CA1-PU-14

CA1: CMP Upgrade 2013/14

Page 1

Su b ject CA 1 CMP Upgrade 2013/14 CMP Upgrade This CMP Upgrade lists all significant changes to the Core Reading and the ActEd material since last year so that you can manually amend your 2013 study material to make it suitable for study for the 2014 2014 exams. It includes replacement pages and additional pages where appropriate. appropriate. Alternatively, you can buy a full replacement set of up-to-date Course Notes at a significantly reduced price if you have previously bought the full price Course Notes in this subject. Please see our 2014 Student Brochure for more 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 and Answer Bank that will make them suitable for study for the 2014 exams.

The Actuarial Education Company

© IFE: 2014 Examinations Examinations

Page 2


1

Changes Changes to the Syllabus objectives obj ectives and Core Reading Reading

1.1 1.1

Syllabus objecti ves Syllabus objective 1.3 has been changed to: 1.3

1.2 1.2

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

Core Reading 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 and Faculty of Actuaries”. All references to open-ended investment companies (OEICs) have been removed (this is most 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 the futur e” indic ates ates the areas areas where the actuarial techniques learnt in th e CT CT subjects, and the application skills in this course and elsewhere lead to a particular rol e for actuaries.

Chapter 7 Page 9

The first sentence now reads: “ A pure endowment endowment pro vides a benefit benefit on sur vival ...” ...”



Page 2


1

Changes Changes to the Syllabus objectives obj ectives and Core Reading Reading

1.1 1.1

Syllabus objecti ves Syllabus objective 1.3 has been changed to: 1.3

1.2 1.2

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

Core Reading 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 and Faculty of Actuaries”. All references to open-ended investment companies (OEICs) have been removed (this is most 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 the futur e” indic ates ates the areas areas where the actuarial techniques learnt in th e CT CT subjects, and the application skills in this course and elsewhere lead to a particular rol e for actuaries.

Chapter 7 Page 9

The first sentence now reads: “ A pure endowment endowment pro vides a benefit benefit on sur vival ...” ...”




Page 3

Chapter 16 Page 4

The first sentence of Core Reading now reads: The runnin g yield (ie ( ie rental rental yield) yield) on property varies with t he type of building.

Chapter 18 Page 7

As stated above, all references to OEICs have 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 you remove pages 3 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 th e model using selected values of the variables 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 use replacement pages 7 8c provided below. 





Page 4


Page 11

The following sentence of Core Reading has been added to the section on just-in-time funding: If the anticipated risk event does not happen then terminal funding or a pay-as-youpay-as-you-go 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 use replacement 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 Policy Committee and and the Prudential Regulation Regulation A uthori ty.

Chapter 43 Page 5

The Core Reading and ActEd text on Tail VaR has has been re-written. We recommend that 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 use replacement pages 7 8e provided below. 






Page 5

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 been deleted.


© IFE: 2014 Examinations

Page 6

2


Changes to the ActEd Course Notes All references to the “Board for Actuarial Standards (BAS)” have been changed to “the Financial Reporting Council (FRC)”. All references to “the Actuarial Profession” have been changed to “the Institute and Faculty of Actuaries”. All references to open-ended investment companies (OEICs) have been removed (this is most 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 on government 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.”




Page 7

Page 25

The section on running yields now reads: “Historically, running yields on conventional bonds have typically been higher than running yields on equities and property. This is because income on equities and property is expected to grow over time, creating capital gains. Conversely, since the income 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 to increased 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 uncertainty that followed 2008 however, running yields have been more volatile, which makes a comparison 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...”



Page 8


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 life insurance company of investments, such as bonds, which have historically offered a higher running yield.

Chapter 24 Page 3

6

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



Chapter 32 Page 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 and use replacement pages 7 8c provided below. 






Page 9

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 Notes and 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 recommend that 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 being a shortfall. Page 17

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





Page 10


Chapter 44 Page 3

The last sentence has been corrected and now reads: “...such as critical illness insurance ...”

Chapter 47 Page 8

As stated above, 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 use replacement pages 7 8e provided below. 



Page 17

The Chapter Summary now reflects the new Core Reading on Basel III. We recommend that you remove pages 17 18 from your Course Notes and use replacement pages 17 18c provided below. 






3

Page 11

Changes to the Q&A Bank Part 4 Solutio ns 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

[½]

Page 16

In the section on “ Return”, the last half mark now reads: Running yields have been more volatile since the economic uncertainty that followed 2008 however, which makes comparisons between the two asset classes more difficult. [½]



Page 12

4


Changes to the X Assignments This section provides details of material changes that have been made to the 2013 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 the 2014 version of the assignments.

As si gn men t X3 Sol ut ion s Page 17

The section on reinvestment risk now reads: Historically, conventional bonds have generally earned a higher running yield than equities. Consequently, they involve a greater risk of reinvestment of income on uncertain terms. [½] However, recent economic uncertainty has made it more difficult to compare running yields for different asset classes. [½]


The sixth bullet point under “ Differences” now reads: 

property has historically offered higher running yields

[½]


In Solution X5.8, another half mark has been added to the section on conventional government bonds. This reads: This assumes no default risk on government bonds.


[½]



Page 13

As si gn men t X6 So lu ti on s Page 5

The second point now reads: Ordinary shares (and most properties) have historically given a lower running yield than government bonds. [½]

As si gn men t X7 So lu ti on s Page 12

In Solution X7.5 part (ii), replace the second and third points with: … because this is mainly a unit linked product ...

[½]

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

[½]

Page 14

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

waiting periods starts

this is the period after the sale of the policy, before cover



[½] 

deferred periods this is the amount of time the policyholder must be ill for, before the benefit becomes payable [½] 



Page 14

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 ActEd’s 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 great alternative to a tutorial)

For further details on ActEd’s tutorials, please refer to our latest Tuition Bulletin , which is available from the ActEd website at www.ActEd.co.uk .




5.3

Page 15

Marking You can have your attempts at any of our assignments or mock exams marked by ActEd. When marking your scripts, we aim to provide specific advice to improve your chances of success in the exam and to return your scripts as quickly as possible. For further details on ActEd’s marking services, please refer to the 2014 Student Brochure, which is available from the ActEd website at www.ActEd.co.uk .



Page 16

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 certain sections of the notes or particular questions) or general suggestions about how we can improve the study material. We will incorporate as many of your suggestions as we can when 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 .



CA1-24: Valuation of asset classes and portfolios

1.3

Page 3

The analysis The relative value of different asset classes can be analysed by considering the relationship between the expected and required returns . The expected return and the required return can each be broken int o compo nent 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 three components, based on a return in excess of inflation and a premium to compensate for the risk and all ot her features of t he 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 t he expected return is dif ferent from the required return. If there is a market in index-linked government bonds the required risk-free real yield can norm ally be taken as the real yield on these bonds. In the discus sion below a number of simplify ing assumpti ons are made: ●

that all investors want a real rate of return

●

all investors have the same time horizon for investment decisi ons

●

tax differences between investors can be ignored (in particular, we assume

that we can use gross yields) ●

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

equations below ●

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

In reality all o f th ese assumpt ions are questionable.



Page 4


Under these assumptions, the expected returns between different asset categories should be consistent with each other. Note that “consistent” does not necessarily mean “equal”, eg the expected return from a risky asset might be consistent with the expected return 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 as the timing and reinvestment of investment income. For each of the main asset categories, the expected return from a portfolio of assets will be equated with the required return for that asset category. The equations derived are valid if th e assets consi dered are fair v alue relative to each other.

1.4

Convention al gov ernment bon ds The expected return i s taken to be the gross redemption yield (GRY), if the bond is consi dered to be free from th e risk of default. Equating the expected return with 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 on government 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 2½% pa and we might require an inflation risk premium of 1% pa to cover the risk of higher inflation eroding our real returns. Now, if we know that we can earn a risk free real return of 2% pa on indexlinked government bonds, then conventional government bonds will be cheap to us if their gross redemption yields exceed 5½% pa.




Page 5

Question 24.2 An investor with real liabilities expects future inflation to average 2½% pa. The investor requires a return from conventional government bonds of 1% pa more than the return from index-linked government bonds in order to compensate for the inflation risk on conventional government bonds. If the yield on conventional government bonds is 5% pa would the investor choose to purchase index-linked stocks yielding 2% pa real or the conventional stocks?

1.5

Corporate loan sto cks A si mi lar dev elopm ent of th e gr os s redemp ti on yi eld (GRY) is po ss ib le fo r corporate loan st ocks: GRY = required risk-free real yi eld + expected inf lation + bond risk premium Investors require a higher yield than from conventional government bonds to compensate for the greater risk of d efault and the lower marketability. Therefore the bond risk premium has three main compo nents: ●

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 it until redemption, provided that the bond does not default (and ignoring reinvestment risk, 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 may wish 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 redemption yield reflecting the expected losses from defaults which are incorporated in the default premium.

For comparison purposes, as the expected return is net of the impact of expected defaults, 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 the uncertainty surrounding defaults ( ie the risk that the actual level of defaults turns out to be different to the expected level).



Page 6a


In the discussions for other asset classes below, the formulae for the expected returns ignore the expected impact of default (and other) risks, and the formula for required returns 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 th e income stream, ie the dividend yield g is the expected capital gain, ie the expected annual growth in dividends.

Therefore: d + g = required risk-free real yield + expected inflation + equity r isk premium The equity risk p remium is needed to comp ensate the investor fo r: ●

possible default

●

marketability

●

high vol atility of share prices and dividend income.

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

1.7

Property The form of the equation for property investment is very similar to the equation for equities: rental yield + expected growt h in rents = required risk -free real yield + expected inflatio n + property risk premium




Page 6b

Question 24.3 How would you expect the property risk premium to compare with the equity risk premium?

1.8

Two reminders 1.

With all of the yield models we developed above, the equalities apply only where the assets are correctly priced. To demonstrate that an investment sector is cheap or dear, we need to show that the equality does not hold.

2.

We could develop similar equations using nominal yields ( eg those available on long-dated conventional government bonds) rather than real yields as the benchmark.



Page

6c


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



CA1-32: Expenses

2

Page 7

Expense allocation – princip les This section provides an overview of the principles of expense allocation. Expenses need to be allocated between: ●

classes of business, and

●

functions.

By “function” we mean “activity” or “operation”. For example, the expense might relate 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 they can 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 about loading expenses into premiums later in this section.

Question 32.3 Other than determining the expense loading for premiums, for what other purposes do expenses 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 be allocated to different types of business i n 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 lo catin g di rec t expens es Direct expenses may arise from a department dealing purely with one class of business, in which case the expenses relating to that department can immediately be allocated to the relevant class. If direct expenses arise from areas dealing with more than one class of business then timesheets can be kept (either for a period o r permanently) to help sp lit c osts between classes.



Page 8a

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 each of these classes based on the time that was recorded as being spent underwriting each of them. Staff timesheets can be used to collect this information.

Al lo cating in di rect expen ses The indirect expenses are harder to allocate. By definition , the departments concerned are not related directly to any particular class of business, but form a suppor t funct ion for the provider. In this case, it is necessary to find a sensible apportionm ent of the expenses across di rect business activit ies.

We must allocate indirect expenses to the different classes of business. There is no single correct approach for this, but it may help to allocate the expenses to different departments (ie business activities) first, as an intermediate step. Finally, we must allocate expenses according to the timing of when the expenses were incurred (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 and related staff c ould be charged to the direct func tion departments based on actual use.

Computer usage Some computer usage will be readily identifiable as belonging to one product line and one 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 relevant class of business. However, some expenses, eg a company’s internal electronic mail system, would not be readily identifiable as belonging to any one department or product. They could first be allocated 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 class of business in the same proportion as the salary allocation of the employees in each department, ie according to a timesheet analysis.



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 to allocate the salary cost. Different companies will take different approaches to allocating these remaining staff costs, one approach may be to allocate them to product line (and function) in the same proportions as for the costs that have already been identified. 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’ co sts can be allocated by f loor space taken up b y a department.

If a company owns a property, then this is an asset to the company and ought to be earning a return (rental income) from its tenant. However, since the company is occupying its own property, no such rent is forthcoming. In effect, this is a cost to the company. Therefore, a notional rent needs to be charged to the departments who occupy the building. This notional rent, plus property taxes, heating costs etc, can be split, for example, by floor space occupied, between departments. Thereafter, property costs can be allocated to a class or classes of business in proportion to the allocation of the salaries of the employees of that department (which should already 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 or computer 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.



Page

2.2

8c

CA1-32: Expenses

Allocating expenses by functio n As wel l as appor ti on in g exp ens es to a li ne of bu si ness, co st s need to be apportioned by function, so that they can be allowed for in determining product pricing or the provisions for future liabilities.



CA1-39: Sources of risk

Page 11

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

Liquidity risk for co llective investment schemes Similarly, collective investment schemes and insurance funds that invest in real property need to protect t hemselves if cl ients request access to their funds w hen the underlying properties cannot be sold. Such funds frequently have the power to defer withdrawals by up to six months if necessary, to allow time for property sales. Hedge funds that invest in illiquid assets also often have lock-in periods to 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 than expected wish to sell their units.

Managing liquidity risk Financial companies will maintain a degree of liquidity to deal with anticipated liability withdrawals. In the event of these withdrawals being greater than expected, the company may have to convert some of its less liquid assets to cash or else try to borrow additional funds (which may be unavailable or expensive). Financial companies can allow for liquidity risk to some extent, by allowing a margin for withdrawals being higher than they expect and by allowing for predictable seasonal variations (eg higher bank withdrawals pre-Christmas). Typically, the biggest liquidity risk issues for a financial company arise as a result of a sudden surge in liability withdrawals.

Question 39.6 Why might there be a sudden surge in customers withdrawing their deposits from a bank?



Page 12

3.2

CA1-39: Sources of risk

Market liqu idit y ris k In the context of the financial markets, liquidity risk is where a market does not have the capacity to handle (at least, without a potential adverse impact on the price) the volume of an asset to be bought or sold at the time when the deal is required. In general, the larger a market is, the more liquid it wi ll be, because more participants in th e market will be trading at any one time. Thus when any member of the market wishes to complete a trade, it is likely that the market will be able to find a count erparty willi ng to accept the trade. This partic ular definition of liquidity is frequently also called marketability.

The terms marketability and liquidity are often used interchangeably. Strictly speak though, 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 a short-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 if required.

2.

The amount of cash it will or could become is (almost) certain. (For example, 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 the market value is quite volatile.)

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

Example A seven day fixed-term deposit at a bank is a highly liquid asset because it will become cash within a week. However, such deposits cannot be traded, so they are completely unmarketable. 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 the market value is quite volatile. (We discussed the relative marketability of short-term and long-term bonds when we met the liquidity preference theory in Chapter 14.)



CA1-43: The risk management process (2)

Page 5

Probability

5%

-10

0

Underperformance relative to benchmark

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

Remember that the normal distribution bell cuts off at around three standard deviations from the mean. However, if the underlying distribution is not normal, but skewed, the tail may be much longer than three standard deviations. Unfortunately, portfolios exposed to credit risk, systematic bias or derivatives may exhibit non-normal distri butio ns. The usefulness of VaR in these situatio ns depends on modelling skewed or fat-tailed distributions of returns, either in the form of statistic al distr ibuti ons or via Monte Carlo simulation s. However, the further one gets out into the “ tails” of the distributions, the more lacking the data and, hence, the more arbitr ary the choice of th e underlying pro bability becomes.

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

2.4

Expected shortf all (or Tail VaR) You may find some of the material below familiar, if you have recently studied Subject CT8. Closely related to both shortfall probabilities and VaR are the Tail VaR and Expected Shortfall m easures of risk .



Page 6a


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

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

Expected Shortfall = E ÈÎ Max (L - X ,0 ) ˘˚ =

Ú (L - x )f ( x )dx

-•

where L is t he chosen benchmark level. If L is chosen to be a particular percentile point on the distribution, then the risk measure 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 conditional on there being a shortfall.

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

Questi on 43.1

(CT8 revi sion)

Consider an investment portfolio of £100m whose returns per annum follow a continuous uniform distribution with probability density function: f ( x) =

1 for -0.05 £ x £ 0.05 0.1

(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 ition al VaR

●

worst conditional expectation.




Page

6b

They all measure the risk of underperformance against some set cri teria. Downside risk measures have also been proposed based on an increasing function of (L - x ) , rather than (L - x ) itself in th e integral above.

In other words, for continuous random variables, we could use a measure of the form: L

Ú -• g ( L - x) f ( x) dx Two particular cases of note are when: 1.

g ( L - r ) = ( L - r )2 – this is the so-called shortfall variance

2.

g ( L - r ) = ( L - r ) – the average or expected shortfall measure defined above.

Shortfall measures are useful for monitoring a fund's exposure to risk because the expected underperformance relative to a benchmark is a concept that is relatively easy t o und erstand.

Shortfall measures do ignore upside risk however, ie returns in excess of L are ignored. Example If we believe our average loss on the worst 5% of the possible outcomes for a portfolio is $5 million, then we could say our expected shortfall is $5 million for the 5% tail.



Page

3

6c


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 a range of high impact but low probability risks. These are among the most difficult to manage; they are likely to include both risks related to normal business activities and operational risks. It is important to manage such ris ks in a measured way. In partic ular because credit rating agencies and regulatory authorities pay significant interest to the ability of a company to withstand rare events, there is a temptation for management to concentrate unduly on such risks at the expense of the broad range of risk s 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 loss of business premises by fire, but has attendant additional costs if a total loss by fire does not occur.

●

can be passed to an insurer or reinsurer, usually by some form of catastrophe 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 to determine the amount of capital that it is necessary to hold against the risk event. The techniques of scenario analysis , stress testing and stochastic modelling di scuss ed in the next section enable this to be done. Finally a company will have determined its own risk tolerance – for example the ability to withstand an event that might occur with a 0.5% probability within one year. This means that the company accepts that it might be ruined by a rarer event, and has decided not to take such events into account in its risk management.




Page 17

Chapter 43 Solution s Soluti on 43.1 (i)

VaR

The VaR is given by t such that: t

1

Ú

VaR =

-0.05 t

Ú -0.05

1 0.1

0.1

dx = P( X < t ) = 0.05

dx = 0.05

Hence: t

È 1 ˘ = 0.05 ÍÎ 0.1 x ˙˚ -0.05 t - ( -0.05)

0.1

= 0.05

t = - 0.045 ie the VaR is 0.045 ¥ 100 m = £4.5 m over the next year.

In other words, we are 95% certain that we will not make a loss of more than £4.5 m over the next year. (ii)

Tail VaR

The Tail VaR is given by: -0.045

Ú

-0.05

( -0.045 - x)

1 0.1

dx = -

1 0.1

-0.045

Ú

(0.045 + x) dx

-0.05 -0.045

1 È 1 2˘ =+ 0.045 x x 0.1 ÍÎ 2 ˙˚ -0.05

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



Page 18a


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

(iii)

Conditional Tail VaR 12,500 0.05

= £0.25 m

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

Soluti on 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 property are both correlated to inflation.

Soluti on 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- and long-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 of cyclical effects linked to the economy.




Page 1 8b

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

Soluti on 43.4 Stochastic modelling could involve the following steps: ●

●

●

specify the purpose of the investigation, including a time horizon, a measurable criteria and a probability confidence limit collect, group and modify data choose a suitable density function for each of the variables to be modelled stochastically

●

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 past year 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 chosen density function(s) produce a summary of the results that shows the distribution of the modelled results after many simulations have been run.

Soluti on 43.5 May be less than the sum of individual risks due to the impact of diversification or negative correlation.



Page

18c


This page has been left blank so that you c an slot t he replacement pages into your Course Notes



CA1-47: Capital management (2)

Page 7

Under Pillar 1, in relation to credit risk , there is a standardised approach (which is a modification of the Basel I risk weightings approach) and an internal-ratings based approach that may be adopted by banks able to demonstrate that they have sufficiently sophisticated systems, allowing them to hold less capital. Additional capital requirements apply for market and operational risk. Pillar 2 deals wit h superviso ry iss ues, economi c capital and interest rate risk and is based on four interlocking pr inciples: 1.

Banks are required to have a process for assessing their capital requirements 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 minimu m.

4.

Supervisors shoul d intervene at an early stage to prevent capital from falling below the level required to sup port t he bank’s ri sk characteristic s.

Here interest rate risk refers to the potential risk arising from a mismatch of duration between a bank’s assets (eg mortgages) and liabilities (eg customer deposits). Under the provisions of Pillar 2, the bank’s 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 risk management 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 bank’s risk profile and risk management systems? Pillar 3 deals with the disclosure requirements of the Accord. These include quantitative and qualitative details on the bank’s: ●

financial condition and performance

●

business activities

●

risk profile

●

risk management activities.



Page 8a


The Basel Committee envisages that, as a result o f th e Accord, th e total amount of regulatory capital supporting banks world-wide will remain unaltered, but that its distribution will shift from less risky activities to more risky activities. One outstanding problem, however, is how a bank’s exposure to operational risk can be measured.

This is largely due to the lack of historical and publicly-available data that can be used to assess this risk compared to say credit risk and market risk.

Basel III Basel III, introduced in 2013 for implementation by 2019, is intended to strengthen bank capital requirements by increasing bank liquidity and bank leverage.

There has been much discussion around what changes should be made to banking regulation following the financial collapse of 2008 and the economic turmoil which followed. Basel III aims to address these concerns. It is divided in two main areas: Regulatory capital and asset and liability management.

We now discuss these two areas below. Regulatory capital requirement The regulatory capital requirement is that banks must progressively reach a minimu m solvency ratio , where the solvency ratio is defin ed as: Solvency ratio =

Regulatory capital Risk-weighted assets

The minimum solvency ratio is to be 7% by 2019 compared with the previous minimu m requirement of 2%.

The effect of a minimum solvency ratio is to reduce the amount of lending that banks can offer to companies and consumers. Note that banks do not have to reach this minimum solvency ratio immediately, because this would cause severe strain to many banks. Instead, they are being allowed to work towards this target over several years. Basel III also introd uces a “ leverage ratio” such t hat the amounts of assets and commitments should not represent more than 33 times the Regulatory Capital. This is regardless of the level of their risk-weighting and of whether credit commit ments are drawn down.




Page

8b

Let’s define the leverage ratio as (broadly): leverage ratio =

assets and commitments regulatory capital

.

Therefore the maximum leverage ratio achieves a similar objective to the minimum solvency 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 bank’s ability to manipulate its solvency ratio by adjusting its risk-weighting and credit commitments. The European Commission has also added requirements that: ●

The minimum s olvency ratio should be 9% for EU banks (instead of 7%)

●

EU banks m ust compl y wit h th is level in June 2012 (inst ead of 2019).

Asset and liability management On the asset and liability management side two new ratios have been introduced: ●

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

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

Net Stable Funding Ratio (NSFR) this requires that long-term financial resources exceed long-term commitments, where long term means more than one year.

In other words, this requires that banks always have sufficiently longer-term assets to meet their longer-term liabilities. The main change for banks is i n the liquidit y ratios (LCR and NSFR). definitio ns are very severe for the corpor ate sector.

The

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 in the private sector and the government sector.



Page

8c


This threatens economic growth at the same time as the debt crisis puts pressure on governments to s pend 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 th e design of Basel III has meant that the corporate sector must rely, to a large extent, solely on funding and hedging from outsi de of the banking sector. The basic role of redistribu ting financial risk and fund tr ade has been taken from th e banks.

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

1.3

Solvency II for insu rers The Basel Accords p rovid e a measure of capital adequacy for banks. Solvency II is a comparable solvency requirement for insurance companies’ risks . It is intended that this will be a required regulatory regime for all European Union (EU) states.

Solvency II will succeed Solvency I(!). Solvency I prescribes minimum additional solvency capital amounts that apply to EU insurance companies. However, these additional solvency capital amounts are not very sensitive to the actual risks faced by insurance companies and they “sit on top of” provisions that vary considerably in their levels of prudence between the different EU member states with the result that the overall solvency capital requirement also varies considerably. Solvency II will be much wider ranging than Solvency I and consider more than just additional solvency capital amounts, eg it will include the determination of the value of the assets, the valuation of provisions and assessment of companies’ risk management systems. The new fr amework w ill b e based on th ree Pillars: 1.

quantific ation of risk exposures and capital requirements

2.

a superviso ry regime

3.

discl osure requirements.

You’ll notice the similarity between these three and the three Pillars of Basel II.




Page

8d

Pillar 1 of Solvency II will include rules for valuing both the assets and provisions for liabilities and also the determination of two levels of capital requirement , ie a minimum capital requirement (MCR) and a solvency capital requirement (SCR). These two are described further below. Whereas Pillar 1 is quantitative , Pillar 2 deals with qualitative aspects, eg a company’s internal controls and risk management processes. As in Basel II, the Pillar 2 supervisory regime includes monitoring visits to companies by the regulator.



Page

8e


This page has been left blank so that you c an slot t he replacement pages into your Course Notes




Page 17

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 Acco rd) 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 bank’s 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 capital instruments.

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 / management systems 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.



Page 18a


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 requirements and 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 will no longer be permitted to trade Solvency Capital Requirement (SCR) – the target level of capital below which companies may need to discuss remedies with their regulators.

The SCR may be calculated using a prescribed standard model or a company’s internal model. Using the standard model has the advantage that the SCR calculation is less complex and 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 in modelling risks which mean that it is not necessarily appropriate to the actual companies that need to use it.




Page 1 8b

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 be able to withstand.



CA1-PU-14

Recommend Documents