes from income and capital gain. Therefore:

expected return = init ial income yield + expected capital growth

The term expected capital growth means the annualised rate of increase in price.

2. The nominal return an investor requires from an asset is the sum of threecomponents, based on a return in excess of inflation and a premium to

compensate for the risk and all other features of the asset:

required nominal return = required risk-free real yield+ expected inflation + risk premium

You have come across required return and expected return in Chapter 22, Relationship between returns on asset classes.

Cheapness or dearness can be established if it appears that the expected returnis dif ferent from the required return.

If there is a market in index-linked government bonds the required risk-free realyield can normally be taken as the real yield on these bonds.

In the discus sion below a number of simplify ing assumptions are made:

that all investors want a real rate of return

all investors have the same time horizon for investment decisions

tax differences between investors can be ignored (in particular, we assumethat we can use gross yields)

reinvestment can occur at a rate equal to the expected total return on theasset , in other words, we make no allowance for reinvestment risk in theequations below

we are not allowing for other risks, eg expense risk or liquidity risk (whichmight apply if we wish to sell a bond before redemption).

In reality all o f these assumpt ions are questionable.

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Page 4 CA1-24: Valuation of asset classes and portfolios


Under these assumptions, the expected returns between different asset categories should be consistent with each other. Note that consistent does not necessarily meanequal, eg the expected return from a risky asset might be consistent with the expectedreturn from a risk-free asset if it is 3% pa higher to compensate for the extra risk.

The discussion will be very broad-brush. We will not get distracted by issues such asthe timing and reinvestment of investment income.

For each of the main asset categories, the expected return from a portfolio ofassets will be equated with the required return for that asset category. Theequations derived are valid if the assets considered are fair value relative to eachother.

1.4 Conventional government bonds

The expected return i s taken to be the gross redemption yield (GRY), if the bondis considered to be free from the risk of default. Equating the expected returnwith the required return:

GRY = required risk-free real yield + expected inf lation+ inflation risk premium

For the purposes of this analysis, it is conventional to assume that the risk of default ongovernment bonds is minimal.

We can use this relationship to decide whether government bonds are cheap or dear.

Example

We might believe that future inflation will average 2% pa and we might require aninflation risk premium of 1% pa to cover the risk of higher inflation eroding our realreturns. Now, if we know that we can earn a risk free real return of 2% pa on index-

linked government bonds, then conventional government bonds will be cheap to us iftheir gross redemption yields exceed 5% pa .

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CA1-24: Valuation of asset classes and portfolios Page 5


Question 24.2

An investor with real liabilities expects future inflation to average 2% pa . The

investor requires a return from conventional government bonds of 1% pa more than thereturn from index-linked government bonds in order to compensate for the inflation riskon conventional government bonds. If the yield on conventional government bonds is5% pa would the investor choose to purchase index-linked stocks yielding 2% pa realor the conventional stocks?

1.5 Corporate loan stocks

A similar development of the gross redemption yield (GRY) is poss ib le fo rcorporate loan st ocks:

GRY = required risk-free real yield + expected inf lation+ bond risk premium

Investors require a higher yield than from conventional government bonds tocompensate for the greater risk of default and the lower marketability. Thereforethe bond risk premium has three main components:

inflation risk premium

default premium

marketabilit y premium.

Recall that the GRY is the return you would expect to achieve on a bond if you hold ituntil redemption, provided that the bond does not default (and ignoring reinvestmentrisk, tax, expenses etc ). Exposure to these risks means that the expected return will in

practice be lower than the GRY.

In many practical applications ( eg pension scheme or insurance valuations), we maywish to consider the expected return on an asset or asset class net of, for example,default risk.

The expected return on corporate loan stocks is less than the gross redemptionyield reflecting the expected losses from defaults which are incorporated in thedefault premium.

For comparison purposes, as the expected return is net of the impact of expecteddefaults, the required return should not contain a risk premium for expected default.(Note though that the required return may still contain a risk premium reflecting theuncertainty surrounding defaults ( ie the risk that the actual level of defaults turns out to

be different to the expected level).

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Page 6 a CA1-24: Valuation of asset classes and portfolios


In the discussions for other asset classes below, the formulae for the expected returnsignore the expected impact of default (and other) risks, and the formula for requiredreturns include premia in respect of such risks.

1.6 Equities

The total expected return from equities can be expressed as:

d + g

where: d is the income stream, ie the dividend yield

g is the expected capital gain, ie the expected annual growth individends.

Therefore:

d + g = required risk-free real yield + expected inflation+ equity r isk premium

The equity risk p remium is needed to compensate the investor fo r:

possible default

marketability

high volatility of share prices and dividend income.

Note that g is made up of expected inflation plus real dividend growth. We couldtherefore remove expected inflation from each side of the equation. By makingestimates of future real dividend growth, we can estimate the equity risk premium thatis implied by the current level of equity yields.

1.7 Property

The form of the equation for property investment is very similar to the equationfor equities:

rental yield + expected growth in rents = required risk -free real yield+ expected inflation+ property risk premium

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CA1-32: Expenses Page 7


2 Expense allocation principles

This section provides an overview of the principles of expense allocation . Expensesneed to be allocated between:

classes of business, and

functions.

By function we mean activity or operation. For example, the expense mightrelate to the activity of underwriting or the operation of administering the contract.

One of the main reasons that expenses need to be allocated in this way is so that theycan be loaded into premiums. This will mean that each policy contributes an

appropriate amount to the total level of expenses. We discuss how we might go aboutloading expenses into premiums later in this section.

Question 32.3

Other than determining the expense loading for premiums, for what other purposes doexpenses need to be allocated?

Expenses form an important component of the total outgo analysed in internal

management account s and financial plans. Hence, expenses need to beallocated to different types of business in as realisti c a manner as possib le.

However, the approach should be pragmatic as well as realistic.

2.1 Allocating expenses by class of business

Al locating di rec t expenses

Direct expenses may arise from a department dealing purely with one class ofbusiness, in which case the expenses relating to that department canimmediately be allocated to the relevant class. If direct expenses arise fromareas dealing with more than one class of business then timesheets can be kept(either for a period o r permanently) to help sp lit costs between classes.

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Page 8 a CA1-32: Expenses


Example

Staff in an underwriting department may deal with several classes of business ( eg term

assurance, whole life assurance and endowments). Their costs can be allocated to eachof these classes based on the time that was recorded as being spent underwriting each ofthem. Staff timesheets can be used to collect this information.

Al locating indi rect expenses

The indirect expenses are harder to allocate. By definition , the departmentsconcerned are not related directly to any particular class of business, but form asuppor t funct ion for the provider. In this case, it is necessary to find a sensibleapportionment of the expenses across di rect business activit ies.

We must allocate indirect expenses to the different classes of business. There is nosingle correct approach for this, but it may help to allocate the expenses to differentdepartments ( ie business activities) first, as an intermediate step.

Finally, we must allocate expenses according to the timing of when the expenses wereincurred ( ie by function). We discuss this in more depth in Section 2.2 below.

Example 1

For some costs a charging out basis could be used computer time andrelated staff could be charged to the direct func tion departments based on actualuse.

Computer usage

Some computer usage will be readily identifiable as belonging to one product line andone function. For instance, valuation runs would be a renewal expense while quote

calculations would be new business, and both can be readily allocated to the relevantclass of business.

However, some expenses, eg a companys internal electronic mail system, would not bereadily identifiable as belonging to any one department or product. They could first beallocated to each department pragmatically perhaps in proportion to the other (known)computer costs, or in proportion to staff numbers. They could then be allocated to classof business in the same proportion as the salary allocation of the employees in eachdepartment, ie according to a timesheet analysis.

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CA1-32: Expenses Page 8b


IT staff

For IT staff, where tasks can be readily identified as contributing to a particular function

and product line, salaries could be allocated according to the time spent on each task.

For other tasks, eg fixing a server problem, it may not be so easy to decide how toallocate the salary cost. Different companies will take different approaches toallocating these remaining staff costs, one approach may be to allocate them to productline (and function) in the same proportions as for the costs that have already beenidentified.

Note that this example talks exclusively about IT staff and computer usage. However, parallel arguments could apply to other indirect costs, eg the salaries of actuarial staff.

Example 2

Premises costs can be allocated by f loor space taken up by a department.

If a company owns a property, then this is an asset to the company and ought to beearning a return (rental income) from its tenant. However, since the company isoccupying its own property, no such rent is forthcoming. In effect, this is a cost to thecompany. Therefore, a notional rent needs to be charged to the departments whooccupy the building.

This notional rent, plus property taxes, heating costs etc , can be split, for example, byfloor space occupied, between departments.

Thereafter, property costs can be allocated to a class or classes of business in proportionto the allocation of the salaries of the employees of that department (which shouldalready have been done using, for example, timesheet analysis).

We have mentioned that a pragmatic approach may be necessary. This is because in practice, many companies will not keep detailed enough records of timesheets orcomputer logs to be able to use the methods above. Instead, a simplified approach may

be used, eg costs may be allocated to product line in proportion to the number of policies in force, or the number of new policies written.

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Page 8c CA1-32: Expenses


2.2 Allocating expenses by function

As wel l as apportioning expenses to a line of business, cost s need to beapportioned by function, so that they can be allowed for in determining productpricing or the provisions for future liabilities.

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CA1-39: Sources of risk Page 11


So banks face liquidity risk if more customers than expected demand cash, ie withdrawtheir deposits.

Liquidity risk for co llective investment schemes

Similarly, collective investment schemes and insurance funds that invest in realproperty need to protect themselves if cl ients request access to their funds w henthe underlying properties cannot be sold. Such funds frequently have the powerto defer withdrawals by up to six months if necessary, to allow time for propertysales. Hedge funds that invest in illiquid assets also often have lock-in periodsto mitigate liquidity risk.

The reference to insurance funds here means that unit trusts face liquidity risk if more policyholders than expected surrender their policies.

Similarly, collective investment schemes face liquidity risk if more customers thanexpected wish to sell their units.

Managing liquidity risk

Financial companies will maintain a degree of liquidity to deal with anticipated liabilitywithdrawals. In the event of these withdrawals being greater than expected, thecompany may have to convert some of its less liquid assets to cash or else try to borrowadditional funds (which may be unavailable or expensive).

Financial companies can allow for liquidity risk to some extent, by allowing a marginfor withdrawals being higher than they expect and by allowing for predictable seasonalvariations ( eg higher bank withdrawals pre-Christmas). Typically, the biggest liquidityrisk issues for a financial company arise as a result of a sudden surge in liabilitywithdrawals.

Question 39.6

Why might there be a sudden surge in customers withdrawing their deposits from a bank?

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Page 12 CA1-39: Sources of risk


3.2 Market liqu idity risk

In the context of the financial markets, liquidity risk is where a market does nothave the capacity to handle (at least, without a potential adverse impact on theprice) the volume of an asset to be bought or sold at the time when the deal isrequired. In general, the larger a market is, the more liquid it wi ll be, becausemore participants in the market will be trading at any one time. Thus when anymember of the market wishes to complete a trade, it is likely that the market willbe able to find a counterparty willing to accept the trade. This particulardefinition of liquidity is frequently also called marketability.

The terms marketability and liquidity are often used interchangeably. Strictly speakthough, the two are slightly different:

Marketability is how easy it is to convert an asset into cash.

Liquidity is a measure of how quickly the asset can be converted into cash at a predictable price.

A highly liquid asset therefore has two characteristics:

1. It either will quickly become cash because of the terms of the asset itself ( eg ashort-term bank deposit or a government bond with one week until redemption)or else there is a high degree of certainty that the asset could be sold quickly ifrequired.

2. The amount of cash it will or could become is (almost) certain. (For example, along-term government bond is a marketable asset because there are many market participants willing to trade at any one time, however it is not a liquid asset because the market value is quite volatile.)

Marketability considers only the characteristic of how certain it is that an asset can besold quickly if required.

Example

A seven day fixed-term deposit at a bank is a highly liquid asset because it will becomecash within a week. However, such deposits cannot be traded, so they are completelyunmarketable.

A long-term government bond is a marketable asset because there are many market participants willing to trade at any one time, however it is not a liquid asset because themarket value is quite volatile.

(We discussed the relative marketability of short-term and long-term bonds when wemet the liquidity preference theory in Chapter 14.)

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CA1-43: The risk management process (2) Page 5


Underperformance relative to benchmark

It can be measured either in absolute terms or relative to a benchmark. Again,VaR is based on assumptions that may not be immediately apparent. Inparticular, it is frequently calculated assuming a normal distribution of returns.If the distribution of returns is fat-tailed , or skewed, tracking error (with itsfocus on the standard deviations o f returns) may be misleading.

Remember that the normal distribution bell cuts off at around three standard deviationsfrom the mean. However, if the underlying distribution is not normal, but skewed, thetail may be much longer than three standard deviations.

Unfortunately, portfolios exposed to credit risk, systematic bias or derivativesmay exhibit non-normal distributions. The usefulness of VaR in these situationsdepends on modelling skewed or fat-tailed distributions of returns, either in theform of statistical distr ibutions or via Monte Carlo simulations. However, thefurther one gets out into the tails of the distributions, the more lacking the dataand, hence, the more arbitr ary the choice of the underlying probability becomes.

The main weakness of VaR is that it does not quantify the size of the tail. Anotheruseful measure of investment risk therefore is the Tail Value at Risk .

2.4 Expected shortfall (or Tail VaR)

You may find some of the material below familiar, if you have recently studied SubjectCT8.

Closely related to both shortfall probabilities and VaR are the Tail VaR andExpected Shortfall measures of risk .

0-10

Probability

5%

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Page 6 a CA1-43: The risk management process (2)


The risk measure can be expressed as the expected shortfall below a certainlevel.

For a continuous random variable, the expected shortfall is given by:

( )Expected Shortfall ,0 ( ) ( )L

E Max L X L x f x dx-

= - = -

where L is the chosen benchmark level.

If L is chosen to be a particular percentile point on the distribution, then the riskmeasure is known as the Tail VaR.

The (1- p) Tail VaR is the expected shortfall in the pth

lower tail. So, for the 99%confidence limit, it represents the expected loss in excess of the 1% lower tail value.

However, Tail VaR can also be expressed as the expected shortfall conditionalon there being a shortfall.

This is often called the conditional Tail VaR. Using this definition, we take theexpected shortfall formula and divide by the shortfall probability.

Question 43.1 (CT8 revision)

Consider an investment portfolio of 100 m whose returns per annum follow acontinuous uniform distribution with probability density function:

1( )

0.1= f x for 0.05 0.05- x

(i) Calculate the 95% VaR over one year.

(ii) Calculate the corresponding Tail VaR over one year.

(iii) Calculate the corresponding conditional Tail VaR over one year.

Other similar measures of ri sk have been called:

expected tail loss

tail conditional expectation

condi tional VaR

tail cond itional VaR

worst conditional expectation.

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Page 6c CA1-43: The risk management process (2)


3 Low likelihood high impact risks

Dealing with low likelihood but high impact risks is a particular issue that may arise as part of the Risk control stage of the management process.

The risk portfolio analysis described in the last chapter will have identified arange of high impact but low probability risks. These are among the mostdifficult to manage; they are likely to include both risks related to normalbusiness activities and operational risks.

It is important to manage such risks in a measured way. In particular becausecredit rating agencies and regulatory authorities pay significant interest to theability of a company to withstand rare events, there is a temptation formanagement to concentrate unduly on such risks at the expense of the broad

range of risks accepted.

Low probability, high impact risks :

can only be diversif ied in a limited way

Example

Production of a major product line on two sites diversifies the risk of a total lossof business premises by fire, but has attendant additional costs if a total loss byfire does not occur.

can be passed to an insurer or reinsurer, usually by some form ofcatastrophe insurance or whole account aggregate excess of loss cover(commonly called stop loss cover). (We will discuss these reinsurance

products amongst others in the later chapters on risk management tools.) can be mitigated by management control procedures, such as disaster

recovery planning.

Some such risks can only be accepted as part of the consequences of the

business undertaken, and the management issue then becomes how todetermine the amount of capital that it is necessary to hold against the riskevent. The techniques of scenario analysis , stress testing and stochasticmodelling di scussed in the next section enable this to be done.

Finally a company will have determined its own risk tolerance for example theability to withstand an event that might occur with a 0.5% probability within oneyear. This means that the company accepts that it might be ruined by a rarerevent, and has decided not to take such events into account in its riskmanagement.

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Chapter 43 Solutions

Solution 43.1

(i) VaR

The VaR is given by t such that:

0.05

1VaR ( ) 0.05

0.1-= = < =

t

dx P X t

0.05

10.05

0.1-=

t

dx

Hence:

0.05

10.05

0.1

( 0.05)0.05

0.1

0.045

-

=

- - =

= -

t

x

t

t

ie the VaR is 0.045 100 4.5 =m m over the next year.

In other words, we are 95% certain that we will not make a loss of more than 4.5 mover the next year.

(ii) Tail VaR

The Tail VaR is given by:

( ) ( )0.045 0.045

0.05 0.05

0.0452

0.05

1 10.045 0.045

0.1 0.1

1 10.045

0.1 2

0.000125

- -

- -

-

-

- - = - +

= - +

=

x dx x dx

x x

ie the Tail VaR is 0.000125 100 12, 500 =m over the next year.

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Note: If we had been asked to find the expected shortfall under a benchmark loss of4.5m, then we would have calculated the same result. In other words, the expectedshortfall starts with a benchmark amount (in this case a loss of 4.5m) whereas the TailVaR starts with a required confidence level.

(iii) Conditional Tail VaR

12,5000.25

0.05= m

In other words, if we take the worst 5% of scenarios, the average loss on these scenarioswould be 4.5 0.25 4.75+ =m m m .

Solution 43.2

Examples of assets with a positive correlation:

assets in the same particular sector, eg two shares in the same industrial sector

assets from different sectors that react in the same way, eg shares and propertyare both correlated to inflation.

Solution 43.3

Commercial bank

A commercial bank is exposed to substantial amounts of credit risk and market risk(particularly with regards to interest rates). As such, useful stress tests might include:

testing how the asset and liability values respond to a 3% increase in short- andlong-term interest rates

testing the impact of a worsening of the credit rating of all borrowers

testing the impact of a widening of credit spreads on assets held.

The assessment should be carried out over long enough periods to take account ofcyclical effects linked to the economy.

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Life insurance company

Life insurance companies are exposed to market risk (not just from interest rates butfrom volatility of all asset categories), risk relative to liabilities and credit risk. Thereare many other tests worthy of carrying out ( eg for liquidity risk), but the two exampleschosen here are:

testing solvency in the event of a fall in asset prices ( eg 20% equities, 10% bonds and some allowance for currency depreciation)

testing solvency in the event of a widening of credit spreads on assets held.

Solution 43.4

Stochastic modelling could involve the following steps:

specify the purpose of the investigation, including a time horizon, a measurablecriteria and a probability confidence limit

collect, group and modify data

choose a suitable density function for each of the variables to be modelledstochastically

specify correlation between variables

ascribe values to the variables that are not being modelled stochastically

construct a model based on the expected cashflows

check that the goodness of fit is acceptable. This can be done by running a pastyear and comparing the model with the actual results.

attempt to fit a different model if the first model does not fit well

run the model many times, each time using a random sample from the chosendensity function(s)

produce a summary of the results that shows the distribution of the modelledresults after many simulations have been run.

Solution 43.5

May be less than the sum of individual risks due to the impact of diversification ornegative correlation.

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This page has been left blank so that you can slot the replacement pagesinto your Course Notes

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Under Pillar 1, in relation to credit risk , there is a standardised approach (which is amodification of the Basel I risk weightings approach) and an internal-ratings basedapproach that may be adopted by banks able to demonstrate that they have sufficientlysophisticated systems, allowing them to hold less capital.

Additional capital requirements apply for market and operational risk.

Pillar 2 deals wit h superviso ry issues, economic capital and interest rate risk andis based on four interlocking pr inciples:

1. Banks are required to have a process for assessing their capitalrequirements in relation to their individual risk profiles.

2. This process will be evaluated by supervisor s.

3. Banks are expected to operate with capital above the Pillar 1 minimum.

4. Supervisors should intervene at an early stage to prevent capital fromfalling below the level required to support the banks ri sk characteristics.

Here interest rate risk refers to the potential risk arising from a mismatch of duration between a banks assets ( eg mortgages) and liabilities ( eg customer deposits).

Under the provisions of Pillar 2, the banks internal processes and risk systems will be

under direct supervision. It is likely that the regulator will make regular visits to the banks they regulate and discuss the risk measurement and management systems,accounting management information systems and the reporting lines between riskmanagement personnel and the top management of the bank.

Question 47.4

What factors would you expect the regulator to take into account in assessing a banksrisk profile and risk management systems?

Pillar 3 deals with the disclosure requirements of the Accord. These includequantitative and qualitative details on the banks:

financial condition and performance

business activities

risk profile

risk management activities.

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Lets define the leverage ratio as (broadly):

assets and commitmentsleverage ratio =

regulatory capital.

Therefore the maximum leverage ratio achieves a similar objective to the minimumsolvency ratio, because if the leverage ratio increases, the solvency ratio decreases.

So why bother with both requirements? The leverage ratio is in place to limit a banksability to manipulate its solvency ratio by adjusting its risk-weighting and creditcommitments.

The European Commission has also added requirements that:

The minimum solvency ratio should be 9% for EU banks (instead of 7%) EU banks must comply wit h th is level in June 2012 (instead of 2019).

Asset and liability management

On the asset and liability management side two new ratios have beenintroduced:

Liquidity Coverage Ratio (LCR) this requires that the high-quality highly-liquid assets held must exceed the net cash outflows for the following 30days.

In other words, this requires that banks always have sufficiently liquid assets tomeet their short-term liabilities.

Net Stable Funding Ratio (NSFR) this requires that long-term financialresources exceed long-term commitments, where long term means morethan one year.

In other words, this requires that banks always have sufficiently longer-termassets to meet their longer-term liabilities.

The main change for banks is i n the liquidit y ratios (LCR and NSFR). Thedefinitions are very severe for the corporate sector.

Effects of Basel III

Basel III aims to sharply deleverage the economy.

Deleveraging the economy means reducing the levels of debt in the economy, ie inthe private sector and the government sector.

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This threatens economic growth at the same time as the debt crisis putspressure on governments to spend less.

This is because lower levels of borrowing will lead to lower spending and hence lower

economic growth.

The need to deleverage the economy is import ant, but the design of Basel III hasmeant that the corporate sector must rely, to a large extent, solely on fundingand hedging from outsi de of the banking sector. The basic role of redistribu tingfinancial risk and fund trade has been taken from the banks.

In other words, by reducing the levels of debt in the economy ( ie, banks being unable tolend as much money), the corporate sector has had to raise finance through other means,such as hedging arrangements.

1.3 Solvency II for insurers

The Basel Accords p rovide a measure of capital adequacy for banks. Solvency IIis a comparable solvency requirement for insurance companies risks . It isintended that this will be a required regulatory regime for all European Union(EU) states.

Solvency II will succeed Solvency I(!). Solvency I prescribes minimum additionalsolvency capital amounts that apply to EU insurance companies. However, theseadditional solvency capital amounts are not very sensitive to the actual risks faced byinsurance companies and they sit on top of provisions that vary considerably in theirlevels of prudence between the different EU member states with the result that theoverall solvency capital requirement also varies considerably.

Solvency II will be much wider ranging than Solvency I and consider more than justadditional solvency capital amounts, eg it will include the determination of the value ofthe assets, the valuation of provisions and assessment of companies risk managementsystems.

The new framework will be based on th ree Pillars:

1. quantific ation of risk exposures and capital requirements

2. a superviso ry regime

3. disclosure requirements.

Youll notice the similarity between these three and the three Pillars of Basel II.

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Pillar 1 of Solvency II will include rules for valuing both the assets and provisions forliabilities and also the determination of two levels of capital requirement , ie a minimumcapital requirement (MCR) and a solvency capital requirement (SCR). These two aredescribed further below.

Whereas Pillar 1 is quantitative , Pillar 2 deals with qualitative aspects, eg a companysinternal controls and risk management processes. As in Basel II, the Pillar 2supervisory regime includes monitoring visits to companies by the regulator.

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Chapter 47 Summary

Regulatory capital

A regulatory solvency capital requirement is the total of:

the margins between the best estimate basis and the regulatory liability valuation basis

an amount of additional capital in excess of the regulatory provisions.

Basel I (the Basel Accord)

Basel I required banks to hold capital equal to 8% of the value of their assets, with risk

weightings for the various categories of assets.

A banks available capital is split into two types:

1. Tier 1 capital or core capital shareholders equity and disclosed reserves

2. Tier 2 capital or supplementary capital revaluation reserves, general provisions, hidden reserves, subordinated debt and certain other approved capitalinstruments.

At least half of the required capital amount should be covered by Tier 1 capital.

Basel II

The main rationales behind Basel II are:

to provide a capital adequacy methodology that is more clearly driven by risk

to reward banks that have developed effective risk measurement / managementsystems by allowing them to hold less capital.

Basel II is based on three Pillars:

1. quantification of regulatory capital requirements

2. a supervisory regime

3. disclosure requirements.

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Basel III

The main aims of Basel III are:

to reduce the amount of debt in the economy by restricting banks ability to lend increase the security of banks by ensuring they have enough funds to meet their

liabilities.

Basel III attempts to achieve these aims by means of regulatory capital requirementsand asset / liability management.

However, this comes at the cost of increasing strain on already struggling economies.

Solvency II

Solvency II is also based on three Pillars:

1. quantification of risk exposures and capital requirements

2. a supervisory regime

3. disclosure.

Solvency II will establish two levels of capital requirements:

Minimum Capital Requirement (MCR) the threshold at which companies willno longer be permitted to trade

Solvency Capital Requirement (SCR) the target level of capital below whichcompanies may need to discuss remedies with their regulators.

The SCR may be calculated using a prescribed standard model or a companys internalmodel.

Using the standard model has the advantage that the SCR calculation is less complexand less time-consuming. However, the standard model has the disadvantage that it

aims to capture the risk profile of an average company, and approximations are made inmodelling risks which mean that it is not necessarily appropriate to the actualcompanies that need to use it.

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Economic capital

Economic capital is the amount of capital that a provider determines is appropriate to

hold given its assets, its liabilities, and its business objectives.

It is an internal, rather than a regulatory, capital assessment.

Typically it will be determined based upon:

the risk profile of the individual assets and liabilities in its portfolio

the correlation of the risks

the desired level of overall credit deterioration that the provider wishes to beable to withstand.

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