Faculty of Actuaries Institute of Actuaries
EXAMINATION
April 2006
Subject CA1 Core Applications Concepts
Paper 1 (Assets)
EXAMINERS REPORT
Introduction
The attached subject report has been written by the Principal Examiner with the aim of
helping candidates. The questions and comments are based around Core Reading as the
interpretation of the syllabus to which the examiners are working. They have however given
credit for any alternative approach or interpretation which they consider to be reasonable.
M Flaherty
Chairman of the Board of Examiners
June 2006
Comments
Individual comments are shown after each question and after each part question where
relevant.
General comments
As the title of the course suggests, this subject examines applications of the core techniques
and considers broad actuarial concepts in practical situations. To perform well in this
subject requires good general business awareness and the ability to use common sense in the
situations posed, as much as learning the content of the core reading.
The notes that follow are not to be interpreted as model solutions. Although they contain the
majority of the points that the examiners were looking for, they also contain more than even
the best prepared candidate could be expected to write in the time allowed in the examination
room.
Faculty of Actuaries
Institute of Actuaries
Subject CA1 Core Applications Concepts, Paper 1 (Assets) April 2006 Examiners Report
1 (a) A lifetime mortgage with interest added to capital.
The mortgage amount (less any associated costs) will be received immediately
and no capital or interest payments will be made.
On death, the estate will have the proceeds from the sale of the property, but
will need to pay the capital cost of the mortgage along with all accrued
interest.
(b) A lifetime mortgage with repayments each year (or other regular times).
The mortgage amount (less any associated costs) will be received immediately.
Repayments, which may be fixed or variable, will be payable at regular times.
On death, the estate will have the proceeds from the sale of the property, but
will need to pay the capital cost of the mortgage only.
(c) The home (or a proportion of it) could be sold to a company in return for a
lump sum and the right to live in the property until he died.
The value less associated costs will be received immediately. The value
received would be less than the open market value in view of the right of
residence.
On death, nothing will be received if the entire home was sold. If a proportion
were sold, then the estate would receive the value of the remaining proportion.
(d) The owner could sell the home and move to a cheaper property or rent.
The difference between the two property values after costs have been paid
would be received on sale. Alternatively the net sale price is received, and
regular rent (certain or uncertain) is paid out.
On death, there will be no monies due and the value of the new home (if there
is one) would form part of the estate. If not, the new residence is not part of
the estate.
Comments on question 1:
Marks were given for any two sets of answers under (a) to (d) above. Equity release or home
reversion plans generally address the need for additional income, and were not appropriate
answers, unless the description of the cash flows clearly involved the homeowner receiving
capital. Other methods that involved the homeowner gaining capital were also given credit.
The question was generally well answered. The better candidates included mention of the
costs associated with the options they chose, and concentrated on describing the cash flows,
rather than the plan in general.
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Subject CA1 Core Applications Concepts, Paper 1 (Assets) April 2006 Examiners Report
2 (i) The general formula is:
V= Dt v(t )
t 1
where:
V is the value of the share
Dt is the amount of the tth dividend payment
v(t) is the discount factor applied between time 0 and the time of the tth
dividend payment
The simplified formula is:
D0 (1 g )
V=
(i g )
where:
D0 is the most recent dividend received.
i is the required rate of return
g is dividend growth rate
Credit was also given for defining D0 as the next dividend due provided that the (1 +
g) term was omitted.
(ii) Dividends are paid annually, and the next dividend is payable in one year s
time.
Dividends grow at constant rate g.
The required rate of return is independent of the time at which payments are
received.
Shares are held in perpetuity or are sold at a price consistent with the formula.
Comments on question 2: Many candidates attempts at general formulae were not actually
general; for example they assumed a constant discount rate i. Otherwise the question was
generally well answered.
3 The key features of indices that are suitable to be used with index tracking fund are:
The index should be representative of the equity market.
It needs to be practical to be used as an index tracker, for example avoiding
frequent changes in constituents or being calculated with reasonable frequency
(real time pricing is best).
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Subject CA1 Core Applications Concepts, Paper 1 (Assets) April 2006 Examiners Report
Firms for inclusion should have sufficient liquidity so that full index replication is
possible without causing prices for individual equities to be too volatile.
All firms within the index should be subject to the same financial
reporting/accounting and other standards as far as possible e.g. same market
regulation standards, this is particularly important for investors from overseas
where lack of information, language and poorer market regulation represent
barriers to investment.
For all the above reasons the smallest firms and those firms with a low proportion of
free-float shares are likely to need to be excluded.
A small number of firms may be very large. It may be necessary to restrict the
weighting of these firms because their performance could dominate the whole index.
The country is unlikely to achieve the implicit aim of encouraging investment in a
wide range of firms.
Similarly it may be necessary to restrict weightings where there are large proportions
of closely held holdings that are not traded as they could cause distortions to the
index.
Restricting the representation of the largest firms and non-free float shares will
increase the diversity within the index and therefore reduce the level of specific equity
risk.
Having identified firms and the extent to which they are suitable for inclusion then the
country needs to consider how many indices/sub-indices should be created. Initially
the country is likely to restrict the number of indices to a few as it will be easier to
create a domestic and international profile for the indices and therefore assist the
encouraging domestic equity investment.
There may be a variety of tax bases applying to potential users of the index. The
country may want to calculate indices that allow for these differences (e.g.
withholding tax for overseas investors).
The index should try to reflect the actual accrual of dividend income in the market.
Comments on question 3: This question was not well answered. The main problem was that
many candidates gave a good list of what needed to be considered when constructing indices
in general (coverage, weightings, calculation frequency, updating constituents, etc.), but then
did not relate their answers to the specific circumstances of a developing economy. In the
type of question that requires a general concept to be considered in specific circumstances it
is necessary to give equal attention to the specific circumstances and to the general concept.
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Subject CA1 Core Applications Concepts, Paper 1 (Assets) April 2006 Examiners Report
4 Corporate bonds may have enjoyed very good performance relative to all other asset
classes. This may have encouraged new investors.
There may be a general trend towards more secure assets, as there may be uncertainty
in the political or economic climate. For example, it may be felt that the economy is
moving towards recession and future returns on equities will be poor, or that investors
are taking profits from other classes and reinvesting in corporate bonds.
There may have been an overall change in investors liabilities, or recognition of such
a change. For example, pension schemes may have come to realise that a greater
proportion of their liabilities are guaranteed than they have thought guaranteed in the
past, and may have moved into bonds.
There may have been an improvement in investor education so that bonds have been
purchased as a better match for particular liabilities.
In the opinion of investors, the difference between returns on corporate bonds and
government bonds may more than allow for the additional risks. This may have
caused investors to accept the additional risks in exchange for the extra return. One
reason for such a market distortion could be supply related (either oversupply of
corporate or undersupply of government bonds)
There may have been a change in the regulatory regime. For example, the
government may have forced benefit schemes to match their liabilities more closely
by investing in bonds.
There may have been a change in the tax regime so that bonds are now treated more
favourably relative to other assets.
It may be part of investor fashion. If bonds are seen to be popular, more and more
investors may move into them. Being out of step with everyone else is a risk.
If this is not an industry trend, the fund may have had good past performance relative
to competitors, which has attracted new investors. The fund may be managed by a
highly rated fund manager.
There may have been improved marketing and publicity of this fund, for example an
advertising campaign, new literature or a special offer.
Comments on question 4: Performance on this question was very variable. Many candidates
seemed to find several different ways of saying bonds looked cheap . The better candidates
considered matching issues; looked at the yield differentials with other asset classes and
argued risk versus return; and then picked up some of the softer points such as quality of
manager.
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Subject CA1 Core Applications Concepts, Paper 1 (Assets) April 2006 Examiners Report
5 The price of an equity that is regularly traded is a figure that equates the expectations
of a willing buyer and a willing seller.
The key drivers of price are the current level of income, the growth in that level of
income and the uncertainty over that growth. There are elements of subjectivity in
assessing these items, and the further the amounts are in the future the greater the
uncertainty.
There are also elements of sentiment that drive the precise price level, such as the
market s view of the ability of the board and management team.
The price of shares will reflect the latest information including:
announced post balance sheet events
trading conditions affecting the market sector
market speculation about unannounced events, such as mergers and takeovers
The company s earnings is a retrospective accounting measure. The level of
retrospective earnings may not be representative of the future, for example they may
include the effect of historical events such as exceptional items, or particularly good
or poor past results. Different accounting policies may make comparison of quoted
earnings tricky.
Earnings may result from a period where the company was fundamentally different,
due, for example, to corporate restructuring.
The companies may be in completely different industries or market sectors, which
traditionally trade at different P/E ratios. Some companies (e.g. property companies)
are not valued on an earnings basis and P/E ratios are largely irrelevant to them.
The way in which earnings are distributed may distort P/E ratios.
P/E ratios of two firms may also differ due to a combination of all the factors outlined
above.
Comments on question 5: Although price earnings ratio is not a defined term in the core
reading, the concepts of market price and corporate earnings are both well covered. Sadly a
number of candidates based their answers on dividend yield issues (i.e. price/dividend ratios)
and scored few marks. Potential distorting effects were not well covered, but most
candidates pointed out the effects of different industries or market sectors.
6 (i) Stock markets in developing countries are more risky markets. They offer
higher returns than developed markets to reflect the additional risk.
Due to rapid industrialisation the rate of economic growth is also expected to
be high. In addition, possible market inefficiencies also generate opportunities
for profitable investment.
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Subject CA1 Core Applications Concepts, Paper 1 (Assets) April 2006 Examiners Report
The economies and markets of many smaller countries are less interdependent
than those of the major economic powers. Therefore investment in emerging
markets may provide diversification.
Competitor funds may be similarly invested, and this fund wants to be in the
pack .
(ii) Emerging markets will differ from each other in practice but points to consider
will generally include the following:
current market valuation
possibility of high or volatile economic growth rate
currency stability and strength
level of marketability
degree of political stability
market regulation
restrictions on foreign investment such as exchange controls
range of companies available
communication problems such as language or time delays
availability and quality of information and accounting standards.
withholding taxes could be more of an issue
expertise in these markets
extra costs such as custody fees
the extent of additional diversity generated.
(iii) Markets in small economies can be affected by the enormous flows of money
generated by changes in sentiment of international investors. For example,
domestic factors in the US that cause investors to repatriate funds, can
completely swamp economic fundamentals in determining the level of local
markets.
Marks were given for any sensible example that specifically related to small
economies.
Comments on question 6: In part (i) many candidates spent too much time talking about
overseas markets in general rather than concentrating on developing economies. Part (ii)
was largely bookwork and was well answered. In part (iii) most candidates made the point
about lack of liquidity, but often it was described in the context of a given investor moving the
market or not being able to sell. The bigger issue of other investors moving the market a lot
due to large cash flows was missed.
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Subject CA1 Core Applications Concepts, Paper 1 (Assets) April 2006 Examiners Report
7 (i) (a) Arbitrage The simultaneous buying and selling of two economically
equivalent but differently priced portfolios so as to make a risk free
profit.
(b) Spot interest rate The n year spot interest rate is the geometric
average of the interest rates that are expected to apply over the next n
years. It is the redemption yield on an n year zero coupon bond.
(ii) (a) Expectations theory Expectations theory describes the shape of the
yield curve as determined by economic factors which drive the
market s expectations for future short-term interest rates.
(b) Liquidity preference theory Investors require a greater return to
encourage them to commit funds for a longer period so yields should
be higher for long-dated stocks.
(c) Market segmentation theory Yields at each term are determined by
supply and demand from investors with liabilities of that term so yields
on short and long bonds may therefore move somewhat independently.
(iii) To cost the guarantee, it is necessary to estimate future 1 year yields (using the
above theories and the yield curve) and compare these rates to the possible
guaranteed rate.
The yield curve is upward sloping so based on the expectations theory the
market expectations for future short-term (1-year) interest rates is that the one-
year rates will progressively increase.
Part of the upward slope of the yield curve relates to liquidity rather than the
expectation of increases to short-term rates. Thus based on the liquidity
preference theory using the yield curve to estimate future short-term rates risks
overestimating future rates therefore understating the cost of the investment
guarantee.
Market segmentation theory says that the yields on long and short bonds may
move somewhat independently, so the yield curve does not necessarily predict
the future short-rates so care should be exercised in using the yield curve to
anticipate the future cost of investment guarantees.
Using the initial yield curve to anticipate the cost of investment guarantees
risks mis-stating the anticipated cost, however, there may be no better
objective information available.
If there is other market information indicating that future short-term yields
will be different from those predicted from the initial yield curve then this
suggests an arbitrage opportunity exists.
Initial market yield information should therefore be used carefully and with
judgement when estimating the cost of investment guarantees.
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Subject CA1 Core Applications Concepts, Paper 1 (Assets) April 2006 Examiners Report
The yield curve will vary over time. Uncertainty over predicting future yield
curves will increase the further in the future the prediction is required there
is an expanding funnel of doubt. Therefore the actual cost of the investment
guarantee may be considerably different from that anticipated at outset.
Comments on question 7: This was the least well done question on the paper. Considering
that part (i) was bookwork definitions, very few did well. Part (ii) was much better;
definitions tended to be both tight and relevant. Very few candidates did well on part (iii).
Many started by not understanding how the contract works overestimating future zero-
coupon yields results in underestimating the cost of the guarantee; inadequate reserves will
be established and the company will be financially exposed. The question was designed to
explore the effects of the three theories together on the overall approach, not each theory
separately.
8 (i) The main factors that will influence a long term investment strategy are:
The nature of the existing liabilities fixed in monetary terms, fixed in
real terms, or varying in some other way.
The currency of the existing liabilities.
The term of the existing liabilities.
The level of uncertainty of the existing liabilities both in amount and
timing.
The tax treatment of different investments and the tax position of the
investor.
Statutory, legal or voluntary restrictions on how the fund may invest.
The size of the assets, both in relation to the liabilities and in absolute
terms.
The expected long term return from various asset classes allowing for
expenses.
Statutory valuation and solvency requirements.
Future accrual of liabilities.
The existing portfolio.
The strategy followed by other funds.
The amount of risk that the investor is prepared to take.
The investor s objectives.
Liquidity requirements.
Features of the available assets.
The risks associated with those assets either absolutely or relative to the
liabilities.
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Subject CA1 Core Applications Concepts, Paper 1 (Assets) April 2006 Examiners Report
(ii) (a) The investor s need for income or capital (allowing for existing assets).
In particular, a low risk investor may wish to repay any debt including
mortgage and invest for retirement. A high risk investor will wish to
choose investments with the highest expected return.
The inheritance could be viewed as a windfall so just spend it for fun.
Some assets may be precluded due to the amount of capital available to
invest. A desire for a diversified portfolio may suggest collective
investments.
Individuals will need to consider their tax position and will wish to
invest in tax efficient products.
(b) The investment objective is to create as large a fund or pension as
possible on retirement, although as retirement approaches some
defence against the possibility of falling interest rates is also desirable.
The likely strategy would involve investment in equities and possibly
bonds as well for diversification, transferring more into bonds as
retirement approaches.
The key issues should centre around finding the optimum time to begin
transferring which, may be linked to the contributor s age, and how
regularly to transfer and in what proportions of the fund.
(c) The first priority must be to ensure all liabilities can be met.
The amount of risk that can be taken depends on the financial strength
and on the uncertainty over liabilities. Funds with low financial
strength will need to be invested in high quality bonds of appropriate
terms. If a slightly higher risk can be taken with part of the fund then
equities and property could be considered.
The position of the fund would need to be monitored carefully and
investments changed as it matures.
Unit-linked funds would be invested in accordance with the fund
descriptions issued to policyholders.
(d) The first priority must be to ensure that all liabilities can be met,
allowing for the length of time it might take to achieve settlement and
uncertainty over amounts and timings of payments.
Competitive premiums may require the highest investment return using
asset types permitted by regulations.
It may be important to stabilise profits.
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Subject CA1 Core Applications Concepts, Paper 1 (Assets) April 2006 Examiners Report
Investment policy depends on size of free reserves, and reinsurance
arrangements.
(e) Investment policy may impact on the reputation of the charity, which
will have broad objectives and constraints. The attitude to risk of
trustees/management and contributors should be considered.
It will also be necessary to consider the specific purpose of charity, its
operating considerations, need for investment income and capital.
Impact of the tax status on expected returns.
The amount and timing of contribution income will be relevant.
Comments on question 8: This question was answered well by most candidates. In part (i)
the command verb is outline , indicating that a bit more than a list is required, but not
much more, given the number of marks available. Most candidates tied the answer to pat (i)
to the different scenarios on part (ii) fairly well.
9 (i) The main purpose of any initial appraisal is to ascertain whether the project is
likely to satisfy the minimum criteria that have been established by the
company for projects to proceed. A major consideration could be opportunity
costs e.g. better use of resources might be possible in other projects.
Other possible criteria include achieving synergy or compatibility with other
projects undertaken by the company, or satisfying political constraints, both
within and exterior to the company.
The return on the project could be determined as the net present value (NPV)
or the Internal Rate of Return (IRR) or the payback period for the project. As
the IRR can give multiple solutions it is less popular than NPV. Alternatively,
the project could be viewed in terms of an option, and option pricing
techniques could be used
The NPV method would yield a satisfactory result if the answer were positive
when an appropriate discount rate was used. The result of the IRR and the
payback period would be regarded as satisfactory if they exceeded the pre-set
requirement of the company.
Following this analysis a sensitivity analysis should be conducted in order to
ascertain how sensitive the result is to varying the parameters around their
most likely levels.
If the results proved very unsatisfactory then the new range should not be
launched. If the results show a satisfactory outcome then a detailed risk
analysis should be conducted.
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Subject CA1 Core Applications Concepts, Paper 1 (Assets) April 2006 Examiners Report
(ii) The capital cost of the project could be underestimated. All areas of the
project should be well planned and researched and costed at each stage.
The time to be operational could be underestimated. Each part of the project
should be planned in advance to ensure the project is completed on time.
Action should be taken at the first sign of overrun.
Sales are overestimated. Market research should be carried out to determine
demand for organic foods and sensitivity of sales to price.
Costs are underestimated. Thorough research will be needed for realistic
estimate of costs. Could try to set up fixed price deals with suppliers so that
they are bearing some of the risk.
Market issues could be a problem. For example there could be difficulties in
quality and quantity of supplies or you may have to replace otherwise
profitable lines with the organic range. The market should be researched
initially and continue to be monitored for any potential problem areas.
Regulations relating to organic produce change. This may be very costly. Be
aware of all regulations and ensure that company produces its range to the
required standards at all times. Also research any likely changes and ensure
company can meet these as soon as possible if required.
(iii) The starting point is the current cost of raising incremental capital for the
company in order to carry out the project. This is the rate of return that needs
to be earned on the capital if the existing shareholders are to be no better off
and no worse off.
This should be the company s normal cost of raising capital, taking this as a
weighted average where the weights are based on the optimum capital
structure for the company as between equity and debt. (If the company s
capital structure is not currently optimum, it could be made optimum through
a separate decision).
The cost of debt capital should be taken as the cost in real terms of new
borrowing for the company, by taking an appropriate margin over the current
expected total real return on index-linked bonds, having regard to the
company s credit rating, and multiplying by (1 t), where t is the assumed
rate of corporation tax.
The cost of equity capital should be taken as the current expected total real
return on index-linked bonds plus a suitable margin to allow for the additional
return that equity investors seek to compensate them for the risks they run.
This would generate a real discount rate, to be applied to cash flows expressed
in present-day monetary values, or adjusted by the assumed future inflation
rate and used with cash flows in nominal terms.
The project might be considered a slightly higher risk as this is a new area for
the retailer. The project should be appraised on a slightly higher discount rate
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Subject CA1 Core Applications Concepts, Paper 1 (Assets) April 2006 Examiners Report
than would be considered for projects exhibiting normal degrees of risk for the
company.
A guide may be the discount rate used by other organic food businesses. In
practice these rates may be hard to obtain and therefore an arbitrary addition to
the discount rate the company normally uses may be the only solution.
Care should be taken to avoid spurious accuracy and to avoid the rate being
too high and so distorting relative weights of short and long term values.
Comments on question 9: In part (i), the better candidates grasped the scope of the initial
appraisal and so kept their answers focused on relevant points. The weaker ones went
overboard on risk or went into too great depth on the methods, in some cases writing down
everything they could think of, relevant or not. In part (ii), most people said many sensible
things and gave examples and justifications of mitigating options. Answers were generally
well structured and easy to follow, without too much padding. Part (iii) was one of the best
answered sections. The good answers fleshed out WACC and explained all terms, the
rationale, and how it needs to be tweaked for this project. There were some good discussions
on why it was riskier (but not hugely different/riskier). Candidates who did not hang their
answer around WACC ended up rambling in circles.
END OF EXAMINERS REPORT
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