Understanding Confidence Levels in Time

What's the right understanding of the concept of 'confidence level' for a financial institution?

That's not an easy question....

A short (popular) definition of confidence level in terms of Solvency and Basel regulation would be:

The probability that a financial institution doesn't default within a year.


In this blog I'll discuss and compare three more or less accepted confidence levels (CFLs):

1. Dutch Pension Funds: CFL= 97.5% 
2. Life Insurers (Solvency II): CFL = 99,5%
3. Banks (Basel II/III): CFL = 99.9%

Understanding Confidence Level
Before we get into the details, let's first shine a light on a widespread misunderstanding regarding the concept of 'confidence level'.

To make the concept of confidence level more understandable, one might argue as follows:

1. The confidence level of a Dutch pension fund is defined as 97.5%
2. This implies that there's a one years probability that the pension fund has an one year default probability of 2.5% (= 100% - 97.5%)
3. This implies that the pension fund on average defaults once every 40 years (= 1 / 0.025)

This method of reasoning is completely

WRONG

The mistake that's been made is more or less the same as the next two fallacies:

1. If one ship crosses the ocean in 12 days. 12 ships will cross the ocean in one day
2. I fit in my jacket, my jacket fits in my suitcase, therefore I fit in y suitcase

Explanation
The probability of a pension fund with a confidence level of 97,5% going default, can be approximated by a simple Poisson distribution as follows:

From this we can conclude:

• In 40 years the pension fund has a 63% default probability.
• The probability that the pension fund defaults more than once is 26%
• The probability that the pension fund defaults exactly once in a 10 years period is 19.47% 

Insurer Confidence Level
For an insurance company with a confidence level of 99.5% the results are:

So even an insurer has a 4.88% default probability in a 10 years period on basis of a 99.5% confidence level. Keep this in mind if you take out a life insurance policy!!!


Banking Confidence Level
It starts getting serious when it comes down to a 99,9% confidence level for banks:

Comparison
Comparing the default probability of (Dutch) pension funds, insurers and bank on the long run:

Finally
Although this blog gives some more insight about the consequences of confidence levels on the long run, the real question of course is: what's the price you have to pay to avoid default risks?
That's something for another blog.....


Sources/Links
- Spreadsheet with tables used in this blog

Bonds: a Crisis Risk Indicator?

As a risk professional you've learned to classify an increase in bond's interest volatility (or standard deviation) as an indicator that bonds have become more risky. Right you are....

Now, with this knowledge, let's take a look at the next chart, presenting the long-term (10Y) interest rate of some of the leading EU member states from January 1993 to April 2014:

This chart clearly shows that :

• Since the introduction of the Euro in 1999, country spreads start declining
• Interest rates converge to the year of the famous (Lehman) crisis in 2008
• After the 2008 crisis, rating agencies wake up and spreads explode again

Let's take a look in more detail, by some log scale zooming......

To find out if the convergence of interest rates really is a kind of early warning crisis indicator, let's add some more EU countries to the chart.

Now the picture becomes clear: A structural decline in bond's standard deviation is not a decline in risk, but more the opposite....

As standard deviation decreases, (crisis) risk increases!

We can check this by looking at the cross-country standard deviation development in time:

These charts, presented on a vertical linear and log scale basis, clearly  illustrate that as soon as the standard deviation hits the 0.2% level, crisis can be expected soon.

Not only is the 0.2% SD-level an early warning indicator for the 2008 crisis that started with the bankruptcy of the Lehman Brothers bank, but it's also an indicator of 'Dot Com' crisis in 2000....

Finally
Meanwhile... as from February 2012, standard deviations are declining  again. Time to worry?

Key questions are:

• when will standard deviation hit the 0.2% floor again? 
• and when it does, will there be another crisis?

Remember lesson number 1 in risk management: Crises are unpredictable!
Nevertheless, once 0.2% SD  turns up: fasten your investment seat bells....

Links/Sources:
- Spreadsheet of charts used in this blog
- EU Interest Rates
- Big Picture Chart

Discussing Life-Cycle Pensions & Longevity

In this blog I'm going to discuss two persistent pension topics:

1. One of the most common misunderstandings in pension fund land is that an individual (member) investment policy weighs up to a collective investment approach.
2. Is there a rule of thumb that expresses 'longevity risk' in terms of the yearly return?  

1. Collective vs. Individual Investing Approach

In case of a 'healthy pension fund', new members will join as time continues. In a mature pension fund the balance of contributions, investment returns, paid pensions and costs will stabilize over time.

Therefore the duration of the obligations of a pension fund will more or less stabilize as well. The duration of an average pension fund varies often between 15 and 25 years. Long enough to define a long term investment strategy based on a mix of risky equities (e.g. 60%) and fixed income (e.g. 40%). Regardless of age or status, all members of a pension fund profit from this balanced investment approach.

In case of an individual (member) investment strategy, the risk profile of the individual investments has to be reduced as the retirement date comes near. In practice this implies that 'equities' are reduced in favor of 'fixed income' after a certain age. As the age of a pension member progresses, the duration of the individual liabilities also decreases, with an expected downfall in return as a consequence.

Let's compare three different types of investment strategies to get a clear picture of what is happening:

1. Collective Pension Fund Strategy Approach: Constant Yearly Return
   40% Fixed Income à 4% return + 60% Equities à 6% = 5.2% return yearly
    
2. Life Cycle I Approach ('100-Age' Method)
   Yearly Return (age X): X% Fixed Income à 4% + (100-X)% Equities à 6%
    
3. Life Cycle II Approach (Decreasing equities between age 45 and age 65)
   Yearly Return (age X) = MIN(MAX((6%+(44-X)*0.1%);4%);6%)

All visually expressed in the next chart:

Pension Outcomes

Now lets compare the pension outcomes of these three different investment strategies with help of the Pension Excel Calculator on basis of the next assumptions:

- Retirement age: 65 year

- Start ages 20 and 40

- 3% and 0% indexed  contributions and benefits

- Life Table NL Men 2012 (NL=Netherlands)

Results Pension Calculations (yearly paid pension):

Conclusion  I

From the above table we can conclude that switching from a collective investment approach to an individual investment approach will decrease pension benefits with roughly 10%. Think twice before you do so!

2. Longevity Risk Impact

To get an idea of the longevity impact on the pension outcomes, yearly paid pensions are calculated for different forecasted Dutch life tables (Men).

Life Tables

Forecast Life Table 2062 is calculated on basis of a publication of the Royal Dutch Actuarial Association.

The Forecast Life Table 2112 is (non-official; non scientific) calculated on basis of the assumption that for every age the decrease in mortality rate over the period 2062-2112 is the same as over the period 2012-2062.

Pension Outcomes per Life Table

Here are the yearly pension outcomes on basis of the forecasted life tables:

From the above table, we may conclude that the order of magnitude effect of longevity over a fifty to seventy year period is that pensions will have to be cut  roughly by 25%-30%.


Another way of looking at this longevity risk, is to try to fund the future increase in life expectation from the annual returns.

The next table shows the required return to fund the longevity impact for different forecasted life tables:

Roughly speaking, the expected long-term longevity effects take about 0.7%-1.2% of the yearly return on the long run.

Finally

Instead of developing a high tech approach, this blog intended to give you some practical insights in the order of magnitude effects of life-cycle investments and longevity impact on pension plans in general.

Hope you liked it!

Links/Downloads:

- Excel Pension Calculator including Dutch Life Tables 2012-2062 

- Excel Tables of this Blog
- Forecasted NL Life Tables  2012, 2062, 2112

- Original Pension Excel Calculator

- Publication Dutch Life tables 2012-2062 (Dutch)

- Excel Spreadsheet Forecast Dutch Life Tables 2012-2062