Presented to the Staple Inn Actuarial Society on 16 February 1999 THE PRICE OF ACTUARIAL ...

37 Pages·2005·2.07 MB·English

Presented to the Staple Inn Actuarial Society
on 16th February 1999
THE PRICE OF ACTUARIAL VALUES
by
Tim Gordon
The price of actuarial values Contents
Contents
1. Introduction 1
2. Traditional approach 3
3. Modern finance theory 6
4. Application to UK pension schemes 13
5. Commercial aspects 24
6. Non-commercial barriers 29
7. Conclusion 31
Acknowledgements 32
References 33
Appendix 35
The price of actuarial values Introduction
1. Introduction
"Behavioural psychologists introduce another phenomenon - cognitive dissonance .... This
is the mental anguish that results from being presented with evidence that our assumptions
or beliefs are wrong. In order to counteract it, we hang on to our biases, however irrational,
because we do not want life to become too complicated. Indeed, people will often
deliberately ignore new information or develop convoluted arguments in order to maintain
their beliefs or assumptions." (Urwin, 1999)
I confess that it had always puzzled me why actuarial methods applied in relation to pensions
seemed to be fundamentally different from methods applied elsewhere in finance.
Nevertheless, I assumed that the examinations I had to pass in order to become a pensions
actuary had covered the basics of finance to the extent they were applicable to actuarial
work. It came as a considerable shock after having qualified to find that, other than the
elementary use of compound interest, the basics of finance had been completely omitted.
The original application of modern finance theory to corporate pensions was carried out by
such notable financial economists as Black, Sharpe, Tepper and Treynor in the late 1970s
and early 1980s in the USA (which has a pensions regime similar enough to that of the UK
to make much of their work directly applicable in the UK). The penetration of these ideas
amongst practitioners both in the USA and the UK has been slow because the ideas were so
different from the generally accepted views and because of practitioners' unwillingness to
learn new techniques.
Within the UK, the profession has only relatively recently been forced to face up to the
inconsistencies in the traditional methods used by actuaries to fund and cost pensions
liabilities. The pensions apple cart was first upset by Dyson & Exley (1995) who argued that
instead of using off-market values for assets and implicit smoothing methods, actuaries
should use market-consistent methods. Then the paper by Exley, Mehta & Smith (1997)
(which I refer to as EM&S) showed precisely how modern finance theory should be applied
to pensions actuarial work in a UK context.
My impression is that, within the UK actuarial profession, the methodology proposed by
EM&S is viewed as exotic with little relevance to practitioners. However, our claim to be
practical at the expense of getting the basics right strikes me as particularly hollow.
Accordingly, this paper has as its aim the propagation of modern finance theory amongst
practising pensions actuaries. In particular, I have tried to nail myths which masquerade as
sound actuarial advice in some quarters.
There has been debate within the profession regarding the level of mathematics required to
use the methodology proposed by EM&S. It is true that some aspects are mathematically
involved, but it should be noted that:
• an understanding of the basic principles does not require sophisticated
mathematics, and
• in any case, we claim to be a mathematically literate profession.
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The price of actuarial values Introduction
There is considerable confusion regarding terms such as "market value valuation", "market-
based valuation" or "market-led valuation", some of which appears to be a result of
consultants trying to claim that they have always carried out market-contsistent valuations
and that no fundamental change was proposed.by EM&S. For the sake of clarity, I will use
the term "market-consistent valuation" to refer to a valuation which is consistent with
modern finance theory (as specified in EM&S) and the term "traditional valuation" to refer
to any other actuarial valuation, including those which:
• place a value (an "assessed value") different from market value on assets (often
derived using a primitive dividend or corporate earnings discount model applied to
a notional portfolio of assets),
• apply the ratio of market value to assessed value as a multiplier to liabilities
determined on a "long-term" basis,
• use "smoothed" market values, or
• use economic assumptions (usually described as "long-term" or "actuarial
judgement") which contradict market values (including any double counting of the
equity risk premium).
The remaining sections of this paper cover the following topics:
• section 2 - problems with the traditional approach,
• section 3 - a brief summary of relevant modern finance theory,
• section 4 - how modern finance theory can be applied to UK pension schemes,
• section 5 - commercial issues affecting actuarial methods,
• section 6 - non-commercial barriers to the adoption of modern finance theory, and
• section 7 - conclusion.
The appendix sets out further reading on modern finance theory.
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The price of actuarial values Traditional approach
2. Traditional approach
2.1. Summary
The following is a summary of the approach advocated by the reading for subjects 304 and
404 of the UK actuarial examinations for pensions valuations. Contact with the work of
pensions consultancy firms other than my own and briefing documents released by these
firms suggest that this approach is still the most common in the UK.
The approach is characterised by the following:
(a) the treatment of company-sponsored pension schemes as isolated entities,
(b) the application of expectation (averaging) over a long period of time to determine
value,
(c) an ad hoc allowance for risk usually achieved by using lower estimates than
implied by history for economic assumptions and usually in consultation with the
party or parties for whom the valuation is being carried out,
(d) the treatment of pension schemes open to new entrants as continuing indefinitely,
(e) a check on the solvency of the scheme if it were to be discontinued (but which
cannot be relied upon by the trustees of the scheme - see section 3.8 of guidance
note GN9: Retirement Benefit Schemes - Actuarial Reports v6.0), and
(f) a conviction that the equity market is irrationally volatile and cheap for long-term
investors.
Parsons (1990) and Thornton & Wilson (1992) contain good descriptions of how pensions
actuaries derive assumptions in accordance with (b) above.
I have not found a well-defined explanation of how the allowance for risk under (c) is
determined other than general references to actuarial judgement or the use of asset-liability
modelling (which also tends to be poorly defined). The core reading for subject 404 for
1999/2000 is vague to say the least:
"The approach to the on-going valuation is likely to be cautious, as the trustees
must endeavour to provide funds that are sufficient to meet the liabilities. ... This
caution is applied by making adjustments to the assumptions rather than to the
calculated values. However, some actuaries prefer to demonstrate the caution by
making explicit loadings to values determined by 'best estimate' assumptions."
This approach suffers from the following key problems:
• Lack of objectivity. The answer varies enormously depending on which actuary
carries out the calculation - even one actuary can come up with a large range of
answers (all of which he or she may be prepared to describe as "prudent best
estimates").
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The price of actuarial values Traditional approach
• Lack of comparability. Actuarial values cannot be compared with other company
costs because the actuary is using a non market-consistent basis. In effect, the
actuary is confusing valuation and investment advice - this is covered in §2.3.
These problems arise because of the use of judgmental and market-inconsistent methods. I
cover these below.
2.2. Judgmental methods
It would appear that, because of actuaries' conviction that:
• pension schemes can simultaneously ignore the risk of under-performance on
equities and take credit for extra return rewarded for this risk compared with risk-
free investments, and
• actuarial judgement is the only technique for valuing long-term liabilities,
actuaries assume that judgmental methods are the only methods available which give
sensible answers. What is more, the judgement involved is something which apparently only
comes with years of experience. In other words, we claim to know the answer but cannot tell
anyone else how to derive it in advance.
The problem is that the difference that actuarial judgement can make to valuations using the
traditional approach is enormous. It means that:
• we are exposed to pressure from clients seeking to move answers in the direction
which favours them, and
• we lose credibility because we are unable to explain precisely how we arrive at an
answer.
It is important to stress that a move to methods based on modern finance theory will not
remove the requirement for actuarial judgement. Instead, it will help to define the areas
where actuarial judgement really is required and provide better methods than we currently
have available on which to base our advice.
2.3. Market-inconsistent methods ("price v value")
Price is the means by which different commodities can be traded against each other. Clearly
it has drawbacks, for instance:
• there may be no market at all,
• if a market is not frequently traded, the information can be out of date,
• dealing expenses and other forms of market friction mean that the underlying price
is subject to uncertainty, and
• markets can be subject to deliberate manipulation (for instance, a derivatives trader
with a position in a barrier option may trade to ensure the barrier is triggered).
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The price of actuarial values Traditional approach
However, for UK pension schemes, their typical investments and the assets which best match
their liabilities are traded very frequently. Moreover, their holdings in less frequently traded
assets tend to be well diversified. Accordingly, the above drawbacks are unlikely to be
significant.
Companies assessing costs need to use a consistent method. In addition, it would be
reasonable for them to use a method which takes their shareholders' views into account. By
definition, a market-consistent basis achieves these aims (because shareholders can trade
only at market price).
UK pensions actuaries are taught to use an approach based on "fundamental value" or "long-
term value" which requires that current market conditions are ignored - see, for instance,
Pemberton (1998a). The most notable aspect of "fundamental value" is its lack of definition.
Its existence is usually asserted without proof, presumably because its meaning is thought to
be so obvious.
This "price v value" debate appears to me to be wholly spurious.
• We all have different views on the relative values of different assets - that is the
reason we hold different portfolios of assets and liabilities.
• Price is the medium for exchange and, therefore, to quote value in a different,
"actuarial" currency seems rather pointless.
• Placing a different monetary value on an asset or a liability compared with market
value is a form of (poorly-specified) investment advice. If an actuary states that
equities with a market value of £1.00 are actually worth £1.20 (or, equivalently,
that a liability is lower if it is backed by equities rather than, say, gilts), then this
contains the implicit recommendation to buy the equities (although it does not
indicate how much of equities should be bought). An analogy would be for
investment managers to report what they think the investments they have bought
are worth instead of the actual market price of the investments.
Actuaries often justify their use of market-inconsistent values by asserting that internal
consistency is all that is required. This is not true. To establish that a valuation is not
making an implicit statement regarding investment advice, one needs to carry out the market-
consistent valuation first.
In summary, using values which are inconsistent with market prices:
• relies on the claimed superior knowledge of the actuary (although this is not given
credence by the rest of the market),
• contains implicit investment advice,
• is not comparable with other market-inconsistent valuations, and
• ignores the views of shareholders.
For the remainder of this paper, I will use the terms "value" and "price" interchangeably.
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The price of actuarial values Modern finance theory
3. Modern finance theory
3.1. Outline
Modern finance theory dates from 1958 when Markowitz and Tobin were working on the
theory of portfolio selection and Modigliani and Miller were working on capital structure
and valuation. It is frequently also called "financial economics".
It is important for actuaries or actuarial students who wish to familiarise themselves with
modern finance theory to note that they should be wary of the many negative presentations
within the actuarial literature. Typically, these presentations distort modern finance theory
beyond all recognition. The best example I can find of this is Clarkson (1996). The
comments in the abstract of the discussion by Bowie, Hardy, Macdonald and Smith all draw
attention to the minimal resemblance of the caricature of financial economics presented by
Clarkson to reality.
Modern finance theory is an attempt to understand the behaviour of markets using models. It
is characterised by:
• quantifiable and testable theories,
• intellectual coherence, and
• a healthy suspicion of subjectivity.
Although some parts of modern finance theory are mathematically involved, especially those
using stochastic calculus, the subject as a whole should be accessible to any qualified
actuary.
In the remainder of this section, I have outlined the main results in modern finance theory of
which actuaries should be aware. I have commented on market pricing models and market
efficiency not because they are required in day-to-day pensions actuarial work but because
they are so frequently misrepresented by actuaries.
3.2. Law of one price/no arbitrage
If there are two different prices for things which are for all material purposes the same then
the opportunity to trade them off against each other without risk means that these price
differences are unable to remain. Achieving a risk-free profit is called arbitrage (although
the word is sometimes misused by actuaries to refer to a perceived anomaly in the market
which cannot be used to make a risk-free profit). The well-publicised failure of LTCM in
1998 was an example of the dangers of speculation (taking high risks to generate a high
return) rather than an example of arbitrage.
The best description of arbitrage I have seen is in the prologue and first chapter of Baxter &
Rennie (1996). If actuaries read this, maybe they will have second thoughts before
advocating the traditional expected value approach.
A simple example of arbitrage is valuing a "forward". A forward is an agreement now to
exchange a fixed amount of cash for a fixed number of shares at a specified date in the
future.
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The price of actuarial values Modern finance theory
When pricing a forward, the instinct of pensions actuaries who are unfamiliar with
derivatives is to price it using the expected return on the equity and then to worry about how
much risk to take. However, because one can borrow money at a fixed rate to buy the shares
now and then wait until the exchange date, the price of the forward can be determined now
without reference to risk. If you quote a different price from this risk-free price, your
forward will simply be bought or sold (depending on whether you priced too low or too high
compared with the risk-free price). Your expected return may still be positive but it will be
very risky whereas those you sold to or bought from have a risk-free profit and will be
laughing all the way to the bank. This is an example of an arbitrage opportunity. It is not a
game - this is how forwards are actually priced in practice.
Five important points emerge from this example:
• our actuarial training has not equipped us to deal with such a simple pricing
problem,
• where arbitrage is possible, reliance on expected value can be seriously misleading,
• the value does not depend on the extra return for taking risks on equities (because
the discount rate has nothing to do with the expected return on the underlying asset
- it is a feature of the arbitrage formula),
• the general solution to this problem would be no different if the timescale were
short or long, and
• not only did the method yield a value but it also yielded the matching investment
strategy.
Pricing a forward is a simple example of "hedging". Hedging is covered in more detail in
the next section.
3.3. Hedging
The fact that a forward can be priced by eliminating arbitrage opportunities compared with
another combination of investments is called hedging. For a forward, the hedge is static - it
can be valued with no requirement to trade after an initial transaction. If one allows for
dynamic hedging, in other words, the regular updating of the hedge, then more complicated
liabilities can be valued. Most famously, these include valuing options using the Black-
Scholes formula. This is covered at length in Kemp (1997).
The discussions of Kemp (1997) and Clarkson (1997)+ are well worth reading. They
illustrate that actuaries tend:
• to suppose that the reliability of hedging depends on the existence of efficient
markets and the validity of a particular market pricing model such as the capital
asset pricing model (it is dependent on neither of these),
+ As a footnote to Clarkson's contribution to the discussion of Kemp (1997), Scholes and Merton have
since been awarded the Nobel prize for economics. Undoubtedly, Black would have been similarly
honoured if he were still alive but the prize cannot be awarded posthumously.
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The price of actuarial values Modern finance theory
• to find the mathematics confusing (especially references to "risk neutrality" which
is a mathematical term, not a reference to risk in the conventional sense), and
• to dwell on imperfections of these models as if they were not well known and
allowed for by actual practitioners.
Regarding the last of the above points, Wilmott (1998) provides lucid descriptions of the
problems encountered using simple formulae and demonstrates that practitioners in
derivatives are in fact extremely suspicious of idealised models, are well aware of these
models' deficiencies and make considerable effort to take account of these deficiencies.
The reality is that hedging is used extensively to value complicated liabilities.
I sometimes wonder whether actuaries are actually solving a different problem which
involves maximising the likelihood of meeting the liabilities with no credit for meeting any
amount less than 100% of them. The following is equivalent:
If I start with £10, how can I maximise my chances of it becoming £20 in a year's
time?
Clearly, if a risk-free return of 100% pa over one year is not available then I have to invest in
a risky asset, otherwise I have no chance of meeting the £20.
The point which seems to give rise to confusion is that hedging has nothing to do with how
expensive it is to hedge. If:
• asset A will always meet a liability exactly and costs £100, and
• asset B fails to meet the liability 5% of the time and costs £1,
then holding A is still the best hedge. This is true even if £99 of Bs may still fail to meet the
liability (whatever their expected return is).
The same five points made at the end of §3.2 apply equally well to hedging in general. I
have summarised them again below for emphasis:
• our actuarial training has not equipped us to deal these problems,
• expected value (in the actuarial sense) can be seriously misleading as a guide to
financial value,
• value does not depend on the extra return for taking risks,
• the general formula does not depend on whether the timescale is short or long, and
• not only does hedging yield the value but it also yields the matching investment
strategy.
In the remainder of this paper I tend to use the word "match" instead of "hedge" because this
is more conventional actuarial terminology.
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