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