Oct 31, 2009

The first Actuary

As the story goes, insurance began around 1688 at a coffeehouse in London called Lloyds, where shipman discussed and divided their risks.

That 'explains' the birth of non life insurance.

But what about life insurance?

Who developed the first life table?

Answers...
The answer to this question depends on who you ask...
  • Definitely Graunt in 1662 (statistical analyzes of data)
  • Surely De Witt in 1671 (life insurance tables)
  • Undoubtedly Halley: 1693 (life insurance tables)

Depending on what you define as a life table, answering this question often leads to a never ending semantic discussion.

Don't worry, there's help... In his Google-book, "A history of probability and statistics and their applications before 1750", Anders Hald explains the origin and development of life tables.

First Life Tables
An indeed, the 'first' life tables, based on more or less empiric data and interest rates were developed at the end of the 17th century.
The first actuary....
However, already in the 3rd century the Roman jurist Ulpian devised a table for the legal conversion of a life annuity to an annuity certain.
It was pointed out by Greenwood that the valuation (duration) of the annuities was deliberately chosen to high, in order to protect the interests of the legal heir.

This would implie that Ulpian not only did a tremendous job by estimating life annuities, but also developed and applied the first primitive 'Solvency Zero' principles...

With his 'simple table', Ulpian was more than ahead of his time.

So, we may rightfully conclude that the one and only first actuary was a jurist: Domitius Ulpianus, alias Ulpian

Strange that it took more than 1500 years to develop more sophisticated life- and annuity tables.

Related links & Sources:

Oct 24, 2009

Pension Fund Market Valuation ParaDox

Is Market Valuation (MV) the right tool for pension funds?

Mid 2009, the new appointed ABP chairman Nijpels and - previously - the ABP CFO ten Damme (picture on the right), stated that the relatively new method of MV is inadequate for pension funds.

Both think that valuation of pension funds could be better based on a (seven year) moving average interest rate.
Nijpels en Ten Damme are supported in their view by Albert Röell, Chairman of KAS BANK, who advises the Dutch regulator DNB to reassess its policy.

Nevertheless DNB doesn't seem to respond.
Neither Roëll nor the world's third-biggest pension fund gets an answer. Is ABP crying over spilt milk?

Why MV?
At first sight, there seems nothing wrong in calculating the value of a pension fund, on MV basis. Market (consistent) valuation implies that the value of an asset or liability is defined by it's market price. If the market is too thin, a mark-to-model approach can be used....

Clearly MV increased the transparency and accountability of pension funds. However, 2008/2009 show that MV, based on the actual term structure of interest rates, leads to excessive volatility in funding ratios.

Is MV the best method?
Of course MV can be a best practice method in helping to define the pension fund value in case of a merger, a takeover or with regard to managing assets. But is MV also the best method for managing the pension fund as a whole, from a board, regulator or 'pension fund member' perspective?
  • Future certainty
    The first fundamental question is :

    can we define the value of long-term
    ( 60 years or more) cash flows at all?


    The answer is: No, we can't!. Just take a look at an average CFO, who's proud to present his next quarterly company result with 60% certainty. What would be the certainty of the long-term company result of - let's say - 20 years ahead. Exactly: Almost zero.

    It's impossible for anyone, no Nostradamus Actuary included, to predict the compound and correlated long term effects of interest rate, stock market, derivates, inflation, salary increases, mortality, disability, longevity and costs. Therefore, if it's not possible....., don't pretent you can.

  • Pension fund: Not for Sale
    Second important subject for consideration is that a pension fund (in general) is not listed on the stock market. Also, in general, it is not for sale on the market. Therefore, the hourly, daily or monthly calculated MV is only of limited interest with regard to the pension fund's strategy, policy or control.

    Neither is MV the right base for monthly adjusting of the contribution rates, funding rates or indexation capacity.

Principles
Simply stated, it's important that a pension fund:
  1. can meet its obligations "on the long-term"
  2. is sufficiently liquid to pay his annuities "on the short-term"

Moving average
The first statement implies that if you take the funding ratio as steering/testing parameter (there are more!), there is - given the mentioned long term uncertainty - no other option than to base the valuation on a more (term dependent) 'moving average' of interest rates in combination with the moving average value development of other asset classes. The choice of the moving average period is critical.

Dead Money
Even more, if the pension fund is forced to act on basis of MV, it has to keep extra (non-volatile) buffers to withstand the possible effects of non-relevant short-term market fluctuations. On top of this many pension funds tried to downplay their indexation ambition.

The consequence of all this is that MV generates a substantial amount of structural "dead" capital into the balance sheet. "Dead" capital that - besides - is withdrawn from the national economy and therefore weakens the pension fund's country position in the international level playing field.

Paradoxical measures
In case - due to market developments - the MV goes down , short-term prudential constraints (as enforced or stimulated by the regulator) will moreover endanger the long-term objectives of pension funds. Consequently leading pension funds from the frying-pan into the fire.

There's another interesting aspect that pleads against MV. In general (Dutch) pension funds cannot go bankrupt, as they are allowed to cut back on the participants’ entitlements in extreme (emergency) situations. So the key question is what kind of minimum security level we enforce upon ourselves. Just an example to illustrate this:

Example
What would you prefer:
  1. 100% of the yearly pension that you have been promised, on basis of a 125% funding ratio
  2. 125% of the yearly pension that you have been originally promised, at a 100% funding ratio target

Remember there is no ultimate warranty whatsoever in either situation.

The only difference is that in scenario A the chance that your entitlements will be cut down is slightly smaller than in scenario B. But this last situation is as hypothetic as it can be, as contributions will be raised first, before any cut down scenarios will be considered.

So its better to use the funding ratio surplus for legalized controlled indexation and pension benefits improvement than as 'dead' money.

A final argument in the war against MV for pension funds is the next illustration .....

ParaDox
Let's take a look at a company called ParaDox.... ParaDox produces parasols (sunshades) for the high season.

In winter, ParaDox produces at full speed in order to achieve a top level inventory at the start of the summer.

In winter, however, hardly any parasols are sold. During this cold season the price of the parasols on the market (in the shops) drops to about 50% of the summer price. Even more, parasols sales go 80% down in winter (cf. long-term investment market).

If ParaDox would apply MV based techniques, it would have to depreciate their current stock to 50% of the (summer)value. Surely ParaDox would go bankrupt. No, every sensible human being, including actuaries, would decide that in this situation it's best to value the stock of ParaDox on basis of the 'moving average' (realized) sales price over one or more recent years.
N.B. Even if ParaDox would have one or two 'bad summers', deprecation would not be considered.

If in this ParaDox case it's clear that market valuation (i.c. deprecation) is unwise, the more it must be clear that in a company with long-term obligations and high uncertainties , like a pension fund is, it's naive to operate and steer on basis of MV.

Moving Average Period
Now that's illustrated that the Moving Average Method (MAM) is preferable above the MV method (MVM) for pension funds, there's still one thing to decide: the 'MAM period'.

If the MAM period is chosen too short, it will suffer the same disadvantages as the MVM.

If it's chosen too long, there's the risk of not being able to adapt fast enough to realistic contribution levels, if needed. In this situation there's also the risk of unintentional intergenerational financial effects. However, these effects can be yearly calculated and translated into a sound policy.

From this perspective it seems reasonable to fix the MAM periode to the average duration of nominal pension liabilities, which is (in The Netherlands) about fifteen years (in real terms, it is even longer).

Hope
Let's trust that DNB listens to ABP and KAS BANK, so that 'pension funds' and 'pension fun' become one again!

Related links:
- P&I/Watson Wyatt World 300 Largest Pension Funds
- Market-consistent valuation of pension liabilities (must read!)

Oct 22, 2009

Actuagram

If you want something to chew on, something that challenges your actuarial brain and associative power, try to solve the next Actuagram.
This actuarial brain teaser is a mix of an actuarial crossword puzzle and a cryptogram.

How to play the puzzle:
  1. Click on the word you would like to solve.
  2. Fill in your suggestion, click on OK
  3. Only if you do not know the answer, click on the 'solve button'

Can you manage, without using the 'solve button' ?

Congratulations! Actuaries, have fun!

[ If your browser doesn't allow you to play here, click on this link]

Actuagram

by Joshua Maggid
EclipseCrossword © 2000-2007




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