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The Actuary The magazine of the Institute & Faculty of Actuaries

Mistakes and myths from the previous century

Do you ever stop to consider why derivatives
pricing is not dominated by actuaries? After
all, the techniques which are used to reduce these risky contracts into holdings of shares and bonds are the epitome of certum ex incertis. If that colossal missed opportunity does not worry you then how do you feel about our profession’s failure to:
– produce a minimum funding requirement (MFR) which worked; and
– substantiate the traditional approach to valuing defined benefit pension liabilities it initially recommended to the Accounting Standards Board (ASB)?
The past reluctance of the profession to take on board the lessons of modern finance (also known as financial economics) is at the root of these problems. We thought it timely to tackle some of the common myths concerning modern finance.

Fundamental or actuarial value
What is value? When evaluating an investment opportunity it is natural to construct a value for the asset under consideration and compare this with its price. However, as instinctive as this approach may feel, it fails to capture the actual decision one has to make: given my net wealth, what overall portfolio best meets my objectives? For instance, if I determine that a unit of an asset with a market price of £100 is worth £200, I still need to determine:
– how much of it I should buy;
– what else I should sell to finance the purchase;
– how this asset fits into my ongoing strategy.
The ‘valuation’ of £200 is, by itself, simply useless.
Unfortunately, we as actuaries tend to regard a job as finished once we have come up with a market-inconsistent value. Even worse, we seem to have concluded that our values are better than the ones everyone else uses (ie market values). A direct analogy to actuaries carrying out valuations using assumptions which contradict market values would be to allow investment managers to produce their quarterly reports using their assessment of the value of the assets they manage. Both would be guilty of the same offence: confusing an investment call with a valuation.

Expected value is not value!
One reason why we as actuaries have a tendency to reject market values is that our roots in insurance lead us to turn first to average or expected values. Life is full of examples which show that averages do not work universally: a man with his head in the oven and his feet in the freezer is, on average, comfortable.
Most investors are risk-averse they give more weight to bad outcomes than good outcomes. In addition, many risks cannot be diversified. These two facts together mean that, in a liquid market, the sum of the discounted expected cashflows from a risky asset which cannot be diversified will always be higher than its market value. This principle indicates that:
– although investing in equities to meet a liability best matched by a long-dated gilt gives a net positive expected return, it does not add value; and
– expected value has a role to play only in calculating the value of risks which can be diversified.
Individuals who confuse expected value with value often use phrases like ‘maximise return subject to an acceptable risk’. This sounds, and is, reasonable unless, as is unfortunately often the case, an inappropriate measure of risk is used. A recent example of an inappropriate measure was the spectacular failure of LTCM which, according to Philippe Jorion, was maximising expected returns subject to an inadequate risk constraint (based on value at risk).
It is tempting to use expected return arguments to give advice and sell unnecessary services to financially less sophisticated clients. However, we suggest that you dwell for a while on the following disturbing analogy. In the 1980s, salesmen sold personal pensions to naive deferred pensioners using misleading ruses such as comparing the rate of revaluation on the deferred pension with investment returns. Of course, they were eventually made to pay for this type of advice.

Time diversification of risk
A principal actuarial hang-up with the difference between expected value and market value relates to long-term investors, usually a variation on one of these misconceptions:
– long-term investors can wait until equities outperform the matching investment and then cash in their equity risk premium;
– there is, in effect, a guarantee that over the long term equities will outperform the matching assets; or
– because the likelihood of equity underperformance is low in the long term, the cost of, in effect, guaranteeing that it will not happen is also low.
These are all versions of what is known as ‘time diversification of risk’.
Before you fall into this trap for the financially unwary, consider the graphs shown in figures 1 to 3, all of which relate to equity investment to meet a liability matched by gilts. Figure 1 (opposite) shows the all-too-familiar ‘funnel of doubt’, with the 5th percentile line increasing with time. The view that the probability of a shortfall declines with time is reinforced by figure 2 (top right). But we need to place a value on this risk. Luckily the (modified) Black-Scholes formula provides a simple way of valuing the risk of shortfall as is shown in figure 3 (bottom right). The point is that, while probability of shortfall decreases with time, the relevant measure, ie the value of the risk, increases.
There are numerous other problems with the time diversification of risk arguments:
– Advocates usually take a scheme-centric viewpoint. But if a company pension scheme’s assets fall by £10m then this still leaves shareholders £10m worse off, irrespective of whether the magic 100% funding level is breached.
– We do not have enough data to make reasonable long-term predictions the previous century has only five independent 20-year time periods. Even then, radical changes in the economic environment make historic data of dubious value.
– We selectively ignore other stockmarkets. The history of UK and US stockmarkets is very reassuring but what of other major markets such as Russia, China, Germany, and Japan? Each of these markets has had one or more major interruption, which means that they are typically excluded from long-term studies.
– Our data may be flawed. Recent research suggests that using the Barclays Capital Equity-Gilt Study to derive the real return on equities for the period before 1955 may overstate the figure we should be using by some 5% pa.
– The post-Second World War period has been particularly favourable for the UK stockmarket with its absence of banking panics, depressions, civil wars, and constitutional crises, with victory in the Cold War and with no nuclear missiles fired over Berlin, Cuba, Korea, or Vietnam.
In case it is not clear, these are not reasons for avoiding equity investment in general our point is simply that equities are not appropriate for funding all long-term liabilities, defined-benefit pension liabilities in particular.
Financial economics: ‘too simplistic’
Many opponents of financial economics claim that this system is too simplistic to deal with the real-life problems actuaries tackle. Often their arguments are based on misunderstanding of the system, such as:
– it means the same thing as modern portfolio theory;
– it depends on the efficient market hypothesis;
– it fails because it cannot take account of autocorrelations (it can);
– it always assumes that investment returns are normally (or log-normally) distributed.
– it always measures risk using standard deviation.
Of course, simple models are often used in financial economics, especially in educational textbooks. The key point is that, in many cases, simple models are sufficient for the task in hand. If you are interested in testing this then why not use one of the many proprietary market-inconsistent, over-engineered stochastic actuarial asset/liability models to price a simple option and see how it performs against market professionals who use a deterministic Black-Scholes model?

The future
When we were studying for the actuarial exams, we (possibly naïvely) assumed that the education material was written by people who knew more than we did. Now we frequently encounter students who are well aware of how severely outdated the actuarial syllabus is. We therefore conclude with the plea that the profession should be at pains to correct this at the forthcoming educational review. We would like the next generation of actuaries to be properly equipped to face the new century.