Showing posts with label actuarial science. Show all posts
Showing posts with label actuarial science. Show all posts

Dec 20, 2013

Relationship Confidence Level & Funding Ratio

Dutch Pension funds constantly keep their members informed about the development of the funding ratio. But actually..., what is the confidence level that belongs to a certain funding ratio?

The answer to this question varies greatly by pension fund. To create some sort of insight in the relationship between the Funding Ratio (FR) and confidence level, we will discuss a highly simplified, but certainly realistic example.

Confidence and Equity
The required confidence level for Dutch pension funds is anchored in the Dutch Pension Act (Pensioenwet), at a 97.5 %  level.

Article 132 , paragraph 2 of the Pension Act  states:
A pension fund will set the regulatory own funds so that the probability of the pension fund having 
less assets at its disposal than the amount of the Technical Facilities (TF) within a year is reduced to 97 1/2 %

Funding ratio
Under the Dutch Pension Act, the required one-year confidence level of 97.5 % is directly related to the Regulatory Own Funds (ROF) and thus to the Required Funding Ratio (RFR). In a simplified formula stated: RFR = (ROF + TF) / TF.

At higher funding ratios than the RFR, the actual confidence level will be more than 97.5 % and vice versa: if the actual funding ratio is lower than the RFR, the corresponding confidence level will be less than 97.5%.

In practice, calculations show that the required funding ratio of most Dutch pension funds has an outcome somewhere between 120% and 130% .

Funding Ratio and Investment Risk
The fluctuation of the funding ratio depends largely on the investment risk that a pension fund is willing to take. Netherland's largest pension fund, ABP, adopted an investment policy that aims at roughly 40% fixed income and 60% equities. This policy resulted in the next yield and 5-year backward moving annual volatility (risk) :

The average ABP annual return over the past 5 years was about 5 % with a volatility of 15.9%.

Volatility Funding Ratio
The volatility of the funding ratio depends not only on the volatility of investments, but also on the volatility of the discounted liabilities. In the Netherlands, liabilities are discounted at a risk-free rate, with help of the so-called 'ultimate forward rate' (UFR).

On balance, the ABP's annual funding level volatility over the past 10 years turns out to be approximately 17 % .

This percentage has the same order of magnitude as the annual funding level volatility of an average pension fund in the Netherlands .

As the funding volatility has the same order of magnitude as the investment volatility, we may conclude that the confidence level that corresponds to a certain funding ratio is mainly determined by the investment risk .

To get sight at the 'one year confidence level' for various funding levels, please take a look at the the next chart that's based on a highly simplified approach. We do not seek exactness, but want to get an impression of the confidence sensitivity. Therefore, we abstract from the additional volatility effects that may arise from other risks (like liabilities and expenses ). The calculation is performed for two different risk strategies of a pension fund :
  1. The 'current risky' investment strategy with an expected investment volatility of 15 %
  2. A 'risk-averse' investment strategy with an expected investment volatility of 4%
Here are the results :

On the basis of graph above a first serie of important conclusions can be drawn:
  • A 100% funding ratio corresponds with a 50% confidence level
  • If the funding ratio exceeds 100%, the 'current risky' investment strategy results - as expected - in a lower confidence level than a risk-averse strategy.
  • Although perhaps at first sight surprising, the reverse is also true:
    If the funding ratio falls to a level less than 100% , a risky investment strategy results in a higher confidence level than the 'risk-averse' investment strategy. And this is exactly the situation in which a number of Dutch pension funds, but also many foreign pension funds, are in.
To draw some more specific conclusions, we zoom in on the graph:

Now, a second set of interesting conclusions becomes visible:
  • Required Funding Ratio
    The 'current risky' investment strategy of Dutch pension funds in combination with the legally required confidence level of 97.5 %, urges a funding ratio of about 130 %.  In a risk-averse strategy the required funding ratio would be somewhere around 110 % .
  • Actual Confidence Level
    A legally required confidence level of 97.5% with a funding ratio of 110% for a risk-averse fund would result in an actual confidence level of about 75% in case of a risky investment strategy .
    As most Dutch pension funds have adopted a risky investment strategy, the actual average confidence level is about 75% in case of a 110% funding ratio and about 50% in the case of a 100% funding ratio.
  • Maximum Confidence Level Decline?
    There's a maximum decline of 24% in confidence level in case of a transition from a risk-averse to a risky investment. The maximum decline corresponds with a funding ratio of approximately 108%.
  • Indexation Potential?
    The current average funding ratio of Dutch pension funds fluctuates around 100%. This implies that as far as future actual annual returns result in an excess return above the required return on liabilities, this so-called 'excess-return' should first be used to achieve the required funding ratio of about 130%.  In most cases this leaves no room for indexation in the coming 10 years.
  • Partial Indexation?
    It's quite common to apply 'partial indexation', above a 105% funding ratio. However, if the actual funding ratio is still below the minimum required confidence level (of 130%), "partial indexation" lowers the funding ratio and diminishes the recovery-rate. In this case, the (partial) indexation policy should be tested for feasibility. The expected return minus the (future expected) indexation and minus the required return on liabilities, should be sufficient to grow to the required funding ratio of 130% within the statutory recovery period of 10 years .
Solvency II to pension funds ?
Finally, we zoom in on the possible introduction (IORP legislation) of a required 99.5% confidence level, as is valid for insurers under Solvency-II:

A final set of key conclusions now becomes visible :
  • Solvency II
    Increasing the current confidence level of 97.5 % (Pensions) to 99.5% (Solvency II ) implies an increase of the required funding ratio from 110% to about 113% for risk-averse pension funds and an increase from 129% to 139%  for pension funds with a (current) risky investment policy.
  • Unrealistic Solvency-II Growth Path
    Based on the current average funding ratio of around 100%, pension funds should be able to climb to a funding ratio of around 139% within a (statutory limited) 10 years period to reach a Solvency-II confidence level of 99,5%. I think most of us will agree that this is a complete unrealistic scenario. In this case pension funds will ultimately be forced (by the regulator) to de-risk their investment portfolio. De-risking will result in lower (expected) returns and further loss of indexation potential.  Implementing Solvency-II requirements will turn pension funds into 'nominal pension insurers'.
  • Basel
    Confidence levels in the financial markets seem to know no end. If, in the long term, the confidence level requirement of 99.9 % ( Basel banking regulations requirement) should become obligatory for pension funds, things would really get out of hand. In this case, the funding ratio requirement would increase further to 116 % ( risk-averse strategy ) or even 147 % ( risky strategy).
The question is whether it's wise to judge pension funds with long term liability structures and corresponding investment policies, on basis of a one-year 97,5% confidence level. It would probably be more realistic and practical to scale up to a 99.5 % confidence level on basis of a 5 or 10-years period:

Illustration: In case of a portfolio with a 15% risky investment strategy, the 5-year average 99.5 % confidence level would lead to a required funding ratio of 118 % .

Based on the global approach above, the following conclusions can be drawn:
  • The actual confidence level of Dutch pension funds is far below the (statutory) required confidence level of 97.5 %. For pension funds with a risky (= 15% volatility) investment strategy and a funding ratio between 100% and 110%, the actual confidence level varies from 50% (at a 100 % funding ratio) to 75%  (at a 110 % funding ratio).
  • There's only very limited indexation potential for pension funds with a funding ratio between 100% and 130 %, due to the obligation to grow the actual funding ratio (with priority) to the statutory required level (130%).
  • Introduction of an IORP risk framework based on a Solvency-II confidence level of 99.5% would imply that pension funds are forced to de-risk their portfolio. De-risking will result in lower (expected) returns and further loss of indexation potential. Implementing Solvency-II requirements will turn pension funds into 'nominal pension insurers'.
  • Due to their long-term obligations and corresponding investment strategies, pension funds can be more adequately controlled and steered on basis of a five-year average 99.5 % confidence level, instead of the actual one-year 97.5% confidence level.
The calculations and conclusions in this blog are very rough approximations which by definition do not apply to an individual pension fund and are only intended for discussion purposes. Please consult your own pension fund if you are interested in the confidence level results regarding your own pension fund. In this case don't forget to ask your pension fund to report according the template style of this blog!

Aftermath: International Funding Ratios Comparison
The funding ratio's and mentioned statutory requirements in this blog are based on the actual situation in the Netherlands. Funding ratio's in other countries vary considerably!

In an excellent rare Netspar thesis  (2010) the diverse funding ratios of public sector pension funds are compared regarding three kinds of Methods:
  1. Reported Ratio: Funding ratios officially reported by each scheme.
  2. Fair Value: This method, inspired by Dutch plans, uses a market discount rate to account for pension liabilities. Dutch pension industry refers discount rates to nominal swap rates since the market of government bonds is not deep enough for the industry. 30-year nominal swap rate, which roughly has the same duration of 15 years as a typical pension fund, is used as the market discount rate for nominal liabilities
  3. Expected Return: This (actuarial) method, following the U.S. practice, is based on an assumed discount rate of 8% which reflects the American’s expectation of annualized long term pension asset return.
Here are the results:

For example: if you would like to compare the Netherlands with the US on basis of Fair Value (the Dutch mandatory method), the funding ratio of the US would be 31% compared to around 90% in the Netherlands. Please keep this in mind if you examine the above charts in this blog!

But let's stay optimistic about US pension funds, the funding ratio ofl US corporate plan's is already rising!

US Pension Fund Fitness Tracker

Find out what your actual pension confidence level is!!!

Used Links & Sources
- Dutch Pension Act (in English)
- Advisory Report of the UFR Committee
- A fixed UFR, a costly mistake?
- Long duration bond benchmarks for U.S. corporate pension plans
 - Netspar Thesis (2010): What Explains the Diverse Funding Ratios..
US Pension Fund Fitness Tracker

Apr 2, 2009

Wiki Book of Actuarial Science?

Wikibooks is great!

Wikibooks is a Wikimedia community for creating a free library of educational textbooks that anyone can edit.

Since the start in 2003, Wikibooks has grown to include over 35000 pages (year 2009) in a multitude of textbooks created by volunteers.

A great example of Wikibooks is the Wikibook Chess.

In exactly 12 chapters a variety of aspects like, Playing, Notating, Tactics, Strategies, Openings and Endgames, are clearly explained.

Wikibook of Actuarial Science
There is also a Wikibook of Actuarial Science. Although all the required chapters of 'Actuarial Science' are already there and structured, the content has to be taken care of.

So, if you like to contribute? Work for voluntary actuaries!