Question

Suppose the average return on an asset is 12.3 percent and the standard deviation is 21.9 percent. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to determine the probability that in any given year you will lose money by investing in this asset.

Answer 1

Average return = Mean = 12.3%, Standard deviation = 21.9%

It is given that returns are normally distributed

In any given year if one looses money by investing in asset, then it implies that returns of asset are less that 0% in than year

To find the probability that in any given year one will loose money, we will need to find the probability that return in that year is less than 0% for a given normal distribution of returns with mean = 12.3% and standard deviation = 21.9%

This can be found out using NORMDIST function in excel

Formula to be used in excel : =NORMDIST(x,Mean,Standard_dev,Cumulative)

We need to find probability that return in any year is less than 0%, thererfore in formula x = 0% and Cumulative = 1 since we will be using cumulative distribution function to find the probability

                                       =NORMDIST(0%,12.3%,21.9%,1)

Finding probability of loosing money in a year
x	0%
Mean	12.30%
Standard_dev	21.90%
Cumulative	1
Probability of loosing money in a year	0.2872

Using NORMDIST function in excel we get probability of getting return less that 0% in a year = Probability of loosing money in a given year = 0.2872 = 28.72%