long-term daily stock returns ~ N(m, sigma)

Label: intuitiveFinance

A basic assumption in BS and most models can be loosely stated as

“Daily stock returns are normally distributed, approximately.” I used

to question this assumption. I used to feel that if the 90% confidence

interval of an absolute price change in IBM is $10 then it will be

that way 20 years from now. Now I think differently.

When IBM price was $1, daily return was typically a few percent, i.e.

a few cents of rise or fall.

When IBM price was $100, daily return was still a few percent, i.e. a

few dollars of rise or fall.

So the return tends to stay within a narrow range like (-2%, 2%),

regardless of the magnitude of price.

More precisely, the BS assumption is about log return i.e. log(price

relative). This makes sense. If %return is normal, then what is a

-150% return?

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