Lognormally distributed share returns

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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.

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.

See also