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stochastic model - lognormal distribution

S

sahildh

Member
Can anyone please explain me the relation between mean and variance of annual growth rate (1+i), it's lognormal distribution and the normal distribution.
How are the mean and variance of each related?
A detailed explanation would be a great help.
Thank you :)
 
sahildh said:
Can anyone please explain me the relation between mean and variance of annual growth rate (1+i), it's lognormal distribution and the normal distribution.
How are the mean and variance of each related?
A detailed explanation would be a great help.
Thank you :)
Click to expand...

Lol @ "a detailed explanation would be a great help". Work on your persuasive writing.

If your question is:

If the annual growth rate of a fund is Normally/Lognormally distributed, what is the relationship between the mean and the variance?

Normally:
There is no relationship

Lognormally:
Variance is proportional to the mean squared.

I don't think that this is the actual question you're interested in as they're not very interesting answers.

Please go into more detail behind your question.
 
What i meant by my previous question was that if mean and variance of any one is given then how to calculate the mean and variance of the rest?
 
sahildh said:
What i meant by my previous question was that if mean and variance of any one is given then how to calculate the mean and variance of the rest?
Click to expand...

If X ~ LogN(mu, sigma^2) then
Ln(X) ~ N(mu, sigma^2)

If X ~ N(mu, sigma^2) then
exp(X) ~ LogN(mu, sigma^2)

For Normal distribution, the parameters "mu" and "sigma^2" are it's mean and variance respectively. (Formula given on page 11 of the tables)

For Lognormal Distribution, the formula for mean and variance(in terms of mu and sigma^2) are given on Page 14 the tables.
 
If the mean and variance of interest rate is given and we know that (1+i) is lognormally distributed then how do we calculate the parameters of this lognormal distribution?:p
 
sahildh said:
If the mean and variance of interest rate is given and we know that (1+i) is lognormally distributed then how do we calculate the parameters of this lognormal distribution?:p
Click to expand...

Recall this:

E[1 + X] = 1 + E[X] and
Var[1 + X] = Var[X]

So if i has mean "m" and variance "v" then mean and variance of 1 + i will be
"1 + m" and "v" respectively.

Equate these to the mean and variance of LogNormal (formula given in the tables) and workout the parameters of the distribution.
 
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