What is the probability of this investment return using excel's normdist?

Question

Hi

If the average return = 10%

Standard deviation = 15%

Then probability of getting a return greater than 12% in year one is normdist(12,10,15,True)

Ok - what if I wanted to know what the probabilty of getting at least 12% was over 5 years?

I assume we do someting to the 15% volatility because we are compounding the returns but what?

Thanks

Answer 1

For any normal random variable X with mean μ and standard deviation  ÃÂƒ , X ~ Normal( μ ,  ÃÂƒ ), (note that in most textbooks and literature the notation is with the variance, i.e., X ~ Normal( μ ,  ÃÂƒÃ‚² ).  Most software denotes the normal with just the standard deviation.)

You can translate into standard normal units by:

Z = ( X - μ ) /  ÃÂƒ

Where Z ~ Normal( μ  = 0,  ÃÂƒ  = 1).  You can then use the standard normal cdf tables to get probabilities.

If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed.  This is called the Central Limit Theorem.

If a sample of size is is drawn from a population with mean μ and standard deviation σ then the sample average xBar is normally distributed

with mean μ and standard deviation  ÃÂƒ /√(n)

An applet for finding the values

http://www-stat.stanford.edu/~naras/jsm/...

calculator

http://stattrek.com/Tables/normal.aspx

how to read the tables

http://rlbroderson.tripod.com/statistics...

In this question we have

Xbar ~ Normal( μ = 0.1 , σ² = 0.0225 / 5 )

Xbar ~ Normal( μ = 0.1 , σ² = 0.0045 )

Xbar ~ Normal( μ = 0.1 , σ = 0.15 / sqrt( 5 ) )

Xbar ~ Normal( μ = 0.1 , σ = 0.06708204 )

Find P( Xbar > 0.12 )

P( ( Xbar - μ ) / σ > ( 0.12 - 0.1 ) / 0.06708204 )

= P( Z > 0.2981424 )

= P( Z < -0.2981424 )

= 0.3827972