Annual portfolio returns (before fees) are normally distributed with a mean of 10% and a standard dev. of 15%. All managers charge fees of 0.5% per year. The probability that a portafolio manager’s net annual return (after fees) is greter than -5.5% is closest to: A)16% B)68% C)84% D)95%

Mean 9.5% sd. 15% Z-score: [-5.5-9.5]/15 Z-score = -1 P(Z<=-1) = P(Z=>1) = 1-P(Z<=1) = 1-0.84 = 16% edit: oops was looking at the wrong table

mean 0.10-0.005 = 0.095 -0.055-0.095 =- 0.15/0.15 = -1 is it C?

C: 84% The -5.5% they show here is -1 std of the normally distributed curve. 1 std equals 68%. The portion of the normal distribution below -5.5% is half of (100-68) or 16%. So, 84% is above -5.5%

Supersharp… you gave the answer for less than -5.5%

you’re right mcf, thanks it should be P(Z>=-1) = P(Z<=1) = 0.84

I wanted to see something about quanto options or something.

C is correct.

JoeyDVivre Wrote: ------------------------------------------------------- > I wanted to see something about quanto options or > something. Joey, I think that hypothesis testing is a bit useless unless you work at uni, I dont know why I keep studying it since I went to uni. The king is Mr Bernulli, followed by Ito and the risk-neutral “apparent” probability. :slight_smile:

Ahaa, CP thought be this stuff last week, lets see if I got the lesson 1. mean (10-5 )9.5% 1 std deviation each sides leaves -5.5 and 25 and this is 68% on each tail there remains 16% so 68+ 16 on the right tail gives 84% the probability of a return less than -5.5 should be the remaining 16% on the left tail the answer is A. CP, did i get the lesson?

Nope. 1) Draw a normal curve, and put 9.5% as mean (also call it zero so you can see that with a normalized Z). 2) Calculate Z=(-5.5 - 9.5)/15 = -1 3) Since 9.5% is at zero, and you have a value of -1, you are clearly to teh left of zero. 4) The question is asking what’s teh probability of a return greater than (-1), whiiwch is the area from -1 all the way to the far right. 5) That’s teh same as a probability of 1.0 - (the area from -1 all the way to the left). 6) Just look up proabbiltiy of Z <= -1, and then answer is 1.0 - Pr(Z<=-1).

i definately mis read the question which means if I read propery my answer should have been 84%. but with what your method Dreary i found 84.13% which is the same as B. So I think I am not doing badly but now i have one more way of doing it as you have demonstrated. Thank you guys you are great. Am off now. join you tomorrow.