Lognormally distributed share returns: Difference between revisions
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If share returns are lognormally distributed it means that the logarithm of [1 + the share return] has a normal probability distribution. | If share returns are lognormally distributed it means that the logarithm of [1 + the share return] has a normal probability distribution. | ||
Normal distributions have infinitely long ‘tails’ both upside and downside - so implying unlimited downside potential when used for modelling share returns. | Normal distributions have infinitely long ‘tails’ both upside and downside - so implying unlimited downside potential when used for modelling share returns. | ||
But the theoretically worst outcome for a share investor is to lose the whole of their investment - in other words a negative return of -100%. It is not theoretically possible to suffer a return of worse than -100%. | But the theoretically worst outcome for a share investor is to lose the whole of their investment - in other words a negative return of -100%. | ||
It is not theoretically possible to suffer a return of worse than -100%. | |||
Lognormal distributions - unlike normal distributions - also have a limited downside, so they do not suffer from this theoretical shortcoming. | Lognormal distributions - unlike normal distributions - also have a limited downside, so they do not suffer from this theoretical shortcoming. | ||
== See also == | == See also == | ||
* [[Lognormal frequency distribution]] | * [[Lognormal frequency distribution]] | ||
* [[Normal distribution]] | * [[Normal frequency distribution]] | ||
* [[Volatility]] | * [[Volatility]] | ||
[[Category:The_business_context]] | |||
[[Category:Financial_products_and_markets]] | |||
Latest revision as of 20:55, 1 July 2022
If share returns are lognormally distributed it means that the logarithm of [1 + the share return] has a normal probability distribution.
Normal distributions have infinitely long ‘tails’ both upside and downside - so implying unlimited downside potential when used for modelling share returns.
But the theoretically worst outcome for a share investor is to lose the whole of their investment - in other words a negative return of -100%.
It is not theoretically possible to suffer a return of worse than -100%.
Lognormal distributions - unlike normal distributions - also have a limited downside, so they do not suffer from this theoretical shortcoming.
