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
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?
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?
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.
