Hi Could someone explain me the reason why in currc Reading 9 page 446 in example 9 question 3 the largest ratio .090625 has negative N(-0.91)? question in task was: Q:What is the probability that return on SFr optimal portoilio will be less that the shortfall level? P(R<3.75) = N(- .90625)? What is the reasoning here that we use negaitve sign N(-x)? thanks R
Need some more info, but the mean must be greater than 3.75. Anyway the z value must be a negative number or your “safety first” portfolio will have a prob > 50% of not achieving its shortfall level which shouldn’t make sense.
Thanks for answer After I woke up today look at it again I got the point. Shortfall level is the level below which returns are unacceptable for the investor as the probability rules says P(Z>=x) =1.0-N(x) thus to obtain that x must be negative as inequation rule holds: number Z >= x implies Z < -x easy 
ps example was: $800 000 portolio, you are reponsible for research assets allocation, min liquidate level at the end of year $30 000. Data of portolios A Er 25% stnd dev 27% B Er 11% stnd dev 8% C Er 14% stnd dev 20% What is the probability that return on SFr portolio will be less that shortfall level solution has three steps: 1)short fall level RL= 30 000 / 800 000 = 3.75% 2)Best Portolio is portfolio B with safety first ratio = (11%-3,75%)/8% = .90625 is the best alternative according to safery first ratio then last one: 3) P(Rb<3.75) so we create inequality need to be standardized using equation Z=(x-u)/stnd dev x normal rv and u mean Z <= (3,75-11)/8 gives -.90625 rounded to -.91 look into N tables we find .8186 for .91 or ,1814 for negative substract from 1 gives 1-.8186 = .1814 is the probability that return on SFr portolio will be less that shortfall level