Morgan Stanley says stocks could fall 10%

[crazy canuck]

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Question for the statistically minded:

If you have an asset with a 17% standard deviation, how often can you say it will fall at least 10% in the next six months and end up being right on purely the basis of statistical fluctuation (incorrectly assuming a Gaussian dsd).

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N(d2) in the BS formula gives you the probability that the stock will be bigger than a certain strike under geometric brownian motion assumptions. N() is cumulative normal distribution.

So assume S (stock price) = 100.
Strike K = 90
Time = T = 0.5 years
std = sigma = 0.17

So probability that stock bigger than strike = N(d2)

d2 = (log(S/K)+(r-sigma^2/2)T)/(sigma*sqrt(T))


So I get 85% with 5% interest rate.

Therefore, based on these assumptions there is a chance of 15% that Morgan-Stanley is right and the market will drop more than 10%.