value of σ

Any one tell me,where I make mistake ,for finding the value of 'σ' in folowing question:
An investment bank models the expected performanance of its assets over a 5day period . over that period the return on bank's portfolio i, has a mean value of .15% and S.D .3% .(1+i)is lognormally distributed.
Cacculate the value of j such that the probability that i is greater than or equal to j is .9 .
Solution- mean(1+i) =1.0015 ,var(1+i)=.003^2
exp(μ+σ^2/2)= 1.0015 ............(1)
exp(2μ +σ^2)(exp{σ^2} - 1)=.003^2 ........(2)
1.0015^2(exp{σ^2}-1)=.003^2
exp{σ^2} = .003^2/1.0015^2 +1
σ^2= 0
(but this make infinite value for solving the probability)
& μ =log 1.0015
μ =.00149

 

Neetu

I have asked before that you include a reference to where your questions are from when you post threads. Please do this - it makes your questions easier to answer and of more use to other users.

This question is from 102 September 2003, Question 5.

Your equation for sigma-squared is correct - but your use of your calculator appears not to be.

I get sigma-squared = 8.973 x 10^(-6) (which is small, but not zero).

 

Sir, I have ASI past question paper.So this is the reason that not include a reference to where question are come from.

Sir,but this is the value =.003^2/1.0015^2=8.973 x10^(-6)
and my equation is
exp{σ^2} = .003^2/1.0015^2 +1
I am so confuse ,Please clarify this point.How can I say sigma-squared =8.973 x10^(-6).

 

doesn't ln(1+ the smallnumber) also equal the small number

 

take logs of both sides ie

ln(exp{σ^2}) = ln(1+(0.003/1.0015)^2)
σ^2 = ln(1.000008973) (on calculator)
σ^2 = 8.972959743x10^-6

σ^2 = 8.973x10^-6

 

Thanks a lot for this help.
Neetu