Showing posts with label default. Show all posts
Showing posts with label default. Show all posts

Jul 6, 2014

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


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

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:

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

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.....

- Spreadsheet with tables used in this blog