Lognormal distribution

Here I explain an idea that is confusing the first time you see it: a variable is lognormally distributed if its log (or natural log) is normally distributed. I use an example of future stock price: it the rate of return is normally distributed (it can be negative), the future stock price level is lognormally distributed (it cannot be negative!).

Category:

Education

Tags:

• Finance
• Quant
• Excel

[renay18g]

Hi David. Thanks for the video. I understand how to get the lognormal distribution but I don't understand how this is beneficial over a normal distribution. Why use a lognormal distribution to model asset prices?

Thanks.

[bionicturtledotcom]

Right, the motive is indeed to treat periodic asset RETURNS as continuous and normal. So, it does start with normal but for returns. If $10 goes to $11, that's a return of LN($11/10) = 9.5% because 10*EXP(9.5%) = $11. The return is normal which implies that price LEVELS or RATIOS ($11/$10) are lognormal. It is difficult idea but the meaning of lognormal is that the log [i.e., LN()] is normal.

[alphaferrari]

so what you're saying is thhis;' this share price distribution follows simple geometric distribution, therefore, we can also use geometric mean too.'

if you do not agree with this, then plz explain.

[bionicturtledotcom]

Well, i don't know about geometric distribution. But if the distribution of price levels is lognormal, then its mean is different from its median (unlike the normal, where they are the same); i.e., future expected price median not equal to to future expected prce mean. So, there can be two meanings of expected average future price

[DURound]

I would have thought it would have helped to show the normal distribution of the logged values of the stock price.

[Eisaal]

Thank you for the helpful videos

[easykill102]

Thanks, really helped

[saleemo20]

I already figured out the bin ranges! thanks for the video. quick questions, why do we do 1000 trials? can i access most of the spreadsheets on ure site? where in your site can they be found?

[saleemo20]

thanks for the video david. However, i am having a hard time as to ow you got the bin and freq. it would be helpful if you get explain me how the bins were achieved. thank you!

[DannyZ225]

Great illustration! Thanks, David.

[doveisle]

Bravo!! I didn't quite get it this time but much better than my teacher taught me. I'll get it in a couple of times.

[YoyoTube125]

Hi David,

Thank you for this clip. I was over-whelmed by the ideas of lognormally distributed & normally distributed. Your clip really saved me and the screen shot of excel helps a lot as well. Thank you!