European Financial Stability Facility and Lognormal frequency distribution: Difference between pages

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The European Financial Stability Facility (EFSF) was established in 2010 as a temporary rescue mechanism.
A lognormal distribution is one where the logarithm - for example log(X) or ln(X) - of the variable is normally distributed.  


The EFSF’s mandate was to safeguard financial stability in Europe by providing financial assistance to Euro zone Member States.
Lognormal distributions have a minimum - usually 'worst case' - value, whilst having an infinitely high upside.


A simplified illustration is set out below.


The Facility was replaced by the European Stability Mechanism (ESM) in 2012 which finances new programmes. 
A simple (non-symmetrical) lognormal distribution includes the following values:


Its final assistance programme for Greece expired in 2015.
0.01, 0.1, 1, 10 and 100.


However, it continues to administer outstanding loan repayments and payouts to bond holders in close co-operation with the ESM.
The median - the mid-point of the distribution - being 1.
 
This distribution is skewed: most of the values being in the lower (left) part of the distribution, the upside being infinitely high, and the downside limit being 0.
 
The logs - for example to the base 10 - of these values are:
 
log(0.01), log(0.1), log(1), log(10) and log(100)
 
= -2, -1, 0, 1 and 2.
 
When the parent values are lognormally distributed, the transformed (log) values follow a (symmetrical) normal distribution.
 
So for example the mean, mode and median of the log values above (including -2, -1, 0, 1 and 2) would all be the same, namely the middle value 0.




== See also ==
== See also ==
* [[euro zone]]
* [[Frequency distribution]]
* [[Stability Bond]]
* [[Leptokurtic frequency distribution]]
* [[European Stability Mechanism]]
* [[Lognormally distributed share returns]]
* [[Median]]
* [[Normal frequency distribution]]

Revision as of 10:58, 22 August 2013

A lognormal distribution is one where the logarithm - for example log(X) or ln(X) - of the variable is normally distributed.

Lognormal distributions have a minimum - usually 'worst case' - value, whilst having an infinitely high upside.

A simplified illustration is set out below.

A simple (non-symmetrical) lognormal distribution includes the following values:

0.01, 0.1, 1, 10 and 100.

The median - the mid-point of the distribution - being 1.

This distribution is skewed: most of the values being in the lower (left) part of the distribution, the upside being infinitely high, and the downside limit being 0.

The logs - for example to the base 10 - of these values are:

log(0.01), log(0.1), log(1), log(10) and log(100)

= -2, -1, 0, 1 and 2.

When the parent values are lognormally distributed, the transformed (log) values follow a (symmetrical) normal distribution.

So for example the mean, mode and median of the log values above (including -2, -1, 0, 1 and 2) would all be the same, namely the middle value 0.


See also